RICE UNIVERSITY. 461nm Laser For Studies In Ultracold Neutral Strontium. by Aaron D Saenz

Transcription

1 RICE UNIVERSITY 461nm Laser For Studies In Ultracold Neutral Strontium by Aaron D Saenz A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree Master of Science Approved, Thesis Committee: Thomas C. Killian, Chairman Assistant Professor of Physics and Astronomy Randall G. Hulet Fayez Sarofim Professor of Physics and Astronomy Stanley A. Dodds Associate Professor of Physics and Astronomy Houston, Texas July, 2005

2 ABSTRACT 461nm Laser For Studies In Ultracold Neutral Strontium by Aaron D Saenz A 461 nm laser was constructed for the purposes of studying ultracold neutral strontium. The dipole-allowed 1 S 0 1 P 1 transition at nm can be used in laser cooling and trapping, optical imaging, Zeeman slowing, and photoassociative spectroscopy. We produce light at this wavelength by converting infrared light at 922nm from various IR sources, notably a Ti:Sapphire laser, via second harmonic generation in a frequency doubling cavity using a potassium niobate crystal. This thesis will discuss the motivation, optical resonator, locking electronics, and characterization of a 461 nm laser.

3 Acknowledgments I would like to thank my committee: S.A. Dodds, R.G. Hulet, for their time and patience, and especially my advisor T.C. Killian for his guidance and assistance both in the thesis and my work in general. Many thanks go to my colleagues at the Killian Lab: S. Laha, P. Gupta, P.G. Mickelson, Y.N. Martinez, S.B. Nagel, and C. Simien who gave good advice and valuable suggestions. Y.C. Chen was sorely missed but continued to serve as the apotheosis of post-doctoral excellence. I give my thanks to my family and friends whose support is vital and appreciated. G.D. Wiley, it would not have been fun without you. Finally: Thanks Mom and Dad, for everything.

4 Contents Abstract Acknowledgments List of Figures ii iii vi 1 Introduction Ultracold Neutral Strontium Laser Cooling and Trapping Absorption Imaging Photoassociative Spectroscopy Frequency Doubling Outline Optics and Beam Coupling Frequency Doubling Cavity Spatial Modes of the Cavity Beam Coupling and Alignment Output Beam Profile Electronics Error Signal

5 v 3.2 Locking The Cavity Characterization of Electronics Characterization of the 461nm Laser Efficiency of Frequency Conversion Thermal Effects Conclusion Summary Improvements and Future Work A Computational Analysis of Beam Profiles 54 B Computational Modelling of Beam Profiles 60 References 64

6 List of Figures 1.1 Strontium Energy Diagram Laser Cooling on Strontium Absorption Imaging Photoassociative Spectroscopy Energy Diagram Photoassociative Spectroscopy Results Optical Elements of Doubling Cavity Close-up of Potassium Niobate Crystal Beam Waists Beam Waists Inside Resonator Infrared Beam Profile nm Beam Profile Logic Flow of Feedback Loop Schematic of Locking Circuit Coincidence of IR Transmission and Blue Output Modes Transmission Modes of Cavity Close-up of Transmission Modes Output Modes of Cavity

7 vii 3.7 Close-up of Output Modes Switching Noise Comparison of Sweep Versus Lock Power in Blue Power Out vs. Temperature Efficiency of Cavity Temperature Controller Calibration Optimum Temperature for Input Power A.1 Matlab A.2 Matlab A.3 Matlab A.4 Matlab A.5 Matlab B.1 MathematicaCode B.2 MathematicaCode B.3 MathematicaCode B.4 MathematicaCode B.5 MathematicaCode B.6 MathematicaCode

8 Chapter 1 Introduction This thesis describes the construction of a 461 nm laser in the form of a frequency doubling cavity that facilitates various experiments on ultracold neutral strontium. This laser excites an allowed dipole transition from the 1 S 0 to the 1 P 1 states, in Sr and is the basis through which optical trapping and cooling, fluorescence and absorption imaging, and photoassociative spectroscopy (PAS) can all be performed. The following chapters will describe the physics and construction of the laser as well as characterize its performance. Designed to compensate for a gap in available commercial laser sources in the blue spectral range, the laser utilizes second harmonic generation (SHG) to frequency double near infrared light (IR) from 922 nm to 461 nm. We will first review the various experimental uses of the 461 nm laser, and touch upon the theory behind SHG before detailing the operation of the laser itself. 1.1 Ultracold Neutral Strontium Ultracold neutral strontium atoms provide unique opportunities for research with narrow intercombination line transitions that may lead to all optical means of obtaining quantum degeneracy [2][3][4], and/or may be utilized for optical frequency standards [5] [6] [7] [8]. There are several available bosonic isotopes for quantum degeneracy including the most abundant 88 Sr. Strontium displays interesting atomic

9 2 Figure 1.1: Strontium Energy Diagram. Strontium energy levels for commonly used transitions. Selected decay rates (1/s) and excitation wavelengths are shown *Taken from [1]. properties due to the absence of nuclear spin and the subsequent lack of hyperfine structure. Strontium atoms also approach the ideal two level theoretical systems used to commonly describe atomic laser cooling and trapping [9]. In such cases, the modelled atomic transition is in a J=0 J=1 system. In strontium, the two valence electrons may couple in parallel or anti-parallel, corresponding to triplet or singlet states that approximate the model [10]. Figure 1.1 shows a partial energy diagram of 88 Sr, with emphasis given to the transitions used within our laboratory. 1.2 Laser Cooling and Trapping We recently completed construction of a new apparatus for studying laser cooled strontium. The doubling cavity I built generates the nm photons for laser cooling and trapping of strontium along the 1 S 0 1 P 1 allowed dipole transition.

10 3 Magneto-Optical Traps (MOT), thoroughly discussed in Metcalf and van der Straten s Laser Cooling and Trapping, are now commonly used tools in many atomic physics laboratories [11]. In such traps, three orthogonal counter propagating beams cool and trap atoms inside a quadrupole magnetic field. In our setup, such atoms are provided by heating solid strontium to create an atomic beam that is collimated and Zeeman slowed using the same 1 S 0 1 P 1 transition. Optical cooling is performed by the well known Doppler technique, cooling strontium atoms to sub-kelvin temperatures, and obeying the well known Doppler limit given by: k B T doppler = Γ 2 (1.1) Where T doppler 760 µk is the Doppler limit temperature and Γ is the transition rate. For the 1 S 0 1 P 1 transition the Doppler limit is many time greater than the limit set by photon recoil: k B T recoil = 2 k 2 M (1.2) Where k is the wavenumber of the light, and M the mass of the atom, and T recoil 1 µk. In order to trap, orthogonal circular polarization is chosen for each propagating/counter propagating beam, and anti-helmholtz coil pairs provide magnetic field gradients to generate Zeeman shifts in the atoms traveling away from the intersection of the three MOT beams. The MOT cooling and trapping provides us with cold,

