Design Of AgGaS₂ Optical Parametric Oscillator

Optical parametric oscillators (OPO) can generate coherent radiation fromUltra-violent to Far-Infrared as a broadly tunable laser source, which canmake up for some wavelengths which some gas or solid-state lasers could notradiate. OPO has been applied to laser spectroscopy, differential absorptionlidar, directional infrared countermeasure (DIRCM), large screen projectiondisplay, engine combustion diagnosis ect. It has been an important lasersource which can not be replaced by other one in scientific research, militaryand civilian fields. In the thesis, the key techniques of optical parametricoscillators operating in the range of atmospheric transparency ( 3 ? 5μm) arestudied. AgGaS2 optical parametric oscillator pumped by a Q-switchedNd:YAG laser operating at 1.064 μm is investigated theoretically , which itcan to achieve phase-matched down-conversion into the λ > 5μm region.Optimal designs of AgGaS2 optical parametric oscillator at 3-5 microns aremade. The analyses in detail are listed below:1, Phase-matching Angle of AGS OPOBased on the principle of interaction of three waves and the relation betweenthe effective nonlinear coefficient and the output wavelength for the twophase-matched types, figure 1 and figure 2 show the variations of the tuningcurve of parametric output wavelength and the effective nonlinear coefficient.The phase-matching angle 470 for type I AGS OPO is concluded for the3-5 μm tuning curve.40 42 44 46 48 50 52 54 56123456λ(nm)θ(o)2.550 55 60 65 70 75 80 853.03.54.04.55.05.56.0λ(nm)θ(o)(a) Type I phase-matching (b) Type II phase-matchingFig. 1 Angle tuning curve of AGS OPO pumped by Nd:YAG (1064nm)1 2 3 4 5 64681012deff(pm/v)λ (μm)I 类相位匹配II类相位匹配Fig.2 Effective nonlinear coefficients of AGS OPO pumped by Nd:YAG(1064nm)2,Walk-off Angle of AGS OPOThe walk-off angle of AGS OPO for type I pumped by Nd:YAG laser(1.064 μm ) is calculated. Fig.3 shows that the walk-off angle is smaller than1.3 degree for output wavelength of 3-5 μm . It can be inferred that thewalk-off effect is not serious for type I AGS OPO.3.0 3.5 4.0 4.5 5.0 5.5 6.01.2841.2881.2921.2961.300Walk-off Angle α (0)λ(μm)Fig.3 Walk-off angle of AGS I OPO pumped by Nd:YAG(1064nm)3,Allowing Angle of AGS OPO-0.042.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5-0.020.000.020.04BA?θ(0)λ(μm)Fig.4 Allowing angle of AGS I OPO pumped by Nd:YAG(1064nm)Under the small signal approximation for the interaction allowing the threewaves, the effects of allowing angle on the output wavelength for AGS isstimulated. As shown in Fig.4, the longer the output wavelength, the smallerthe allowing angle and the more difficult the operation of AGS OPO. In orderto realize the effective operation of long wavelength and improve theconversion efficiency of infrared tunable OPO, it is necessary for a pumpinglaser with better dispersion angle and stability.4,Conversion Efficiency of AGS OPOSome other effects of conversion coefficient on the angle allowed and onthe crystal length are also discussed for AGS OPO under the phase mismatchpermitted.0.0-0.06 -0.03 0.00 0.03 0.060.20.40.60.81.0ηm?θ(0)0.904.010 0.015 0.020 0.025 0.0300.950.960.970.980.991.00 ?θ=0.0010?θ=0.0020?θ=0.0050ηmL(m)Fig.5 Variation of mismatching coefficient Fig.6 Variation of phase matching coefficientwith mismatching angle with length of crystalAs shown in Fig.5, when ?θ =0, η m=1, the conversion efficiency reachthe maximum which is the ideal one η 0. With increasing of ? θ, the anglebetween the direction of light and θ of phase match so the value of η mdecreases. When η m=0, the conversion efficiency equals to 0, and then themismatch angle is the largest one permitted, ? θmax. It is inferred that for aparametric oscillator, especially the tuning infrared one, the coefficient ofphase mismatch is very sensitive to the mismatch angle, and so as to theconversion efficiency.Fig.6 shows that the phase mismatch coefficient decreases with increasingthe crystal length, as well as the conversion efficiency. And η m decreaseseven faster with increasing ?