Novel configurations for optical parametric oscillators without any cavity
Authors: Ding Yujie J. , Khurgin Jacob B. , Lee Seung-Joon 
Published: February 2023

Forward optical parametric oscillators (OPO’s) based on quasi-phase matching (QPM) were implemented in LiNbO3 [1], However, a forward OPO requires a cavity to establish oscillation. Harris [2] introduced the concept of a backward OPO (BOPO) based on conventional phase matching: a cavity is not required to establish oscillation. However, in Ref. [2], only a threshold condition was obtained. Here, we present our results on BOPO’s [3] and transversely-pumped counter-propagating OPO’s (TPCOPO’s) [4]. A TPCOPO does not require a cavity to establish oscillation either. Second-order susceptibility of a nonlinear medium is spatially modulated with a period the pump wavelength in the medium to achieve QPM. A pump wave at the wavelength in vacuum λ3 propagates along a waveguide for a BOPO or onto the surface for a TPCOPO. Two counter-propagating waves at the wavelengths λ1 and λ2 can be generated in the nonlinear medium. To tune the output frequencies of the signal and idler, we can change the incident angle of the pump wave in the TPCOPO or BOPO. The gain for the signal or idler is effectively balanced by the loss of the signal or idler at the respective exit plane to reach a steady-state oscillation. Because a cavity is eliminated, a BOPO or TPCOPO is more stable while a forward OPO is sensitive to the slight mirror translation. For a TPCOPO [4], there is an optimal pump power ≈3.4Pth (where Pth is the threshold, pump power) at which η reaches the maximum value of 44%. If P3≫Pth, there is a huge build-up of the oscillating fields inside the medium. The efficient sum-frequency generation saturates the TPCOPO. Consider GaAs/Al0.8Ga0.2 As multilayers [5] with the optimized structure dimensions: if λ3≈0.49μm, Pth≈7.3kW and tuning range: 1.4-2.6 μm (or 3.1-5.8 μm if λ3≈2μm). Consider ZnSe/ZnS multilayers: if λ3 ≈ 0.49 μm, Pth≈0.92kW and the tuning range: 0.7-1.7 μm, Consider GaAs/AlAs asymmetric coupled quantum-well domain structure [6]: if λ3 = 10 μm, Pth ≈ 10W and the tuning range: 15-29 μm. Consider a nondegenerate BOPO: |k1 − k2| ≫ 1/L, where k1,2 are the corresponding wave vectors and
L
is the length of the medium. If P3≈1.1 Pth, the conversion efficiency for the BOPO is η ≈ 20%. When P3 ≈ 3.4Pth, η ≈ 44% for the TPCOPO and η ≈ 95% for the BOPO. Consider a degenerate BOPO: λ1=λ2. A mirror for the pump wave with the reflectivity R2ω is attached to the right facet to increase the conversion efficiencies, However, it is not required for the oscillation to occur. When the pump intensity is Ip≈4I′th≈Ith/4, where Ith and I′th are the thresholds for a nearly-degenerate and degenerate BOPO, η ≈ 99.7% if R2ω=99%. Therefore, compared with the nondegenerate BOPO, the degenerate BOPO offers higher conversion efficiencies. The decrease of the conversion efficiency as Ip (>4I′th) increases is due to generation of a backward wave at the pump wavelength, which propagates along the direction opposite to that of the pump wave. Consider a poled LiNbO3 [1], If the spatial period of the domains is Λ=4μm, λ3=1.1μm, λ1,2≈2.2μm, and L≈2.6cm, the threshold pump intensity for the degenerate BOPO is I′th=2.9×108 W/cm2. For a QPM KTP [7]: Λ=0.7μm, λ3=1.3μm, λ1,2≈2.6μm, and L≈3cm, I′th=2.8×106 W/cm2. In the presence of a cavity for the signal and idler, the thresholds can be reduced by several orders of magnitude. Both the BOPO and TPCOPO can be also implemented in nonlinear optical polymers. Our parametric processes can be used to achieve large amplifications and difference-frequency generation [8].