11 4 dense, and spatial constrained samples aptly suited for atomic experiments. Typical results for our 461 nm MOT are < 7 mk, > atoms/m 3, and sizes 1 mm 3. Figure 1.2 highlights the MOT setup in our laboratory including the doubling cavities which are the heart of the 461 nm laser described in this thesis. Not pictured is the red, 689 nm, intercombination line MOT that follows the 1 S 0 3 P 1 transition from Figure 1.1, and is the subject of S. Nagel s master s thesis [10]. Notice that the setup also includes absorption imaging which is further discussed below. 1.3 Absorption Imaging We are able to probe cooled and trapped strontium atoms through purely optical means utilizing absorption imaging. My doubling cavity is used to provide an imaging beam of 461 nm light. That image beam is split off the main MOT beam using an acouto-optic modulator (AOM), making it slightly detuned from resonance ( 40 MHz), and passed through the atoms inside the MOT which absorb photons along the 1 S 0 1 P 1 transition. The absorbed photons are emitted in a randomized manner such that relatively few travel along the same k vector as the imaging beam. Effectively, the atoms cast a shadow in the path of the beam, and by placing a CCD camera behind the atoms we can capture an image of that shadow. The shadow contains a plethora of valuable information about the atomic cloud. Not only can the camera capture information about the spatial outline and movement of the cloud, we can use the intensity of the absorption to determine the number of

12 5 Imaging Camera Magneto- Optical Trap Zeeman-Slowed Atomic Beam Strontium Reservoir Zeeman Beam Magnetic Coils 461 nm To MOT Imaging Beam Frequency Doubling To Zeeman Slower Ti-Sapphire Laser 922 nm Figure 1.2: Laser Cooling on Strontium Diagram of our experimental setup for studies on ultracold neutral strontium.

13 6 Image Beam Atoms Camera Figure 1.3: Absorption Imaging A beam slightly detuned from the 1 S 0 1 P 1 transition is incident upon the trapped atoms. The image of the cast shadow is recorded by a CCD camera and the corresponding Optical Depth is calculated.

14 7 atoms and approximate density. Using Beer s Law, we can relate the optical density (OD) of the MOT to the image intensity with (I atoms ) and without (I background ) the atomic cloud: OD(x, y) = ln[i background (x, y)/i atoms (x, y)] (1.3) OD(x, y) = α(ν) OD(x, y) = α(ν)n 0 e x 2πσz n i (x, y, z) dz (1.4) 2 2σ 2 x + y2 2σ 2 y (1.5) Where α(ν) is the aborption cross section at the image beam frequency ν, n 0 is the peak atom density, and we assume a Gaussian distribution of atoms consistent with our MOT [12]. We image along the z axis, perpendicular to the magnetic coils. For σ z we must infer a value, typically σ x σ y where sizes in the x and y axis are typically similar to each other within a factor of two. In Figure 1.3, we see an overview of the imaging process as well as an example of an OD distribution for our MOT. Absorption imaging along the 1 S 0 1 P 1 transition is the most commonly used and definitive diagnostic for ultracold neutral strontium in our lab. By varying the time between capture and camera exposure, we can watch our MOT spatially expand, yielding information on temperature and lifetime of our system. It is through this simple but powerful technique that we can analyze the results of the various other experiments we perform.

15 8 Energy ν = Σ g 1 Πu 1 S0 + 1 P 1. 1 Πg 461 nm SC 1 Σ + u RE 1 Σ + g 1 S0 + 1 S 0 Internuclear separation Figure 1.4: Photoassociative Spectroscopy Energy Diagram Abbreviations: State Changing Collision (SC) and Radiative Emission (RE) We only concern ourselves with the 1 Σ + u potential *Taken from [13]. 1.4 Photoassociative Spectroscopy Before we built the new apparatus, the doubling cavity was used to generate light to perform photoassociative spectroscopy (PAS), which provides valuable insight into molecular potentials and excited state lifetimes as well as scattering lengths of the 88 Sr and 86 Sr isotopes. Several papers have been recently written on PAS at both short and long range [13] [2] [14]. Figure 1.4 gives the atomic and molecular potentials as functions of internuclear separation. Notice the levels in the excited molecular potential, ν. During PAS, atoms in close proximity to one another can be optically driven to combine into molecular states by excitation into these levels. This light

16 9 assisted combination is the foundation of photoassociation. Atoms paired into the steep molecular potential quickly gain energy as they move along the curve. Many will transition back to the atomic state and gain enough kinetic energy to leave the trap - called radiative emission (RE). Even more kinetic energy is gained if the paired atoms go through a state changing collision (SC) wherein the molecular state changes to a lower-lying electronic configuration of free atoms [13]. In either case, photoassociated atoms no longer remain inside the atomic MOT. This absence of atoms that have been photoassociated allows us to set the number of atoms in the MOT as a direct indicator of how effectively atoms are being coupled into the molecular state. During our PAS experiments, a 461 nm beam was detuned from the 1 S 0 1 P 1 resonance and made incident upon 88 Sr or 86 Sr atoms that were trapped and cooled in the intercombination line MOT briefly alluded to earlier in this section. By varying that detuning, the PAS beam scanned the molecular potential. When on resonance with a quantum level, the number of atoms in the MOT would be reduced, often by more than 50%. When these experiments were performed at small detunings (0-2 GHz) corresponding to large internuclear spacings ( nm) they are known as PAS studies at long range and gave insight into long range parameters of the excited state potential. Figure 1.5 shows typical results for our PAS studies at long range ( 88 Sr only), which were normalized for intensity and duration of the beam. The level spacings allowed us to determine the 1 P 1 lifetime at 5.22 ±.03 ns [2].

17 10 number of atoms fraction remaining obs. calc. (MHz) x (a) data fit detuning (MHz) 1 (b) detuning (MHz) (c) quantum number Figure 1.5: Photoassociative Spectroscopy Results Typical spectra taken for long range PAS studies on 88 Sr (a)the signal from a single quantum level has been fit using a lorentzian curve (b)various quantum levels (ν from Figure 1.4) at long range show the decrease in signal strength nearing the atomic resonance (c) Results corresponded well with theoretical calculations *Taken from [13]. PAS studies at short range occured at larger detunings ( GHz) corresponding to smaller internuclear spacing (< 4 nm). These studies allowed us to probe the molecular potential further, determining the ground state wavefunction, and giving values for the scattering lengths of 88 Sr and 86 Sr that look promising for achieving quantum degeneracy [2] [4] [3].

18 Frequency Doubling Second harmonic generation of light is a prime example of non-linear optical phenomena in which the frequency of light is doubled through polarization waves in a medium. The polarization of the medium can be expressed as: P = ε 0 χ 1 E 1 + ε 0 χ 2 E 2 + ε 0 χ 3 E 3... (1.6) Where E is the electric field imposed on the medium and χ i is the i th order susceptibility of the medium. If an electromagnetic wave of frequency ω is incident on such a medium with a non-trivial χ 2 then a corresponding E-M wave will propagate with frequency 2ω. The power of that wave will follow the relation: P ω2 = [ 2η3 oω1d 2 2 eff L2 ]Pω 2 A 1 ( kl sin 2 ) 2 = ξ kl nl Pω 2 1 ( 2 kl sin 2 ) 2 (1.7) kl 2 k = 2ω 1(n 1 n 2 ) c (1.8) Where A is the area, k is the wavevector, L the length of the medium, c is the speed of light in vacuum, n 1 and n 2 are indices of refraction for each frequency, ξ nl is the nonlinear conversion efficiency, d eff is the nonlinear coefficient of the doubling crystal, and η 0 = 377/n 1 [15]. Typically, k is non zero, and the power of the frequency doubled wave is small [15]. If the two waves can be phase-matched, however, k goes to zero and the power