θ , conversion efficiency varies obviously. On thecondition of fixed phase mismatch angle permitted, increasing the length ofcrystal can improve the gain of parametric light. As a result, in order tooptimize the output characters of OPO device, the length of crystal mustsatisfy the two sides which we have mentioned above.-0.120.01 0.02 0.03 0.04 0.05-0.08-0.040.000.040.080.12?θ(0)L(m)Fig.7 Effect of crystal length on allowing angleThe function of the length of crystal on the allowing angle is shown in Fig.7,at a fixed output wavelength. The curve of ?θ >0 means that the directionangle of wave-vector is larger than phase match angle. With increasing thelength of crystal, the allowing angle becomes smaller continuously, and itresults in the phase mismatch, so that higher tuning precision is required. Itcan be concluded that changing the length of crystal can result in changing ofallowing angle, and so as to the conversion efficiency.5,Threshold of AGS OPOFig. 8 Schematics of double-pass pump AgGaS2 SRO OPO.AGS is AgGaS2 crystal;FRI is Faraday rotator isolator.Due to the relatively low damage threshold for AGS crystal at nanosecondpumping, the threshold of double-pass pump nanosecond AgGaS2 type I SROOPO has been investigated theoretically. Simplified theoretical model isestablished by Brosnan and Byer . The simple DSRO schemes are shown inFig. 8.As the same time, the methods to reduce AGS OPO oscillation thresholdare discussed.The threshold energy density is changed with the cavity length between thetwo cavity mirrors. The relation is shown in Fig. 9 for a diameter 2 mm, 10 nsduration pump beam and crystal length of 2 cm. The longer the cavity lengthis, the higher the threshold is. And the threshold operating on longer wave ishigher than that for the shorter one obviously. So reducing the cavity lengthshould be considered in the design of OPO. For 2 cm crystal length, the cavitylength should be less than 3 cm, just at the minimal distance allowed fortuning.2 4 6 8 100.150.200.250.300.350.40Threshold energy density (J/cm2)Cavity length (cm)3 μm4 μm5 μmFig. 9 DSRO threshold energy density as a function of cavity lengthThe DSRO threshold as a function of crystal physical length is shown inFig. 10 for a pump beam with a 2 mm spot in diameter, 10 ns pulse width and3 cm cavity space. It is clear that when the crystal length is less than 1 cm, thethreshold is abruptly increased, when the length is more than 2 cm, it nearlykeeps flat. Meanwhile, for the different parametric wavelength, there is littlediscrepancy. Considering that the effect of pump beam Poynting vectorwalk-off is evident for the much longer crystal and prices and so on, the goodcrystal length is approximately 2 cm.0 1 2 3 4 5 60.00.81.62.43.24.0Threshold energy density (J/cm2)Crystal length (cm)3 μm4 μm5 μmFig. 10 DSRO threshold energy density as a function of crystal length0.0 0.2 0.4 0.6 0.8 1.00.150.300.450.600.750.90Threshold energy density (J/cm2)γ3 μm4 μm5 μmFig. 11 DSRO threshold energy density as a function of the ratio of backward to forward pumpfield amplitude in the crystalγFor a double-pass pump singly resonant OPO, the ratio of backward toforward pump field amplitude in the crystal γ is an important parameter.The DSRO threshold dependence on γ is shown in Fig. 11 for the samepump beam as in Fig. 10 and 3 cm cavity length, 2 cm crystal length. It can beinferred from the prediction that bigger γ is contributed to the lowerthreshold. So it is required that the cavity mirror M2 should be highreflectivity and the crystal surfaces to the mirror have to be high transmissionat the pump wavelength. Considering the case, the Au mirror (reflectivityR>98% for all the wavelengths) can be suit for the mirror M2 in the scheme ofFig. 1(b) under the low power density.0.150 1 2 3 4 5 60.180.210.240.270.30Threshold energy density (J/cm2)Pumping spot diameter (mm)3 μm4 μm5 μmFig. 