High repetition rate fiber laser

Transcription

1 University of Karlsruhe (TH) Institute of Photonics and Quantum Electronics (IPQ) Bachelor's thesis of Ms. Fan Yang High repetition rate fiber laser Start: End: Instructor: Supervisor: Prof J. Leuthold, Prof. Franz X. Kärtner KIT, MIT Michelle Sander, Dr. Amir Nejadmalayeri MIT

2 I hereby certify that this bachelors thesis has been composed by myself, and describes my own work, unless otherwise acknowledged in the text. All references and verbatim extracts have been quoted, and all sources of information have been specifically acknowledged. Karlsruhe, den Fan Yang

3 Abstract Abstract This thesis presents the design and characterization of a compact Erbium-doped fiber laser that uses a Saturable Bragg Reflector (SBR) and soliton mode-locking. The laser produces pulses with a of 160 fs at a 1GHz repetition rate, has an output power of 26 mw, a stable elliptical polarization and good self-starting characteristics. It was further shown that thermal damage could be prevented by pump-reflective coating and an additional short piece of single mode fiber (SMF). For the purpose of building a home-made Erbium-doped fiber amplifier for the laser, the behavior of Erbium-doped fibers with high and low doping was studied with respect to pump power, fiber length, type and seed wavelengths. Based on these experiments, an optical amplifier with a gain of 26 db for a signal wavelength of 1560 nm was developed as well as an ASE source with a 3 db bandwidth of 10 nm at a center wavelength of 1555 nm. 3

4 Acknowledgement Acknowledgement It was an honor for me to work on such an exciting field for my bachelor s thesis which was only possible with the support by Professor Franz Kaertner, Professor Jürg Leuthold and Professor Wolfgang Freude. Without them I would have never been able to visit MIT and work for such a great group. I also want to thank them for their kindness and patience whenever I approached them with my humongous amount of questions. I also own my deepest gratitude to my two advisors Michelle Sander and Dr. Amir Nejadmalayeri who spent endless hours listening to my concerns and questions of any kind, having inspiring discussions on experimental results and procedures while introducing me to scientific research at the highest level. I have learned so many skills while working on the projects which I will need for the rest of my life. For all of this I cannot express with words how grateful I am. Furthermore I would like to thank Andrew Benedick, Aleem Siddiqui, Li-Jin Chen, Hyunil Byun, Dr. Guoqing Chang, Ali Motamedi, Jonathan Cox, Hung-Wen Chen, Jonathan Morse and Shu-Wei Huang for sharing their time to answer my questions and helping me whenever I needed them. I m also grateful for the help and kindness of Dorothy Fleischer welcoming me and introducing me to the group during my first days. Moreover, many thanks go to Frederike Ahr for her generous support. Last but not least I will never be able to return the amount of selfless support my parents gave me. Even from miles away their care and unconditional love carried me throughout my stay. I wish all basketball players of the group many many thrilling games in the gym and good luck to all group members for the rest of their career! 4

5 Table of contents Table of contents Abstract...3 Acknowledgement...4 Table of contents...5 List of Figures...7 List of Tables Introduction Ultrafast Optics Fiber lasers and amplifiers Laser Fundamentals Quantum mechanical background Introduction Rate equations Real system Laser CW operation Resonator modes Pulsed operation Soliton theory Mode-locking Passive Mode-locking Master Equation of Mode-locking Fast Saturable Absorbers Soliton Mode-locking Polarization Saturable Bragg Reflector Semiconductor Saturable Absorber Bragg Reflector Summary GHz Erbium-doped fiber laser Laser Design Fiber type

6 Table of contents Fiber length Mirrors Wavelength-Division Multiplexer Building the laser Measurements CW operation Mode-locking operation ASE and EDFA Introduction Erbium-doped fiber amplifier Amplified Spontaneous Emission Structure and parameters Measurement Setup Procedure Preprocessing Erbium-doped fiber amplifier Amplified Spontaneous Emission source Conclusion and future work Conclusion Future work EDFA and ASE source Laser Appendix A: Bibliography Appendix B: List of Acronyms Appendix C: List of Symbols Appendix D: Components D.1. Gain Fibers D.2. Diode: EM4 D D.3 Coupler D.4. WDM Appendix E: Results E.1. Laser E.2. EDFA E.3. ASE source

7 List of Figures List of Figures Fig A Two-Level system with energy levels W 2 and W 1. N th is the number of photons with the frequency f = (W 2 -W 1 )/h in the free field which are responsible for induced emission and absorption. 21,sp is the upper state lifetime equivalent to the average time it takes for electrons to relax by spontaneously emitting a photon into any mode. The two terms represent the absorption and emission rate as in (2.3) and (2.4) Fig Three-Level-System of an Er 3+ Ion with energy states W 1 = 4 I 15/2, W 2 = 4 I 13/2, W 3 = 4 I 11/2. Stark splitting takes place when the ion is placed inside a crystalline host. For transitions between W 1 and W 2, induced emission takes place with a rate of 21 L where L is the photon flux at 1530 nm, the spontaneous emission rate into the laser mode equals to 1/ 21,spm. With P being the photon flux at 980 nm, the absorption of pump light happens with the time constant 13 P Fig Absorption and emission interaction cross sections of an EDF. Taken from [5] Fig Energy level structure for two sublevel systems. W mi is the energy separation between the sublevel state W mi and W i Fig Gain coefficient of an EDF as a function of wavelength for different degrees of population inversion. The highest curve corresponds to the case of maximum, the lowest curve to the case of minimum population inversion. Taken from [4] Fig. 2.6 General setup of a laser consisting of a partially reflective mirror and a highly reflective mirror which together with the gain medium itself form the cavity. The amplification of light at the desired wavelength happens inside this cavity while every roundtrip adds more and more intensity to the existing light until saturation occurs. Additionally, optical or electrical pumping is necessary to achieve population inversion Fig Ultrashort pulses in the time and frequency domain. E(t) and its fourier transform Ê(f) represent the actual pulse whereas A(t) and Â(f) describe the shape of the envelope. Furthermore, f = f R = 1/ T and FWHM = Fig The propagation of a fundamental soliton. Adapted from [10] Fig Net gain window of a saturable absorber, amplifying the high power sections of the pulse Adapted from [10] Fig The structure of a typical Saturable Bragg Reflector (SBR). The alternating layers of GaAs and AlGaAs represent the Bragg Reflector, which is mounted on a copper substrate, while InGaAs is the Saturable Absorber directly grown on the outermost GaAs layer. Pump light is effectively kept away from the SBR by pump-reflective coating which is another Bragg Reflector on its own but specifically designed for the pump wavelength. Taken from [13] Fig Time response (a), adapted from [10], and carrier dynamics in a band diagram (b) of a semiconductor saturable absorber after a high energy pulse in 3 stages: 1) Electron-hole pairs are generated similarly to a two-level system 2) Electrons then start to relax into the minima of the valence and conduction band 3) Recombination of electrons and holes Fig (a) Power-dependent reflectivity of the SBR with (red) and without (black) pump-reflective coating. You can clearly see that the major difference lies in the absorption at the pump wavelength at around nm. A drawback is the drop in reflectivity at around 1550 nm of 8%. (b) Intensity distribution of the light inside the SBR, Saturable Absorber and in free space. Taken from [13] Fig Thermally damaged SBR Taken from [13] Fig Schematics of the 1 GHz laser with reference between the components of the 1 GHz laser design and the elements in the principal laser setup. A 980 nm laser diode acts as an optical pump, an 7

8 List of Figures output coupler with 10% transmission for the signal wavelength corresponds to the transmissive mirror and the SBR plays the role of the reflective mirror while an Erbium Doped Fiber serves as the gain medium Fig Setup of the CW measurement Fig Setup of the mode-locked measurement Fig An undesired mode-locked state with one sideband shown in the RF spectrum (a) and OSA spectrum (b) with I pump =700 ma and P out = 13 mw. The sideband in the RF spectrum suggests amplitude modulation of the envelope Fig RF spectrum of the 1 st and 2 nd successfully mode-locked state with stable polarization (a) and OSA spectrum of the 2 nd mode-locked state with I pump = 1100mA and P out = 26 mw (b). No sidebands are visible and the repetition rate equals to GHz Fig A second undesired mode-locked state with two sidebands shown in the RF spectrum (a) and OSA spectrum (b) with I pump =700 ma and P out = 16.5 mw Fig OSA spectra of the 1 st (a) and 2 nd (b) successfully modelocked state for different pump currents and the comparison of the two spectra (c) Fig OSA spectrum in a linear scale of the 2 th successfully mode-locked state with I pump = 900 ma, P pump = 420 mw, P out = 20 mw Fig Setup of the mode-locked measurement with losses and characteristic powers Fig Power development of the laser over 24 hours starting at 6 pm. Clearly the power stays constant in 1) and 3) whereas in 2) it drops by approximately 5% Fig OSA spectra of the 2 nd successfully mode-locked state at I pump = 700 ma on the first (blue) and second (violet) day. Apparently the alignment changed overnight, while it stayed fairly constant during the day Fig Power development of the 980 nm pump diode output power over 7 hours after the modelocked overnight test at I pump = 700 ma Fig ASE spectrum in which the 3 db flatness and its corresponding 3 db bandwidth are marked Fig Different possibilities of Amplifier/ASE source setup: (a) Co-directional pumping for an Amplifier (b) Two-Stage ASE source (c) Contra-directional pumping for an Amplifier Fig Setup for the EDFA and ASE source measurement Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Color plots of gain (a), output power (b) and SNR (c) as a function of wavelength and length Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: Gain as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: SNR as a function of fiber length for different wavelengths (a) and as a function of wavelength for different fiber lengths (b) with a cut-off at 50 db so that the spectra with zero noise are suppressed in favor of the important trends in the relevant SNR range Fig M-12 fiber with I pump = 500 ma, P pump = 230 mw, P seed = 0.1 mw: Color plots of the SNR as a function of wavelength and length Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, seed = 1590 nm, P seed = 0.1 mw, L = 31 m: OSA spectrum with no ASE noise Fig M-12 fiber I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: A new ASE spectrum evolves with increasing fiber length for a seed wavelength of 1560 nm (a) which dampens the SNR whereas it doesn t really emerge for 1595 nm (b)

