Pulse shaping with a phase-shifted fiber Bragg grating for antisymmetric pulse generation

Transcription

1 Pulse shaping with a phase-shifted fiber Bragg grating for antisymmetric pulse generation G. Curatu, S. LaRochelle *, C. Paré **, and P.-A. Bélanger Centre d Optique, Photonique et Lasers, Université Laval, Québec, Canada GK 7P4 ABSTRACT Pulses of arbitrary temporal shape can be generated by spectrally filtering a short pulse. Frequency selective reflectors, such as fiber Bragg gratings, can be designed to obtain the desired pulse shape. The required distribution of the refractive index modulation, amplitude and phase, can be calculated using inverse scattering techniques. For weak gratings, under the Born approximation, the impulse response of the grating is directly related to the refractive index distribution. The specified refractive index can be photo-written in an optical fiber using standard phase-mask scanning techniques. Two Bragg gratings were specially designed to shape a train of gaussian pulses into antisymmetric Hermite-Gauss pulses. The first grating had a length of 4 mm producing a spectral response over.5 nm (peak-to-peak). This grating was interrogated by ps pulses produced by a CW tunable laser with an external modulator. The second grating (L = mm and λ = nm) was interrogated with a mode-locked fiber laser (7 ps). The pulses were characterized in the frequency and time domain. The antisymmetric pulses were propagated in standard fiber to verify the presence of the phase shift between the two lobes. These Hermite-Gauss pulses could be used to study antisymmetric dispersion-managed soliton pulses. Keywords: Fiber Bragg gratings, pulse shaping, pulse propagation, antisymmetric pulse, soliton.. INTRODUCTION During the past years, the increased interest in soliton-based communication systems raised the need in pulses having particular shapes. A rather challenging task has been the generation of odd-symmetry pulses to study dark solitons. Their generation is less straightforward than for bright solitons because dark solitons require a local change in phase. If such a pulse does not contain the appropriate phase shift, it evolves into a symmetric pair of dark pulses with opposite velocities. Several techniques have been developed for generating dark solitons, with the first attempt made in 987. The odd-symmetry dark pulses were created by spectrally filtering a 6 nm beam in which a phase shift of π was introduced. The filtering was done using a grating, and the phase shift was introduced by means of a phase plate. In 988, dark soliton pulses at 62 nm were obtained using a spatial amplitude and phase mask in combination with a grating pair 2. Later, in a 993 experiment 3, dark solitons were obtained from an 85 nm Ti:sapphire. The pulse shaping setup was based on a selective amplitude and phase filtering of the longitudinal modes of the laser cavity. More recently, a technique based on fiber Bragg grating pulse shaping was suggested for the generation of dark solitons 4. A uniform fiber Bragg grating was used as a passive filtering element at the output of a mode-locked laser, in order to transform the train of bright pulses into a train of odd-symmetry dark pulses. However, in this case, it was only by coincidence that the uniform grating introduced the required amount of phase shift between the modes of the mode-locked laser. Recent research in the dispersion-managed systems for optical communications imposes new challenges in generating dispersion managed soliton pulses. A periodic dispersion map can support the propagation of a pulse called dispersionmanaged soliton, whose shape reproduces itself every period of the dispersion map 5. By deriving an approximate ordinary differential equation for the shape of the fundamental dispersion managed soliton, the existence of higher-order dispersion managed solitons was predicted 6. The first antisymmetric solution was theoretically demonstrated to be robust enough to propagate without distortions over thousands of kilometers. This second mode can be well approximated by the odd Hermite-Gauss function. * larochel@gel.ulaval.ca; Tel: (48) ext.3559; Fax: (48) ** Now with Institut National d Optique, 274 rue Einstein, Québec, Canada GP 4S4