19 12 can be optimized. This matching can only occur if the indices of refraction for each frequency are identical. Potassium Niobate (KNbO 3 ) is aptly suited for frequency doubling in the bluegreen portion of the visible spectra. KNbO 3 is transparent in both the visible and near infrared regimes, and has a large d eff suitable for efficient doubling as seen in equation 1.7. Potassium Niobate is often used in frequency conversions to the blue-green spectra with reported efficiencies > 80% [16]. If the fundamental and second harmonic have orthogonal polarizations, the crystal s birefringence may make it possible for n 2 to equal n 1. The equality is fine tuned by varying incident angles of light with respect to the axes of the crystal, or through varying the temperature of the crystal. The first technique is utilized, in our case, as the crystal is being manufactured: the crystal is cut at an angle, with respect to its optical axes, to phase-match the 922 nm and 461 nm light near room temperature, as discussed in [17] [18] [19]. We also use the second technique: the temperature susceptibility of the crystal is such that the indices of refraction in the two perpendicular axis, which correspond to the two polarizations of IR and blue light, are widely tunable [19] [20]. This allows us to find and fine-tune near-room temperature for which n 2 is equal to n 1. For further information on the indices of refraction, the reader is referred to Figure 7 in [20]

20 Outline The thesis will describe the process through which the 461 nm laser was built and operates. The motivation for the 461 nm laser, as well as the theory of SHG, is discussed earlier in this introductory chapter. Chapter 2 will discuss the pertinent optical resonator beam parameters of the laser, as well as detailing some of its optical characteristics. Chapter 3 concerns itself with electronic feedback and stabilization and relates the electronic parameters of the lock-loop setup with the transmitted and output modes of the laser s doubling cavity. Characterization of the laser, including overall efficiency and temperature response is given in chapter 4, along with comparisons to similar systems from within and outside our laboratory. The final chapter gives a brief conclusion to this thesis and discusses possible improvements and avenues for future work. Appendices describing the computational techniques involved in modelling the beam profiles of the cavity are included.

21 Chapter 2 Optics and Beam Coupling In order to create the 461 nm visible laser light, an infrared 922 nm beam couples into a Potassium Niobate crystal within a resonant optical cavity. That 922 nm source has varied over the history of the 461 nm laser. The ideal source would be commercially available, easily tuned in frequency, able to be locked to an atomic reference, of sufficient power and intensity, and stable over long periods of time. These requirements suggest either a diode or Ti:Sapphire laser. Diode lasers are easily tunable by means of optical feedback. Using a diffraction grating in Littrow to form an extended cavity setup, they can be continuously tuned in frequency by 10s of GHz as the grating is adjusted via a piezo-electric transducer (PZT). Utilizing temperature and current control, the diffraction grating can be adjusted even further for discontinuous tuning over 1000s of GHz. This high range in tunability was ideal for the short range photoassociative spectroscopy studies described in section 1.4. For those experiments, the doubling cavity was fed by a TEC100 diode laser from Sacher Lasertechnik with output of 60 mw and able to be continually tuned without mode hops by > 8 GHz using compensating current as a PZT adjusted grating angle. Later, IR power was boosted to 125 mw using the more powerful TEC120. Laser linewidth was measured using a Fabry Perot etalon

22 15 and was approximately 85 MHz. The diode lasers, though aptly suited for the PAS studies, do not provide sufficient power for laser cooling and trapping as detailed in section 1.2. For the PAS experiments, relative measurements to a locked source using a Burleigh WA-1000 wavemeter were required. Coherent s MBR-110 is a Verdi-10 pumped Ti:Sapphire infrared laser that provides > 1 W of IR power for 10 W of pumped power. Using a standard bow-tie configuration and with a variably angled Fabry-Perot etalon, it can be easily tuned over the near infrared spectrum (670 to 1090 nm), and can be continuously scanned over 10 GHz while the etalon locks its frequency [15]. Two other 461 nm lasers built previous to the one characterized in this thesis are already supplied by the Ti:Saph. laser in our laboratory. A saturated absorption cell is pumped using one of those lasers, and the corresponding signal locks the Ti:Saph. to the 1 S 0 1 P 1 transition. The large available power makes the Ti:Saph laser ideal for the 461 nm laser for use in the MOT or Zeeman beams. Long range studies in PAS were also accomplished by passing the 922 nm beam through acousto-optic modulators (AOM) before entering the doubling cavity, and again after exit [13]. In this case the detuning in the IR beam was doubled as it was converted to blue light. This means that we were able to obtain detunings > 2 GHz using AOMs with maximum detunings < 350 MHz a piece. For the setup described in this thesis, the IR source is always the Ti:Saph. laser

23 16 tuned to 922 nm and passed through a fiber optic cable. This fiber is designed for transmission in the near IR, and has a high coupling efficiency > 75%. The optical fiber passes the IR beam onto another optical table where it is coupled into the doubling cavity as described below. 2.1 Frequency Doubling Cavity At its heart, the frequency doubling cavity is a simple optical resonator formed by two mirrors. Such a resonator, often referred to as a Fabry-Perot etalon, has two helpful qualities for frequency doubling. First, for high reflectivity of the mirrors, light circulates many times in the resonator before it escapes, creating higher intensities of light inside the resonator. Frequency conversion of infrared to blue light is directly proportional to the square of incident power in the crystal, as seen in equation 1.7. Accordingly, increases in the IR intensity within the crystal are desirable to maximize IR to blue light conversion. Second, destructive interference of the circulating light limits the possible wavelengths of light allowed inside the resonator to λ = 2L N Where N is any integer, and L is the length of the cavity. For a given wavelength of our IR source, the cavity will not generally allow the light inside. We scan L in order to match λ and see a resonant peak in transmission out of the back of the cavity when the two are in sync. Keeping the cavity on resonance is accomplished using a servo-lock described in section 3.2. For the 461 nm laser, the first mirror of the optical resonator is formed by the input

24 17 Cylindrical Lens Collimation Lens IR Fiber Coupler Mode Matching Lens Input Coupler Potassium Niobate Crystal Fast Photo- Diode KNbO3 n~2.28 Mirror Dichroic Mirror PZT Input Coupler Thermo-electric cooler Figure 2.1: Optical Elements of Doubling Cavity. Figure 2.2: Close-up of Potassium Niobate Crystal. coupler, and the second mirror by the back surface of the KNbO 3 crystal. Figure 2.1 diagrams our setup and Figure 2.2 provides an enlarged look at the resonator. Typically, optical resonators are characterized by three properties: the free spectral range (FSR), finesse (F ), and full width half maximum of a resonance (FWHM). For a cavity without loss, that is a cavity where the crystal does not frequency double but merely acts as a transparent medium, relations for each are given by: With F SR = F = π R 1 R F W HM = F SR F c 2L eff (2.1) (2.2) (2.3) L eff = D air + D crystal n crystal (2.4) R = R 1 R 2 (2.5) Where c is the speed of light in vacuum, D air 15 mm is the distance in air in the resonator, D crystal 5 mm is the crystal length, n crystal 2.28 is the index of

25 18 refraction for the crystal. Using these values for our doubling cavity, we can expect F SR 5.7 GHz, F inesse 239, and F W HM 23.7 MHz. Our doubling cavity, however, loses IR power due to conversion to blue light, power lost out the input coupler, and inherit losses of the system (L sys ). For a system with losses, we consider the follwing relations [21]: P ω2 = 16T 2 1 ξ nl P 2 ω 1 [2 R 1 (2 L sys ɛξ nl P ω1 )] 4 (2.6) P ω2 T 2 1 CP ω1 [1 2 R 1 (2 L sys ɛc)] (2.7) Where T 1 = 1 R 1 is the transmittance of the input coupler, ɛ P ω 2 P ω1 is the overall conversion efficiency of IR to blue, C = ξ nl P ω1 is the infrared to blue conversion per pass, and other variables are as in equation 1.7. If we maximize equation 2.7 with regards to T 1 [21]: T optimized 1 = L sys 2 + L 2 sys 4 + C (2.8) As we will always have some losses, and hopefully quite a bit of conversion to blue light, T optimized 1 will be greater than 0. Thus the optimized input coupler would have reflectance less than 1, as is our case. Finding the right T for a an optical resonator with losses is known as impedance matching, and is analogous to the concept in electronics [21].