9 List of Figures Fig M-12 fiber with seed = 1560 nm for I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: OSA spectra for different lengths in full span (a) and peak zoom (b) Fig M-12 fiber with seed = 1570 nm for I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: OSA spectra for different lengths in full span (a) and peak zoom (b) Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Development of the spectrum over seed for L = 5.2 m (a), L = 16.2 m (b) and L = 47.2 m (c) in which for other wavelengths there was only noise. The power levels beyond the chosen wavelength range were all below -70 dbm and therefore cut off for these graphs Fig Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Color plots of gain (a), output power (b) and SNR (c) as a function of wavelength and fiber length Fig Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: Gain as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) Fig Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: SNR as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) Fig Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1mW: Development of the spectrum over seed for L = 45 cm (a), L = 80 cm (b) Fig Er-110 fiber with seed = 1560 nm for I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: OSA spectrum for different lengths in full span (a) and peak zoom (b) Fig M-12 fiber unseeded with a fixed flatness of 3 db: Output Power (a), Bandwidth (b) and = center (c) as a function of pump current and fiber length Fig M-12 fiber unseeded: OSA spectra for L = 8m (a) and L = 11m (b) for increasing pump powers. The light blue and green traces are potentially useful for a good ASE source, showing a reasonably wide 3 db bandwidth and center at around 1555 nm Fig Er-110 fiber unseeded with a fixed flatness of 3 db: Output Power (a), Bandwidth (b) and = center (c) as a function of pump current and fiber length Fig RF spectrum of the 1 st and 2 nd successfully mode-locked state with stable polarization (a) and OSA spectrum of the 2 nd mode-locked state with I pump = 1100mA and P out = 26 mw (b). No sidebands are visible and the repetition rate equals to GHz Fig M-12 fiber, L = 16 m (a) and Er-110 fiber, L = 85 cm (b) with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: OSA spectra for different wavelengths Fig M-12 fiber unseeded: ASE spectra for different pumping levels. The green and blue traces represent the spectra which all have a similar bandwidth and desired peak wavelength while the output power drops with decreasing pumping levels Fig. D. 1. Absorption losses over wavelength in db/m of the Fibercore M /125 fiber (a) and the Liekki Er110-4/125 fiber (b) Fig. D. 2. Optical output spectrum Fig. D. 3. Power output fluctuations of the diode over 10 hours at I pump = 700 ma Fig. D. 4. Insertion losses with respect to wavelength at bith ports Fig. D. 5 WDM and the illustration of its different insertion losses Fig. D. 6. Insertion losses of the 1550 port seeded with 1550 nm (a) and isolation loss of the 980 port seeded with 1550 nm (b)

10 List of Figures Fig. E. 1. M-12 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: Gain as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) Fig. E. 2. M-12 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: SNR as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) Fig. E. 3. Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: Gain as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) Fig. E. 4. Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: SNR as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b)

11 List of Tables List of Tables Table 3.1. The two stable mode-locked states and their characteristic quantities Table 3.2. EM4 Pump diode D power characteristics: I pump and the corresponding pump power at the output of the isolator. The values at 1100 ma and 1150 ma were calculated by linear interpolation Table 4.1. M-12 fiber with I pump = 1100 ma, P pump = 513 mw: Characteristic values for the ASE source Table D. 1. Pump power measured at the angle cleaved output of the diode P diode and after connectorisation and connecting it with the isolator P pump. The powers corresponding to I pump = 1100 ma and Ipump = 1150 ma were calculated by linear interpolation Table D. 2. Insertion losses of 10%/90% Couplers and their coupling ratios Table D. 3 Insertion and isolation losses of the AFW (above) and AFW Table E GHz fiber laser in CW Operation, see Fig Table E GHz fiber laser in mode-locked states with rotating elliptical polarization and the location of the side peaks in the RF spectrum Table E. 3. M-12 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Gain [db] as a function of seed wavelength and fiber length. Zeros were assigned to values below zero to improve the facility of inspection Table E. 4. M-12 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Outpower power [mw] as a function of seed wavelength and fiber length Table E. 5. M-12 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: SNR [db] as a function of seed wavelength and fiber length. Zeros were assigned to values below zero to improve the facility of inspection Table E. 6. Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Gain [db] as a function of seed wavelength and fiber length. Zeros were assigned to values below zero to improve the facility of inspection Table E. 7. Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Output power [mw] as a function of seed wavelength and fiber length Table E. 8. Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: SNR [db] as a function of seed wavelength and fiber length. Zeros were assigned to values below zero to improve the facility of inspection Table E. 9 M-12 fiber unseeded with a flatness of 3 db: Output power [mw] of an ASE source with the given parameters Table E. 10. M-12 fiber unseeded with a flatness of 3 db: Bandwidth [nm] of an ASE source with the given parameters Table E. 11. M-12 fiber unseeded with a flatness of 3 db: Center wavelength [nm] of an ASE source with the given parameters

12 Introduction 1 Introduction 1.1. Ultrafast Optics In the past few years, ultrashort laser pulses in the picosecond and sub-picosecond range have found widespread applications in communication, sensing, machining or medical applications. Their short pulse durations imply an enormous concentration of pulse energy and hence high peak powers at modest average optical powers. These high powers can be used for material processing and surgery as well as nonlinear frequency generation. The broad spectrum on the other hand enables high spatial resolution for Optical Coherence Tomography [9]. Furthermore, high repetition rate mode-locked lasers create frequency combs which can be used for frequency metrology [3] and laser-based spectroscopy involving the tracing of ultrafast physical or chemical processes Fiber lasers and amplifiers In general, ultrafast light sources are either solid state or fiber lasers. Compared to their solid state counterparts, fiber lasers are much more compact, cheap and easy to handle. Moreover, light distribution e.g. for optical communication is commonly operated with fiber optics for which laser pulses directly coming from a fiber are more advantageous in terms of coupling quality. Pulses that transverse the ocean have to be amplified because of power attenuation inside the fiber. A strong signal is also necessary for a good signal-to-noise ratio. Moreover, high powers are obligatory for applications where nonlinear effects are involved. Fiber amplifiers are therefore as crucial as the laser sources themselves. In this thesis I will discuss the latest design of an Erbium-doped fiber laser optimized for a high repetition rate and output power as well as a short pulse duration. As the laser output needed amplification, a home-made optical amplifier was designed which could significantly reduce the overall operating costs for the experiments. In order to obtain the parameters for optimal characteristics, the behavior of two different gain fibers with high and low doping was studied in a cut-back experiment, at the same time exploring the influences of pump power and seed wavelength. Since Amplified Spontaneous Emission (ASE) sources use a similar setup as the amplifier, the measurement data was also analyzed with respect to ASE characteristics. 12

13 Laser Fundamentals 2 Laser Fundamentals 2.1. Quantum mechanical background Introduction The basic function of a laser is the emission of coherent light at a certain wavelength. Light emission occurs through radiative transitions from an excited state to a ground state, coherence results from induced emission. In order to excite electronic states, either optical or electrical pumping is necessary. In the first case, optical pumping creates a population inversion by exciting electrons to a third energetic state with a very short lifetime but higher energy eigenvalue. In the second case, electrons are accumulated in certain spatial areas by the injection of carriers which, for example, can be achieved in heterojunction diodes. This thesis will only deal with the first case since fiber lasers are doped with rare earth ions which require optical pumping Rate equations Two-level system The simplest model for transitions in a laser is represented by a system with two eigenstates, and corresponding eigenvalues W 2 and W 1 (Fig. 2.1). The Schrödinger equation (2.1) predicts the time evolution of the actual electron state, with the Hamilton (2.1) Operator (2.2) representing the energy of the two states. The bigger c e is compared to c g, the more electrons are likely to be found in the excited state which in reality would express itself through more dominant emission over absorption. Therefore, in order to have a net gain, the population inversion has to be positive, where the absolute squares stand for the probabilities to find an electron in the particular eigenstate. If we do not consider strong induced emission inside a lasing cavity yet, the total emission and absorption rate and in (2.3) and (2.4) only account for spontaneous emission from (2.2) 13

14 Laser Fundamentals the excited state as well as induced emission and absorption by weak photons in the free field [10]. is the average time it takes for electrons to relax by spontaneously emitting a photon into any mode and the free field. denotes the number of thermally excited photons in (2.3) (2.4) Fig A Two-Level system with energy levels W 2 and W 1. N th is the number of photons with the frequency f = (W 2 -W 1 )/h in the free field which are responsible for induced emission and absorption. 21,sp is the upper state lifetime equivalent to the average time it takes for electrons to relax by spontaneously emitting a photon into any mode. The two terms represent the absorption and emission rate as in (2.3) and (2.4). The populations N 1 and N 2 of the two energy levels then behave according to (2.5) (2.6) The time derivative of the population inversion can thus be expressed by (2.7) with T 1 representing the time constant for energy relaxation. In steady state, both time derivatives in (2.5) and (2.6) equal to zero which leads to an equilibrium population inversion of. (2.8) 14

