Birefringent Medium Research Articles

Efficiency of second harmonic generation for partially coherent light in anisotropic crystals

Abstract This paper analyzes the second harmonic generation (SHG) efficiency of light with partial temporal coherence due to depolarization effects in birefringent media. It discusses relations between SHG efficiency fading, light source spectrum, crystal birefringence, and phase matching conditions. The efficiency of SHG pumped by the partially coherent light beam that may depolarize light in nonlinear birefringent crystal is also analyzed. The basic theory of SHG with its modification for partially coherent light with depolarization and some numerical calculations of the SHG process are described.

Compact spatial polariscope for light polarization state analysis

A new setup established to measure the light polarization state and the birefringent media parameters is proposed. The described setup consists of two pairs of the linear Wollaston compensators and circular compensators which form a set of two spatially modulated elliptical compensators. These compensators could be used separately as a spatial generator of polarization states and as an analyzer. Using them together allows us to establish a polariscopic setup in which the birefringent media parameters could be measured. When analyzing both the light polarization state and the birefringent media parameters the singular points in the output light intensity appear. The coordinates of these points depend linearly on the azimuth and ellipticity angles of the examined light or on the eigenvectors of the birefringent medium, while the measured light maximum value corresponds to the phase shift for the measurements of the birefringent medium parameters. Neither movable parts nor active elements are needed and no complicated analysis of output light should be made to calculate the desired quantities.

Measurements of elliptically birefringent media parameters in optical vortex birefringence compensator

A new application of the optical vortex birefringence compensator has been presented. Two parameters of elliptically birefringent medium, an ellipticity angle and an optical path difference, can be measured simultaneously in the setup based on the C polarization type singularities generated using two Wollaston compensators. The theory and numerical investigations of the proposed method have been presented as well as some experiments verifying our theoretical predictions.

Electronic control of soliton power transfer in silicon nanocrystal waveguides

We demonstrate numerically that the power transfer from one polarization component of a (1+ 1)D vector spatial soliton to the other in a birefringent nonlinear medium can be controlled via the electro-optic Kerr effect by varying the externally applied electric field. We show how several all-optical operations involving fundamental vector solitons can be electronically controlled. We also discover that the split-up of the higher-order vector solitons due to the two-photon absorption (TPA) can be suppressed by adjusting the external electric field. The soliton trapping along the slow optical axis is realized by a planar waveguide, filled with a silicon-nanocrystal material. The external electric field is applied along the fast optical axis of the waveguide.

Erratum: Scattering-matrix analysis of periodically patterned multilayers with asymmetric unit cells and birefringent media [Phys. Rev. B77, 035324 (2008)

Erratum: Scattering-matrix analysis of periodically patterned multilayers with asymmetric unit cells and birefringent media [Phys. Rev. B<b>77</b>, 035324 (2008)

Higher-order statistics of Stokes parameters in a random birefringent medium

We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher-order statistics of the reduced Stokes parameters along the irreducible representations of the rotation group. We show how this model allows a detailed description of the propagation, giving analytical expressions for the probability densities of the Mueller matrix and the reduced Stokes vector throughout the propagation. It also allows an exact description of the evolution of averaged quantities, such as the degree of polarization. We also discuss how this model allows a generalization of the concepts of reduced Stokes parameters and degree of polarization to higher-order statistics. We give some notes on how it can be extended to more general random media.

A Field Equation of the Stokes Parameters –Spin Texture of Light Polarization–

A field equation is studied for the light polarization in anisotropic media. The field of polarization is given by a spatial distribution of the Stokes vectors which is naturally deduced from the two-component Schrodinger type equation. The evolution equation is derived for the Stokes parameter (pseudo-spin) field by constructing the effective Lagrangian, which is similar to the equation of motion of texture in anisotropic fluid; superfluid He3 or liquid crystal. Some analytic solutions are obtained for a special case of nonlinear birefringent media for which the dielectric tensor is given by the Kerr effect.

