Theory of second harmonic generation of ultrashort pulses for collinear achromatic phase matching

Abstract

Achromatic phase matching (APM), a favorable method in increasing phase matching bandwidth, is explored for second harmonic generation of ultrashort pulses based on a typical grating telescope system. A set of coupled equations incorporating angular dispersion is constructed in the space-time domain. An analytic solution with a pump of tilting pulsed Gaussian beam to the equations is given under the undepleted pump approximation. With the aid of matrix formalism, some properties of the conversion are demonstrated. Though a maximal phase matching bandwidth is obtained, angular dispersion makes the conversion active only around the geometrical focus. Theory shows that APM does not require an overall pulse-front matching in the conversion process.

Second harmonic generation in the presence of walk-off and group velocity mismatch

“…Although the PFT can hinder further applications, it is well known that it is equivalent to angular dispersion [13,14], and can be controlled, and removed, using angularly dispersive optical components such as prisms and gratings. This would correspond to the inverse of a technique that has been studied over the last 25 years [15][16][17][18][19],…”

The Optical Design of Achromatic Phase Matching System Based on ZEMAX

“…In order to overcome this difficulty, extremely short crystals are employed which drastically lowers the efficiency. To increase the phasing-bandwidth and no lower the efficiency, a scheme called APM is proposed [10][11][12]. APM is a dispersive arrangement where the different spectral components of a pulse are spectrally dispersed so that each component falls on the crystal under the proper phase-matching angle.…”

Highly efficient broadband sum-frequency generation in the visible wavelength range

“…Thin nonlinear crystals can support the broadband threewave mixing process but at the expense of efficiency. Several techniques have been suggested to enhance the efficiency over a broad bandwidth, such as quasi-phasematching with chirped grating design [2,3], phase matching in bulk polycrystal [4], achromatic phase matching [5][6][7][8], temperature gradient phase matching in a quasiphase-matched crystal [9], and use of several crystals [2]. While these methods improve efficiency or bandwidth of the conversion process, all exhibit a trade-off between bandwidth and efficiency.…”

“…The conversion of each frequency component occurs in a different location along the nonlinear crystal, correlating with the location of Δkz ≈ 0 for the interacting waves involved. When the phase matching is tuned over the entire signal spectrum, one can obtain full-photon conversion for very broadband spectra [5][6][7][8].…”