15 Laser Fundamentals It is obvious that is valid with (2.3) and (2.4) which implies that for all cases in thermal equilibrium, a two-level system yields a greater population in the ground state than in the excited state Three-level system This can only be changed if an additional term for case of optical pumping: (2.4) is introduced for example in the (2.9) The new quantity denotes the number of photons at the pump wavelength so that according to (2.8), population inversion can be achieved above a certain threshold for which and. Optical pumping requires a three level system (Fig. 2.2) as can be found in rare earth ions. For - doped fibers (EDF), pumping the medium with a wavelength of 980 nm raises electrons from the into the state from which they relax into fairly quickly [1]. If we now consider induced emission by strong incident light which happens for high population inversion, we will obtain a coupled system of equations: (2.10) (2.11) (2.12) where and are the optical intensities at the lasing wavelength and pumping wavelength respectively. Since is now depleted by the pumping, the photon absorption from to was neglected in (2.11) and (2.12). For <<, the population as well as transitions from this state will always be negligible so that we can simplify the system to the two-level case, merging the state to form the so-called rate equations [10] and 15

16 Laser Fundamentals (2.13) (2.14) The first term in (2.13) accounts for various relaxation processes, the second for induced emission and the third represents the absorption of pump light from to. The evolution of the photon number at the lasing wavelength is then determined by the time constant of the resonator loss related cavity decay and induced and spontaneous emission (2.14). Furthermore, now only includes the emission of photons into the specific laser mode whereas is the general upper state life time including all effects that lead to electron transition like scattering and electron-lattice interaction. Fig Three-Level-System of an Er 3+ Ion with energy states W 1 = 4 I 15/2, W 2 = 4 I 13/2, W 3 = 4 I 11/2. Stark splitting takes place when the ion is placed inside a crystalline host. For transitions between W 1 and W 2, induced emission takes place with a rate of 21 L where L is the photon flux at 1530 nm, the spontaneous emission rate into the laser mode equals to 1/ 21,spm. With P being the photon flux at 980 nm, the absorption of pump light happens with the time constant 13 P Real system Atom-field interaction The assumption of negligible induced emission, which was made in order to derive (2.3) and (2.4), was only legitimate for a closed system without optical pumping. Notice that in (2.10) and the following, we introduced a new quantity for the terms with induced emission, which 16

17 Laser Fundamentals is defined as the interaction cross-section for a particular transition. This is due to the fact that in reality when the lasing process starts, the optical power of the incident photons will be very strong compared to the former so that the equations of motion for the atomic dipole moments have to be taken into account. The radiation process can intuitively be understood as follows: When the atom is in an energy eigenstate, there will be no permanent dipole moment [10]. Once an incident photon excites the electrons, they will be transferred into the state with,. The expectation value of the dipole moment is now different than zero and will vary with time since is not a Hamiltonian eigenstate. This vibration of the dipole will result in an induced photon and is the reason why the induced and incident light beams are in phase. In order to take this oscillation into account, we have to add to the Hamilton another operator (2.15) which describes the energy of the electric dipole in the incident electric field. (2.15) The new Schrödinger equation now yields: ( 2.16) Following this equation we obtain a coupled pair of equations of motion for the dipole moment and population inversion which are discussed in [10]. Assuming a quasi steady state for the dipoles, introducing the interaction cross section, the saturation intensity I S as well as the so-called lineshape function with being the frequency of the incident light, the time derivative of now obeys (2.17) The second term on the right hand side describes the induced emission whereas the first term has already been introduced for spontaneous and free space induced emission in (2.7). The lineshape function emerges from calculations with the coupled equations of and and can e.g. have a Lorentzian or Gaussian shape with a maximum at The steady state population inversion is inversely proportional to closer is to the eigen frequency, the less populated will be. which means that the The interaction cross section represents the atom field interaction and is defined as. (2.18) 17

18 Laser Fundamentals Another commonly used quantity is the photon flux photons per second per surface area. which is equal to the number of Gain spectrum For isolated ions, the above image of a simple Three-Level system is totally acceptable. However, interactions between ions and phonons as well as the destruction of the symmetric environment when they are placed in crystalline hosts (Stark splitting) cause the broadening of the distinct energy levels, meaning that each level in Fig. 2.2 would then consist of multiple sublevels. This is the reason why we do not only find one particular emission wavelength at spectrum (Fig. 2.3). but a whole Fig Absorption and emission interaction cross sections of an EDF. Taken from [5] Notice that the spectra in Fig. 2.3 do not overlap completely. This is due to the different definitions of the emission and absorption interaction cross sections. According to [1], and can be determined by the weighted sum of all sublevel cross sections: (2.19) (2.20) temperature. are called the partition functions, k B is the Boltzmann constant and T the Fig Energy level structure for two sublevel systems. W mi is the energy separation between the sublevel state W mi and W i 18

19 Laser Fundamentals The gain spectrum of an atom is then described by (see [4]) (2.21) The following graph shows the gain spectra of an Erbium doped fiber where each curve represents a fixed population inversion. Fig Gain coefficient of an EDF as a function of wavelength for different degrees of population inversion. The highest curve corresponds to the case of maximum, the lowest curve to the case of minimum population inversion. Taken from [4] 2.2. Laser CW operation Fig. 2.6 General setup of a laser consisting of a partially reflective mirror and a highly reflective mirror which together with the gain medium itself form the cavity. The amplification of light at the desired wavelength happens inside this cavity while every roundtrip adds more and more intensity to the existing light until saturation occurs. Additionally, optical or electrical pumping is necessary to achieve population inversion. 19

20 Laser Fundamentals The most principal setup of a laser is shown in Fig In continuous-wave (CW) operation, the laser emits exactly at the wavelength for which the gain spectrum has its maximum. However, the output bandwidth in reality is much narrower than the curve may suggest. This is intuitively due to the fact that after several roundtrips in the cavity, the dominant wavelength will be significantly higher than the rest of the spectrum which can thus be neglected. As it can be seen in Fig. 2.5, Erbium doped fibers exhibit particularly high gain for wavelengths around 1530 nm Resonator modes Although the sublevel system might suggest a spectrum with an almost continuous amount of eigen frequencies, a laser cavity only allows constructive interference if the optical length of the cavity equals to integer multiples of the wavelength (2.22) is the propagation length in the gain medium with an refractive index whereas corresponds to the path length in free space. The allowed frequencies are hence (2.23) As explained in , this would result in a rather broad discrete spectrum emitted by the laser but only if the amplification path is short (e.g. in an optical amplifier, see 4.1.1) or in the case of pulsed operation Pulsed operation For applications it is often necessary to provide optical pulses with a certain repetition rate. According to the Fourier transformation, the periodicity in time is inversely proportional to the frequency spacing (Fig. 2.7). Therefore, if pulses are desired to be separated by, the laser needs to be designed for frequency and time bandwidth are related to each other by. Fourier transformation laws further state that the (2.24) As a consequence, a measure has to be found to maintain the spectral width of the laser if short pulses are desired this technique is called Mode-locking which will be discussed in 0. 20

21 Laser Fundamentals A mode-locked state can be examined using an optical spectrum and RF spectrum analyzer (OSA and ESA). In principle, the OSA spectrum should display discrete lines because only certain discrete wavelengths can survive inside the cavity. But the finite bandwidth of the OSA causes the user to see a smooth curve and is therefore commonly used to provide an overview over the entire optical spectrum. The RF spectrum on the other hand is mainly used to determine the exact frequency spacing which is equivalent to the repetition rate, as well as possible sidebands or modulations. The RF detector converts optical pulses into electrical signals which then undergo Fourier Transformation in the ESA. Typical observations which suggest that the desired mode-locking state is close but has not yet been successfully reached are for example a modulation of the peaks in the RF spectrum arising from multiple pulsing or sidebands coming from amplitude modulation (2.3.5) Soliton theory In addition to high repetition rates, we usually want short pulses to exit our fiber at the output. In order to achieve this, there are two possibilities: one of them is a soliton-laser where a short pulse maintains its time width throughout the fiber whereas the other is a stretched-pulse laser which first broadens a pulse before it is recompressed. A dispersion managed stretched-pulse laser needs to include both gain and passive fiber in one round trip. This often requires modelocking mechanisms which depend on polarization and can have self-starting problems and a bulky setup. As the initial goal was to build a compact fiber laser, this option would not have been feasible. Fig Ultrashort pulses in the time and frequency domain. E(t) and its fourier transform Ê(f) represent the actual pulse whereas A(t) and Â(f) describe the shape of the envelope. Furthermore, f = f R = 1/ T and FWHM =

22 Laser Fundamentals (2.25) In normally dispersive media a pulse broadens as it propagates because of group velocity dispersion (GVD) D which causes a chirp. A very profound and detailed study of the propagation of a Gaussian pulse in dispersive media can be found in [6]. Self-phase modulation (SPM) based on the nonlinear Kerr-effect also leads to spectral broadening. If two chirps of different signs act on the pulse, for example a positive SPM and a negative GVD, their effects compensate each other so that the pulse shape stays constant. This follows from the nonlinear Schrödinger equation (NSE) for the envelope function. The fundamental soliton with a steady state potential for is a sech-shaped function (see Fig. 3.8): (2.26) Substituted into (2.25) we obtain (2.27) Comparison of the coefficients yields: (2.28) Intuitively this describes the compensation of nonlinear and linear effects. Moreover, (2.28) shows that the group delay dispersion has to be negative for > 0 in order to obtain a soliton. The combination of (2.28) and [10] results in the fundamental relation (2.29) 22