Paraxial imaging and walk-off effects with birefringent media in refracting surfaces, lenses, and slabs

The paraxial theory of spherical refracting surfaces, spherical lenses, and slabs with one birefringent medium is investigated analytically: using walk-off effects in the paraxial domain, a number of relations between objects and images are deduced, along with cardinal elements, in the case where the optic axis is parallel to the optical axis. This method naturally shows that in some cases first-order astigmatism appears. An argument based on the wavefront (and phase) transformation shows that any spherical birefringent thin lens is stigmatic in the paraxial domain, because the first-order astigmatisms due to the two surfaces of such a lens compensate each other. This is a priori not the case with thick birefringent lenses -- but two such cases are detailed.

Scattering-matrix analysis of periodically patterned multilayers with asymmetric unit cells and birefringent media

Fourier analysis has been successfully applied to study optical properties of photonic crystal structures, usually composed of optically isotropic media. In a commonly used formulation [D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999)], inversion symmetry of the unit cell is required. Here, we extend the treatment of Whittaker and Culshaw to structures with asymmetric unit cells that can be composed of birefringent media. As applications we consider a high-refractive-index membrane with a triangular lattice of triangular holes, where the presence of a TE-like gap at $\ensuremath{\omega}$ and of a TM-like gap at $2\ensuremath{\omega}$ is established, and a slot waveguide made of (birefringent) porous silicon, where coupling of guided modes to radiative modes is achieved through a one-dimensional periodic grating.

Second-harmonic power generated in the absorbing and birefringent nonlinear medium

Considering the absorption of the nonlinear medium to the second-harmonic (SH) wave and using the complete boundary conditions for the reflections of the fundamental and SH waves at the input and output faces of the nonlinear medium, a formula for calculating the second-harmonic power generated in the absorbing and birefringent nonlinear medium was derived from the Maxwell's equation that the SH field E2 satisfies. The result shows that the formula for calculating the second-harmonic power generated in the nonzero absorption medium can be used for calculating the second-harmonic power generated in the absorptive medium if the complex refractive index, instead of the ordinary refractive index is used.

Two-frequency radiative transfer: Maxwell equations in random dielectrics

The paper addresses the space-frequency correlations of electromagnetic waves in general random, bianisotropic media whose constitutive tensors are complex Hermitian matrices. The two-frequency Wigner distribution (2f-WD) for polarized waves is introduced to describe the space-frequency correlations, and the closed form Wigner-Moyal equation is derived from the Maxwell equations. Two-frequency radiative transfer (2f-RT) equations are then derived from the Wigner-Moyal equation by using the multiple-scale expansion. For the simplest isotropic medium, the result coincides with Chandrasekhar's transfer equation. In birefringent media, the 2f-RT equations take the scalar form due to the absence of depolarization. A number of birefringent media such as chiral, uniaxial, and gyrotropic media are examined. For the unpolarized wave in an isotropic medium the 2f-RT equations reduces to the 2f-RT equation previously derived in part I of this research [J. Opt. Soc. Am. A24, 2248 (2007)]. A similar Fokker-Planck-type equation is derived from the scalar 2f-RT equation for the birefringent media.

Mutual coherence of polarized light in disordered media: two-frequency method extended

The paper addresses the two-point correlations of electromagnetic waves in general random, bi-anisotropic media whose constitutive tensors are complex Hermitian, positive- or negative-definite matrices. A simplified version of the two-frequency Wigner distribution (2f-WD) for polarized waves is introduced and the closed form Wigner–Moyal equation is derived from the Maxwell equations. In the weak-disorder regime with an arbitrarily varying background the two-frequency radiative transfer (2f-RT) equations for the associated 2 × 2 coherence matrices are derived from the Wigner–Moyal equation by using the multiple-scale expansion. In birefringent media, the coherence matrix becomes a scalar and the 2f-RT equations take the scalar form due to the absence of depolarization. A paraxial approximation is developed for spatially anisotropic media. Examples of isotropic, chiral, uniaxial and gyrotropic media are discussed.