12 DSRO threshold energy density as a function of pumping spot sizePumping laser is another important factor for effective OPO operation. Thepump spot size dependence of parametric gain for critically phase-matchedinteractions is well known. The good pump laser parameters not only decreasethe pump threshold, but also increase the conversion coefficient. Fig. 12shows that the increase in threshold as well as the decrease in gain is due tothe small pump spot size as a result of Poynting vector walk-off. It can besuggested that the spot diameter larger than 2 mm for AGS DSRO isnecessary.The threshold as a function of the pump pulse width is shown in Fig. 13.The pump pulse width and energy can be adjusted by operating the Nd:YAGoscillator and amplifier, respectively. The longer the pulse width, the higherthe threshold. It is clear from the figure that the relatively shorter pulse widthis benefit to the lower threshold.10 20 30 400.20.40.60.8Threshold energy density (J/cm2)Pulse width (ns)3 μm4 μm5 μmFig. 13 DSRO threshold energy density as a function of pumping pulse widthIt is evident that the threshold operating at the relatively longer parametricwavelength is higher (threshold at 5 μm >that at 4 μm >one at 3 μm ) from theFig. 9, 10, 11, 12, 13. It can be interpreted as follows: 1) the oscillationthreshold is inversely proportional to the product of the idler and signalangular frequency, so as to the product of the two wavelength;2) the effectivenonlinear coefficient d eff is decreasing at the range of 3 ? 5μm as well asthe gain in the AGS crystal, the threshold is inversely proportional to d eff, too.Thus a larger threshold is predicted certainly.Fig. 14 Comparison between the oscillation threshold of the single and double pump passIn order to compare the threshold between SRO and DSRO for AGS crystal,Fig. 14 shows the threshold dependence on the cavity length for twoconfigurations operating at 4 μm . It is obvious that the AGS DSRO thresholdis much lower than the one for SRO. The same results can be concluded forother parameters such as AGS crystal length, backward to forward rate ofpump field amplitude, pump spot size and pulse width.6,ConclusionIn this thesis, the principle and design method of 3-5 μm angle tuning AGSoptical parametric oscillator are investigated. The method to determine the cutangle for the phase match of the nonlinear crystal is demonstrated. The AGSOPO angle tuning curve pumped at 1.064 μm is simulated. Under the smallsignal approximation, the effects of allowing angle on the output wavelength,crystal length are shown, respectively. Some other effects of conversioncoefficient on the angle allowed and on the crystal length are also discussed.The results provided are the reference for optimal design of the new waveband laser. The theoretical analysis indicate that, the high quality pump lightbeam quality, the strict angle harmonious phase matched condition, the highquality non-linear crystal and the best length are the important parameters forthe OPO conversion efficiency. That should be considered for the design ofOPO.AGS OPO design diagram for experiment has been given in this thesis. Thethreshold of double-pass pump nanosecond AgGaS2 type I SRO OPO hasbeen investigated theoretically. The influences of the parameters such as OPOcavity length, AGS crystal physical length, backward to forward rate of pumpfield amplitude, pump spot size and pulse width, on the threshold energydensity are analyzed in detail. A comparison between the oscillation thresholdof the single and double pass pump indeed shows that double pump passlowers the oscillation threshold significantly. Considering the low damagethreshold for AgGaS2 crystal, it is quite important and necessary for AGSSRO OPO to operate under the relatively lower threshold. The suitableparameters such as over 2 cm crystal length, minimal cavity length, highquality antireflection coating on both ends of the crystal and high reflectivityforward mirror at pump wavelength, narrower nanosecond pulse width andlarger pump spot are all helpful and significant for the designing of AGS OPO.The results provided are helpful of the design of AGS OPO.In summary, the thesis investigates an applicable method for 3 ~ 5 μm OPO.In further job, we should improve the coating craft at infrared wavelength;enhance membrane efficiency of mirror and conversion efficiency of OPO.