A COMPACT, TOTALLY PASSIVE, MULTI-PASS SLAB LASER AMPLIFIER BASED ON STABLE, DEGENERATE OPTICAL RESONATORS

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1 A COMPACT, TOTALLY PASSIVE, MULTI-PASS SLAB LASER AMPLIFIER BASED ON STABLE, DEGENERATE OPTICAL RESONATORS John J. Degnan, Sigma Space Corporation, Lanham, MD 76 USA FAX: Abstract Low energy, picosecon pulse oscillators typically require several orers of magnitue amplification to be useful in khz satellite laser ranging systems, altimetry, or other applications. The present paper escribes a totally passive amplifier esign, base on egenerate optical resonators, which permits high multipass amplification of ultrashort pulses in a compact package, requires no active switching components, an shoul be relatively simple to align. INTRODUCTION New kilohertz satellite laser ranging systems rely on either passively Q-switche microchip or SESAM (SEmiconuctor Saturable Absorbing Mirrors) laser oscillators for the generation of picosecon pulsewiths. Microchip lasers (e.g. SLR) typically generate several microjoule pulse energies at few khz rates with pulsewiths on the orer of a few hunre picosecons. SESAM evices (e.g. Graz) can prouce much shorter pulses between an psec but with significantly lower energies, typically sub-microjoule. Furthermore, if one operates at khz fire rates, the amplifiers can be pumpe with CW ioe laser arrays for longer life an reliability, but the resulting gain per pass is relatively low compare to pulse-pumpe systems. As a result, the pulse must pass through several stages of low-gain amplification in orer to reach pulse energies of several hunre microjoules require for robust photon-counting of satellite returns. In the NASA SLR system, the oscillator pulse is passe six times through a single amplifier hea using three carefully aligne mirrors while, in the High-Q system use at Graz, the SESAM oscillator pulse is input to a relatively large regenerative amplifier with complex pulse switching electronics followe by a conventional amplifier. As an alternative, we propose a totally passive, multipass amplifier base on the concept of stable egenerate optical resonators [Ramsay an Degnan, 97]. A comparison of the three multipass amplifier techniques is illustrate in Fig.. STABLE DEGENERATE OPTICAL RESONATORS The characteristics of any optical resonator are efine by the raii of curvature of two mirrors, b an b, an the istance between them. Paraxial rays will never walk out of the resonator, i.e. the resonator is stable, if the following stability conition is satisfie () b b At certain mirror separations, the resonator becomes egenerate an can be characterize by an integer N. These iscrete separations are efine by the equation ± b + b πk K= for N= N ( N K ) = ± b + b + b b cos, < K<N/ for N > provie K > is not ivisible into N ()

2 For each value of K an N, there are two istinct separations which prouce the egeneracy. Table illustrates the vali values for K up to N =8 N = K= Table : Vali K-values as a function of the egeneracy factor, N. Passive Amplifier/Multiple Mirrors (e.g. Q-Peak laser in SLR) Laser Slab HV HV Regenerative Amplifiers (e.g. NASA STALAS Laser or High-Q laser at Graz) Q- switch Laser Ro out Q- switch in Out Degenerate Optical Resonators In 7.7 xn j mm Laser Slab a 7.7 z j Figure : Some multipass amplifier approaches. Degenerate resonators exhibit a number of interesting physical effects, among them: The Hermite-Gaussian (TEM mnq ) resonator moes ivie into N iscrete frequencies separate by c/nl where L is the resonator length; thus, N= represents the highest egeneracy where all spatial moes oscillate at the same frequency. Hole-couple lasers exhibit large power losses because the frequency-egenerate TEM moes can couple together to create a low loss composite moe with a null at the coupling hole Internal ray paths can be efine which repeat themselves after N roun trips in the resonator It is this last feature which suggests their use in passive multipass amplifiers.

3 SPECIAL CASE #: SYMMETRIC RESONATORS If the two mirror raii of curvature are equal (b = b = b), the egeneracy equation simplifies to: ± πk ( N, K ) = b ± cos N Figure isplays the resonance positions of a symmetric resonator for N = to 6. The vertical scale inicates the level of egeneracy, N. 6 Degeneracy, N Resonator Length (normalize to b) Figure : Degenerate mirror separations for a symmetric resonator for N = to 6. The stable range is < < b. The + an - positions are inicate by the re an blue lines respectively. For each egenerate separation, there are two types of ray paths, ecliptic or non-ecliptic, as illustrate in Figure for N = an K =. Ecliptic rays make N passes through the amplifier slab before retracing the same path in the opposite irection. Non-ecliptic rays, on the other han, never retrace the same path an therefore have the following potential avantages over ecliptic rays:. The angularly separate input an output beams o not require aitional optical isolation between the oscillator an amplifier. There is no nee for an inepenent means (e.g. polarization rotation) of separating the input an output beams. The circulating beam samples more of the pumpe amplifier volume for better energy extraction Ecliptic ray paths, on the other han, may offer avantages in terms of ease of alignment since the input an output beams are coaxial an normal to the reflecting surface of the input mirror. Furthermore, as we shall see later, ecliptic paths also len themselves more easily to variable pass amplifier systems.

