Abstract

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 ≈3.4P_th (where P_th is the threshold, pump power) at which η reaches the maximum value of 44%. If P₃≫P_th, there is a huge build-up of the oscillating fields inside the medium. The efficient sum-frequency generation saturates the TPCOPO. Consider GaAs/Al_0.8Ga_0.2 As multilayers [5] with the optimized structure dimensions: if λ₃≈0.49μm, P_th≈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, P_th≈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, P_th ≈ 10W and the tuning range: 15-29 μm. Consider a nondegenerate BOPO: |k₁ − k₂| ≫ 1/L, where k_1,2 are the corresponding wave vectors and L is the length of the medium. If P₃≈1.1 P_th, the conversion efficiency for the BOPO is η ≈ 20%. When P₃ ≈ 3.4P_th, 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 R_2ω 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 I_p≈4I′_th≈I_th/4, where I_th and I′_th are the thresholds for a nearly-degenerate and degenerate BOPO, η ≈ 99.7% if R_2ω=99%. Therefore, compared with the nondegenerate BOPO, the degenerate BOPO offers higher conversion efficiencies. The decrease of the conversion efficiency as I_p (>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, λ_1,2≈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, λ_1,2≈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].

© 1997 Optical Society of America