26 19 Losses also affect the finesse of our cavity [22]: F 2π L sys + C + ln 1 R (2.9) Which does approach equation 2.2 as L sys and C go to 0. For our doubling cavity, this means that F 239 and F W HM 23.7 MHz as we calculated before. We continue this discussion in section Spatial Modes of the Cavity In order to successfully couple into the resonator the infrared light must match specific spatial modes. These modes are determined by the design of the optical resonator which has a preferred transverse Gaussian waist at a preferred position. This preferred beam profile is stable within the resonator and by coupling into it, we insure that circulating power within the resonator is maximized. The lowest order transverse spatial mode, T EM 00, is circular in pattern and behaves simply as it focuses, making it relatively easy to model within the crystal. It is Gaussian in both transverse axes and is the preferred spatial profile for most optical beams in atomic physics. Gaussian beam behavior is generally understood and is discussed in Lasers and Electro Optics by C.C. Davis as well as in many other references [23]. The optical cavity is described by a discrete set of resonance frequencies which correspond to integer number, N, of half wavelengths of the incident light such that

27 20 λn = L. These longitudinal modes are set by cavity spacing, L, and for a cavity 2 with sufficiently high finesse, can be very narrow. For our setup impedance matching requires a relatively low finesse and broad linewidth. Thus, with a relatively narrow IR source, it is the position, and not width of these resonances that will concern us. In our cavity, a piezo-electric transducer (PZT) attached to the input coupler allows us to vary cavity spacing and resonances. Typically, longitudinal modes are not a large concern during alignment, but become critical when we discuss locking the cavity to a particular resonance, as in section Beam Coupling and Alignment Maximizing power within the cavity requires exact alignment of the infrared light into the resonator. This alignment is dependent on incident angle and position, as well as beam waist position and size. Before attempting to couple the IR source into the doubling cavity, we first model the spatial modes of both resonator and IR beam and determine what beam shaping must occur to match the two. If the incoming mode of the infrared light does not match the fundamental mode of the cavity, light will be coupled into various transverse spatial modes, limiting the conversion efficiency of the doubling cavity. We can avoid this loss of efficiency by passing the IR beam through a lens before it enters into the doubling cavity. This mode matching lens will be chosen such that the new waist of the IR beam will coincide with the natural waist of the cavity.

28 21 IR Waist out of Fiber Mode- Matching Lens Input Coupler Virtual Cavity Waist Natural Cavity Waist Figure 2.3: Beam Waists This diagram is not to scale W aist S iz e HmL Input Coupler (Lens) Virtual Waist Natural Cavity Waist Crystal Position HmL Figure 2.4: Beam Waists Inside Resonator Using a Mathematica script (see Appendix B), we can model the natural cavity waist and the virtual waist used for mode matching. The dashed line is the natural cavity waist propagated out of the cavity ignoring the input coupler. The solid line to the left of the input coupler is the beam profile for both the virtual beam and the natural cavity waist propagated out of the cavity with the input coupler acting as a lens. The natural waist of the cavity, however, is calculated as if light originates in the resonator and stays there [23], allowing us to consider the input coupler as a focusing mirror. In such a case the natural waist is typically on the back mirrored surface of the crystal as depicted in Figure 2.3. We can calculate the exact size of this waist using standard ABCD matrix formulation, as described in [23]. In such formulation we consider the beam to travel through a repeating unit cell consisting of the crystal medium, open air, the reflective surface of the input coupler as a focusing

29 22 lens, open air again, and the crystal again. Once the ABCD matrix for this unit cell is calculated, we can use the equation found in [15]: w 2 0 = 2λ 0 B nπ 4 (A + D) 2 (2.10) Where w 0 is size of the natural cavity waist, and A,B, and D refer to the corresponding values of the matrix. Notice that the formula contains λ 0 n which is the wavelength of light in vacuum over the index of refraction of the medium. For a single media unit cell as discussed in [15] this formula is sufficient, but for our case, with two media of different n, we must alter the technique. We include the effect of the change of indices of refraction in the ABCD matrices themselves. We are then free to use a modified equation: w 2 0 = 2λ 0 B π 4 (A + D) 2 (2.11) Where the direct dependence on n has been moved to within the values of A,B, and D. If we wish to model light as it enters into the resonator, we should consider how that natural waist looks from outside. Here we introduce the concept of a virtual waist that mimics the position and size of the natural cavity waist as seen from outside the cavity. In order to model the virtual waist, we propagate the natural waist out of the cavity and towards the IR source. We then retrace the beam back towards the crystal, but ignore the input coupler. The radius of curvature of the input coupler is

30 23 25 mm, and has a focal length 50 mm for beams passing through. This gives us a virtual waist that is smaller and further from the back surface of the crystal than the natural waist as seen in Figure 2.4. We use the mode matching lens to match the IR beam to the size and position of this new waist. Determination of the virtual waist given cavity spacing and input coupler radius of curvature is excellently discussed in C. Simien s masters thesis [24]. We determine our virtual waist to be 39.6 µm, 3.85 mm from the front surface of the crystal. Correctly matching the real and virtual beam waists is simplified using computer modelling. Measurements of the IR beam using a Beam Master beam profiler are run through a Matlab script which then fits suitable Gaussian parameters to them using the equation: w 2 (z, w 0 ) = w0[1 2 + ( λ(z z 0) ) 2 ] (2.12) πw0 2 Where the beam waist, w, can be determined at any position, z, given the initial beam waist w 0 and position z 0. Equations for modelling Gaussian beams are taken from [23] and entered into a Mathematica notebook which takes the Gaussian waists and positions determined by Matlab and virtual waists from Mathematica, see Appendix B, and plots them over distance. Modelling the two profiles as they pass through various simulated thin-lenses allows us to mode match the IR beam into the cavity. Figure 2.5 shows the results of such a program. The horizontal and vertical profiles of the incoming IR light travel from left to right and are overlapped with the virtual

31 24 beam that propagates right to left out of the cavity. Sharp turns in the profiles correspond to the passage through a lens, as detailed in the caption. Although we could model a perfect mode-matching lens, we are limited in reality by available focal lengths lenses, and millimeter spatial resolution in positioning. The model in Figure 2.5 uses a single commercially made lens and we allow for some astigmatism in our IR beam. Appendix B provides a more thorough look into the beam coupling programs. The reader will notice in Figure 2.5 that the horizontal and vertical beam profiles out of the IR fiber vary widely from the virtual beam profile. This is NOT ideal. After completion of this thesis and many hours successful use of the 461 nm laser, an error was detected in the calculation of the natural cavity waist, and virtual waist. When corrected, the virtual waist was about half the previous size, causing the virtual profile outside of the cavity to be proportionally larger. The parameters for the virtual waist we listed above are the corrected values. Figure 2.5 shows this correct virtual waist, and the real beam profiles out of the IR fiber as currently used in our setup. Obviously, our current mode matching lens, while sufficient, is not ideal, and likely leads to coupling into higher order spatial modes, as seen in Figure 3.4 and discussed in Chapter 4. Future improvements in the 461 nm laser will include a better mode matching lens. Once the mode matching lens has been chosen and placed, alignment into the cavity can begin. After passing through the mode matching lens, the IR beam is