4 Ecliptic z i slab := i i Non-Ecliptic + Ecliptic Ray Trace for + slab Non-Ecliptic Ray Trace for + slab Ecliptic Ray Trace for - slab Non-Ecliptic Ray Trace for - slab (a) (b) Figure : Ray traces for a symmetric resonator with egeneracy N = an K =; (a) Ecliptic ray traces for + (top) an - (bottom) ; (b) Non-ecliptic ray traces for same geometries. SPECIAL CASE #: FLAT-CONCAVE RESONATORS (b = ) If one mirror raius of curvature is infinite ( b = ), the egeneracy equation simplifies to: b πk ( N, K ) = cos N Figure isplays the resonance positions of the flat-concave resonator for N = to 6. The vertical scale again inicates the level of egeneracy, N. Unlike the general or symmetric resonator cases, there is now only one egenerate mirror separation for each value of N an K. For each egenerate position, one can again efine ecliptic an non-ecliptic ray paths which repeat themselves after N roun trips through the resonator.

5 6 Degeneracy, N Resonator Length (normalize to b) Figure : Degenerate mirror separations (normalize to the raius of curvature b of the non-flat mirror) for the generalize flat-concave resonator for N = to 6. The stable region is now efine by < < b. Ecliptic Ray Trace Non-Ecliptic Ray Trace (a) (b) Figure : Ray traces for a Flat-Concave resonator with egeneracy N = an K =; (a) Ecliptic ray trace; (b) Non-ecliptic ray trace. The flat mirror is assume to be locate to the left of each ray trace. VARIABLE PASS AMPLIFIER DESIGN Figure (a) suggests a esign for a simple variable pass amplifier. As illustrate in Figure 6, the incoming collimate p-polarize beam from the oscillator passes through the polarizer an is rotate to circular polarization by a quarter-wave plate. Assume that the left ege of the slab is coate with a highly reflecting mirror at 6 nm except for a small section at the top which is antireflection (AR) coate. The input beam is then inserte normal to the slab surface in the ARcoate region, makes an arbitrary number of passes (N) through the amplifier epenent on the positioning of the single translatable mirror on the right, exits the multipass amplifier through the same AR-coate surface as the entry beam, is rotate to s-polarization by the secon pass through the quarter-wave plate, an is reflecte off the input polarizer. Dioe pumping of the slab can be accomplishe through the eges of the slab or through the top of the slab The

6 amplifier esign also transfers the Gaussian properties (raius, phasefront curvature) of the input beam to the exit beam at all egenerate mirror separations since the roun trip ray matrix for the resonator taken to the Nth power always equals the ientity matrix [Ramsay an Degnan,97]. Thus, the exit beam will have the same spot size an ivergence as the input beam [Degnan, ]. In orer to suppress self-oscillations along or near the amplifier optic axis where the two mirror surfaces are approximately parallel, it may be necessary to introuce a region of low reflectivity in the center of the spherical mirror by either () leaving the center uncoate, () AR-coating the center, or () introucing a central hole. This has no effect on the amplification since the ecliptic rays entering from the flat sie of the resonator never reflect off the center of the spherical mirror. However, the iameter of the low reflectivity area will impose an upper limit on the number of rountrip passes that can be achieve without having the amplifie beam attenuate by the low reflectivity spot. IN λ/ plate N = 7 6 HR Mirror OUT LASER SLAB Mirror on Translation Stage K = Figure 6: Concept for a compact, passive, multipass amplifier base on ecliptic rays in a flat-concave egenerate resonator. The egeneracy N, an the number of passes through the amplifier (N), can be varie by moving the spherical mirror on a precision translation stage. Differently colore rays are associate with ifferent values of N (re =, blue =, green =, etc) SUMMARY Microchip an SESAM oscillators can generate picosecon pulses at multi-khz rates but only at low single pulse energies (several microjoules or less). Since many applications (SLR, D imaging liar, etc.) require pulse energies ranging from several tens of microjoules to several millijoules, there is a general nee for high amplifications in a compact, efficient, ioe-pumpe package. Furthermore, since CW-ioe pumpe amps typically have low single pass gains, many passes through the amplifier may be require to reach the require pulse energies an to extract the store energy efficiently. Regenerative amplifiers can achieve this, but they are usually quite large an require high spee, high voltage electro-optic switches Totally passive egenerate resonator multipass amplifiers are an attractive alternative to multiple mirror systems as use in SLR an can potentially provie : High multipass gain in a compact, easily aligne package

7 . A fair amount of isolation from the oscillator an reuce internal feeback for suppressing self-oscillations within the amplifier Variable number of passes with one translating mirror which can be set for optimum performance or compensate for a egraation in oscillator power Excellent beam control since it preserves the gaussian parameters of the input beam at the output ue to perioic refocusing REFERENCES Ramsay, I. A. an J. J. Degnan, "A Ray Analysis of Optical Resonators Forme by Two Spherical Mirrors", Applie Optics, Vol. 9, pp. 8-98, February, 97. Degnan, J.J., Ray Matrix Approach for the Real Time Control of SLR Optical Elements, these proceeings,.