Quasi-phase-matched second harmonic generation: tuning and tolerances

Abstract

Quasi-phase matching is a technique for phase matching nonlinear optical interactions in which the relative phase is corrected at regular intervals using a structural periodicity built into the nonlinear medium. The theory of quasiphase-matched second harmonic generation is presented in both the space domain and the wave vector mismatch domain. Departures from ideal quasi-phase matching in periodicity, wavelength, angle of propagation, and temperature are examined to determine the tuning properties and acceptance bandwidths for second harmonic generation in periodic structures. Numerical examples are tabulated for periodically poled lithium niobate. Various types of errors in the periodicity of these structures are then analyzed to find their effects on the conversion efficiency and on the shape of the tuning curve. This analysis is useful for establishing fabrication tolerances for practical quasi-phasematched devices. A method of designing structures having desired phase-matching tuning curve shapes is also described which makes use of varying domain lengths to establish a varying effective nonlinear coefficient along the interaction length.

Second Harmonic Generation, Beam Dynamics and Spatial Soliton Generation in Periodically Poled KTiOPO4

“…Howev er, for pro pa gati on at an ang l e˚f rom the x -axi s, the wal k-o˜is dom i nated by the QPM condi ti on gi vi ng an ang ul ar wa lk-o˜ê = sin À 1 [ sin˚2 ¤ = k (2 ! )Ê ] [15]. The experi m ental system used i s shown schemati cal ly i n Fi g. 2.…”

Multistep parametric processes in nonlinear optics

“…In general, the simultaneous phase-matching of several parametric processes is hard to achieve by using the traditional phase-matching methods, such as those based on the optical birefringence effect, except some special cases discussed above. However, the situation becomes quite different for the nonlinear media with a periodic variation of the sign of the quadratic nonlinearity, as it occurs in the fabricated one-dimensional (1D) QPM structures (Fejer, Magel, Jundt, and Byer [1992]) or two-dimensional (2D) χ (2) nonlinear photonic crystals (Berger [1998]; Broderick, Ross, Offerhaus, Richardson, and Hanna [2000]; Saltiel and Kivshar [2000a]). In this part of the review, we describe the basic principles of the simultaneous phase-matching of two (or more) parametric processes in different types of 1D and 2D nonlinear optical superlattices.…”

“…6 which is described by the system of parametrically coupled equations, (3.6) where ∆k SHG = k 2 −2k 1 +G m and ∆k DFG = k 2 −k sig −k out , σ 1 to σ 5 are the coupling coefficients proportional to the second-order nonlinearity parameter d ef f . The vector G m is one of the QPM vectors used for achieving the phase matching (Fejer, Magel, Jundt, and Byer [1992]) in the QPM structure. If the birefringence phase matching is used, then G m = 0.…”

Narrowband Biphotons: Generation, Manipulation, and Applications

“…4, where the generated fieldâ 1 propagates along the +z direction andâ 2 along the -z direction. For SPDC with χ (2) nonlinearity, this geometry can be achieved by quasiphase matching [29] to submicron periodicity and driven by a single pump laser beam [30,31,32]. For SFWM driven by χ (3) nonlinearity, the phase matching condition can be satisfied by aligning two coherent driving laser beams [33,26].…”

“…Following Eq. (16), the two-photon wave amplitude now is determined by the Fourier transform of the nonlinear coupling coefficient (29) to give ψ(τ) = BLe −γ e τ e −iϖ as τ sin Ω e τ 2 Θ (τ), = i 2 BLe −γ e τ e −iϖ as τ [e −iΩ e τ − e iΩ e τ ]θ (τ).…”