23 Laser Fundamentals Fig The propagation of a fundamental soliton. Adapted from [10] 2.3. Mode-locking Passive Mode-locking There are several categories of mode-locking which are all used in order to preserve a wide emission bandwidth as well as high repetition rates. A detailed discussion on the various possibilities can be found in [10]. The idea behind all mode-locking mechanisms is to extract and amplify a short section of a pulse, which could have evolved by a random disturbance, in the time domain. For this purpose, one is looking for a mechanism that causes the difference between resonator losses and gain to vary with time, acting like a shutter (Fig. 2.9). Active mode-locking enforces such a modulation of the loss medium using electro- or acoustooptical components. Passive mode-locking ([12]) on the other hand leaves it to the pulse itself to produce the net gain window for powers above a certain threshold. Because there is no additional electronic device involved in this case, the noise performance is slightly more favorable. It can also produce shorter pulses without having to use pulse compression methods which is desirable to avoid phase fluctuations. For our laser we chose the soliton mode-locking method with a Saturable Bragg Reflector (SBR), also called SEmiconductor Saturable Absorber Mirror (SESAM) based on the power dependent losses of a semiconductor saturable absorber ([8], [11]) Master Equation of Mode-locking The master mode-locking equation is given by (2.30) 23

24 Laser Fundamentals see [10]. represents the curvature of the gain which acts like a bandpass filter, is the GVD, the SPM, the absorber loss and and the cavity gain and losses per round trip. stands for the time evolving with and the travelling of the pulse whereas the small is the time centered at the peak of the pulse for a fixed Fast Saturable Absorbers In general, a negative GVD is not necessarily available in which case the saturable absorber together with the filter losses can help to shape the pulse [10]. This means that the time response of the saturable absorber modulates the losses in such a way that they are much higher than the gain far away from the pulse so that each time, only a short section of the pulse experiences a net gain (Fig. 2.9). The behavior of a fast saturable absorber which only modulates the cavity losses can be described as follows (2.31) which is, if expanded for small intensities, (2.32) If we neglect and in (2.30), we obtain a soliton as a steady state solution with the following identity (2.33) [10]. As one can clearly see, the filter losses now took over the GVD part in equation (2.29) whereas the saturable absorber plays the role of the self-phase modulation. 24

25 Laser Fundamentals Soliton Mode-locking Soliton mode-locking exploits the saturable absorber dynamics to ensure self-starting and stability against continuum break-through whereas the pulse-shaping is controlled by the positive SPM and negative GVD of the gain fiber. The losses of the saturable absorber can be described by (2.34) where is the absorber recovery time and E A the saturation energy of the saturable absorber. Problems can emerge if the pulses become very short and have very high power. Once the saturation fluence is exceeded, the recovery time will produce a long net gain window. At the same time the power will be very high and the pulse very short. In this case, the continuum may experience lower total losses than the soliton which eventually enables its breakthrough. Another possible scenario is the break-up into multiple pulses with reduced energy and reduced filter losses, as the system always occupies the state with the overall lowest possible energy loss. Fig Net gain window of a saturable absorber, amplifying the high power sections of the pulse Adapted from [10] According to [10], as a rule of thumb, the absorber recovery time should satisfy order to maintain stability. in Polarization The coherent laser light at the output generally consists of two linearly polarized electrical field components which have a random phase relation and therefore form a rotating elliptic polarization. This is an unwanted effect because a propagation of such polarized light in birefringent media would lead to differing output signals for identical input signals which might cause misunderstandings between the sender and receiver. The bend of the gain fiber strongly influences birefringence properties and group velocities which greatly affect the dynamics of the relative phase. At a certain degree of bending, the phase relation between the components at the output stay constant and the polarization remains stable. 25

26 Laser Fundamentals 2.4. Saturable Bragg Reflector As mentioned, we chose a Saturable Bragg Reflector (SBR) for the soliton-modelocking mechanism comprising a III-V semiconductor quantum well (InGaAs) which represents the absorber layer and is grown on a Bragg Reflector. The combination of the two acts as our reflective mirror (Fig. 3.1) with power-dependent reflectivity. Fig The structure of a typical Saturable Bragg Reflector (SBR). The alternating layers of GaAs and AlGaAs represent the Bragg Reflector, which is mounted on a copper substrate, while InGaAs is the Saturable Absorber directly grown on the outermost GaAs layer. Pump light is effectively kept away from the SBR by pump-reflective coating which is another Bragg Reflector on its own but specifically designed for the pump wavelength. Taken from [13] Semiconductor Saturable Absorber In the Semiconductor Saturable Absorber photon absorption by electrons in the valence band causes their transition into the conduction band. This process of photon absorption naturally corresponds to cavity losses. However, if the photon intensity becomes too high, the conduction band will eventually be saturated so that further photons cannot be absorbed anymore which causes the instantaneous loss to decrease and the reflection to increase. There will hence be a net gain window during which the pulse experiences effective gain (Fig. 2.9) as long as the carriers in the conduction band have not relaxed into their ground state yet. This process is reversed for very high powers when high fluence nonlinear effects like Two- Photon-Absorption and Free-Carrier-Absorption ([7]) get involved which will not be discussed in detail. The impulse response for the reflectivity of the absorber is depicted in Fig (a). In addition to the recovery time A, a saturable absorber can be furthermore characterized by the following quantities: The saturation fluence is the energy per surface area in order to reduce the absorption to 1/e of its initial value. The maximum change in reflectivity is called modulation depth and depends on the material composition, optical wavelength and optical intensity. 26

27 Laser Fundamentals (a) (b) Fig Time response (a), adapted from [10], and carrier dynamics in a band diagram (b) of a semiconductor saturable absorber after a high energy pulse in 3 stages: 1) Electron-hole pairs are generated similarly to a two-level system 2) Electrons then start to relax into the minima of the valence and conduction band 3) Recombination of electrons and holes The relaxation happens in three different time scales corresponding to various quantummechanical effects (Fig (b)). At first, electron-hole pairs are generated similarly to a two-level system. This process lasts for about fs after which the saturable absorber is saturated. Electrons then start to scatter into the minimum of the conduction band whereas holes relax towards the maximum of the valence band. This can either take place through nonradiative scattering in a time-scale of about fs or through interaction with the lattice with a time constant of about 300 fs - 1 ps. Once the carriers arrive at the extrema of the corresponding energy band they will recombine within 100 fs 100 ps. The duration of this period is among others strongly influenced by the number of defects in the semiconductor Bragg Reflector The reason to choose a Bragg Reflector instead of a commercial silver mirror was on the one hand to enable the growth of a Saturable Absorber layer and on the other hand because it has higher reflectivity. Its design is wavelength specific. Alternating layers of media with high and low refractive indices are grown on each other with a spacing of a quarter-wavelength. As a wave propagates into a denser medium it is reflected with a phase jump of whereas when it hits a medium with lower density, the phase jump is zero. It is easy to see that with an optical path spacing of a quarter-wavelength, the reflected light rays with the desired frequency will interfere constructively. The intensity profile in Fig (b) shows how the amplitude of the standing wave decreases towards the end of the mirror, since the number of interfering light beams also decreases accordingly. In this way it is possible to engineer field penetration into the absorber layer for the different desired purposes. 27

28 Laser Fundamentals (a) (b) Fig (a) Power-dependent reflectivity of the SBR with (red) and without (black) pump-reflective coating. You can clearly see that the major difference lies in the absorption at the pump wavelength at around nm. A drawback is the drop in reflectivity at around 1550 nm of 8%. (b) Intensity distribution of the light inside the SBR, Saturable Absorber and in free space. Taken from [13] Since significant powers of pump light which arrive at the Bragg Reflector can potentially destroy the mode-locked state and the SBR itself (Fig. 2.13), pump-reflective coating (PRC) is added at the input of the Bragg mirror. Its structure is a Bragg Reflector on its own but engineered specifically for the pump wavelength. As we can see in Fig (a), the PRC successfully increased the reflectivity for light at 980 nm by 70% Summary Fig Thermally damaged SBR Taken from [13] Compared to Fast Saturable Absorbers, the long recovery time of SBRs does not enable very short pulses as elaborated above. It is also very sensitive to overload heating which can lead to irreparable thermal damage. However, SBR soliton mode-locking allows reliable self-starting and can easily be engineered to suit a specific range of signal wavelengths at the same time allowing a very compact design. Like other passive mode-locked lasers, it also exhibits excellent noise performance compared to active mode-locked lasers which are subject to additional noise from the electronic modulators. A detailed study on engineering limitations for certain parameters and how this influences the optimal laser performance can be found in [2]. 28

29 1 GHz Erbium-doped fiber laser 3 1 GHz Erbium-doped fiber laser 3.1. Laser Design After the theoretical introduction above, the right components have to be chosen in order to achieve our goal of building a self-starting and compact high-repetition rate fiber laser ([13]) Fiber type Soliton Mode-locking requires a gain fiber with both negative group delay dispersion and a positive nonlinearity coefficient. For compactness and a high repetition rate, short fiber lengths with high absorption are preferred. Also, the dopant is expected to emit light in the L- Band. Considering all these criteria above, we chose the Liekki Er80-8/125 with D = -20 fs 2 /mm and absorption db = 80 db/m at 1530 nm Fiber length The repetition rate we were aiming at was 1 GHz with an expected output bandwidth centered at around nm. With the known refractive index for silica glass = 1.45, equation (2.23) yields a total length of 100 mm Mirrors As illustrated above, the Bragg Reflector and Saturable Absorber structure combined with pump-reflective coating constitute the optimal constellation for our purposes. The chosen SBR gives us a modulation depth of 2,5%, a saturation fluence of 25 µj/ and a recovery time of 6 ps. In order to prevent thermal damage of the SBR, pump-reflective coating was used and a short piece of SMF spliced to the gain fiber which was then butt-coupled to the SBR. An alternative way to avoid heat issues could have been free-space coupling which however would have added unnecessary noise to the signal. As a partial reflector we decided to use an output coupler coated upon the ferrule of an FC/PC connector with an output coupling ratio of 10% Wavelength-Division Multiplexer In order to complete the laser design, 980 nm light has to be pumped into the cavity to create population inversion at the same time allowing the extraction of the signal light at 1550 nm 29