2 In this paper, we present a new and simple method of generating a train of antisymmetric Hermite-Gauss pulses by reflecting a short pulse from a phase-shifted fiber Bragg grating. The impulse response of the grating, or equivalently its transfer function, will determine the reflected pulse shape. This principle has been used in the past to generate a train of rectangular pulses by reshaping short optical pulses 7. In the following section of this paper, we discuss the requirements on the reflectivity and index modulation of the Bragg gratings to produce the antisymmetric pulses. We find that an apodization profile with a double lobe structure and a π phase-shift is a good approximation of the exact solution for a weak reflectivity grating. In Section 3, we discuss experimental results on the writing and characterization of the fiber Bragg gratings. Finally, in Section 4 we present the impulse response of the two filters designed to produce antisymmetric Hermite-Gauss pulses of 2 ps and 26 ps width between the peaks. We then verify the presence of a π phase-shift between the two lobes by propagating the pulses in standard fiber. 2. DESIGN OF FIBER BRAGG GRATINGS The appropriate distribution of the index change along the grating was calculated using an inverse scattering technique based on the solution to the Gel Fand-Levitan-Marchenko coupled equations 8. The specification of the required reflectivity and phase allows the determination of the index modulation amplitude and phase. This technique does not however guaranty the feasibility of the resulting grating profile. The apodization profile of the index modulation required for the generation of Hermite-Gauss pulses is shown in Figure for gratings with peak reflectivities of 2%, 5%, and 95%. The reflectivity is represented as a function of the wavenumber detuning δ= β π/λ, where βis the fundamental mode propagation constant, and Λ is the grating period. The detuning is normalized to δ o = mm -. The solid line represents our ideal target spectrum, and the dotted curve is the calculated spectrum given by the corresponding index modulation for a grating length limited to 2 mm. The target reflectivity spectrum has a Hermite-Gauss shape only because the Hermite-Gauss function is an auto-fourier transform (i.e. its Fourier transform is also a Hermite-Gauss). From Figure it can be seen that, as the specified grating reflectivity is increased, the apodization profile becomes more complex. At the same time, the difference between the target and the actual reflectivity increases due to the finite length of the grating. Figure. (a) Required apodization profile calculated by inverse scattering; (b) Comparison between the target (solid line) and the achievable (dashed line) spectral response for a 2 mm long grating. To simplify the design and fabrication process by avoiding complicated index profiles with multiple phase shifts, low reflectivity gratings can be considered. For these weak gratings, in which light penetrates through the full grating, the Born approximation specifies that the reflectivity spectrum is proportional to the Fourier transform of the index modulation pro- 2

3 file along the grating length. The impulse response in the time domain is the inverse Fourier transform of the reflectivity spectrum of the grating. Therefore, for a short input pulse, the temporal shape of the reflected pulse is proportional to the refractive index profile along the grating length. So, to obtain a Hermite-Gauss pulse, the apodization profile of the refractive index modulation has to be modulated after a Hermite-Gauss shape. In most writing regime, the photo-induced index change produced by ultra-violet exposure is strictly positive. However, an effective negative apodization profile can be obtained by introducing a phase shift of π where the sign change must occur. Figure 2 shows an example of a 4 mm fiber Bragg grating with a Hermite-Gauss index profile (the period of the grating is not to scale)..5 x -4 Refractive index change phase shift Length [mm] Figure 2. Refractive index change within a fiber Bragg grating with a Hermite-Gauss index profile. Two gratings were designed for two different pulse shaping experiments. Several factors had to be taken into account for the design of the gratings: length, spectral width, reflectivity, phase shift, etc. To effectively obtain the impulse response of the gratings, the filter bandwidth should ideally be much smaller than the spectral width of the source. The bandwidth of a fiber Bragg grating depends on the length and on the index modulation of the grating. For weak gratings, the bandwidth is inversely proportional to the grating length. In this work, we consider two different scenarios: input gaussian pulses of FWHM = ps and FWHM = 7 ps. In the design of the gratings, we also had to consider experimental constraints limiting the grating length to 5 mm for narrow-band gratings and mm for wideband gratings. In the latter case, the constraint arises from the difficulty to write a short apodization profile with sufficient spatial resolution considering the UV beam width of mm. Assuming a Hermite-Gauss apodization profile, the reflectivity of the gratings were calculated using the matrix transfer method 9. For the first scenario, the length of the grating was chosen such that its spectral width was of.5 nm (peak-to-peak), with a reflectivity of 3%. This resulted in a 4 mm long grating with a maximum index change n =.3-5. In the second case, the grating length was mm, with a maximum index change n =.5-4. The spectral width was of nm (peak-to-peak), with a reflectivity of 65%. The final parameters for both cases are shown in Table. Figure 3 shows the calculated wavelength and time domain pulse shaping results. Input Pulse (FWHM) Grating Length Table. Simulation parameters and results. Maximum Index Change Grating Bandwidth (peak-to-peak) Grating Reflectivity Shaped Pulse Width (peak-to-peak) ps 4 mm nm 3% 2 ps 7 ps mm.5-4 nm 65% 26 ps 3

