Passive mode locking of optical parametric oscillators - OSA Publishing

Passive mode locking of optical parametric oscillators: an efficient technique for generating sub-picosecond pulses J. Khurgin1, J-M. Melkonian2, A. Godard2*, M. Lefebvre2, and E. Rosencher2,3 1 Johns Hopkins University, Baltimore MD 21218, USA Office Nationale d'Études et de Recherches Aérospatiales, Chemin de la Hunière, 91761 Palaiseau, France 3 Département de Physique, École Polytechnique, 91128 Palaiseau, France *Corresponding author: [email protected]

2

Abstract: We show that optical parametric generation in a nonlinear crystal with a large group velocity mismatch between the pump and nearlydegenerate signal and idler is analogous to laser amplification in the medium with a gain recovery time comparable to the walk-off time. Based on this conclusion we propose to combine an OPO with a nonlinear saturable absorber or Kerr lens to generate directly high peak power subpicosecond pulses using pump pulses ranging from tens of picoseconds to quasi-CW. Our analytical model predicts better than 80% photon conversion efficiency and pulse lengths that are of the order of a few hundred femtoseconds. Numerical simulations confirm our predictions and show that repetitive passive mode locking is feasible with a quasi-CW pump. ©2007 Optical Society of America OCIS codes: (190.4970) Parametric oscillators and amplifiers; (190.7110) Ultrafast nonlinear optics

References and links 1.

E. S. Wachman, D. C. Edelstein, and C. L. Tang, “Continuous-wave mode-locked and dispersioncompensated femtosecond optical parametric oscillator,” Opt. Lett. 15, 136 (1990). 2. J. M. Melkonian, N. Forget, F. Bretenaker, C. Drag, M. Lefebvre, and E. Rosencher, “Active mode locking of continuous-wave doubly and singly-resonant optical parametric oscillators,” Opt. Lett. 32, 1701 (2007). 3. S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. QE-4, 598 (1968). 4. R. Laenen, H. Graener, and A. Laubereau, “Broadly tunable femtosecond pulses generated by optical parametric oscillation,” Opt. Lett. 15, 971 (1990). 5. K. Wolfrum, R. Laenen, and A. Laubereau, “Intense bandwidth- and diffraction-limited picosecond pulses with large tuning range,” Opt. Commun. 97, 41 (1993). 6. J. D. V. Khaydarov, J. H. Andrews, and K. D. Singer, “20- fold pulse compression in a synchronously pumped optical parametric oscillator,” Appl. Phys. Lett. 65, 1614 (1994). 7. J. D. V. Khaydarov, J. H. Andrews, and K. D. Singer, “Pulse compression in a synchronously pumped optical parametric oscillator from group-velocity mismatch,” Opt. Lett, 19, 831 (1994). 8. J. D. V. Khaydarov, J. H. Andrews, and K. D. Singer, “Pulse-compression mechanism in a synchronously pumped optical parametric oscillator,” J. Opt. Soc. Am. B 12, 2199 (1995). 9. A. Umbrasas, J.-C. Diels, J. Jacob, and A. Piskarskas, “Parametric oscillation and compression in KTP crystals,” Opt. Lett. 19, 1753 (1994). 10. C. Rauscher, T. Roth, R. Laenen, and A. Laubereau, “Tunable femtosecond-pulse generation by an optical parametric oscillator in the saturation regime,” Opt. Lett. 20, 2003 (1995). 11. L. Lefort, K. Puech, S. D. Butterworth, Y. P. Svirko, and D. C. Hanna, “Generation of femtosecond pulses from order-of magnitude pulse compression in a synchronously pumped optical parametric oscillator based on periodically poled lithium niobate,” Opt. Lett. 24, 28 (1999). 12. R. S. Kurti and K. D. Singer, “Pulse compression in a silver gallium sulfide midinfrared, synchronously pumped optical parametric oscillator,” J. Opt. Soc. Am. B 22, 2157 (2005). 13. G. Arisholm, “General analysis of group velocity effects in collinear optical parametric amplifiers and generators,” Opt. Express 15, 6513 (2007)

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Received 7 Sep 2007; revised 23 Oct 2007; accepted 25 Oct 2007; published 25 Mar 2008

31 March 2008 / Vol. 16, No. 7 / OPTICS EXPRESS 4804

14. 15. 16. 17. 18. 19. 20.

21. 22. 23. 24. 25.

26.