32 Mode Matching Lens W aist S iz e HmL Horizontal Waist Input Coupler (Lens) Vertical Waist Virtual Waist Position HmL Figure 2.5: Infrared Beam Profile The horizontal and vertical beams propagating from the left begin at z=0, the face of the IR fiber coupler. They then encounter the f=200 mm lens at z=0.37 m. The IR beams focus down onto the input coupler (effectively a f=-49 mm lens) at z=0.595 m and end at the back surface of the crystal located at z=0.62 m. The virtual beam propagates from right to left seeing the same elements in reverse. centered onto the input coupler and the reflection is aligned back onto the incoming beam. The crystal is then adjusted in the transverse axes such that the beam falls roughly along its longitudinal axis. Crystal angular alignment is then adjusted as cavity spacing is scanned, until transmission modes appear out the back end of the crystal. A high speed photodiode, see Figure 2.1, carries those transmission modes onto an oscilloscope where they can be maximized using the various IR turning mirrors and input coupler angle. Gross cavity spacing can be adjusted by moving the crystal itself, and the angle of the crystal may sometimes be altered to maximize transmission. A dichroic mirror at an angle close to 45 o from the incident beam, separates the incoming IR beam from the outgoing blue visible beam.

33 26 In order to maximize the efficiency of the cavity both the first and second harmonic frequencies of light must be phased matched within the crystal using temperature, as discussed in section 1.5. The fundamental and second harmonic are polarized at different axes, and indices of refraction in different axes have different temperature dependences. Temperature tuning matches the index of refraction of the fundamental frequency with that of the second harmonic. Coatings on the back surface of the crystal are used to provide the corresponding high reflectivity of the resonator mirror for both frequencies. The coatings must be of proper thickness such that the nodes of the fundamental and second harmonic coincide on the back surface of the crystal [25]. Small variations in coating thickness will lead to slightly different node positions causing destructive interference inside the optical resonator. Second harmonic losses due to coating thickness are non-trivial and may explain low conversion efficiencies discussed in section 4.1 [25] [26]. 2.4 Output Beam Profile The second harmonic generation of light provides a relatively ideal beam out of the doubling cavity. Figure 2.6 shows the beam profile of the 461 nm laser as it comes out of the doubling cavity and passes through a collimating lens, and two cylindrical lenses for beam shaping. In our current setup, the 461 nm laser provides light for a MOT, image beam, and 2D collimator (version of optical molasses). There are several excellent discussions of losses in SHG from the near IR to the

34 Vertical Waist W aist S iz e HmL Horizontal Waist Position HmL Figure 2.6: 461 nm Beam Profile Horizontal and vertical waists propagate from the left starting at z=0.62 m - the outer most edge of the input coupler. A f=200 mm spherical lens at z=0.815 m collimates the horizontal waist over long distances. Two cylindrical lenses (f=500mm and f=-400 mm) at z=1.215 m and z=1.3 m respectively help match the vertical waist to the horizontal. high end visible spectra [27][16][24][28][29]. Common optical culprits of loss include thermal lensing and blue light induced infrared absorption (BLIIRA). Thermal lensing occurs as temperature gradients form in the longitudinal and transverse axis due to heating from the circulating IR light. These temperature gradients change the indices of refraction of the KNbO 3 crystal and alter the position and typically increase the size of the resonator waist. Shifts in waist position and size affect the beam coupling into the cavity and adversely affect SHG [27]. More importantly, increases in beam waist lower intensity within the crystal and thus conversion efficiency. See section 3.3 and 4.2 for further discussion of thermal issues. BLIIRA is not completely understood, though extensive studies have been per-

35 28 formed to model its behavior and determine a coefficient for the process [28] [29]. It is typically modelled as blue light depopulating low-level traps inside the crystal lattice through photo-ionization, permitting increased IR absorption [27][29]. Infrared photons are normally absorbed into the crystal at a small yet measurable rate, but as blue photons are incident upon the crystal, that rate dramatically increases [28]. This absorption is significant with as little as 10 3 W/cm 2 of blue light, begins to increase exponentially near 100 W/cm 2 and continues so well past 10 4 W/cm 2 (for reference our laser intensity 1300 W/cm 2 ) [28] [29]. BLIIRA, combined with other loss mechanisms, helps explain why KNbO 3 crystals fail to maintain a quadratic dependence on incident power as suggested by theory, and instead enter into a linear regime and fixed efficiency [16]. Although BLIIRA can be reduced at longer wavelengths or higher crystal temperatures [28], this does not match our phase-matching criteria.

36 Chapter 3 Electronics Feedback electronics prove necessary in order to compensate for fluctuations in cavity spacing and crystal properties. Acoustic vibrations provide the greatest interference in cavity stability but thermal drifts may also contribute. By monitoring the transmission through the doubling cavity and correspondingly varying cavity spacing through a piezo-electric transducer (PZT), feedback electronics can lock the cavity on resonance and compensate for the fluctuations. An overview of the feedback process is outlined in Figure 3.1. Demonstrative samples of various signals have been provided for clarification. Important to cavity stability but not pictured in the figure are crystal temperature, high voltage amplification for the PZT, voltage offset on the PZT, and beam alignment into the cavity. Alignment has been discussed in the previous section and will be considered to already have been maximized in discussion of electronic feedback - likewise with crystal temperature, discussed in the next section. High voltage amplification and voltage offset will briefly be discussed with the ramp signal. 3.1 Error Signal A modified Pound-Drever-Hall method generates an electronic error signal to provide feedback into the cavity. In a standard P-D-H setup, the incoming laser light is

37 30 Use VCO & EOM to place sidebands on IR light Ramp cavity to vary resonance frequency Mix Transmission with VCO to form Error Signal Transmission > Set? NO YES Feed back Error into cavity (Locking) A B C D E ν 0 ν 0 -β ν 0 +β Intensity (Arb.) Ramp Signal Transmission Modes Time (ms) Intensity (Arb.) Error Signal Transmission Mode Time (ms) Intensity (Arb.) Set Point Transmission Mode Time (ms) Intensity (Arb.) Error Signal Locked Transmission Time (ms) Figure 3.1: Logic Flow of Feedback Loop. A) Frequency sidebands are placed on either side of the IR laser center frequency. An Idealized example below where β is 15 MHz. B) A triangular wave ramp is sent to the cavity which passes through resonances with the IR laser. C) An error signal is generated by demodulating the mixed sideband and IR center frequency signals. This error signal is anti-symmetric about peaks in transmission. D) A comparison between IR transmission level and a manually determined set point allow the locking mechanism to distinguish between off and on resonance conditions. E) The anti-symmetric error signal is fed back into the cavity PZT, causing cavity spacing to follow transmission peaks thus locking the cavity to the IR resonance. modulated and the reflected beam off the cavity is phase detected at the modulation frequency using an electronic mixer to produce a demodulated signal [30]. We have modified this setup to use the transmitted rather than reflected signal. This requires that the transmitted and outgoing light have coincident peaks, but this will always be the case for our setup as shown later in section 3.3. Infrared light from the Ti:Sapphire pumping laser passes through an Electro-Optic Modulator (EOM), acquiring frequency sidebands. These sidebands occur at roughly