30 1 GHz Erbium-doped fiber laser coming out of the laser. For this purpose, a wavelength-division multiplexer (WDM) is used to selectively allow pump and signal transmission through the specified ports Building the laser Fig Schematics of the 1 GHz laser with reference between the components of the 1 GHz laser design and the elements in the principal laser setup. A 980 nm laser diode acts as an optical pump, an output coupler with 10% transmission for the signal wavelength corresponds to the transmissive mirror and the SBR plays the role of the reflective mirror while an Erbium Doped Fiber serves as the gain medium. The Liekki gain fiber represents the main part of the laser cavity. We tested its absorption behavior for different wavelengths before splicing a 93 mm piece of EDF to 7 mm of SMF which was used for thermal protection of the SBR. The next step was to connectorise the spliced piece of bare fiber with FC/APC connectors and polish them on films with different grit sizes. Later we went on to measure the splice loss by determining the transmission of 1310 nm light at which an EDF does not exhibit absorption losses. A relatively low splice loss of 0.12 db could be reported. The remaining parts of the laser setup now needed to be assembled and tested. The combined port of the WDM was spliced to the Output Coupler (OC) and the transmission measured in all relevant directions for pump as well as signal wavelengths. Similar tests were conducted with the optical couplers. Moreover, the power output of the pump diode connected to the isolator was measured over the entire operational pump current range and overnight tests were performed to determine its long-term stability (see Appendix D: Components). 30

31 1 GHz Erbium-doped fiber laser 3.3. Measurements CW operation Fig Setup of the CW measurement After each component was characterized, we first tested the laser in CW operation before investigating its mode-locked characteristics. The reason for this additional step was to make sure that enough intracavity power is generated for mode-locking purposes. For this measurement we butt-coupled our cavity to a silver mirror with high reflectivity and measured its output power. The gain was constant at about 5 db and the intracavity sufficiently high to saturate the saturable absorber which was mainly responsible for self-starting in our design Mode-locking operation Setup For the actual mode-locked measurement, two couplers were used in order to connect the output of the laser to the power meter and the OSA as well as the polarization measurement setup. As the output beam of the laser is most likely elliptically polarized, a polarization beam splitter projects the ellipse onto two linearly polarized components. One of them is then converted into an electrical signal by the photo detector which is connected to an RF spectrum analyzer. The RF spectrum is finally used to determine the repetition rate as well as to examine possible sidebands. This way it is possible to make a statement on the stability of the angle of the ellipse. A rotating ellipse would lead to a modulation of each of the two linear amplitude components which results in sidebands in the frequency domain. As we used a free- 31

32 1 GHz Erbium-doped fiber laser Fig Setup of the mode-locked measurement space polarization beam splitter, the laser output had to be coupled into free space and back into fiber via collimators Results The first mode-locked states which were detected all displayed one or two unwanted sidebands. Two of them can be seen in Fig. 3.4 and Fig Although the powers achieved looked quite promising, it was necessary to continue adjusting the bend of the fiber until a more stable mode-locked state with respect to polarization could be found. In the end we were able to capture two different mode-locked states with stable polarization which you can easily see in Fig. 3.5 where the only peaks are at multiples of the repetition rate of GHz. (a) (b) Fig An undesired mode-locked state with one sideband shown in the RF spectrum (a) and OSA spectrum (b) with I pump =700 ma and P out = 13 mw. The sideband in the RF spectrum suggests amplitude modulation of the envelope. 32

33 1 GHz Erbium-doped fiber laser (a) (b) Fig A second undesired mode-locked state with two sidebands shown in the RF spectrum (a) and OSA spectrum (b) with I pump =700 ma and P out = 16.5 mw. (a) (b) Fig RF spectrum of the 1 st and 2 nd successfully mode-locked state with stable polarization (a) and OSA spectrum of the 2 nd mode-locked state with I pump = 1100mA and P out = 26 mw (b). No sidebands are visible and the repetition rate equals to GHz. Once the states were found, traces of several pumping levels from 700 ma to 1150 ma were recorded, the characteristic quantities calculated and in the end summarized in Table 3.1. The relations between the pump current I pump and pump power P pump at the 980 nm input port of the WDM can be found in Table 3.2. The first state provided measured powers in the orders of mw at a peak wavelength of about 1556 nm. If we now calculate the output power P out which is available at the 1550 port of the WDM (Fig. 3.9) by eliminating the coupler losses with (3.1) we obtain values around mw. The intracavity power with eliminated WDM and output coupler losses ranged from mw, the 3 db bandwidths were around nm. With the assumption of a transform-limited pulse you can then calculate the pulse duration with (3.2) 33

34 1 GHz Erbium-doped fiber laser (see [10]), which were in the order of fs. It is important to note that for powers lower than 300 mw the mode-locking started to fall apart while it was stable until high powers close to 530 mw. The second successfully mode-locked state yielded slightly better values with measured powers from 8-10 mw, P out hence ranging from mw at bandwidths of nm. The corresponding pulse durations were consequently at around fs. However, the peak wavelength was slightly shifted towards longer wavelengths of about 1570 nm (see Fig. 3.7). As opposed to the first state, the second state showed a maximum threshold at P pump = 530 mw. (a) (b) (c) Fig OSA spectra of the 1 st (a) and 2 nd (b) successfully modelocked state for different pump currents and the comparison of the two spectra (c) In addition to the relevant characteristics mentioned above, several other observations could be made which confirmed the behavior predicted in chapter 2. As the pump power increases, the spectral width broadens while the pulse gets shorter (eq. (2.29)). The peak wavelength also experiences a shift which is due to the fact that the total energy loss, which is now spread among a larger number of wavelengths, always seeks for its minimum. Since the loss curve is not only determined by the inherent absorption spectrum of the gain fiber but also influenced by the wavelength dependent characteristics of the SBR and OC as well as the bend of the fiber, it is hard to predict the final position of the center wavelength. However from looking at Fig. 3.7, one can deduce that for state one, the losses are lower for shorter wavelengths while it is the opposite case for the second state. Furthermore, Fig. 3.8 depicts the pulse in the frequency domain with linear scale which shows a nice sech-shape. This is exactly the soliton solution for which we designed the cavity. After 34

35 1 GHz Erbium-doped fiber laser turning the laser off and back on again, the mode-locked state was automatically reached for sufficiently high pump power. This is an indication for a good self-starting mechanism as well as a decent reproducibility of the mode-locked state. The optimal state we found during the measurement for a carrier wavelength of 1556 nm was for I pump = 1150 ma and P pump = mw with an intracavity power of 243 mw and output power of 13.7 mw, a spectral width of 8.2 nm corresponding to a of 316 fs. Shortest durations for carrier wavelengths at 1571 nm were found to be 156 fs at I pump = 1100 ma and P pump = 513 mw with a significantly higher P intracavity = 460 mw and P out = 26 mw. The spectral width was 16.6 nm. Fig OSA spectrum in a linear scale of the 2 th successfully mode-locked state with I pump = 900 ma, P pump = 420 mw, P out = 20 mw 35

36 1 GHz Erbium-doped fiber laser Fig Setup of the mode-locked measurement with losses and characteristic powers I pump P measured P out P intracavity peak Bandwidth FWHM [ma] [mw] [mw] [mw] [nm] [nm] [fs] 1 st mode-locked state nd mode-locked state Table 3.1. The two stable mode-locked states and their characteristic quantities I pump [ma] P pump [mw] Table 3.2. EM4 Pump diode D power characteristics: I pump and the corresponding pump power at the output of the isolator. The values at 1100 ma and 1150 ma were calculated by linear interpolation. 36

37 1 GHz Erbium-doped fiber laser Overnight test In addition to the measurements above, we conducted an overnight test to examine the stability of the second mode-locked state in particular as it was considered the better one of the two with a shorter pulse duration. Over 24 hours several periods could be observed (Fig. 3.10): In the 1 st and 3 rd period, the output power of the laser remained fairly constant with 5% power variations. Between the hours 5 and 15 however a gradual decrease of power is noticeable which corresponds to changes in bandwidth and peak wavelength as shown in Fig Since the experiment was started at 6 pm, it is likely that this trend was due to more distinct temperature changes in the laboratory during the night. Thermal fluctuations can result in changes of the geometrical dimensions which directly affect the alignment. In order to make sure that this development was not due to possible damages of the pump diode, we performed another final long-term test of its power output. Fig shows fluctuations of about 0.3%. Therefore, as the laser displayed good stability during the working hours and it is reasonable to state that the overnight drop was purely due to changes in external parameters, we are confident to claim that our laser fulfills the initial goals of having a short time duration, high repetition rate, long-term stability and can be self-started very easily. Fig Power development of the laser over 24 hours starting at 6 pm. Clearly the power stays constant in 1) and 3) whereas in 2) it drops by approximately 5%. 37

38 1 GHz Erbium-doped fiber laser Fig OSA spectra of the 2 nd successfully mode-locked state at I pump = 700 ma on the first (blue) and second (violet) day. Apparently the alignment changed overnight, while it stayed fairly constant during the day. Fig Power development of the 980 nm pump diode output power over 7 hours after the mode-locked overnight test at I pump = 700 ma 38

