Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

Resonant oscillations of the Stokes parameters in non-linear twisted birefringent media

Ryohei Seto, Hiroshi Kuratsuji, Robert S. Botet

Published Jul 26, 2005• 10 citations
Publisher

Abstract

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.

DOI
10.1209/epl/i2005-10146-7

Related papers

Electromagnetic Gyration: -- Hamiltonian Dynamics of the Stokes Parameters --

Hiroshi Kuratsuji, Robert S. Botet, Ryohei Seto

Starting with a Schrödinger-type equation derived from the Maxwell theory of electromagnetism, a general formalism is presented for the change of light polarization in nonlinear birefringent media, which we call “optical gyration” or more generally, “electromagnetic gyration” and applications are considered. The theory is formulated in terms of the Hamiltonian dynamics of the Stokes parameters which turns out to be the equation for a classical spin. As applications, we consider two models: (a) As the first application, we analyze solvable models admitting analytic solutions, which exhibit the structure change in the behavior of the Stokes parameter caused by the mutual interplay between linear and nonlinear birefringence. (b) The second application is the optical analogue of the so-called nuclear magnetic resonance (NMR) or Rabi resonance. This is investigated in the case of purely linear birefringence and coexisting of linear and nonlinear birefringence.

Progress of Theoretical Physics•Feb 1, 2007•15 citations

Modification of radiation polarisation due to propagation in a resonant medium

G. G. Adonts, D G Akopyan, K V Arutunyan

The optical-pumping theory of the passage of polarised radiation through a resonant medium was developed in the irreducible tensorial formalism. Transitions with arbitrary momenta J 1.2 are considered in the cubic approximation. For transitions with small values of momenta (J 1 =1 to J 2 =0; J 1 = 1 / 2 to J 2 = 1 / 2 ) the vector form of the equation system in density-matrix notation allows the problem to be solved exactly for light intensity. In the general case of an elliptically polarised wave, the equation systems for the interaction between circular components of polarisation of light in a resonant medium are obtained. Numerical calculations for deformation and rotation of the polarisation ellipse in a medium subject to saturation effects are also carried out. Irrespective of the initial state the polarisation tends either to a linear or to a circular form as it propagates, depending on times of collisional relaxation of orientation and alignment. The polarisation of linearly and circularly polarised waves does not change as the waves propagate, but the values of the saturation power for these polarisations differ considerably.

Journal of Physics B Atomic and Molecular Physics•Dec 28, 1986•9 citations

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

Waldemar Jęda, Andrzej Zagorski

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.

Acta Physica Polonica A•Sep 1, 1999•2 citations

Polarized light in an anisotropic medium versus spin in a magnetic field

Valerii S Zapasskii, G. G. Kozlov

The analogy between polarization optics effects and the dynamics of a spin in a magnetic field is analyzed based on the fact that the Bloch equation for a spin in a magnetic field is formally identical to the evolution equation for the quasi-spin vector of a light propagating in an optically anisotropic medium. Among the effects discussed within this framework are light polarization beats in a birefringent medium; optical activity suppression in the media with linear birefringence; suppression of linear birefringence in the media with spatially modulated gyration; 'adiabatic' transformation of light polarization in media of smoothly varying anisotropy, and two- and three-pulse polarization echoes.

Physics-Uspekhi•Aug 31, 1999•20 citations

Laser-induced rotation of the plane of polarisation of light in a resonance medium

G. G. Adonts

The propagation of a strongly polarised electromagnetic wave through a resonance medium with arbitrary angular momenta of the levels is investigated in the adiabatic following approximation. Exact wavefunctions of the two-level atomic system with degenerate levels in the field of a circularly (linearly) polarised wave are constructed and the picture of the energetic level splitting and shift is discussed. Exact formulae for the non-linear refractive index of the medium in the field of the circularly (linearly) polarised wave are found. The propagation of counterpropagating polarised waves-an intense pump wave and a probe light signal-through the resonance medium is studied. The studies are carried out in the scope of a two-level (one-photon resonance) and a three-level (one- and two-photon resonances) medium. Formulae are found for the induced pump angle of rotation of the ellipse (plane) of polarisation for the probing signal that are exact in terms of the intensity of the pump wave. The spectral dependence of the angle of rotation is studied, and it is shown that a series of Stark-shifted resonance poles of atomic absorption and a three-photon scattering process arise.