38 31 15 MHz on each side of the IR laser frequency similar to Figure 3.1A, and are driven by a voltage controlled oscillator (VCO). Actual traces of our sidebands cannot be seen as the resolution of our cavity is greater than 15 MHz, but we cite the EOM technology s reliability and the successful production of an error signal as sufficient proof of their existence. After passing through the EOM, the IR beam is steered into an optical fiber that carries it onto the Neutral Atoms table, where our strontium studies occur, and from that fiber through a mode-matching lens and into the cavity. A simple triangular wave signal ramps the cavity PZT and scans the etalon s transmission frequency. Transmission peaks occur when the cavity spacing is on resonance with the input beam. The ramp varies 15 volts peak to peak at a typical rate of > 10 Hz and inputs directly into the feedback electronics circuit. From there, the ramp can pass into a high voltage amplifier whose input gain is 5. The amplifier also provides a DC offset to the PZT through an amplified battery signal. This offset is largely unimportant to the locking process as long as at least one transmission signal occurs during a ramp cycle. In order to guarantee the transmission peak, the offset is manually set such that peaks occur roughly in the center leg of the ramp signal, and the laser is then locked. The 461 nm laser can operate for many hours before DC offset drift causes it to unlock. One generates the error signal by mixing the transmission signal with the original VCO frequency. The signal is anti-symmetric: negative on one side of the transmission

39 32 peak, zero at resonance, and positive at the other side. Scope traces of the signal can be seen in Figure 3.1C and can be analyzed as in [31]. The anti-symmetry forms the backbone of the feedback signal and allows the locking circuit to center itself on a transmission mode. 3.2 Locking The Cavity Figure 3.2 provides a schematic of the locking circuit, which consists of a switching circuit and a single-path servo-lock. The servo-lock is a standard element in laser control, allowing the error signal derived previously to be amplified and integrated and fed back into the cavity. The switching circuit allows the locking system to determine for itself if the cavity is on or off resonance and respond accordingly. A simple circuit determines if the cavity is near resonance by comparing the transmission signal with a manually controlled set voltage. This set voltage is high enough that smaller, non-desirable modes are not considered to be on resonance. When the transmission signal is less than the set voltage, the switching circuit is sent a low signal. At low input, the switching circuit shorts the integrator and the boost of the locking circuit, resetting the capacitors and preventing the error signal from locking the cavity. Also at low, the switching circuit passes the ramp signal to the cavity causing it to continue scanning. Eventually, the ramped cavity should hit a transmission peak and cause the comparator to send out a high signal. The switching circuit then opens the capacitors to allow integration and stops sending

40 33 Figure 3.2: Schematic of Locking Circuit. The single path lock-loop and switching circuit used to the lock the cavity including relevant passive element values. the ramp signal to the cavity. There is a finite non-trivial time between the cavity nearing resonance and the locking circuit being able to integrate sufficiently to lock the cavity. To compensate for this time a small capacitor has been placed at the ramp signal output from the switching circuit, causing the ramp to come down slowly and assisting the integrator. This measure in of itself is helpful but not sufficient, and the set voltage must be considerably lower than the peak of the transmission to allow for extra integrator time. Thus there is some finesse involved in placing the set point at the correct voltage - high enough to exclude undesirable peaks but low enough to compensate for integrator lag.

41 34 The lock-loop is essentially an integrator with variable gain and boost to maintain a secure lock. Integration follows the standard relation: V out = 1 RC V in dt. (3.1) Where V out is output voltage, V in is input voltage and R and C stand for the input resistor and feedback capacitor respectively. During operation, the cavity will be ramped until it nears a transmission peak and integration begins. The integrated error signal will be fed back into the PZT and control the resonance of the cavity. Variable gain allows for the error signal to adequately shift the PZT without oscillation no matter what the absolute transmission, and thus error signal, strength. Boost gives more gain at low frequencies to provide a more stable lock. Normal procedure for locking the cavity is straightforward. Once cavity alignment and temperature have been optimized, the DC offset is placed appropriately. The locking circuit is then activated, the cavity begins to lock, and gain is adjusted manually to optimize 461 nm output. Fine-tuning of temperature may be required but the system does approach a single switch setup allowing the user a minimum number of tasks before maximum output of the cavity is achieved. 3.3 Characterization of Electronics Typical operation of the feedback electronics provides a robust lock to the IR transmission peaks, and generation of 461 nm light can be characterized in parallel to

42 Transmission Modes Blue Output Modes 5 Volts Time (ms) Figure 3.3: Coincidence of IR Transmission and Blue Output modes. Transmission modes are displaced +1 Volt and Blue Output modes -1 Volt for clarity. Amplitudes are to scale. electronic features. The two best diagnostics of cavity behavior are the transmitted (IR) and output (visible) modes of the cavity. The transmitted modes are a direct ingredient in the creation of the error signal and the output modes are our desired 461 nm laser output. The feedback and locking electronics do have an effect on the optical properties of that laser and the entire electronics system is characterized in those terms below. As we proposed, transmitted and output modes occur in coincidence with each other as seen in Figure 3.3. Figures 3.4 and 3.6 show the transmitted and output modes independently of each other and with the error signal as reference. Secondary

43 Error Signal Locked Transmission Transmission Modes 10 8 Error Signal Transmission Mode Volts 6 4 Volts Time (ms) Time (ms) Figure 3.4: Transmission Modes of Cavity. Error signal is offset by +6 Volts and amplified (x10) for clarity. The smaller transmission modes are due to coupling into non-t EM 00 transverse spatial modes. Figure 3.5: Close-up of Transmission Modes. Error signal is offset by +6 Volts and amplified (x10) for clarity. peaks in the transmission arise from coupling into non-t EM 00 transverse modes of the cavity. These higher order modes limit conversion power of the doubling cavity as discussed in section 2.2. Notice the anti-symmetry of the error signal needed to lock the cavity as we described earlier. A corresponding match between 461 nm light generation and the error signal is demonstrated as well. Noise that occurs during the error signal is problematic during startup when the cavity occasionally locks to a smaller transmission peak. Once locked to the correct mode, however, the switching circuit keeps the cavity from seeing extraneous error signals. The locked versions of each signal are provided as reference and to demonstrate that the transmission falls as the cavity locks while the opposite occurs with the visible light. Explanations and effects will be discussed later in this section.

44 Error Signal Locked Output Blue Output Modes 6 5 Error Signal Output Modes 4 4 Volts 3 Volts Time (ms) Figure 3.6: Output Modes of Cavity. Error signal is offset by +3.5 volts and amplified (x5) for clarity Time (ms) Figure 3.7: Close-up of Output Modes. Error signal is offset by +3.5 volts and amplified (x5) for clarity. The free spectral range (FSR) of the cavity corresponds in time to the separation between peaks. A simple method for experimentally measuring the FSR is taken from [24]. The 922 nm source (Ti:Saph. laser) is manually scanned with part of the beam coupled into the 461 nm and part aligned onto a Burleigh WA-1000 wavemeter. When cavity is on resonance with the laser, the wavemeter reading is recorded, and the distance between resonances is the FSR, measured to be 7.7 ± 0.1 GHZ. This process is akin to our normal sweeping configuration, only we are scanning the laser and not the cavity. Even this simple measurement gets us fairly close to our calculations in section 2.1 of 5.7 GHz. Taking our experimental value for the free spectral range we can determine a constant conversion factor of MHz/s for the given ramping of the cavity. Maintaining that same ramp and examining the inset of each figure gives an experimentally determined full width half maximum of each peak as 50

45 38 MHz for the transmitted and 30 MHz for the output. If we use the experimentally derived values for FSR and FWHM in the IR, we can calculate a finesse for our cavity which includes our losses at 110 mw input power. Using equation 2.3 we find that our finesse is 154, and using equation 2.9 we can say that L sys + C.0145 at 110 mw. Likewise, one can determine that the error signal scans the cavity 0.36 MHz/mV. These error signals have been optimized for the parameters of the laser at the time (110 mw input power, and o C control temperature) and vary as those parameters change Transmission Modes Blue Output Modes 5 Volts Time (ms) Figure 3.8: Switching Noise. The switching circuit of the lock-loop provides unwanted feedback onto the cavity PZT as it is being swept. This noise is manifested as multiple modes occurring after the primary mode, and can be seen on both transmitted and reflected signals. Transmission modes are displaced +1 Volt and Blue Output modes -1 Volt for clarity. Amplitudes are to scale.