39 ASE and EDFA 4 ASE and EDFA 4.1. Introduction Erbium-doped fiber amplifier As Table 3.1 shows us, the output powers emitted by the 1 GHz laser never exceeded 26 mw implying a very low signal to noise ratio which is undesirable in optical communications. High powers are also essential for certain measurements involving nonlinearity. For this and other reasons an optical amplifier is obligatory. Since commercial amplifiers are generally very expensive, the idea was to design a home-made fiber amplifier from scratch providing us with the best possible characteristics. The most relevant quantity for amplifier operation is the gain. The change of the signal intensity propagating in the fiber at the position z for infinitesimal dz is equivalent to g(,z) in equation (2.21). In order to examine the dependence of g(,z) with regard to pump and signal intensity, we consider the case of which leads to (4.1) depending on the level of population inversion, which can be calculated in steady state by (4.2) where N is the total amount of electrons (see [1]) and, respectively. The effective power gain in db of an amplifier with the length of be defined as can then (4.3) In eq. (4.2) we can see that for very high the population inversion vanishes and is therefore not able to provide more net induced emission for increasing signal powers. Moreover, if (4.2) is substituted into (4.1) which yields (4.4), it is obvious that for fixed 39

40 ASE and EDFA moderate and very high, the increase becomes linear with z, independent from the input power. (4.4) This also means that decreases for higher powers and the amplifier is operating in the saturated gain region. Intuitively it can be understood as follows: When the pump power is too high, all the electrons that are abundant in the excited state will have been used up for induced emission so that the spare photons are not able to produce any more amplification. For our applications we are looking for an amplifier which has a high gain and SNR at the carrier wavelength of the laser around nm. In the case that they show opposite trends, a higher gain would be more important than a high SNR Amplified Spontaneous Emission The concept of Amplified Spontaneous Emission (ASE) is the amplification of spontaneous and induced emission which dominates the absorption for high population inversions. It is basically a laser cavity without mirrors so that the amplification path is equivalent to half a roundtrip. The emitted spectrum resembles the gain spectrum of the erbium doped fiber mentioned above. However, the output beam is by no means coherent because every photon is emitted with random phases. Therefore, incoherent ASE light is usually an undesired phenomenon for laser sources because it adds noise and even reduces the coherent laser radiation in the propagating direction. Likewise, ASE in the counter propagating direction inconveniently depletes inversion and lowers the gain. Nevertheless, ASE sources can also prove to be useful for example for characterizing fiberoptic components, for biomedical imaging (optical coherence tomography), spectroscopy and optical sensing. Our final application would be to characterize nonlinear waveguides on silicon wafers with regard to their behavior towards different wavelengths, which could be much faster if all wavelengths were evaluated at once. 40

41 ASE and EDFA Fig ASE spectrum in which the 3 db flatness and its corresponding 3 db bandwidth are marked. Significant characteristics of an ASE include the degree of flatness, meaning absolute power change around the peak power (Fig. 4.1), the corresponding bandwidth as well as the total output power which is the most important factor for our application. The higher the output power for this particular bandwidth the better the final SNR and results of our measurement will be. Our desired center wavelength is at 1555 nm with a 3dB bandwidth ideally around 20 nm and output powers of at least 50 mw Structure and parameters The main part of an ASE source or amplifier is once more the gain fiber. As optical pumping is involved, WDMs are also required. Unlike the laser, there are no mirrors involved and the SBR is replaced by a second WDM which allows us to extract the desired light at 1550 nm after half a roundtrip. The structure of an ASE source and the one of an amplifier only differ in such a way that for an amplifier the 1550 port of the WDM in is seeded with the signal while it remains unconnected for the ASE source. There are several possible setups for an ASE source or amplifier which are shown in Fig This thesis will discuss the co-directional method. Apart from the principal structure, there are several other parameters which affect the performance of the ASE source or amplifier significantly such as the length and type of the gain fiber, the input wavelength and the input power. 41

42 ASE and EDFA (a) (b) (c) Fig Different possibilities of Amplifier/ASE source setup: (a) Co-directional pumping for an Amplifier (b) Two-Stage ASE source (c) Contra-directional pumping for an Amplifier An optimum length with regard to gain can be found at the point where g(,z) becomes zero and any additional fiber would only lead to increasing losses and therefore less effective gain. On the other hand, the ASE spectrum, which evolves in the gain fiber at the same time, results in a deviating behavior of the SNR. The choice of the fiber highly depends on the application for which you want to use your amplifier or ASE source. If nonlinearity and the total dispersion in the fiber do play a role, a highly absorptive gain fiber, for example the Liekki Er110-4/125 (Er-110), is advantageous. For other applications the less doped Fibercore M /125 (M-12) might also be a possibility in case its behavior is more favorable in other aspects. All seed wavelengths exhibit different behaviors because of the wavelength dependent gain spectrum. As mentioned above, the amplifier gain also significantly depends on its actual input power. Because of the gain saturation phenomenon we should not only seed all wavelengths with a constant power, but, if possible, also perform a linearity test in order to detect at which powers it starts to saturate. 42

43 ASE and EDFA 4.2. Measurement Setup In our experiment we focused on obtaining the wavelength, pump power as well as fiber length and type dependent gain and SNR ratio, the latter being dominated by the ASE spectrum. For this purpose we seeded the amplifier with a constant input power of 0.1 mw which was the limitation set by the tunable laser source (TLS). The saturation regime would therefore still have to be examined in future experiments. Fig Setup for the EDFA and ASE source measurement For the measurement we decided to monitor the input power, the output optical spectrum and output signal power as well as the pump power at PM2 (see Fig. 4.3). The purpose of the output signal power measurement in addition to the OSA spectrum is to eliminate any possible calibration imprecision of the OSA. Both the pump diode and the TLS were protected by an isolator to avoid damage by back reflections Procedure Before starting the actual experiment, we once more thoroughly characterized all of our components by systematically seeding them with all wavelengths we would be using for the test. Details on the measured components characteristics can be found in Appendix D: Components. The parameters which were systematically scanned included the wavelength seed, the pump current I pump and the length of the fiber. Certainly the type of the fiber with different doping levels also had a big influence on the results. The wavelength and pump current were both controlled by an automated scan with intervals of 5 nm and 50 ma whereas the gain fiber type and length had to be manually adjusted. The scan itself contained two for-loops: the outer one performed a sweep of the TLS with a wait time of 2 s to make sure that the laser diode has 43

44 ASE and EDFA reached the steady state while the inner loop increased the pump current linearly, each time followed by a 1s pause prior to the power and OSA measurements. After a few scans, we noticed that the GPIB interface started to transfer data from the buffer of the OSA to the computer before the OSA has even finished sweeping. This resulted in misleading spectra which were at times showing data from the previous measurement. Hence we additionally waited 1 s between the OSA sweep and the GPIB transfer. At the end of the two for-loops operated with seeded gain fibers, the pump power was gradually decreased after the TLS had been turned off. These last traces were later used for the ASE source design. Since we wanted to start the scan for inherent losses at about 100 db, the initial length of the M-12 fiber was chosen to be 50 m while we started the cut-back of the Er-110 fiber at 95 cm since it exhibits much higher absorption (Fig. D. 1). After each scan, the EDF was shortened by a reasonable length according to the trend shown on the graphs, before it was respliced to WDM out. The measurements of the spectra and power values do not only allow us to obtain important characteristics of an amplifier or ASE source with the specific lengths but also provide an insight as to how the spectrum develops inside the fiber over length. An additional piece of SMF was used to connect the gain fiber to the output WDM so that the length of the 1550 port was maintained. The splice of the EDF to the input WDM remained throughout the whole experiment Preprocessing After collecting the relevant data, which were the input power at PM1 and the output power at PM3 as well as the OSA spectra (Fig. 4.3), they needed to be preprocessed. All recorded OSA spectra for one fixed fiber length were plotted in one graph immediately after the scan. Additionally, the raw data of the spectra were saved in txt-files for future analysis. The power values were stored in files for fixed wavelengths and fiber lengths showing the collected data for pump currents between 0 and 1100 ma. The pump powers at PM2 were only measured in order to decide whether or not an output WDM is necessary when the amplifier is connected with a subsequent optical device designed for 1550 nm. For intermediate calculations they need not be taken into account. Before the final data analysis could take place, the measured output and OSA power had to be adjusted by eliminating the coupler losses. The losses of the WDM however were kept in order to achieve a realistic estimation as of which powers to expect in case the WDM is required. Other than the power meter values, the OSA power values had to undergo an additional calibration step. They were multiplied by the ratio of the sum over the entire spectrum divided by the power output at PM3. This is only a valid step if the noise is assumed to concentrate in the wavelength range of the OSA spectrum. At this point it is also important to note that all figures in this thesis which include OSA traces display the actual measured spectra according to Fig. 4.3 and were not normalized with regard to coupler and WDM losses. 44

45 ASE and EDFA Above pre-processing measures were applied to both ASE and Amplifier measurements Erbium-doped fiber amplifier Data Processing As mentioned above, the variables of interest for the amplifier are the gain and the SNR. In order to obtain the gain, the signal power inside the 1 nm bandwidth centered at the peak wavelength supposedly equal to seed was calculated from the OSA spectrum and compared with the input power from the TLS into the WDM in. Its ratio was then converted into db. In the case of insignificant power levels I uniformly assigned 3e-8 W to the corresponding variables. The output power which the amplifier provides (P out in Fig. 4.3) for a certain input wavelength was defined as the signal power inside the peak. The noise dominated by the ASE spectrum is reflected by the SNR which is defined as the logarithm of the signal power divided by the noise power within the bandwidth of nm, which was the overall power subtracted by the signal power. The results were then visualized by and as well as plots with a fixed current of 1100 ma, since all parameters were monotonically increasing with I pump. The numeric values can be found in the tables in Appendix E: Results Fibercore M / Gain The contour plots in Fig. 4.4 provide us with a general overview of the amplifier behavior as a function of wavelength and fiber length, when the pump power is fixed at P pump = 513 mw. Gain and output power are proportionally related with each other since the input power stays fairly constant at 0.1 mw throughout the entire experiment which is why only the gain will be discussed in detail. Precise values of all three characteristics can be looked up in Table E. 3 - Table E. 5. Both quantities have their maxima at nm and short fiber lengths below 15 m. Interestingly, Fig. 4.5 (a) shows that for increasing wavelength, the peak gain shifts to longer fiber lengths. In order to explain this fact it is crucial to understand how could actually theoretically be modeled. From equations (4.1) and (4.3) we can see that the overall gain can be calculated by integrating the infinitesimal gain shown in Fig. 2.5 where z is the position of the fiber. is moreover closely related to, since the population inversion in (4.2) is directly dependent on the pump light intensity. The longer z, the lower the absorption and population inversion. 45

