Mode spectrum of multi-longitudinal mode pumped near-degenerate OPOs with volume Bragg grating output couplers

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1 Mode spectru of ulti-longitudinal ode puped near-degenerate OPOs with volue Bragg grating output couplers Markus Henriksson 12 * Lars Sjöqvist 1 Valdas Pasiskevicius 2 and Fredrik Laurell 2 1 Laser Systes Group FOI - Swedish Defence Research Agency P.O. Box Linköping Sweden 2 Laser Physics KTH - Royal Institute of Technology Stockhol Sweden *ahe@foi.se Abstract: Spectral requireents for the first stage OPO used to pup a tande ZGP id-infrared OPO are theoretically investigated. Based on these requireents we deonstrate a singly-resonant type-i OPO including periodically poled KTiOPO 4 and volue-bragg gratings as output couplers. Singly resonant oscillation is deonstrated very close to degeneracy where signal and idler spectra are not well separated. Investigations of the longitudinal ode spectru and the idler spectru with high resolution using a scanning Fabry-Perot interferoeter show the essential role played by the phase correlations of the ulti-longitudinal ode Q-switched pup laser in foration of the nonresonant idler spectru Optical Society of Aerica OCIS codes: ( ) Paraetric oscillators and aplifiers; ( ) Volue holographic gratings. References and links 1. S. Haidar K. Miyaoto and H. Ito Generation of tunable id-ir ( µ) fro a 2 µ puped ZnGeP 2 optical paraetric oscillator Opt. Coun. 241(1 3) (2004). 2. K. L. Vodopyanov O. Levi P. S. Kuo T. J. Pinguet J. S. Harris M. M. Fejer B. Gerard L. Becouarn and E. Lallier Optical paraetric oscillation in quasi-phase-atched GaAs Opt. Lett. 29(16) (2004). 3. S. Brosnan and R. Byer Optical Paraetric Oscillator Threshold and Linewidth Studies IEEE J. Quantu Electron. 15(6) (1979). 4. P. Schlup G. W. Baxter and I. T. McKinnie Single-ode near- and id-infrared periodically poled lithiu niobate optical paraetric oscillator Opt. Coun. 176(1 3) (2000). 5. B. Jacobsson M. Tiihonen V. Pasiskevicius and F. Laurell Narrowband bulk Bragg grating optical paraetric oscillator Opt. Lett. 30(17) (2005). 6. M. Henriksson L. Sjoqvist V. Pasiskevicius and F. Laurell Narrow linewidth 2 µ optical paraetric oscillation in periodically poled LiNbO 3 with volue Bragg grating outcoupler Appl. Phys. B 86(3) (2007). 7. M. Henriksson M. Tiihonen V. Pasiskevicius and F. Laurell ZnGeP 2 Paraetric Oscillator Puped by a Linewidth Narrowed Paraetric 2 µ Source Opt. Lett. 31(12) (2006). 8. M. Henriksson M. Tiihonen V. Pasiskevicius and F. Laurell Mid-infrared ZGP OPO puped by neardegenerate narrowband type-i PPKTP paraetric oscillator Appl. Phys. B 88(1) (2007). 9. M. Henriksson L. Sjoqvist V. Pasiskevicius and F. Laurell Tande PPKTP and ZGP OPO for id-infrared generation Proc. SPIE O (2008). 10. G. Arishol G. Rustad and K. Stenersen Iportance of pup-bea group velocity for backconversion in optical paraetric oscillators J. Opt. Soc. A. B 18(12) (2001). 11. G. Arishol Quantu noise initiation and acroscopic fluctuations in optical paraetric oscillators J. Opt. Soc. A. B 16(1) (1999). 12. M. Iai Y. Ohtsuka and S. Satoh Spatial coherence analysis of light propagation in optical fibers by interferoetric ethods J. Opt. Soc. A. A 3(7) (1986). 13. H. Kogelnik Coupled wave theory for thick hologra gratings Bell Syst. Tech. J (1969). 14. G. Anstett and R. Wallenstein Experiental investigation of the spectro-teporal dynaics of the light pulses of Q-switched Nd:YAG lasers and nanosecond optical paraetric oscillators Appl. Phys. B 79(7) (2004). 15. P. N. Butcher and D. Cotter The eleents of nonlinear optics (Cabridge 1990). (C) 2009 OSA 28 Septeber 2009 / Vol. 17 No. 20 / OPTICS EXPRESS 17582

