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Physical Review A

Second-harmonic generation and photon bunching in multimode laser beams

Yujiang Qu, Surendra Singh

Published Apr 1, 1993• 18 citations
Publisher

Abstract

Second-harmonic generation in multimode laser beams is studied experimentally. A multimode laser beam derived from a laser oscillating simultaneously in many longitudinal modes that have the same transverse profile (${\mathrm{TEM}}_{00}$) is focused into a nonlinear crystal. Noncritical phase matching is utilized to generate the second harmonic. The number of longitudinal modes is systematically varied from 1 to 7 and the dependence of the efficiency of second-harmonic generation on the number of modes in the fundamental beam is studied. Experimental results clearly demonstrate the increasing degree of photon bunching in the fundamental beam as the number of modes increases. Experimental results are discussed and compared with the predictions of theoretical models.

DOI
10.1103/physreva.47.3259

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Second-harmonic generation in multimode laser beams is studied experimentally. A multimode laser beam derived from a laser oscillating simultaneously in many longitudinal modes that have the same transverse profile (TEM00{\mathrm{TEM}}_{00}TEM00​) is focused into a nonlinear crystal. Noncritical phase matching is utilized to generate the second harmonic. The number of longitudinal modes is systematically varied from 1 to 7 and the dependence of the efficiency of second-harmonic generation on the number of modes in the fundamental beam is studied. Experimental results clearly demonstrate the increasing degree of photon bunching in the fundamental beam as the number of modes increases. Experimental results are discussed and compared with the predictions of theoretical models.
Second-harmonic generation (SHG) has been predicted to be very sensitive to photon bunching. Because of its two-photon nature SHG would be more efficient with bunched than with random or antibunched photon sequences of the same mean intensity. We use this phenomenon to demonstrate the bunching of photons in time. The fundamental beam, derived from a laser operating near threshold, was focused into a 90° temperature phase matched nonlinear crystal. The operating point of the laser was varied in the neighborhood of threshold, and a feedback loop stabilized its intensity at each operating point. It is well known that the character of laser light changes in passing the threshold of laser action. Underlying photon sequences are bunched below threshold and random above threshold.
We demonstrate supermode-based second harmonic generation in an integrated nonlinear interferometer made of linear and nonlinear directional couplers. We use a fully-fibered pump shaper to demonstrate second harmonic generation pumped by the symmetric or anti-symmetric fundamental spatial modes. The selection of the pumping mode and thus of a specific SHG spectral profile is achieved through the selection of the fundamental wavelength and via a robust phase setting scheme. We use two methods: either post-selecting or actively setting the pumping mode. Such modal phase matching paves the way for classical and quantum applications of coupled nonlinear photonic circuits, where multimode excitation, encoding and detection are a route for multiplexing and scaling up light-processing.
The effect of the quantum properties of light on nonlinear processes has been well studied theoretically. It has been shown that the efficiency of n-photon nonlinear processes in many cases scales as the normalized n-th order correlation function. For light with high intensity correlation function, the efficiency of the n-th harmonic generation will be considerably higher than for coherent light. The experimental observation of this effect remained difficult until recently, because of the absence of bright sources with strong and fast intensity fluctuations. For the experimental demonstration of statistical effects in optical harmonic generation we use as a pump the radiation of high-gain parametric down conversion. Such light shows quantum properties (e.g. quadrature or two-mode squeezing) and has large number of photons in one mode. The normalized n-th order correlation function for this light is (2n - 1)!!, which makes it more attractive for nonlinear processes than both coherent and thermal light. For the generation of optical harmonics we used broadband parametric down conversion around frequency-degeneracy (1600 nm) produced in 1cm BBO crystal from Ti:Sapphire laser (800 nm, 1.6ps, 5kHz, 3W mean intensity). Due to spectral filtering and post-selection technique we could vary the statistics of light from coherent to super-bunched, which allowed us to demonstrate the efficiency enhancement for second-, third-, and fourth-harmonic generation. The obtained experimental results show a good agreement with the theory.
It is theoretically and experimentally demonstrated that optical second-harmonic generation (SHG) is possible to be observed in atomic media irradiated with an intense laser pulse. The SHG is induced by a static electric field spontaneously generated in the interaction, and any special condition is not required for the SHG. The experiment to observe the SHG has been made using atomic sodium vapor and a mode-locked Nd-doped yttrium aluminum garnet laser system (pulse duration, 28 psec; output energy \ensuremath{\lesssim}50 mJ). The second harmonic (SH) polarization, spatial beam pattern, and dependences of SH signal on the sodium density and on the fundamental intensity have been examined. The experimental results agree well with the theoretical predictions and numerical results.
Three-photon resonance enhancement of third-harmonic generation and multiphoton ionization have been studied in xenon under excitation by the Bessel and the focused annular laser beams. It has been shown that the transformation of a Gaussian beam into a Bessel or an annular one leads to significant changes of third-harmonic excitation profiles and ionization spectra. These changes result from a principal difference of the beams, where either collinear (Gaussian beams) or noncollinear (Bessel and focused annular beams) excitation geometries are realized. It has been shown that the noncollinear ring-type phase matching shifts the maximum of the generated third harmonic to the longer wavelength toward the atomic resonance. Numerical calculations of third-harmonic excitation spectra have been carried out and compared with experimental results. The efficiency of frequency tripling in collinear and noncollinear excitation geometries have been compared. Cancellation of the three-photon 6s6s6s resonance and the influence of harmonic photons on the excitation of the four-photon 4f4f4f resonance in the Bessel beams are discussed.
An experiment is described that investigates certain interference effects for second-harmonic generation within a resonant cavity. By employing a noncollinear geometry, the phases of two fundamental beams from a frequency-stabilized dye laser can be controlled unrestricted by the boundary conditions imposed in an optical cavity containing a KDP crystal and resonant at the second harmonic. The fundamental beams are either traveling or standing waves and generate either one or two coherent sources of ultraviolet radiation within the cavity. The experiment demonstrates explicitly the dependence of second-harmonic phase on the fundamental phases and the dependence of coupling efficiency on the overlap of the harmonic polarization wave with the cavity-mode function. The measurements agree well with a simple theory.