46 ASE and EDFA (a) (b) (c) Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Color plots of gain (a), output power (b) and SNR (c) as a function of wavelength and length. The effective gain in db over a fiber length (4.5) can then be understood as the integration of the consecutively dropping gain spectra for decreasing population inversion and hence increasing. The reason why we can find a gain maximum at all now becomes clearer: At z cross where the changes its sign from positive to negative, itself would have its maximum. The more intuitive picture with Fig. 2.5 suggests that above a certain there is net absorption so that the overall gain which has accumulated throughout the fiber so far would only drop as the fiber length is further increased. Moreover, if one takes a look at the points where the curves cross the x-axis in Fig. 2.5, it is obvious that for longer wavelengths the zero-crossing occurs for lower population inversion, therefore the peak of is located at longer lengths than for shorter wavelengths. This can be physically explained as follows: Although N 2 is already depleted in such a way 46

47 ASE and EDFA (a) (b) Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: Gain as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) that the net emission becomes negative for short wavelengths, there is still enough population inversion for longer wavelengths at lower energies. It is also possible that the higher energetic photons which are absorbed now raise the population of the sublevels responsible for the transitions at lower energies and therefore help to prolong the propagation length with net gain for these seed wavelengths. For a more sophisticated and thorough explanation of this behavior, it is necessary to study the population dynamics of the different sublevels in the three-level system of Er

48 ASE and EDFA One observation for short fibers and short wavelengths was still surprising. According to Fig. 4.5 (a), zero-crossing has just been reached for e.g nm after 5.2 m. If one now integrates all the curves up to this length, a peak is expected at 1530 nm. Fig. 4.5 (b) shows that for short lengths of the fiber we have a relatively flat gain from nm and that for long fiber there is a distinct peak gain at a particular wavelength which shifts to higher values. The latter can be easily explained if one considers exactly as the effective gain as a function of wavelength for a fixed fiber length. As the light propagates through the fiber, the absorption is much higher for shorter than for longer wavelengths so that for longer fiber, the peak is consequently located at longer wavelengths. The former trend however does not match with the prediction by of having a peak at 1530 nm. The behavior is presumably due to gain saturation (4.1.1) which could be verified in future measurements by a nonlinearity test mentioned above Signal-to-noise ratio A short glance at the SNR contour plot in Fig. 4.4 is enough to distinguish two white areas which yield SNR maxima of about 200 db. This is the value I assigned to all cases where the noise was zero and the logarithm hence could not be calculated. Fig. 4.8 shows the spectra for these cases. One could argue that the SNR at these parameter combinations is simply at its maxima which happen to be extraordinarily high. But if you follow the 1600 nm curve in Fig. 4.6 (a) you can see that it actually continues to rise after reaching the supposed maximum. Another possibility is that above a certain threshold the setup behaves like a cavity because of a bad splice and the system starts to lase and therefore concentrates all its energy at one wavelength (2.2.1). But later on, after examining the SNR color plots at different pumping levels and e.g. comparing Fig. 4.7 with Fig. 4.4 (c), it turned out that some of these singularities only appeared for lower currents but vanished for higher pump currents suggesting that this explanation is not the whole truth. For the depiction of the SNR as a function over length as shown in Fig. 4.6 (a), we chose to eliminate the singularities in favor of a higher resolution in the more informative SNR range SNR as a function of fiber length The question now is how the behavior of the gain and noise relate to each other and if theoretical considerations together with Fig. 4.5 (a) can predict Fig. 4.6 (a). An important approach is once again to look at the absorption spectrum of the fiber in order to develop an idea as for what to expect e.g. for dropping gain. When the gain is already decreasing, the zero-crossing for this particular seed and any other shorter wavelength would have already been reached. Furthermore, a close look at Fig. 2.5 reveals that for all curves below zero, the ASE spectrum at nm would generally be more absorbed than the signal for >1530 nm which leads to a rising SNR for dropping gain. Before the gain reaches its maximum, which is the case for longer wavelengths and short fibers, it is still rising and the same argument holds, namely that the SNR rises because decreasing infinitesimal gain 48

49 ASE and EDFA (a) (b) Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: SNR as a function of fiber length for different wavelengths (a) and as a function of wavelength for different fiber lengths (b) with a cut-off at 50 db so that the spectra with zero noise are suppressed in favor of the important trends in the relevant SNR range. for longer > 1550 nm automatically involves increasing absorption for the shorter wavelengths of the ASE spectrum according to the curves in Fig For short lengths, the above predictions are more or less confirmed by Fig. 4.6 (a). However, while the gain drops with longer length for all wavelengths, the SNR also begins to drop for e.g nm at 16.2 m (see Fig. 4.6 (a)) although we would have expected the opposite. In order to understand this behavior, Fig. 4.9 gives a more detailed picture of what exactly happens with the spectra. The drop apparently occurs because the ASE spectrum, as much as it shifts to longer wavelength and is attenuated with length, begins to arise at a completely different wavelength range starting from a length of 16.2 m. 49

50 ASE and EDFA Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, seed = 1590 nm, P seed = 0.1 mw, L = 31 m: OSA spectrum with no ASE noise Fig M-12 fiber with I pump = 500 ma, P pump = 230 mw, P seed = 0.1 mw: Color plots of the SNR as a function of wavelength and length The new ASE spectrum is most likely not based on the population inversion provided by the 980 nm pump diode because the overall power of the ASE spectrum is wavelength dependent for a fixed fiber length. A possibility is that the new spectrum is produced in such a way that the higher energetic signal light now starts to act like a pump. If this assumption was true, the ASE spectrum would at least have to be located at lower energies than the signal light itself which is indeed the case in Fig. 4.9 (a), Fig. 4.9 (b) and (c). As the signal wavelength becomes longer and above 1565 nm, the absorption at seed will not be high enough anymore to produce net emission which is why above a certain wavelength the SNR actually behaves according to the theoretical predictions in the previous paragraph and rises with increasing length SNR as a function of In Fig. 4.6 (b), three different behaviors can be noticed: For short lengths the SNR follows the slope of the gain, for medium lengths the SNR exhibits a maximum which is shifted relative to the maximum of the gain and for long fibers the SNR eventually rises with wavelength after being negligible up to 1560 nm. When the fiber is very short, the ASE spectrum does not change significantly with wavelength since population inversion is so abundant that both the ASE and are provided with enough excited electrons to maintain their gain. For medium lengths between 11 and 21 m, the SNR also follows the gain but in a much more pronounced way. A possible explanation for this could be the competition between the ASE and signal light since population inversion is limited now. This means that an increase of the signal power would subtract from the ASE spectrum whereas when the gain decreases, the noise power grows accordingly. 50

51 ASE and EDFA (a) (b) Fig M-12 fiber I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: A new ASE spectrum evolves with increasing fiber length for a seed wavelength of 1560 nm (a) which dampens the SNR whereas it doesn t really emerge for 1595 nm (b) For long lengths the SNR monotonically rises with wavelength. If we take a look at Fig (c) this can be better understood. The peak gain is at 1560 nm where the absorption and total power are finally sufficient to create a new ASE spectrum. Apparently the signal gain is more dominant so that in total the SNR rises drastically. For longer wavelengths the gain drops again and so does the ASE, since it directly depends on the absorbed power which acts like a pump. In addition, the fact that under these circumstances the SNR continues to rise indicates that the ASE is decreasing faster than the gain. In general, the processes involved are much more complicated and profound which is why numerical simulations would be needed in order to check the validity of the hypotheses above. 51

52 ASE and EDFA Amplifier design After observing several interesting phenomena while exploring the 3D parameters space, the optimal parameters for our amplifier need to be determined. As previously mentioned, we would like to have the highest gain and SNR for around nm. Short lengths in Fig. 4.5 (b) are very favorable in terms of a flat and high gain spectrum. However, if we look at the corresponding curves in the SNR graph, we see that the SNR is higher for 16.2 m, at the same time having a gain reasonably close to the maximum. The decreasing SNR curve at 5.2 m and the rising SNR for 16.2 m cross at the wavelength of 1555 nm which can be seen by comparing Fig with Fig which illustrate the development of the OSA spectrum for both cases). (a) (b) Fig M-12 fiber with seed = 1560 nm for I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: OSA spectra for different lengths in full span (a) and peak zoom (b). 52

53 ASE and EDFA Although the spectrum is not equally flat at 16.2 m, it can be considered a good compromise overall. In the end, we were able to design an amplifier of 16.2 m length with a gain of 26 db, output power of 48 mw and an SNR at 32 db at a signal wavelength of 1560 nm and P seed = 0.1 mw. (a) (b) Fig M-12 fiber with seed = 1570 nm for I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: OSA spectra for different lengths in full span (a) and peak zoom (b). 53

