The exploration into the effects of higher order transversal modes in a singular resonant optical parametric oscillator (OPO), using numerical solutions and mode expansions up to two radial modes, anticipates that lower threshold and higher conversion will be observed at negative dispersion. The 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

Continuous-wave operation of singly-resonant optical parametric oscillators (SRO) has recently been demonstrated for various non-linear materials, including KTP and periodically-poled LiNbO3 (PPLN). In these experiments, significant pump depletion was achieved, up to 93% in some cases. Theoretical studies have been published regarding diffractive effects for continuous wave SROs, but so far, no study of diffractive effects for arbitrary pump depletion in a continuous-wave SRO without beam walk-off has been published.

Idler Beam and Pump Depletion Dependence on Pump Power and Dispersion

Our investigation presents results showing that the idler beam contains higher transverse modes with appreciable amplitudes, and these amplitudes depend weakly on the amount of pump depletion but heavily on the amount of dispersion.

We have found that the threshold for the first higher radial signal mode is about four times higher than for the lowest mode. Consequently, the relationships between pump input power to idler output power are linear, while the pump input power varies as a function of signal power. This implies that the threshold pump power can be determined using these properties.

Influence of Dispersion and Pump Power

In order to understand the influence of dispersion and pump power on the mode content of the idler and pump, it is instructive to consider a mode expansion of the fields. At the threshold with a zero order pump at input, the effect of the dispersion is to favor the n=0 idler mode for particular dispersion values. Above the threshold, the mode content of the idler is modified by higher pump modes generated by pump depletion.

Numerical Model Calculations

Our model calculations involve a numerical integration of the coupled wave equations, and of the coupled mode equations. Using different numerical methods, the diffraction step was accurately executed and the program was validated by propagating Gaussian modes without conversion, and beams with negligible diffraction and full conversion.

Threshold Parameter

Our investigations show the threshold parameter as a function of the dispersion parameter. The different models give varying results, but all results suggest a minimal threshold at particular values of dispersion.

While the details of the study are complex, the outcome is clear: dispersion has a profound effect on the generation of higher order transverse modes in singly resonant OPOs. Further understanding of these dynamics will aid in the development of improved optical parametric oscillators and potentially revolutionize applications in many related fields.