Mirrorless optical parametric oscillator in a stitched GaN waveguide

Summary form only given. Asymmetric GaN planar waveguides grown on (0001) sapphire by molecular beam epitaxy are promissing submicrometric periodically poled (PP) structures required for quasi-phase-matching the counterpropagating three-wave parametric interactions [1, 2]. However, the realization of cm long waveguides presenting a submicronic periodicity is not possible without moving the sample under the writing beam. This displacement introduces stitching errors. The device must then be formed by a chain of multiple PPGaN elements, each of about 100 mm long, jointed by uniformly polarized domains of mm length representing stitching errors. A mirrorless optical parametric oscillator (MOPO) was experimentally realized in a bold KTiOPO₄ crystal by using the periodically-poled PPKTP with sub-mm periodicity [3]. Now we investigate a MOPO for a fragmented PPGaN waveguide. One of the remarkable properties of the PPKTP bulk MOPO with a chirped pump was the strong asymmetry in the spectral bandwidth: the bandwidth of the forward signal was comparable to that of the pump, whereas the bandwidth of the backward idler was typically one to two orders of magnitude narrower [4, 5]. Quite surprisingly here, the structure presenting stitching errors is almost as efficient as a perfect one because the generated coherent phase of the backscattered wave locks the phases of the forward propagating waves in such a way that they are almost unsensitive to the junctions where quasi-phase-matching is not preserved. Regardless if the phase modulation in the pump is deterministic or stochastic, the backward parametric wave always has a bandwidth that is narrow compared to that of the forward wave.This is illustrated by running a simulation with a stochastic pump with a FWHM temporal length of 100 ps and where the spectral FWHM width is Δνp(0) = 6.40 THz. We consider this PPGaN structure where the length L will be shared in N = 64 elements by taking L = 64 l = 6.05 mm, each element having a length l = 94.5 μm. The segmented MOPO will have a length Lseg = 6.38 mm and the jonctions a random length of mean value ( ε_l) = 5.16 μm. The nonlinear waveguide have a section Seff = 3.6 μm2 and a nonlinear effective susceptibility deff = 9 pm/V. For the zpolarized waves in this GaN waveguide and perfectly matching the group velocity of the forward propagating waves, we have for the pump λp = 1.06016μm; np = 2.308566; vp/c = 0.413379; β2,p = 0.286 ps2/m; for the backward signal λs = 1.56242μm; ns = 2.265806; vs/c = 0.418725; β2,s = 0.0647 ps2/m; and for the forward idler λi = 3.29791μm; ni = 2.123532; vi/c = 0.413379; β2,i = -0.418 ps2/m. The quasi-phase matching needs a periodic poled GaN medium of AG = 335.1 nm length, which may be realized by epitaxy. MOPO operation of the stochastic MOPO in both continuous and segmented structures are simulated with such an incoherent pump pulse of Ip = 5.0625 GW/cm2 intensity. It yields 182 W peak power and a pulsed energy of 18.2 nJ. The pump and the parametric spectra are illustrated in Fig.1 By integrating the spectra, it is found that the conversion into parametric waves has an efficiency of 80 % with respect to the continuous MOPO, and a coherence gain of Δνp/Δνs = 216.