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Journal of the Optical Society of America B

Squeezing due to cascaded second-order nonlinearities in quasi-phase-matched media

Ludovic Noirie, P. Vidaković, Juan Ariel Levenson

Published Jan 1, 1997• 35 citations
Publisher

Abstract

We present a calculation on the squeezing performance of a quadratic nonlinear medium in which the phase-matching condition is achieved artificially by a periodic poling of the nonlinear susceptibility. We treat in particular the Kerr-like effect due to cascading of two second-order nonlinearities. We show that interesting performance can be achieved for highly integrable and nonlinear materials, by use of technologies already developed.

DOI
10.1364/josab.14.000001

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We present a calculation on the squeezing performance of a quadratic nonlinear medium in which the phase-matching condition is achieved artificially by a periodic poling of the nonlinear susceptibility. We treat in particular the Kerr-like effect due to cascading of two second-order nonlinearities. We show that interesting performance can be achieved for highly integrable and nonlinear materials, by use of technologies already developed.
The present calculation on squeezing capabilities of quadratic nonlinear media in which the phase matching condition is achieved artificially by a periodic poling of the nonlinear susceptibility shows that interesting performance can be obtained for highly integrable and nonlinear materials, using technologies already developed. The origin of squeezing in quasi-phase matched (QPM) media is the cascading of two second order nonlinearities, which at small second harmonic conversion rates has properties similar to a more familiar, purely third order nonlinear effect—Kerr effect.
Cascading of quadratic nonlinearity has been attracting great interests for its potential application to parametric devices, such as phase conjugators or effective Kerr media. In most configurations, the device consists of a single nonlinear element with uniform phase-mismatch. Cascading of several elements with different phase-mismatch has been theoretically investigated and predicted to improve performance of the device for classical applications. In this paper, amplitude squeezing in second-harmonic generation using cascaded quadratic nonlinear elements is numerically analyzed. The analyses are based on linearization of nonlinear coupling equations, where interacting fields are approximated as plane waves. Phase-mismatch of each element is varied independently and tolerance of squeezing performance to the fluctuation of the phase-mismatch is also investigated. It is predicted that the performance as a squeezing device can be also superior to that of a single element device, if a proper combination of the phase-mismatch of each element is chosen. For the fundamental wave, the tolerance to the fluctuation of the phase-mismatch will improve by nearly tenfold compared with the single element case. For the harmonic wave, squeezing beyond the limit of perfect phase-matched case (3dB) will be available, though the tolerance to the fluctuation of the phase-mismatch is quite small. These improvements can be attributed to the nonlinear phase rotation that keeps squeezed axis coincided with the amplitude phase in a stable manner.
We present a brief overview of the recent developments in quantum optics concerning the control and reduction of quantum noise. The achievements on squeezing, quantum non-demolition measurement and noiseless optical functions are summarized. The present limitations in quantum performance are discussed. We particularly stress the role of nonlinear optics and point out the advantages expected from the implementation of new artificially phase-matched materials, in different configurations including cascaded second-order nonlinearities.
The production of squeezed states in second-harmonic generation is discussed theoretically from the viewpoint of the structure of the nonlinear medium, phase-matching conditions, and the polarization state of the fields. The nonlinear coupling constants are derived in explicit form for all 102 magnetic symmetry groups for crystalline as well as electrically polarized isotropic media. The phase-matching conditions are discussed in detail. Phase mismatch is shown to accumulate along the optical path, and is calculated in full detail for various media and geometries. We refer to this as the mismatch accumulation effect. General formulae for normally ordered variances of the second-harmonic and fundamental fields are derived by perturbative procedure, and are specified for some special cases of practical interest.