2 1. Introduction High average power and high-energy coherent radiation in the id-infrared (MIR) spectral region spanning wavelengths fro 3 µ to about 8 µ is desirable for a nuber of applications including directed countereasures reote sensing and surgery. One of the ethods of obtaining this radiation is by using a tande optical paraetric oscillator (OPO) syste which can be puped by well established Q-switched lasers at 1064 n. Typically such tande OPO consists of a degenerate or near-degenerate OPO operating at 2 µ which in turn pups a id-infrared (MIR) OPO eploying ZGP or orientation-patterned GaAs [12]. The ost critical link in this syste is the first OPO at 2 µ. In designing the tande OPO one needs to take into account that the bandwidth of the radiation generated at 2 µ affects the efficiency of the subsequent MIR OPO. This is a well known fact but to answer exactly how uch the total efficiency suffers as the 2 µ radiation bandwidth is increased is not straightforward. This is the first question we set to answer in this work. Near degeneracy the gain bandwidth in a type I configuration where signal and idler have the sae polarization can be several hundred n. This is especially true for quasi-phase atching (QPM) in periodically poled crystals. OPOs near 2 µ have an iportant application as pup sources for id-ir OPOs. In early realizations of tande OPO systes type-ii interaction in bulk KTP crystals was used for the first-stage OPO. The use of type-i interaction in QPM crystals can iprove the syste efficiency considerably due to the higher nonlinearity and walk-off free interaction. It also enables the use of both signal and idler for puping the MIR OPO. However spectral narrowing is andatory for efficient MIR OPO puping as shown below. The traditional ways to reduce the bandwidth of an OPO by use of etalons and gratings in the cavity [34] are not optial due to additional losses and liited free-spectral range of etalons. Moreover an additional intracavity eleent increases the OPO cavity length which also reduces the efficiency. The use of a volue Bragg grating (VBG) output coupler in an OPO cavity first deonstrated by Jacobsson et al. [5] has been shown to be a ore efficient way of narrowing the spectru of an OPO. We have previously shown narrowband singly-resonant OPO operation near degeneracy with both PPLN and PPKTP crystals [6 9]. Efficient puping of a ZGP OPO by the cobined signal and idler fro a periodically poled KTP (PPKTP) OPO with a VBG was also deonstrated [89]. Thus after theoretically deterining the pup bandwidth liitation in the tande OPO syste we experientally investigate the longitudinal ode spectru of a nearly-degenerate singly-resonant PPKTP OPO (SRO) with VBG output coupler puped by a ultilongitudinal ode laser. In particular we deonstrate that by eploying a narrowband VBG the SRO operation can be achieved even when the signal and the idler spectra start overlapping. This allows effective SRO operation in the type-i QPM OPO very close to degeneracy thus avoiding overconstrained doubly-resonant situation which would result in a highly unstable operation in the OPO without active cavity stabilization. We also show how the teporal coherence of the pup plays a crucial role in foration of the nonresonant idler spectru. 2. Pup bandwidth liitation in tande OPO The acceptance bandwidth of the pup in paraetric devices can be estiated fro the phase atching condition only when one of the paraetric waves has fixed frequency. For instance by assuing a fixed signal wavelength the pup acceptance bandwidth ω p to the first order can be obtained fro Eq. (1) (see e.g [10].): π v ω p < L v v g p g i v g i g p (1) where L is the length of the nonlinear crystal and v gp v gi are the group velocities of the pup and the idler waves respectively. For a 14 long ZGP crystal puped at µ Eq. (1) (C) 2009 OSA 28 Septeber 2009 / Vol. 17 No. 20 / OPTICS EXPRESS 17583

3 gives a axiu pup bandwidth of 275 GHz or 4.1 n for OPA of a single longitudinal ode signal at 3.7 µ. The situation in a free running OPO is uch ore coplicated as both signal and idler have finite spectral bandwidths and can adjust their wavelengths to copensate for a sall change in the pup wavelength. A siulation odel can be used to test the dependence of the OPO conversion efficiency on the pup bandwidth. The siulations were perfored with the OPO siulation engine SISYFOS developed at the Norwegian Defence Research Establishent [11]. As a large nuber of siulation runs were to be perfored with high spectral resolution the siulation was done in plane wave geoetry. The µ pup spectru is described by a Lorentz function and the spectral width given here is the FWHM bandwidth. The individual odes in the pup are assigned