4 (a) (b).9.9 Input pulse Input pulse Reflected pulse FBG Reflected pulse Wavelength [nm] Time [ps] (c) (d).9.9 Input pulse Input pulse FBG Reflected pulse Reflected pulse Wavelength [nm] Time [ps] Figure 3. Pulse shaping simulation results: (a) ps input pulse (wavelength domain); (b) ps input pulse (time domain); (c) 7 ps input pulse (wavelength domain); (d) 7 ps input pulse (time domain). 3. PHOTO-WRITING OF FIBER BRAGG GRATINGS In order to fabricate the desired fiber Bragg grating, an appropriate experimental setup was designed. The technique used falls into the phase mask scanning category. In this setup, the fiber and phase mask move together rather than the laser beam, which remained fixed with respect to the optical table. The phase mask is further mounted on a translation stage driven by a piezo-electric transducer (PZT) (Figure 4). Broadband Source UV beam OSA Phase Mask PZT Optical Fiber PZT Translation Stage DC Motor XY -st order +st order XYZ DC Translation Stage Figure 4. Fiber Bragg gratings photo-writing setup (top view). 4

5 To write a fiber Bragg grating of arbitrary apodization profiles and to introduce phase shifts anywhere along the grating, we used a computer program to control the motion of the PZT and translation stage. By changing the dither amplitude of the PZT stage while maintaining a constant sweep velocity, any apodization profile can be theoretically realized. The dither amplitude varies between and Λ g /2, where Λ g is the period of the grating. Due to the fact that the two-beam interference pattern on the fiber is a sinusoid, the dither amplitude profile corresponding to an apodization profile a(z) can be approximated by 2 d(z)=(2/π)cos - [a(z)]. Introducing a phase shift of π at a certain position within the grating was done by simply adding an offset of Λ g /2 to the dither of the PZT when that position was under the UV beam. Two Bragg gratings were written following the specifications established by the simulations: lengths L = 4 mm and L 2 = mm, and index changes n =.3-5 and n 2 =.5-4. The gratings were photo-written into photosensitive fiber using a frequency doubled Argon laser source, which gave mw of CW power. The beam was focused through a cylindrical lens with a focal length of 5 mm. The scanning speed for the 4 mm grating was. mm/s and. mm/s for the mm grating. After the photo-inscription, the gratings were characterized with a tunable laser source with a resolution of 5 pm. The results were found to be in accordance with the numerical simulations, namely: bandwidths λ =.5 nm and λ 2 = nm (peak-to-peak), and reflectivities R = and R 2 = 5. Figure 5 compares the calculated target reflectivity spectra of the gratings to the measured spectra done on the actual gratings. Even though we measure only the amplitude of the reflectivity, we can examine whether the phase shift between the two reflectivity peaks corresponds well to π. Similar apodization profile without a proper phase shift of π would not result in a two equal lobes reflectivity spectrum. If the phase shift would be close to π (but not π), the two lobes would not be of equal amplitudes. Further, without any phase shift between the peaks, we would obtain a three-lobe reflectivity spectrum. We can conclude from Figure 5 that in (b) the phase shift corresponds well to π, while in (a) the asymmetry suggests an error of % in the phase shift. (a) (b) Reflectivity Wavelength [nm] Reflectivity Wavelength [nm] Figure 5. Reflectivity spectra (solid-measured, dotted-simulated): (a) 4 mm grating; (b) mm grating. 4. PULSE SHAPING AND PROPAGATION After pulse shaping, propagation of the odd-symmetry Hermite-Gauss pulses can be used to experimentally verify the accuracy of a phase shift of π within the pulse. During its propagation, chromatic dispersion broadens the pulses but, due to the phase shift of π between the two lobes of the Hermite-Gauss pulse, the gap between the lobes remains unaltered. If the pulse would not have the phase shift of π, as the lobes enlarge, the field would add up in phase and fill in the gap. Figure 6 (a) presents simulation results of the propagation through 82 km of SMF-28 fiber (D = 7 ps/nm/km) of the Hermite-Gauss pulse generated from a ps input pulse and compares the results to the case where the propagating pulse would be of even symmetry (i.e. no phase shift). In this case, the antisymmetric pulse suffered minimal chromatic dispersion, making difficult to distinguish the dashed line from the solid line in Figure 6 (a). For the 7 ps input gaussian pulse, the Hermite- Gauss pulse propagation was calculated through 5.5 km of SMF-28 fiber and the output pulse with and without the phase 5

