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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Second-harmonic pulse shaping with engineered quasi-phase-matching gratings in the strongly depleted pump regime

Usman K. Sapaev, Gaetano Assanto

Published Jun 1, 2007• 0 citations
Publisher

Abstract

In this paper, a powerful approach for arbitrary pulse shaping based on SHG is discussed in engineered quasi phase matching in the case of strong pump depletion. We used a simulated-annealing algorithm (SAA), numerically solving the coupled-wave equations for fundamental and second harmonic (SH) pulses, taking into account both group velocity mismatch and group velocity dispersion. In order to reduce the SAA iteration time and increase computing speed, we employed simple fast Fourier transform and fourth-order Runge-Kutta algorithms. To design a QPM grating for the generation of an arbitrary target SH pulse, we start the SAA with an initial guess for a fixed number of integration domains and a given fundamental wave pulse.

DOI
10.1109/cleoe-iqec.2007.4386156

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In this paper, a powerful approach for arbitrary pulse shaping based on SHG is discussed in engineered quasi phase matching in the case of strong pump depletion. We used a simulated-annealing algorithm (SAA), numerically solving the coupled-wave equations for fundamental and second harmonic (SH) pulses, taking into account both group velocity mismatch and group velocity dispersion. In order to reduce the SAA iteration time and increase computing speed, we employed simple fast Fourier transform and fourth-order Runge-Kutta algorithms. To design a QPM grating for the generation of an arbitrary target SH pulse, we start the SAA with an initial guess for a fixed number of integration domains and a given fundamental wave pulse.
We propose a spatially chirped quasi-phase-matching (QPM) scheme that enables ultrabroadband second-harmonic-generation (SHG) by using a fan-out QPM grating to frequency-convert a spatially chirped fundamental wave.A "zerodispersion" 4f system maps the spectral contents of ultrabroadband fundamental onto different spatial coordinates in the Fourier plane, where the fundamental is quasi-monochromatic locally in picosecond duration, fundamentally canceling high-order phase mismatch.A fan-out QPM grating characterized by a linear variation of the poling period along the transverse direction exactly supports the QPM of the spatially chirped beam.We theoretically demonstrate the SHG of an 810-nm, 12.1-fs pulse into a 405-nm, 10.2-fs pulse with a conversion efficiency of 77%.
We present a theory of ultrashort-pulse difference-frequency generation (DFG) with quasi-phase-matching (QPM) gratings in the undepleted-pump, unamplified-signal approximation. In the special case of a cw (or quasi-cw) pump, the spectrum of the generated idler is related to the spectrum of the signal through a transfer-function relation that is valid for arbitrary dispersion in the medium. The engineerability of this QPM-DFG transfer function establishes the basis for arbitrary pulse shaping. Experimentally we demonstrate QPM-DFG devices operating in a frequency-degenerate type II configuration and producing pulse-shaped output at 1550 nm from 220-fs pulses at 1550 nm.
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.
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Optical poling is a very simple technique for inducing a quadratic nonlinearity in germanium-doped silica fibers [1] , [2] . By injecting into the fiber fundamental frequency (FF) pulses together with a low power second harmonic (SH) seed, a multi-photon quantum interference process naturally generates a quadratic nonlinearity whose period satisfies the quasi-phase matching (QPM) condition. The nonlinear grating writing process takes a few hours before showing a saturation of the SH conversion efficiency, which is always lower than the best values achievable by resorting to thermal poling [3] . Also, the maximum length of the poled region exhibits saturation, and this hampers the SH generation [4] .
It is shown that coherent quantum simultons (simultaneous solitary waves at two different frequencies) can undergo quadrature-phase squeezing as they propagate through a dispersive ${\ensuremath{\chi}}^{(2)}$ waveguide. This requires a treatment of the coupled quantized fields including a quantized depleted pump field. A technique involving nonlinear stochastic parabolic partial differential equations using a nondiagonal coherent state representation in combination with an exact Wigner representation on a reduced phase space is outlined. We explicitly demonstrate that group-velocity matched ${\ensuremath{\chi}}^{(2)}$ waveguides which exhibit collinear propagation can produce quadrature-phase squeezed simultons. Quasi-phase-matched KTP waveguides, even with their large group-velocity mismatch between fundamental and second harmonic at 425 nm, can produce 3 dB squeezed bright pulses at 850 nm in the large phase-mismatch regime. This can be improved to more than 6 dB by using group-velocity matched waveguides.