R. Laenen, C. Rauscher, A. Laubereau, “Kerr lens mode locking of a sub-picosecond optical parametric oscillator,” Opt. Commun. 115 533 (1995). S. Suomalainen, M. Guina, T. Hakulinen, O. G. Okhotnikov, T. G. Euser , S. Marcinkevicius, “1 μm saturable absorber with recovery time reduced by lattice mismatch,” Appl. Phys. Lett, 89 071112 (2006). A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986). D. J. Kuizenga and A. E. Siegman, “FM and AM mode locking of the homogenous laser,” IEEE J. Quantum Electron. QE-6, 694 (1970). H. A, Haus, ‘Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 11, 736 (1975). H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736 (1975). K. Vodopyanov, J. E. Schaar, P. S. Kuo, M. M. Fejer, X. Yu, J. S. Harris, V. Kozlov, W. C. Hurlbut, Y. -s. Lee, C. Lynch, and D. Bliss, “New Light from Gallium Arsenide: Micro-Structured GaAs for Mid-IR and THz-Wave Generation,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper CMJ1. Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984). M. Ebrahimzadeh, P. J. Phillips, and S. Das, “Low-threshold mid-infrared optical parametric oscillation in periodically poled LiNbO3 synchronously pumped by a Ti:sapphire laser,” Appl. Phys. B 72, 793 (2001) M. L. Bortz, M. A. Arbore, and M. M. Fejer, “Quasi-phase-matched optical parametric amplification and oscillation in periodically poled waveguides,” Opt. Lett. 20, 49 (1995). J. B. Khurgin, “Light slowing down in Moire fiber gratings and its implications for nonlinear optics,” Phys. Rev. A 62, 013821 (2000). R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324 (1996). G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691 (1996)

1. Introduction Optical parametric oscillators (OPO) are efficient sources of tunable radiation due to the exceptionally wide bandwidth of parametric gain that is determined only by the phase mismatch [1]. This gain becomes especially wide near the degeneracy of the idler and signal frequency reaching tens of THz. Spectrally broad radiation can correspond to ultra-short pulses in time domain if all its spectral components are locked in phase – this is exactly what happens in mode-locked lasers where Fourier-limited pulse trains can be generated with a CW or quasi-CW pump. Essentially a mode-locked laser operating with a given duty cycle compresses in time the pump energy by an amount inverse to the duty cycle. It would be common sense then to attempt a similar compressive effect in OPO, but unfortunately the physics of OPO is not conducive to this. While in the laser gain medium the pump energy is stored for a certain gain recovery time, in the OPO the pump energy is constantly on the move with a velocity close to that of the generated signal and idler. Therefore, modulating the cavity loss in an OPO may indeed generate series of short pulses, but only a small fraction of pump energy coming from the pump photons propagating synchronously with the signal and idler will be converted into these short pulses. We checked this fact in a recent work where active mode locking of a CW-pumped OPO has been achieved for the first time [2]. A stable train of short pulses has been obtained, but with a very small efficiency (~ 15 % of the CW efficiency). In this work we explore the means of increasing the conversion efficiency of mode-locked OPOs pumped by CW radiation or by comparatively long pump pulses. It had been noticed in [3] that due to material dispersion the group velocities of the signal (vs) and idler (vi) are larger than the group velocity of the pump vp – hence in the reference frame of the pump the signal photons move and over the length of the crystal cover the interval δtps = L(vp-1-vs-1). Thus all the pump energy contained in this interval can be converted into the signal and idler. This is the principle behind energy compression in synchronously pumped OPO first suggested in [3] and then successfully demonstrated by different groups [4#87330 - $15.00 USD

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8] where up to a 20-fold pulse compression had been achieved in a BBO crystal pumped by a few picosecond pulses way above threshold. Later on similar results were demonstrated using KTP [9,10], PPLN [11], and AgGaS2 [12]. Group velocity management can also lead to a better efficiency in parametric amplifiers, especially when the group velocity of the pump lies between those of the signal and idler waves [13]. With the pump compression achieved solely by gain saturation, the shape and the length of the pulses obtained in these experiments depended critically on the detuning between the resonant cavity round-trip time and the pump repetition rate, and the pulse duration was limited by the dispersion. To the best of our knowledge, the only experiment in which passive mode locking of an OPO had been achieved by a Kerr lens effect did not use the temporal walk-off effect thus the compression achieved in that work was insignificant [14]. In this work we investigate feasibility of introducing a passive mode locker, such as saturable absorber (SESAM) [15] or Kerr lens, into the OPO characterized by large group velocity mismatch. While most of prior work had relied on numerical analysis, we develop a simple analytical model showing that one can treat the nonlinear crystal with a large temporal walk-off δtps as a saturable gain medium with a gain recovery time comparable to δtps. With that in place, we can apply all the classical mode locking theory developed in the works of Siegman and Haus [16-19], in order to ascertain the efficiency and peak power of modelocked OPO operating in the steady state regime. We then perform numerical modeling which confirms our analysis and shows that introduction of a passive mode locker into the OPO with a large walk-off leads to generation of stable sub-picosecond pulses, and, furthermore, even with a CW pumping one can achieve repetitive mode locking, similar to harmonic mode locking in lasers.

t1( /p2)

δ t ps vp

vp

ML vs

Δt1/2 vs

L

vi

α

ts Fig. 1. Mode-locked pump-swept OPO with a walk-off δtps between signal, pump and idler. L crystal length, ML mode locker, α total cavity loss (mirror loss and unsaturated loss), t1/2(p) pump FWHM duration, Δt1/2 signal FWHM duration, ts signal total duration, vp,s,i group velocity of the pump, signal, and idler waves respectively.