6 shift is displayed in Figure 6 (b). For this short Hermite-Gauss pulse, the pulse width (peak-to-peak) is enlarged from 26 ps to 32 ps. (a) (b) Time [ps] Time [ps] Figure 6. Effect of chromatic dispersion for odd (dashed) and even (dotted) Hermite-Gauss pulses: (a) 2 ps pulse propagated on 82 km of standard fiber; (b) 26 ps pulse propagated on 5.5 km of standard fiber. The solid lines are the input pulses. The setup shown in Figure 7 was used to perform the pulse shaping to obtain the Hermite-Gauss pulses, and to propagate them on SMF-28 fiber. The ps gaussian pulses were produced by a CW tunable laser externally modulated by a Mach- Zehnder device. The modulator was driven by a short pulse generator having a repetition rate of MHz. The laser was tuned such that it was centered exactly on the fiber Bragg grating. The pulses were coupled into the grating by means of an optical circulator. The reflected antisymmetric pulses were boosted up by an Erbium-doped fiber amplifier (EDFA), and sent into 82 km of SMF-28 fiber. The input gaussian pulse, the shaped antisymmetric Hermite-Gauss pulse, and the pulse after its propagation on 82 km were measured with a GHz optical oscilloscope, and are shown in Figure 8. The experimental measurements are similar to the simulation results: the peak-to-peak width of the shaped pulse is 2 ps, and the pulse remains almost unchanged after propagating on 82 km. Due to the fact that this pulse is fairly long in time (which implies a narrow wavelength spectrum), it suffers almost no chromatic dispersion during its propagation on 82 km of SMF- 28 fiber. Therefore, it is not easy to assess the quality of the phase shift between the two peaks in this case. Further, even with dispersion, due to the low resolution of the oscilloscope ( GHz), it would not be possible to completely resolve the gap between the two antisymmetric peaks. However, it can be seen from Figure 8 that a slight change in the gap occurred during propagation. This can be attributed to the error in phase shift, but also to the fact that the laser source was not stable enough to remain centered on the grating during the entire measurement. Gaussian Pulse Circulator Short Pulse Source Grating EDFA Detection Hermite- Gauss Pulse SMF-28 Fiber EDFA Detection Figure 7. Pulse shaping and propagation experimental setup. 6

7 3.5E-3 3.E-3 Gaussian input pulse Intensity [Watt] 2.5E-3 2.E-3.5E-3.E-3 Hermite-Gauss pulse Hermite-Gauss pulse after propagation 5.E-4.E Time [ns] Figure 8. Oscilloscope measurements: pulse shaping and propagation ( ps input pulses). In the second case, the 7 ps gaussian pulses were generated by a mode-locked tunable laser at a repetition rate of 2 MHz. The reflected pulses were sent into 5.53 km of SMF-28 fiber. The following three pulses of interest were characterized in terms of their spectral and temporal shape: the input gaussian pulse (coming from the mode-locked laser), the Hermite- Gauss shaped pulse, and the Hermite-Gauss pulse after propagation. Peak powers and spectra of the three pulses were closely monitored to ensure a linear regime pulse propagation (dispersion only). The three spectra were measured with an optical spectrum analyzer, and are shown in Figure 9. Because of the short temporal length of the pulses, the autocorrelation was measured rather than their actual temporal shape. The three autocorrelation curves are shown in Figure. The autocorrelations of the Hermite-Gauss pulses clearly show the expected three peaks structure. The autocorrelation calibration factor is 7.7 ps/ms, which results in 25 ps Hermite-Gauss pulses (peak-to-peak). After propagation, the antisymmetric Hermite-Gauss pulse is enlarged due to dispersion (3 ps peak-to-peak), but maintained the same shape. This proved the quality of the phase shift of π between the two peaks, and therefore the antisymmetry of the pulse. All experimental measurements in this case were consistent with the simulation results shown in Figures 3 (c, d) and 6 (b). 5. CONCLUSION In conclusion, we have developed a simple and flexible new method to generate antisymmetric pulses by shaping a train of short gaussian pulses. Pulse shaping was done by filtering incident pulses using a phase-shifted fiber Bragg grating with an appropriately modulated refractive index and phase along its length. The method is simple because it is based on all-fiber components, eliminating any optical alignments. The flexibility of this method relies on the fact that the amplitude and phase of the reflected frequency components can be precisely controlled during the writing process of fiber Bragg gratings. Also, we can photo-write fiber Bragg gratings at any period, thus generating antisymmetric pulses at any wavelength. Further, adjustment is possible on a range of a few nanometers by strain tuning the grating. The Hermite-Gauss pulses will be further used as antisymmetric DM solitons to study their behavior and stability in a DM communication system. Several other applications in optical communication systems require the use of antisymmetric pulses, which can be generated using this method. 7

