Dispersion-induced Generation of Higher Order Transversal Modes in Singly- Resonant Optical Parametric Oscillators

We study the effects of higher order transversal modes in a model of a singly-resonant OPO, using both numerical solutions and mode expansions including up to two radial modes. The numerical and two-mode solutions predict lower threshold and higher conversion than the single-mode solution at negative dispersion. Relative power in the zero order radial mode ranges from about 88% at positive and small negative dispersion to 48% at larger negative dispersion, with most of the higher mode content in the first mode, and less than 2% in higher modes. Continuous-wave operation of singly-resonant optical parametric oscillators (SRO) has recently been demonstrated for various non-linear materials, including KTP [1-3] and periodically-poled LiNbO 3 (PPLN) [4-6]. Significant pump depletion was achieved, up to 93% in [6]. In these experiments, with zero beam walk-off and confocal parameters of pump and signal comparable to the crystal length, diffractive effects are known to be important [7,8]. Theoretical studies including diffractive effects for cw SROs [7,8] have been published for the case of small pump depletion, and give the dependence of the threshold on the focusing geometry. A treatment of a low-loss SRO for arbitrary pump depletion in the plane-wave approximation was given in [9]. A numerical model including diffraction and pump depletion for a nano-second pulsed SRO with significant birefrigent walk-off was presented in [10]. To the best of our knowledge, no study of diffractive effects for arbitrary pump depletion in a cw SRO without beam walk-off has been published so far. In particular, it is not known how the transverse mode content of the idler beam and the amount of pump depletion depend upon pump power and dispersion. In this letter, we present such results for an SRO with low cavity losses [2]. We find that the idler beam contains higher transverse modes with appreciable amplitudes, and that these amplitudes depend only weakly on the amount of pump depletion, but strongly on the amount of dispersion. We use the coupled wave equations for signal, idler and pump fields A F where κ F =ω F d/(n F c) and d is the effective nonlinear constant. The subscripts x,y and z denote partial derivatives with respect to these spatial coordinates and, for a periodically-poled crystal, ∆=k P-k S-k I-2π/l is the residual dispersion wave vector (l is the period of the poling). In the limit of small cavity loss α S <<1, the signal field …