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Optics and Spectroscopy

Cascaded Second Harmonic Generation with a Half-Order Periodical Orientation

Valentin Yu. Mylnikov, Nikita S. Averkiev, Grigorii S. Sokolovskii

Published Nov 1, 2020• 1 citation
Publisher

Abstract

Abstract We demonstrate theoretically cascaded fourth and second harmonics generation in a periodically oriented nonlinear crystal with a half-order of the periodical orientation. We consider a cascaded process in which four photons of the fundamental harmonic are initially converted into an intermediate photon of the fourth harmonic, which parametrically decays at the second stage into two photons of the second harmonic. We show that fractional phase matching can be achieved by using an asymmetric periodically poled grating. To describe the propagation and transformation of light inside a nonlinear crystal, the quantum spatial Heisenberg equations have been applied, using which the average numbers of photons of the fourth and second harmonics have been calculated as functions of the nonlinear crystal length.

DOI
10.1134/s0030400x2011017x

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Abstract We demonstrate theoretically cascaded fourth and second harmonics generation in a periodically oriented nonlinear crystal with a half-order of the periodical orientation. We consider a cascaded process in which four photons of the fundamental harmonic are initially converted into an intermediate photon of the fourth harmonic, which parametrically decays at the second stage into two photons of the second harmonic. We show that fractional phase matching can be achieved by using an asymmetric periodically poled grating. To describe the propagation and transformation of light inside a nonlinear crystal, the quantum spatial Heisenberg equations have been applied, using which the average numbers of photons of the fourth and second harmonics have been calculated as functions of the nonlinear crystal length.
We theoretically demonstrate cascaded fourth and second harmonic generation in a periodically-poled nonlinear crystal with a half-order of phase-matching period. We consider a cascaded process in which four photons of the fundamental harmonic firstly convert into an intermediate photon of the fourth harmonic, which parametrically decays into two photons of the second harmonic at the second stage. Phase-matching for this cascaded nonlinear conversion is provided by using an asymmetric periodical poling. We use the quantum spatial Heisenberg equations to describe light propagation and conversion inside the nonlinear crystal. With this approach, we calculate second and fourth harmonic average number of photons as a function of the nonlinear crystal length.
We propose an adiabatic scheme for cascaded fourth-harmonic generation (FHG) in chirped dual-period quasi-phase-matched (QPM) crystals, where adiabatic evolution is introduced into the multi-step frequency conversion process. By engineering two chirped QPM gratings for the fundamental-to-second-harmonic ( FF → SH ) and second-to-fourth-harmonic ( SH → FH ) interactions, efficient harmonic generation is achieved through a continuous adiabatic passage in phase-mismatch space, rather than discrete phase-matching conditions in conventional QPM schemes. This approach enables robust and tunable energy transfer among harmonics, allowing controllable generation of second- and fourth-harmonic signals. Numerical results show a maximum FHG efficiency of 94% and a tunable bandwidth of ∼13 nm under realistic conditions. The tunability originates from the controlled shift of QPM resonances along the propagation direction.
The effect of slow light on second-harmonic generation in a periodically poled ${\ensuremath{\chi}}^{(2)}$ nonlinear medium is investigated theoretically. A linear $\ensuremath{\pi}$ phase-shifted grating is used to slow the group velocity of the fundamental frequency, and the resulting field enhancement greatly increases the second-harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.
Abstract A degenerate parametric process and the complete upward generation of ordinary and extraordinary optical waves inside a periodically poled nonlinear crystal (PPNC) with quadratic nonlinearity are considered. A quantum theory is developed for describing statistical characteristics of the polarized states of light in a PPNC. It is found that the degree of polarization can be controlled by creating an imbalance in the intensity of modes at frequencies of ordinary and extraordinary optical waves (i.e., reducing the average number of photons in one and increasing it in the other).