rando coplex Gaussiandistributed aplitudes and the odulation pattern is periodic with a period that is several ties shorter than the ZGP OPO roundtrip tie with no fractional relation between the roundtrip ties. In the siulated exaple a ZGP OPO with paraeters siilar to the ones in earlier experients by the authors [9] three different pup energies were studied. Fro Fig. 1 it can be seen that there is both an increase in threshold energy and a decrease in slope efficiency when the pup bandwidth is increased. The siulation results (see Fig. 1) also show that there is no clear liit of the acceptable pup bandwidth but that the conversion efficiency gradually decreases with increasing bandwidth. Fig. 1. (a) Siulated ZGP OPO output energy as a function of pup bandwidth for three different pup energies. (b) Siulated OPO threshold energy and slope efficiency as a function of pup bandwidth. Operation of the first-stage OPO exactly at degeneracy should be avoided due to the doubly-resonant oscillation nature with increasing output fluctuations owing to backconversion. Without active cavity stabilization and pup retro-reflection the operation of type-i OPOs at degeneracy result in lower conversion efficiency. With signal and idler separated in frequency but having the sae polarization they can still be used for puping of the sae second stage OPO which is not the case when a type II OPO is used for the first OPO stage. Consequently we siulated the effect of detuning fro degeneracy for the firststage OPO on the output energy of the second-stage ZGP OPO. The puping spectra used were not realistic OPO spectra but two identical spectra of the sae type that were used when siulating the effect of the bandwidth. The results for different pup energies are shown in Fig. 2. If the detuning is not too large say below 500 GHz (7.5 n) there is clear evidence that both the signal and idler coherently contribute to the output of the second OPO. This leads to enhanceent of the total syste efficiency. For larger detuning the coherent enhanceent gradually decreases and the ZGP OPO will generate two independent ultiode signal-idler pairs puped by the signal and idler of the first OPO respectively. This effect is illustrated in the right part of Fig. 2 where the siulation with 40 GHz (0.6 n) detuning fro degeneracy of the signal in the first OPO gives a single broad peak for the signal and one for the idler of the ZGP OPO while the siulation with 500 GHz (7.6 n) (C) 2009 OSA 28 Septeber 2009 / Vol. 17 No. 20 / OPTICS EXPRESS 17584

4 detuning in the first OPO gives double peaked signal and idler spectra. The double peaked nature of the spectra has also been observed experientally [9]. Fig. 2. Left: The calculated output energy of the ZGP OPO puped by the signal and idler of an OPO with varying detuning fro degeneracy. Solid lines are the siulations with both pup coponents applied siultaneously and dashed lines with the two coponents siulated separately and the generated energy sued afterwards. The total pup energies were and 700 µj with half of that energy in each coponent. Right: Output spectra fro two of the siulations where the pup was detuned 40 GHz (blue) and 500 GHz (red) fro degeneracy. 3. Experiental setup The pup laser was a coercial ulti-longitudinal ode diode-puped Q-switched Nd:YVO 4 -slab laser providing a axiu energy of 1.8 J in 9 ns-long pulses. For the OPO ode characterization experients the pup laser was operated at 100 Hz repetition rate in order to avoid increased heat-load and associated spectral shift in the reflectivity of the OPO VBG output coupler. The pup laser spectral width was found to be 28 GHz by easuring interference fringe visibility using an iage-rotating Michelson interferoeter where one ar used two irrors in a corner reflector arrangeent while the other ar used a flat irror on a translator (siilar to the arrangeent in [12]). An optical isolator was used to decouple the pup laser fro the OPO cascade while the half-wave plate polarizer cobination was used to adjust pup power. The pup bea was loosely focused to a waist (1/e 2 intensity radius) of in the horizontal and vertical directions respectively. Two different 1 -thick PPKTP crystals having physical lengths