Squeezing in the sum and difference fields in second harmonic generation

Mark S. Hillery

Joji Maeda, Kazuro Kikuchi

We discuss quantum-fluctuation characteristics of a second-harmonic generation system that uses an optical resonator to confine only the fundamental field. It was predicted that the available amount of squeezing is limited to 1.76 dB for the fundamental output and 9.54 dB for the second-harmonic output, respectively, irrespective of system parameters. However, these predictions are based on low-order perturbation theory and are unavailable if the nonlinear coupling between the fundamental and the second harmonic becomes large. We consider the spatial evolution of the fields and reveal that the maximum amount of squeezing depends on the cavity loss: Even an arbitrary amount of squeezing is possible for both the fundamental output and the second-harmonic output. We also consider the possibility of parametric oscillation of empty cavity modes pumped by the generated second harmonic and derive the following prediction: In a system that uses a type I phase-matched crystal, the oscillation of the side mode hardly occurs because of sum-frequency generation with the fundamental and scarcely imposes any limitations on squeezing. On the other hand, a system with a type II phase-matched crystal suffers from the oscillation of the polarization mode orthogonal to that of the fundamental input, and squeezing of the second-harmonic output is limited to 3 dB.

You-Bang Zhan

Jerzy S. Krasiński, Donald F. Heller, Jay R. Ackerhalt +1 more

The theory of three wave mixing was formulated in a classic paper by Armstrong, Bloembergen, Ducuing, and Pershan over 25 years ago.1 A theoretical description of three wave mixing for multimode time-dependent input fields (as opposed to cw single frequency time independent input fields) has recently been presented.2 Analytic solutions were developed for die time-dependent intensities of the output fields. These solutions differ dramatically from those for single-mode fields. New frequencies in the sum-frequency output spectrum and in the input-field output spectrum are created and grow in magnitude as the input intensities are increased. The output spectrum broadens under conditions of strong nonlinear coupling, ultimately reaching the phasematched bandwidth limit. Here, we review the results presented in Ref. 2 for sum frequency generation (SFG) and explicidy compare these results with those for second harmonic generation (SHG). We show that SHG cannot be described as a limit of the SFG formalism for multimode fields. The SFG formulation for the interaction of photons close to frequency ω1 with photons close to frequency ω2 producing photons close to frequency ω 3= ω 1+ ω 2 does not allow ω1(ω2) photons to interact with each other to produce photons close to frequency 2ω1(2ω2). This self interaction is crucial for SHG and must be incorporated. Therefore, a separate formulation is used to describe SHG with multimode input fields.

Toshiaki Suhara, Hiroshi Nishihara

A theoretical analysis based on the fluctuation propagation matrix method proposed by the authors has been performed for systematic study of the generation and conversion of squeezed light in various traveling-wave second-order nonlinear-optic devices. The important insights obtained are: (1) Second-harmonic generation (SHG) allows generation of a highly squeezed fundamental wave, and a highly amplitude squeezed harmonic wave can be obtained by pumping with amplitude-squeezed fundamental wave. (2) Degenerate optical parametric (de)amplification (DOPA and DOPDA) allow generation of squeezed vacuum states and substantial amplitude/phase squeezing of the signal wave. (3) Sum- and difference-frequency generation (SFG and DFG) using a strong pump wave allow wavelength conversion of squeezed light. The results are given in graphic form using normalized parameters which can readily be correlated to device parameters. © 1999 Scripta Technica, Electron Comm Jpn Pt 2, 82(12): 48–56, 1999

S. T. Gevorkyan, Gagik Yu. Kryuchkyan, Karen V. Kheruntsyan