46 39 While close to ideal, operation of the locking-circuit generates a few problematic effects on the 461 nm light. The first and most trivial problem is demonstrated in Figure 3.8 as compared to Figures 3.4 and 3.6. Notice the extra transmission peaks or fuzziness next to the main peak. This effect is caused by erroneous feedback from the switching circuit as it compares the set voltage to transmission signal. Though it has no direct path to the PZT while ramping, the switching circuit can provide an additional path to ground for the ramp signal through a capacitor. This path is necessary and cannot be excluded. It is thought that the switching circuit tries to activate as normal when a transmission peak occurs and causes the ramp signal to fluctuate as the cavity passes through resonance. During locking operation, this behavior is not seen because the switching circuit is directly in control of PZT voltage. Thus, the effect has minimal impact on the cavity and only needs to be eliminated when trying to take characteristic scope traces of the electronics. The effect can be removed by disconnecting the transmission signal from the comparator. Another effect of the locking circuit is seen in Figure 3.9 where power in the blue output is shown. During normal locking procedure, the output light increases as the cavity stops sweeping and locks onto resonance. This increase is expected as the cavity is optimized in temperature for locked output. If instead we optimize the cavity as it sweeps, we notice there is little power difference between the two signals. The temperature difference is non-trivial for our cavity: volts on the temperature

47 Swept Signal Locked Signal Volts Time (ms) Figure 3.9: Comparison of Sweep Versus Lock Power in Blue. Optimizing the crystal temperature for cavity output during swept operation shows that there is little to no power lost during locked operation. controller or 0.6 o C. We know that phase-matching criteria set the temperature in the crystal such that n 2 is equal to n 1 at all times [20][19], so we can surmise that the temperature difference occurs as the temperature controller tries to keep the crystal temperature in the beam path constant. This means that as circulating power increases as we lock the cavity, thermal gradients are formed on the order of 0.4 o C/mm inside the crystal (we assume linear heating and target temperatures occurring at the center of the 3 mm tall crystal) which is small compared to ranges seen in [28] and [20]. Additionally, Figures 3.4 and 3.6 show no signs of thermal locking as described in [28] and [24]. In such cases, as a cavity sweeps from low to high and

48 41 off of the peak, the crystal length changes keeping the cavity near resonance [28]. The absence of thermal locking again suggests that thermal gradients are relatively small. Thus, thermal lensing, or other thermal effects which are discussed in sections 2.4 and 4.2 may be negligible in our system. Non-ideal effects of the feedback electronics on the production of 461 nm light suggest areas where improvement is possible. Power is lost due to thermal and/or absorption effects in the crystal (see section 2.4 as just discussed) [28] [29]. In routine operation, the set voltage is not changed even if input and thus transmission strength is varied, and occasionally the cavity will lock to undesired modes as mentioned earlier in this section. Though this is easily diagnosed by low laser output, and easily remedied by re-locking the cavity, it is non-ideal operation. Overall, the locking electronics on the cavity work remarkably well. The cavity can lock for many hours without need of adjustment. More impressively, however, the cavity recovers from large perturbations without need of manual resetting. Acoustic noise, which plagues the cavity s optical stability, may unlock the cavity briefly, but due to the switching circuit, the electronics will relock the laser quickly and repeatedly as necessary.

49 Chapter 4 Characterization of the 461nm Laser Once the 461 nm laser became operational, care was taken to optimize all available parameters such as beam coupling, beam alignment, crystal temperature, and electronic feedback. We will discuss those four parameters briefly before continuing on to the general characterization of the laser. Beam coupling of the infrared light into the frequency doubling cavity changed as the source of that infrared light changed from the Ti:Sapphire laser, to various diode lasers, and finally back to the Ti:Saph. laser now passed through an optical fiber. The basic assumptions and means of modeling/determining that coupling, however, stayed the same through out. The system for deciding the focal length and position of the mode matching lens, as described in section 2.3, yielded coupling efficiencies 80% in our current setup (as calculated below). Our characterization of the laser in the current setup then should carry over as the pumping source for the 461 nm laser changes again in the future. Beam alignment into the cavity will always be able to be improved upon. Realistically the alignment depends on the stability of at least half a dozen optical elements, all of which have more than one relevant axis of rotation/translation. Great means could be taken to secure each of these elements to the utmost of scientific ability and

50 43 coupling could approach unity. As it is, Figure 3.4 shows that there is still some power lost to higher order spatial modes due to poor alignment and mode matching (see section 2.3). Comparing the heights of those secondary peaks to the primary suggest that the output power may be improved by as much as 21% if all the power in the secondary peaks were instead in the primary (increasing efficiency to 40%).We are satisfied with characterizing the laser at the current beam alignment because the current setup is robust enough to differ very little over the lifetime of several weeks. Please refer to the improvements heading in the conclusion of this thesis for more on maximizing the beam alignment in the future. Optimization of the Potassium Niobate crystal temperature is accomplished by adjusting a temperature controller whose thermo-electric cooling device (TEC) sits as a heat sink under the crystal housing. This setup is discussed further below. Figure 4.1 shows output power versus temperature over a range of input powers. Though not pictured in the figure, care was taken to determine that the peaks of each curve correspond to global and not local maxima of the system. Each peak then coincides with the optimization of the locked cavity, the normal operating mode of the laser, and is satisfactory to characterize the laser s temperature dependence for our purposes. Electronic feedback is optimized by adjusting the error signal gain on the locking circuit as described in Section 3.1. Maximum output of the cavity occurs when the gain is as large as possible without causing strong oscillations in the error signal.

51 Temperature (C) Input Power (mw) Output Power (mw) Temperature (V) Figure 4.1: Power Out vs. Temperature. Given various input powers, output power was traced as a function of the crystal s temperature.