Journal of Physics B Atomic and Molecular Physics•Dec 14, 1987•0 citations

Polarization dynamics in nonlinear birefringent active fibers

S. O. Elyutin, Andrei I. Maimistov

Numerical solutions are obtained of the full self-consistent system of equations for the counter rotating polarization components of the field of short optical pulse propagating in birefringent non-linear fiber and the ensemble of the energy level degenerated dopant resonance atoms implanted in fiber material. In every cross-section of fiber the ellipticity of the polarized wave experiences a complex evolution in time accompanied by rapid changes of the azimuth angle due to interplay of dispersion and Kerr non- linear self- and cross-modulation. The reciprocal effect of the impurities on the traveling pulse causes the oscillations of the pulse envelope able to distort completely the shape of the input signal, while the resonance absorption can drive the birefringence from the non-linear back to linear regime.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 9, 2001•0 citations
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.
Starting with a Schrödinger-type equation derived from the Maxwell theory of electromagnetism, a general formalism is presented for the change of light polarization in nonlinear birefringent media, which we call “optical gyration” or more generally, “electromagnetic gyration” and applications are considered. The theory is formulated in terms of the Hamiltonian dynamics of the Stokes parameters which turns out to be the equation for a classical spin. As applications, we consider two models: (a) As the first application, we analyze solvable models admitting analytic solutions, which exhibit the structure change in the behavior of the Stokes parameter caused by the mutual interplay between linear and nonlinear birefringence. (b) The second application is the optical analogue of the so-called nuclear magnetic resonance (NMR) or Rabi resonance. This is investigated in the case of purely linear birefringence and coexisting of linear and nonlinear birefringence.
The optical-pumping theory of the passage of polarised radiation through a resonant medium was developed in the irreducible tensorial formalism. Transitions with arbitrary momenta J 1.2 are considered in the cubic approximation. For transitions with small values of momenta (J 1 =1 to J 2 =0; J 1 = 1 / 2 to J 2 = 1 / 2 ) the vector form of the equation system in density-matrix notation allows the problem to be solved exactly for light intensity. In the general case of an elliptically polarised wave, the equation systems for the interaction between circular components of polarisation of light in a resonant medium are obtained. Numerical calculations for deformation and rotation of the polarisation ellipse in a medium subject to saturation effects are also carried out. Irrespective of the initial state the polarisation tends either to a linear or to a circular form as it propagates, depending on times of collisional relaxation of orientation and alignment. The polarisation of linearly and circularly polarised waves does not change as the waves propagate, but the values of the saturation power for these polarisations differ considerably.
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.
The analogy between polarization optics effects and the dynamics of a spin in a magnetic field is analyzed based on the fact that the Bloch equation for a spin in a magnetic field is formally identical to the evolution equation for the quasi-spin vector of a light propagating in an optically anisotropic medium. Among the effects discussed within this framework are light polarization beats in a birefringent medium; optical activity suppression in the media with linear birefringence; suppression of linear birefringence in the media with spatially modulated gyration; 'adiabatic' transformation of light polarization in media of smoothly varying anisotropy, and two- and three-pulse polarization echoes.
The propagation of a strongly polarised electromagnetic wave through a resonance medium with arbitrary angular momenta of the levels is investigated in the adiabatic following approximation. Exact wavefunctions of the two-level atomic system with degenerate levels in the field of a circularly (linearly) polarised wave are constructed and the picture of the energetic level splitting and shift is discussed. Exact formulae for the non-linear refractive index of the medium in the field of the circularly (linearly) polarised wave are found. The propagation of counterpropagating polarised waves-an intense pump wave and a probe light signal-through the resonance medium is studied. The studies are carried out in the scope of a two-level (one-photon resonance) and a three-level (one- and two-photon resonances) medium. Formulae are found for the induced pump angle of rotation of the ellipse (plane) of polarisation for the probing signal that are exact in terms of the intensity of the pump wave. The spectral dependence of the angle of rotation is studied, and it is shown that a series of Stark-shifted resonance poles of atomic absorption and a three-photon scattering process arise.
Numerical solutions are obtained of the full self-consistent system of equations for the counter rotating polarization components of the field of short optical pulse propagating in birefringent non-linear fiber and the ensemble of the energy level degenerated dopant resonance atoms implanted in fiber material. In every cross-section of fiber the ellipticity of the polarized wave experiences a complex evolution in time accompanied by rapid changes of the azimuth angle due to interplay of dispersion and Kerr non- linear self- and cross-modulation. The reciprocal effect of the impurities on the traveling pulse causes the oscillations of the pulse envelope able to distort completely the shape of the input signal, while the resonance absorption can drive the birefringence from the non-linear back to linear regime.