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Acta Physica Polonica A

A Model of Optical Bistability and Polarisation Evolution in Birefringent χ(2)Nonlinear Media

Waldemar Jęda, Andrzej Zagorski

Published Sep 1, 1999• 2 citations
Publisher

Abstract

We present a model calculation of optical bistability and polarisation evolution in optically birefringent media based on the interaction of three waves.Second-order optical nonlinearity (described by the third rank susceptibility tensor) is assumed to be dominant.A bistable light transmission is analysed in terms of standard Fabry-Perot model of feedback, and is a direct consequence of the results obtained for a semi-infinite medium.A second effect considered in the paper is evolution of polarisation state of the waves involved in these processes.We derived a closed formula for intensity-dependent refractive index, which corresponds to that used in the case of third-order nonlinear media.As a result, we calculated both intensity • and Stokes parameters of transmitted light.

DOI
10.12693/aphyspola.96.373

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Po land b Facul ty of Physi cs, W arsaw Uni versi ty of T echnology Ko szyko wa 75, 00-662 W arszawa, Po l and ( Recei ved December 10, 2003) In t his work w e present results of calcula tion s concernin g bistabil it y of optical polarisati on in biref ringen t me dia .Second -order optical nonlin eari ty is assumed to be dominant and represented by one parameter.In our mo del the second-harmoni c generation regime is assumed.Light transmission is analysed in terms of standard F abry { Perot mo del of feedback.W e deri ved formulas for the Stokes parameters describin g the polaris atio n state.N umerical results show ed that three parameters may exhibit bistable behaviour.T his creates new possibi li tie s for optical switching.
We study the nonlinear optical bistability and multistability of a nonlinear ferroelectric (FE) Fabry-Perot (FP) interferometer assumed coated with partial dielectric mirrors on its interfaces. The FE material is considered to have an intensity-dependent refractive index where the third order nonlinear susceptibility χ ilmn (3) acts like Kerr coefficient. The nonlinear response of the FE medium is modeled by the Landau-Khalatnikov (LK) dynamical equation. Within a single frequency approximation, the nonlinear wave equation is written in terms of polarization P rather than the electric field E as the dependent variable. The resulting nonlinear polarization equation is numerically integrated across the FP film using the fourth order Runge-Kutta method. The behavior of the resulting polarization and transmission as a function of the field input intensity is investigated.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.
In this pap er w e analyse theoreticall y the trans mission of two strong laser beams through a medium exhibiti ng optical nonlinea rity of the second order combined w ith a linear anisotropy .A standard mo del of two wave mixing w as applie d and closed formulas for intensity and polari satio n state w ere obtained.N umerical calculati ons show that outgoing b eams are very sensitive to the state of incoming beams and to the material characteristics.U nder some realistic condition s we w ere able to obtain bistabil ity of both intensity and polarisati on state.T he results also show how to mo dulate the intensity and polarisati on state of one w ave by another one.PAC S numb ers: 42.
The equations of propagation for the polarisation components of an electromagnetic wave in non-linear birefringent media are often termed “non-linear Schrödinger equations”. In this letter, we pursue the analogy between the quantum dynamics of a 2-states oscillator and the time evolution of the wave polarisation. More specifically, we define exactly the optical analogue of the conditions for nuclear magnetic resonance, leading in the optical medium to resonant oscillations of the polarisation state when birefringence is periodically modulated along the wave propagation direction in addition to a static longitudinal magnetic field. Circular polarisation then exhibits Rabi oscillations. The non-linear influence of light intensity on the shape of the resonant polarisation line is discussed precisely.