54 ASE and EDFA (a) (b) (c) Fig M-12 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Development of the spectrum over seed for L = 5.2 m (a), L = 16.2 m (b) and L = 47.2 m (c) in which for other wavelengths there was only noise. The power levels beyond the chosen wavelength range were all below -70 dbm and therefore cut off for these graphs. 54

55 ASE and EDFA Liekki Er110-4/125 (a) (b) (c) Fig Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: Color plots of gain (a), output power (b) and SNR (c) as a function of wavelength and fiber length. Since the highly doped Er-110 fiber is very expensive, we started at a length which from our experience could be close to the maximum. This is possibly the reason why the graphs do not feature some of the surprising characteristics that the M-12 does. A comparison of Fig (a) with Fig. 4.5 (a) can support this fact as the whole examined range of the Er-110 corresponds to 5-10 m and maybe even shorter lengths of the M-12 which were not recorded. According to Fig. 4.14, the optimal length for nm with respect to gain is at about cm (see Fig. 4.17), for 1565 nm at about 80 cm. For longer wavelength it seems that the maximum of the gain is yet to come for longer fiber lengths which were not recorded. The contour plots of gain and SNR in Fig (a) and (b) are almost identical, which suggests that the population inversion is still so high that gain dominates the behavior of the SNR and the ASE spectrum is still created by the pump power which equals to 513 mw in all graphs. 55

56 ASE and EDFA For our laser we need an amplifier which is as short as possible with a high gain and SNR at nm where the higher gain is the more important criterion. All lengths between 80 and 95 cm exhibit similar gain figures for nm, however the SNR varies drastically. By looking at Fig (a) it is clear that for 1560 nm the SNR rises with length. After consulting the exact values of gain and SNR in Table E. 6- Table E. 8 we came to the conclusion that an Er-110 fiber operates ideally at a length of about 85 cm which gives us a gain of 21 db, an output power of 22 mw and an SNR of 37 db at = 1560 nm and P seed = 0.1 mw. As our laser has higher output powers at about 20 mw and the fiber should be as short as possible, it is very likely that it reaches the gain saturation at lower length which is why an additional cut-back measurement is necessary to optimize the design for our purpose. (a) (b) Fig Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: Gain as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) 56

57 ASE and EDFA In general, the output powers and gain of the Er-110 fiber are slightly less favorable than the M-12 whereas the length of the M-12 could be unacceptable for experiments where pulse broadening is not desired. Hence, depending on the application the M-12 can be chosen when high power outputs are needed while the Er-110 would prove to be more reliable for the amplification of ultrashort laser pulses. (a) (b) Fig Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, seed = nm, P seed = 0.1 mw: SNR as a function of fiber length for different seed wavelengths (a) and as a function of wavelength for different fiber lengths (b) 57

58 ASE and EDFA (a) (b) Fig Er-110 fiber with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1mW: Development of the spectrum over seed for L = 45 cm (a), L = 80 cm (b) 58

59 ASE and EDFA (a) (b) Fig Er-110 fiber with seed = 1560 nm for I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: OSA spectrum for different lengths in full span (a) and peak zoom (b). 59

60 ASE and EDFA Amplified Spontaneous Emission source (a) (b) (c) Fig M-12 fiber unseeded with a fixed flatness of 3 db: Output Power (a), Bandwidth (b) and = center (c) as a function of pump current and fiber length Data Processing The performance of an ASE source is defined by its bandwidth at a certain flatness, center wavelength and output power. As mentioned in 4.1.2, our application requires a wide bandwidth of about 20 nm, small flatness and an output power with a minimum of at least 50 mw. The desired center wavelength is at about 1555 nm. In order to narrow down the search for the optimum and speed up the analyzing algorithm later, the desired flatness was chosen to be 3dB. The characteristic quantities were also calculated for other flatness values but will not be discussed in this text in detail. Compared to the amplifier, a new characteristic quantity for the ASE source was the center wavelength of the spectra which is depicted by its distance to the desired center wavelength center nm in Fig (c). In order to obtain center, the peak wavelength and bandwidth have to be determined first. After using the internal Matlab function max() to find peak I wrote a function which would detect the closest two for which. The bandwidth was then defined as the difference between two 60

61 ASE and EDFA and and the center wavelength as their arithmetic mean. In case the peak power was below -35 dbm, the center wavelength was assigned to be at 1450 nm having a bandwidth of 0 nm (see Appendix E: Results). For the calculation of the output power we used the same function as for the amplifier where the signal range was defined as the above bandwidth determined above Fibercore M /125 The contour plots in Fig convey a very clear message which is that at very high pumping levels, we have maximum output powers of > 16mW for short lengths. But the center wavelength is apparently at about 1530 nm and the bandwidth is narrow. At this center the output power is naturally higher because when the peak is at 1530 nm, it is much more powerful than any other peak wavelength in other spectra (see Fig. 2.5). Unfortunately this is not the desired center wavelength 1555 nm, which is why despite high output powers, a different optimum had to be found. If we move towards longer lengths and lower pumping levels there is a bandwidth maximum of 18 nm with a fairly reasonable ~10 nm at 8 m (see Fig. 4.19). For a fixed length of 8 m, Fig shows how the center wavelength shifts from 1530 nm to 1560 nm and the bandwidth becomes wider with decreasing pump power. Lower pump current causes the population inversion to decrease so that the gain spectrum changes its shape according to When N 2 is low, N 1 is high and the absorption spectrum dominates the gain coefficient according to (2.21) which also means that longer wavelengths have higher emission and therefore the ASE spectrum shifts to the right. However, the output powers at this length are in the sub milliwatt range (Table E. 9) so that we have to continue our search for a satisfying parameter combination. If we stay at high pumping levels and gradually decrease the length, Table 4.1 shows that we can find higher output powers for 11.2 m with relatively wide bandwidth and center closer to 1555 nm. But even so, such output powers in the orders of a few milliwatt are still far too low. This problem could be resolved by building a Two-Stage ASE source consisting of a co-directional ASE source in the first and an amplifier in the second stage (Fig. 4.3). However, since we did not perform a complete nonlinearity study of our amplifier, a sophisticated simulation of the performance of the two stage ASE source is not warranted based on our currently available results. Bi-directional pumping could be another possibility to achieve higher output power levels. 61

62 ASE and EDFA Length (m) Bandwidth (nm) center (nm) Output Power (mw) Table 4.1. M-12 fiber with I pump = 1100 ma, P pump = 513 mw: Characteristic values for the ASE source (a) (b) Fig M-12 fiber unseeded: OSA spectra for L = 8m (a) and L = 11m (b) for increasing pump powers. The light blue and green traces are potentially useful for a good ASE source, showing a reasonably wide 3 db bandwidth and center at around 1555 nm. 62

63 ASE and EDFA Liekki Er110-4/125 A comparison of the ASE performance of Er-110 with M-12 reminds us of the observation for the amplifier measurements. The full range of the Er-110 fiber lengths resembles shorter lengths of the M-12 for the output power. However, a look at the values for center tells us that for these lengths Er-110 mostly operates at center =1530 nm where the bandwidth never exceeds 7 nm. However, if ever a short ASE is needed, it should be worth a try to repeat the experiment with longer lengths of Er-110 since the absorption spectrum would gradually dampen the power at 1530 nm with increasing length. It would then still be significantly shorter than an M-12 based fiber amplifier. A good length to start with would probably be at about m. Fig Er-110 fiber unseeded with a fixed flatness of 3 db: Output Power (a), Bandwidth (b) and = center (c) as a function of pump current and fiber length. 63

64 Conclusion and future work 5 Conclusion and future work 5.1. Conclusion In this thesis, I have presented a design and measurement results for a compact and selfstarting Erbium-doped fiber laser which exhibits a short of 160 fs and an output power of 26 mw at 1570 nm for a pump power of 513 mw into the WDM. Lower pumping levels above a threshold of 300 mw also allow mode-locked operation as well as high P pump < 526 mw which is when the mode-locked state falls apart. Moreover, the laser showed no polarization rotation nor thermal damage after 24 consecutive hours of operation. (a) (b) Fig RF spectrum of the 1 st and 2 nd successfully mode-locked state with stable polarization (a) and OSA spectrum of the 2 nd mode-locked state with I pump = 1100mA and P out = 26 mw (b). No sidebands are visible and the repetition rate equals to GHz. In order to build an EDFA for our laser, we determined the optimal parameter combination for amplifier operation with the M /125 and the Liekki110-40/125 fiber. The M-12 fiber can generally provide higher powers but is undesirable for pulse amplification because pulse propagation in a long dispersive fiber leads to significant pulse broadening. The optimum length of the M-12 fiber for a signal wavelength of 1560 nm was found at 16.2 m for I pump = 1100 ma, P pump = 513 mw and P seed = 0.1 mw which yielded a gain of 26 db, power output of 48 mw and an SNR of 32 db. The Er-110 fiber had its most favorable point of operation at 85 cm, providing a gain of 21 db, output power of 22 mw and an SNR of 37 db at the same signal wavelength and input power. The exact spectra for the relevant range of seed wavelengths at these lengths are depicted in Fig

65 Conclusion and future work (a) (b) Fig M-12 fiber, L = 16 m (a) and Er-110 fiber, L = 85 cm (b) with I pump = 1100 ma, P pump = 513 mw, P seed = 0.1 mw: OSA spectra for different wavelengths Concerning the operation as an ASE source, the initial length of the Er-110 fiber we used proved to be too short to achieve the desired center wavelength of about 1555 nm. However, the M-12 fiber gave us acceptable results with respect to the bandwidth and center wavelength. For 11.2 m, the 3dB bandwidth was 10.8 nm centered at around 1558 nm. This setup gives us an output power of 6 mw at the 1550 port of WDM out in Fig