Characteristic functions for uniformly twisted birefringent media

We present two functions for characterization of birefringent media with application to twisted nematic liquid crystal (LC) cells in the field off state. The first function is for reflective LC cells and the second is for transmissive LC cells. Based on the Stockes formalism, it is shown that these functions describe the ability of a layer of the twisted birefringent medium to change polarization of the output light and are invariant to the layer orientation. The characteristic functions are found in simple procedures and can be used for simultaneous determination of retardation, its wavelength dispersion, and twist angle, as well as for solving optimization problems.

Measurements of birefringent media properties using optical vortex birefringence compensator

We present some applications of the optical vortex birefringence compensator, based on the C polarization type singularities generated using two Wollaston compensators. The theory and experimental results of birefringent media properties measurements are presented. The possibility of the simultaneous measurement of both the azimuth angle and the phase retardance has been analyzed and experimentally verified.

Phenomenological description of quantum gravity inspired modified classical electrodynamics

We discuss a large class of phenomenological models incorporating quantum gravity motivated corrections to electrodynamics. The framework is that of electrodynamics in a birefringent and dispersive medium with non-local constitutive relations, which are considered up to second order in the inverse of the energy characterizing the quantum gravity scale. The energy-momentum tensor, Green functions and frequency dependent refraction indices are obtained, leading to departures from standard physics. The effective character of the theory is also emphasized by introducing a frequency cutoff Ω. The analysis of its effects upon the standard notion of causality is performed, showing that in the radiation regime (Ω R ≫ 1) the expected corrections of the order (ω/Ω) n get further suppressed by highly oscillating terms proportional to $$\sin(\Omega R), \cos(\Omega R)$$ , thus forbiding causality violations to show up in the corresponding observational effects.

Ray equation for a spatially variable uniaxial crystal and its use in the optical design of liquid-crystal lenses

To be able to design optical systems (e.g., variable focus or zoom lenses) made from liquid-crystal devices, it is necessary to be able to ray trace in a birefringent medium where the angle of the optical axis is a function of position in the device. To our knowledge, the theory required to achieve this has not previously been published, and we derive a suitable algorithm and give some examples of its use.

Nonspecular Total Internal Reflection of Spatial Solitons at the Interface between Highly Birefringent Media

We investigate total internal reflection of nonlocal spatial optical solitons at the interface between two differently oriented regions of a highly birefringent nematic liquid crystal. The solitons survive the interaction with an induced index mismatch and undergo nonspecular reflection, with an emerging angle differing appreciably from the incidence angle.

Interpreting magnetization from Faraday rotation in birefringent magnetic media

The Faraday effect is an extremely useful probe of magnetization dynamics on an ultrafast scale. However, the measured Faraday rotation is difficult to interpret in birefringent media. We investigate the link between magnetization and Faraday rotation by solving Maxwell’s equations in a magnetically ordered, birefringent material. We find that the Faraday rotation can depend nonlinearly on the magnetization, meaning that symmetric magnetic oscillations may lead to asymmetric Faraday measurements. Furthermore, sample alignment becomes important—if the incident light is not polarized along a birefringence axis of the sample, the Faraday rotation may be strongly enhanced or weakened, and the interpretation of the magnetization amplitude may be wrong by an order of magnitude.

SOA-fiber ring laser and its application to electric field sensing in frequency domain

We have developed a novel optical fiber ring laser using a semiconductor optical amplifier (SOA) as the gain medium, and taking advantage of polarization anisotropy of its gain. The laser can control the oscillation frequency difference between two counterpropagating lights by incorporating a birefringent medium into the ring resonator. Since the frequency difference is proportional to the birefringence, it can be measured to detect the beat frequency generated by combining two counterpropagating lights and the laser can be applied to an optical fiber sensor whose detecting signal is in frequency domain. Electric field sensor was demonstrated with a lithium niobate crystal as a sensing probe.

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

Starting with a Schrodinger-type equation derived from the Maxwell theory of electro- magnetism, a general formalism is presented for the change of light polarization in nonlinear birefringent media, which we call gyration or more generally, electromagnetic gyration and applications are considered. The theory is formulated in terms of the Hamil- tonian 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 be- havior 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.