2. Gain saturation in an OPO with walk-off and in a laser amplifier We consider the OPO (Fig. 1) to be singly-resonant at the signal frequency. All the amplitudes are normalized in such a way that A2 = p = dn / dt where n is the number of photons. The equations in the nonlinear crystal of length L are then

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∂As 1 ∂As + = κ Ap Ai* e− jΔkz ∂z vs ∂t ∂Ai 1 ∂Ai + = κ Ap As* e− jΔkz ∂z vi ∂t ∂Ap ∂z

+

(1)

1 ∂ Ap = −κ As Ai e jΔkz , v p ∂t

where v denotes group velocities. The coupling coefficient is

κ=

χ ( 2) c

⎛ ω p ω s ωi ⎜ ( p ) ( s ) (i ) ⎝ 2 nr nr nr

η0 S

1/ 2

⎞ ⎟ ⎠

(2)

,

where nr denotes refractive indices, S is the effective area and η0 = 377 Ω. Note that the dimensionality of A is s-1/2 and for κ it is s1/2/cm. In order to operate with real powers rather than photon numbers one can divide κ by the square root of the pump photon energy ( ωp)1/2. For the operation at pump near 1 μm with typical values of χ(2) ~ 20 pm/V which is the case for such state-of-the art materials as GaSe or PPLN and S ~ 10-4 cm2, a typical value of κ ≈ 0.025 cm-1W-1/2 and somewhat higher using quasi-phase matched GaAs [20] with χ(2) ~ 50 pm/V. We also assume (for now) that the group velocities of signal and idler are close to each other because we operate close to the degeneracy region, thus vs ≡ vi. Furthermore, at this point we shall consider the case of perfect phase matching – the effect of the imperfect phase matching on the pulse length will be considered in Section. 4. With perfect phase matching one can assume all field amplitudes to be real. If we now introduce a moving system of coordinates with new time t' = t – z/vp we obtain ∂As ( z, t ') ∂A ( z , t ') − δ v −1 s = κ Ap ( z , t ') Ai* ( z, t ') ∂z ∂t ' ∂Ai ( z , t ') ∂A ( z , t ') − δ v −1 i = κ Ap ( z , t ') As* ( z , t ') ∂z ∂t ' ∂Ap ( z , t ') = −κ As ( z , t ') Ai ( z, t '), ∂z

(3)

where we have introduced the rate of walk-off as δ v −1 = v −p1 − vi−1 . In the moving frame as the signal and idler travel a distance Δz they advance in time by Δzδv-1 i.e. by the total walk-off time δtps over the whole length of the crystal. We now consider the signal and idler short pulses defined in an envelope function approximation as As ,i ( z, t ') = ns ,i ( z ) f ( t '− ( L − z ) δ v −1 ) ; ts

∫

f 2 (τ )dτ = 1; f (τ ) = 0 for τ ts

(4) ,

0

where f(τ), the normalized pulse shape of length ts is assumed not to change as the signal and idler pass through the crystal which is certainly a valid conjecture for the steady-state regime of operation with a stable pulse shape. In the moving frame the signal is delayed by the time δtps = Lδv-1 at the input and emerges from the crystal at t' = 0. Besides, in an OPO resonant at the signal frequency and having small cavity losses one can make the so-called mean field approximation that the signal power does not depend on coordinate z. It follows from (3) and (4) that the pump photons associated with time t' encounter the signal and idler in the spatial

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window L − t '/ δ v −1 < z < L − t '/ δ v −1 + ts / δ v −1 ; outside of that interval they travel unchanged. We then solve (3) to obtain for the depleted pump power following the signal and idler pulses arrival Ap ( z , t ') = Ap 0 − κ ns ∫

z

0

ni ( z ) f 2 (t '− ( L − z1 )δ v −1 )dz1

= Ap 0 − (κ / δ v −1 ) ns ∫

t ' −( L − z )δ v −1

ni ( L − t '/ δ v −1 + τ / δ v −1 ) f 2 (τ )dτ ,

0

(5)

by using the substitution τ = t'–(L–z1)δv-1. Now, if the condition ts