8 .2 Intensity [a.u.]. Input Gaussian pulse Shaped H-G pulse H-G pulse after propagation Wavelength [um] Figure 9. Optical spectrum analyzer measurements (wavelength domain): pulse shaping and propagation (7 ps input pulses)..2. Input Gaussian pulse Voltage [V]. Shaped H-G pulse H-G pulse after propagation Time [s] Figure. Autocorrelator measurements (time domain): pulse shaping and propagation (7 ps input pulses). 8

9 ACKNOWLEDGEMENTS The authors would like to acknowledge G. Baldenberger for his help on the short pulse measurements. This work was supported by the Canadian Institute for Photonic Innovations, by the National Science and Engineering Research Council of Canada, and by QuébecTel. G. Curatu is grateful to the Ontario Ministry of Education and to ITF Optical Technologies for the scholarships awarded during his study. REFERENCES. Ph. Emplit, J.P. Hamaide, F. Reynaud, G. Froehly, and A. Barthelemy, Picosecond steps and dark pulses through nonlinear single mode fibers, Opt. Commun. 62, pp , A.M. Weiner, J.P. Heritage, R.J. Hawkins, R.N. Thurston, E.M. Kirschner, D.E. Learid, and W.J. Tomlinson, Experimental observation of the fundamental dark soliton in optical fibers, Phys. Rev. Lett. 6, pp , M. Haelterman and Ph. Emplit, Optical dark soliton trains generated by passive spectral filtering technique, Electron. Lett. 29, pp , Ph. Emplit, M. Haelterman, R. Kashyap, and M. De Lauthouwer, Fiber Bragg grating for optical dark soliton generation, IEEE Phot. Tech. Lett. 9, pp , M. Suzuki, I. Morita, N. Edgawa, S. Yamamoto, H. Taga, and S. Akiba, Reduction of Gordon-Hauss timing jitter by periodic dispersion compensation in soliton transmission, Electron. Lett. 3, pp , C. Paré and P.-A. Bélanger, Antisymmetric soliton in a dispersion-managed system, Opt. Commun. 68, pp. 3-9, P. Petropulos, M. Ibsen, and D.J. Richardson, Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest, pp , E. Pearl, J. Capmany, J. Marti, Iterative solution to the Gel Fand-Levitan-Marchenko coupled equations and application to synthesis of fiber Bragg gratings, J. of Quant. Electron. 32, pp , M. Yamada and K. Sakuda, Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach, Appl. Opt. 26, pp , K.O. Hill, B. Malo, F. Bilodeau, D.C. Johnson, and J. Albert, Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask, Appl. Phys. Lett. 62, pp , J. Martin and F. Ouellette, Novel writing technique of long and highly reflective in-fiber gratings, Electron. Lett. 3, pp. 8-82, W.H. Loh, M.J. Cole, M.N. Zervas, S. Barcelos, and R.I Laming, Complex grating structures with uniform phase masks based on the moving fiber-scanning beam technique, Opt. Lett. 2, pp ,