of 20 and 10 (with corresponding lengths of QPM periods of 16 and 8 respectively) and QPM periods of µ and 38.8 µ respectively were used as the OPO gain edia. For the longer crystal proper care was taken to prevent parasitic oscillation by AR coating (for pup and signal) and non-parallelis of the crystal optical faces while the shorter crystal was uncoated. The paraetric gain for both crystals was kept at degeneracy by adjusting the PPKTP teperatures (teperatures of 57 C and 89 C for QPM periods of µ and 38.8 µ respectively). Different crystal lengths allowed variation of the OPO longitudinal ode separation and to reach operational regies where the effect of the pup coherence on the idler output spectru could be easily deonstrated. We used a siple linear OPO cavity which eployed a dichroic incoupling irror highly transitting for the pup and highly reflecting for the signal-idler range. The cavity was copleted by one of three available output couplers naely a broadband dielectric irror reflective between 2 µ and 2.4 µ a VBG1 reflective at n and a VBG2 reflective at 2122 n. The VBG reflectivity spectra were 0.5 n (FWHM) in both cases. All output couplers had a noinal axiu power reflectivity of 50%. The VBG optical surfaces were polished to give a sall angle between the surface noral and the grating vector to avoid broadband feedback and then AR-coated for the pup and signal wavelengths. This eans (C) 2009 OSA 28 Septeber 2009 / Vol. 17 No. 20 / OPTICS EXPRESS 17585

5 that the cavity was perfectly singly resonant (at least for VBG2) and that there was no pup feedback. In order to obtain resolution in the easureents of individual longitudinal odes the OPO cavity lengths were kept as sall as possibly ultiately deterined by the echanical constraints. For lower resolution spectral easureents we eployed a grating onochroator with an effective resolution of 0.5 n. The OPO longitudinal odes were resolved using a scanning plane-irror Fabry-Perot interferoeter with a finesse of 70. The Fabry-Perot irror separation of 1.5 gives a frequency resolution of about 1.4 GHz. During easureent the Fabry-Perot was repeatedly scanned over the range of up to 4 free spectral ranges (FSR) with one data point in the frequency scan corresponding to one OPO pulse. The total length of the scans corresponds to up to OPO pulses. The estiated frequency easureent error is about 10% and arises fro the accuracy in deterining the irror spacing and the FSR easureent. 4. Experiental results and discussion The PPKTP OPO output spectra obtained with the three different output couplers are copared in Fig. 3. Here the spectru was easured with the grating onochroator. In the OPO with the dielectric irror output coupler the spectru extends over 14 THz and by reference to Fig. 1 it can be seen that ost of the generated power would be wasted in the cascaded OPO schee. For the VBG output couplers the OPO spectral widths are liited by the onochroator resolution. Figure 4 shows the signal and idler spectra of the OPO containing the 20 -long PPKTP with the VBG2 output coupler (reflective at 2122 n) as easured by the Fabry-Perot interferoeter. The 13 n separation of signal and idler corresponds to 8.6 ties the FSR so that the different orders of signal and idler were interleaved with each other but the signal and idler spectra of different orders did not overlap significantly. In the resonant signal spectru several longitudinal odes are clearly visible with an average ode separation of 3.44 GHz. Fig. 3. Output spectra fro the OPO using three different output couplers shown at two different wavelength scales. This ode separation is well in agreeent with the theoretical value of 3.45 GHz assuing 7.2 optical path in the OPO cavity outside the PPKTP crystal and taking into account the VBG dispersion. Thus the cavity roundtrip tie can be expressed as T ( ω) = T ( ω) + dφ dω. The dispersion of the VBG having a length d can be readily RT cav VBG ω calculated fro the reflectivity phase (Eq. (2)) [13]: 2 2 ( κ δ d) δ φ = arc tan tan h 2 2 κ δ (2) (C) 2009 OSA 28 Septeber 2009 / Vol. 17 No. 20 / OPTICS EXPRESS 17586