52 Power Out (mw) Linear Regime 20 Quadratic Regime Quadratic Fit Linear Fit Power In (mw) Figure 4.2: Efficiency of Cavity. Optimized output power versus input power is shown along with fits to the quadratic and linear regimes. There is a local, much less stable, maxima at lower gain than the optimal one and future users of the system are encouraged to scan thoroughly in gain before determining output power is maximized. For this characterization of the laser care was taken to use only the stable global maximum. 4.1 Efficiency of Frequency Conversion Optimum output for any given input power of the IR pump laser can be seen in Figure 4.2. Typical output power of the Potassium Niobate crystal follows a quadratic increase from zero and later shifts to a linear regime [16]. Accordingly, we have fit our data with quadratic and linear curves as seen, and R 2 values near unity attest

53 46 to the accuracy of those fits. Overall efficiency in the linear regime is 33% and holds steady out to the maximum input achievable in our setup. Though thermal considerations would theoretically start to lower efficiency at higher powers, it is clear that we have not yet entered that regime [16]. Potassium Niobate crystals are the standard for frequency doubling in the high end visible spectrum, but results can vary widely based on individual quality of the specimen. [28] and [27] cite efficiencies of 5% and > 75% respectively and at wavelengths of 423 nm and 461 nm. [16] is the highest we found in our search at > 81% at 471 nm. In context, our results seem to be acceptable but not exceptional. Within our own lab, crystals from the same manufacturer and operating at the same wavelength from the same source yield efficiencies close to 40%. It is important to note, however, that in [27], the reported efficiency is for blue light created, not emitted, from the cavity. Greater than 15% of the claimed efficiency is supposed by accounting for losses due to BLIIRA and non-ideal optical elements. The high efficiency in [16] also compensated for optical elements, though not for BLIIRA. By observing the transmission modes of the cavity as well as the reflected (blue) modes, we can make modest approximations on the limiting factors of our efficiency as discussed in the opening of this section. The 21% gain from beam alignment would give a predicted efficiency of 40%. This would be an improvement but would not approach the results of [16]. Even if operating at other wavelengths was desirable, crystal

54 47 properties would not necessarily yield greater efficiencies at nearby wavelengths such as those used in the references above. It is hard to quantify the losses due to phase mis-matching as discussed in section 2.3 and 1.5 but this may considered along with other thermal effects and losses in the next section. Even if this particular Potassium Niobate crystal, or some systematic portion of our 461 nm laser setup is less than ideal, it is important to note that our results are more than satisfactory for our purposes. Output powers in excess of 125 mw are more than sufficient for the creation of stable Magneto Optical Trap, 2-D collimation, absorption imaging, or photoassociative spectroscopy beams as discussed in the introduction of this thesis. 4.2 Thermal Effects Temperature regulation of the Potassium Niobate (KNbO 3 ) crystal was maintained using a simple HTC temperature controller from Wavelength Electronics. Figure 4.3 shows the conversion curve from monitored voltage on the temperature controller to degrees Celsius. Monitoring of the temperature is accomplished through a 10 kω thermistor positioned at the base of the housing of the crystal. This was also the location of the thermo-electric cooling device (TEC) which acts as a heat sink on the crystal and is the means through which the HTC regulates the crystal temperature. The housing of the crystal is made of aluminum. As seen in Figure 4.1, variations as small as 0.1 o C yield large differences in the output power of the laser. The crystal can

55 Temperature (C) y = x R 2 = Monitor Voltage (V) Figure 4.3: Temperature Controller Calibration. The HTC 3000 temperature controller from Wavelength Electronics utilizes a 10 kω thermocouple to monitor crystal temperature. INSET: Routine operation of the crystal occurs over a relatively smaller portion in temperature space. A linear fit reasonably approximates the voltage to temperature calibration in this regime.

56 49 take several minutes to fully stabilize at a new temperature, depending on the speed at which the temperature controller stabilized, and on the amount the temperature was changed. Furthermore, there is some oscillation in overall monitor voltage on the order of 3 mv (0.075 o C) over a period of a few days. As discussed in sections 1.5 and 2.3, phase matching plays a critical role in the infrared to blue light frequency conversion. The indices of refraction along different axis in the KNbO 3 crystal have differing dependences on temperature, allowing us to temperature tune the 461 nm polarization axis to match the 922nm axis [19]. See the discussion on frequency doubling in the introduction of this thesis for more information. Optimum temperature of the TEC decreases as input power increases as seen in Figure 4.4. Temperature at the crystal near the axis of the incoming beam should remain constant to maintain phase-matching [20][19], suggesting that the difference in TEC temperature likely creates a temperature gradient across the crystal (as we mentioned in section 3.3. Along the longitudinal axis of the crystal, where variation in beam waist size can lead to uneven heating, non-ideal temperature gradients result in a spatial dependence on the index of refraction of the crystal. This effect is sometimes referred to as thermal lensing. Thermal lensing causes distortion in the beam waist as the variation in index of refraction affects the beam profile passing through the medium. Not only does thermal lensing affect spatial mode matching, it can also distort phase matching

57 Temperature (V) Temperature (C) Power In (mw) Figure 4.4: Optimum Temperature for Input Power.

58 51 and leads to an overall reduction in the efficiency of the cavity. See also section 2.4. Large differences in the optimum temperature for a locked versus swept cavity (see Figure 3.9 and section 3.3) suggest that the locked cavity is heated by the incident and circulating IR light. This requires the temperature controller to cool the crystal significantly in order to phase match. A larger beam waist inside the crystal should lessen the heating but this will lead to lower intensities and power conversions. The thermal gradient calculated in section 3.3, however, is small compared to other studies as we mentioned [28] [20]. Thermal expansion of the crystal causes a condition called thermal (self) locking as a cavity is scanned over frequency [28]. The absence of thermal locking in our system, see section 3.3, suggests that thermal gradients along the beam axis are a small source of loss in our system. That thermal losses are small is best seen in Figure 3.9 where, as we mentioned, there are no significant differences in blue power out even as circulating power increases as the cavity locks. Thus despite what temperature gradients we may induce, thermal considerations seem to have minimal effects on cavity efficiency.

59 Chapter 5 Conclusion 5.1 Summary We have detailed the necessary steps in the creation and characterization of a nm laser. We have discussed the relevant concepts in optics, electronics, and atomic physics as pertaining to the construction and use of this device. During normal operation we run the 461 nm laser at output power > 100 mw (125 mw typical), corresponding to conversion efficiencies near 33%. About 30 mw is used in a magnetooptical trap, < 1 mw for an imaging beam, and alternating between 70 mw and 100 mw in a 2D collimator (2D optical molasses), all along the dipole allowed 1 S 0 1 P 1 transition, and all on the new Neutral Atoms setup in our laboratory. The 461 nm has proven itself an essential tool in the cooling, trapping, and study of Strontium. 5.2 Improvements and Future Work Characterization of our doubling cavity suggests that we have not yet reached input powers sufficient to destabilize our 461 nm laser. We can then increase the input power of the cavity and supply the Zeeman beam ( 70 mw required power in the blue) for the new setup as well. Alternatively, using the process detailed in this thesis, we can create additional 461 nm lasers using alternative IR sources similar to the diode lasers utilized during PAS studies at long range. Plans have already been

60 53 considered to use tapered diode amplifiers to provide IR power > 300 mw to various doubling cavities. These sources would be less expensive than the Ti:Saph laser. Beam coupling into the cavity may be improved with greater care in aligning optical mounts. Improved coupling will improve efficiency as we discussed in section 4.1. Drawings have already been made for a new crystal mount which will be more stable than the current one and may increase coupling efficiency. Acoustic noise, which has a devastating but short-term effect on output efficiency, can also be improved upon through standard isolation techniques. Studies in ultracold neutral strontium are reaching a critical point in our laboratory. Results from our studies in photoassociative spectroscopy suggest that 86 Sr may readily be brought into quantum degenerate conditions using purely optical means. Along with the intercombination-line MOT, and a new optical dipole trap, the blue MOT along the 1 S 0 1 P 1 transition will provide an essential ingredient in that process. Quantum degeneracy in 86 Sr will open our laboratory to studies not yet explored in atomic physics.

61 Appendix A Computational Analysis of Beam Profiles This Matlab script is used to fit beam profiles and extract the critical beam parameters (beam waist position and size). Results from this program are typically used in conjunction with the Mathematica modelling programs described in Appendix B. Script begins on next page, with comments in text.

62 Figure A.1: 55