6 where the detuning is ( 1 δ 2π n 1 0 λ λ 0 ) = the coupling coefficient is κ = π n / λ 1 the Bragg wavelength is λ 0 =Λ / 2n0 defined by the VBG period Λ and the index of refraction in the VBG is odulated according to n = n n sin(2 π z / ) Λ. Sall variations of the longitudinal ode spacing due to VBG dispersion are below the resolution of the easureent. The nonresonant OPO idler does not contain obvious spectral odulation. Fig. 4. Spectra of signal (left) and idler (right) with 13 n (900 GHz) separation easured by Fabry-Perot etalon for axiu pup power The situation is qualitatively different in the OPO with the sae VBG2 output coupler but containing a half as long PPKTP crystal and having approxiately half as long OPO cavity. The signal and idler spectra in this OPO are shown in Fig. 5. For this cavity the ode separation is theoretically around 6.25 GHz at the center of the grating and decreases to 6.1 GHz at the first zero in the VBG reflectance spectru. The easured ode separation is 6.2 GHz in close agreeent with the theoretical estiates. This eans that the reflectivity variation between adjacent odes is significant and that only a few odes fits within the 33 GHz FWHM reflectance peak of the volue Bragg grating. The signal spectru contains only three clear longitudinal odes. Obviously single-longitudinal ode operation can be achieved ost easily by further reducing the bandwidth of the VBG output coupler. In contrast to the OPO with a longer cavity (see Fig. 4) the idler spectru in Fig. 5 is odulated with a period corresponding to the signal ode separation in the cavity. The peaks are wider than the easureent resolution and clearly distinguishable. Moreover we verified that the idler spectru odulation persists when the OPO cavity length is slightly changed. Fig. 5. The signal (left) and idler (right) spectra of the short cavity OPO (10 PPKTP crystal) easured by the Fabry-Perot etalon. The signal and idler are separated by 13 n (900 GHz). The differences in the idler spectra for the OPO with long and short cavity cannot be attributed to the resolution of the Fabry-Perot interferoeter because it was at least two-ties (C) 2009 OSA 28 Septeber 2009 / Vol. 17 No. 20 / OPTICS EXPRESS 17587

7 better than the longitudinal odes separation of the longer cavity OPO signal. In order to understand the differences in the idler spectru we need to take into account coherence properties of the ulti-longitudinal ode Q-switched pup pulses. Spectrally resolved streak caera traces in [14] reveal that in an unseeded Q-switched laser adjacent longitudinal ode beating represented by a quasi-period teporal odulation of the intensity envelope are superiposed on apparently rando variation of instantaneous spectral intensity axiu over the whole bandwidth of the Q-switched pulse. This behavior can be understood if one considers that there is certain phase correlation aong adjacent longitudinal odes coprising the Q-switched pulse spectru while the relative phase (and aplitude) variations for the odes separated by ore than a correlation radius specific for each laser reain largely uncorrelated. In principle this correlation radius could be deterined by easuring the RF ode beating spectru of the pup. Next we turn to the issue of the idler generated in a single-resonant OPO puped by such partially coherent pup. The coplex polarization dynaics that generates the idler can be expressed as in Eq. (3) [15]: (2) (2) ε 0 τ i 1 τ 2 p n τ1 φp n τ1 ( ) n (3) P ( t) R E ( t )exp i ( t ) Es ( t τ 2 )exp iφs ( t τ 2 ) dτ1 dτ 2. (2) Here ε 0 is the dielectric constant and R is the second order nonlinear response function related to the ore coonly used susceptibility by the Fourier transfor. (2) Causality deands that R is zero for negative τ 1 and τ 2. That the polarization depends on the field at earlier ties is due to the ass of the charge carriers in the aterial which can ( 2) also be seen in the frequency dependence of χ. E p n and E s are the real slowly varying aplitudes for pup ode n and signal ode respectively while ( t) φ ( t) ω t ϕ s s s φ = ω t+ ϕ and p n p n p n = + are the corresponding tie dependent phases with ω ω ϕ and ϕ s being the frequencies and phase offsets of each ode. The idler will contain energy at frequencies ω = ω p n ωs for all cobinations of pup and signal odes but the aplitude at each frequency depends not only on the ode aplitudes but also on the phases. Considering that the nanosecond OPO cavity length is norally substantially shorter than that of the pup laser (in our case a pup ode separation of about 1 GHz has been easured) then for each OPO signal ode only the pup odes whose phases are correlated with each other will contribute substantially to the idler generation and thus to overall OPO efficiency. So for signal ode separation larger than the pup odal phase correlation radius the idler spectru should contain coherence spikes whose separation corresponds to the signal ode spacing while the width corresponds to the pup odal correlation radius. Fro Fig. 5 we estiate the pup odal phase correlation radius to be about 3 GHz corresponding to approxiately three correlated odes. On the other hand when the OPO signal ode separation is reduced to correspond to the pup odal phase correlation radius the coherence spikes in the idler spectru disappear as adjacent coherence regions start overlapping. Finally it interesting to investigate what happens to the single-resonant OPO spectru when it is forced to operate as close as possible to degeneracy i.e. when the VBG central wavelength is detuned fro degeneracy point by approxiately half of the FWHM bandwidth. This was possible to do with the VBG1 output coupler. The OPO cavity lengths were the sae as those in Fig. 4 and Fig. 5. The spectru of the long-cavity OPO shown in the left part of Fig. 6 reveals that the OPO is indeed singly resonant with the longitudinal odes proinent only on the high-frequency signal part of the spectru. The low-frequency part contains little odulation in agreeent with previous discussion. On the other hand the short-cavity OPO spectru shows narrow (liited by Fabry-Perot interferoeter resolution) p n s p n (C) 2009 OSA 28 Septeber 2009 / Vol. 17 No. 20 / OPTICS EXPRESS 17588

8 longitudinal odes developed on the high-frequency side of the spectru and broader coherence spikes on the low-frequency (the idler) side of the spectru. This is again in agreeent with the above explanation of the spectral behavior for a singly-resonant OPO. Furtherore the OPOs with VBG1 output coupler deonstrate how the superior spectral selectivity of the VBG output couplers allows singly-resonant oscillation to take place even in the case where signal and idler spectra are not well separated. 5. Conclusions Fig. 6. Fabry-Perot spectra of the OPO close to degeneracy containing the VBG1 output coupler. Left: the long cavity OPO with the 20 PPKTP. Right: the short cavity OPO with the 10 PPKTP. We have theoretically deterined the spectral requireents of the first stage OPO operating around the degeneracy point at µ for efficient puping of a subsequent tande ZGP oscillator. These requireents can easily be et in type-i QPM OPOs eploying VBG output couplers. The singly-resonant oscillation in this type of device can be aintained even as the signal and idler spectra are not well separated. Investigations revealed that the relative odal phase correlation of the ulti-longitudinal ode Q-switched pup laser and signal longitudinal ode separation play a significant role in the spectral shape of the nonresonant idler. It should be stressed that the spectra with VBG output couplers reained stable over the whole puping range up to 3.5 ties above the threshold. Finally operating the OPO at 20 khz repetition rate with a cavity containing the 20 PPKTP and the VBG2 output coupler we obtained 7.9 W of output radiation with a 30% conversion efficiency. The signal and idler fro this configuration have also been used to siultaneously pup a ZGP OPO producing 3.2 W of id-ir radiation corresponding to a conversion efficiency of 12% fro 1.06 µ to the id-ir [9]. This is one of the highest efficiencies reported fro a tande OPO syste. Acknowledgeents The authors acknowledge valuable discussions about VBG theory with Björn Jacobsson. The 20 long crystal was poled by Gustav Ströqvist. This work has been supported in part by the EU FP7 project under grant agreeent Nr We also acknowledge suggestions fro one of the reviewers that helped iprove the paper. (C) 2009 OSA 28 Septeber 2009 / Vol. 17 No. 20 / OPTICS EXPRESS 17589