Anisotropic media birefringence

What happens to the diffracted beam in an anisotropic medium (e.g. as in an AOTF device) As given above, the birefringence induced by the acoustic wave causes the diffracted beam polarisation to change. So if, for example, the input beam is P-polarised, then... 

Birefringence In an optically anisotropic medium with axial symmetry, the difference between the refractive index for light polarized parallel to the symmetry axis (extraordinary index) and that for light polarized perpendicular to the axis (ordinary index). 

For perspective, we first consider a z-directed plane wave propagating in an unbounded, slightly anisotropic (birefringent) medium characterized by refractive index n - n + dn, when the electric field is x-directed, and n = h+dny, when the electric field is y-directed, where n is the refractive index of the isotropic medium, and dn, Pny are constants. In an isotropic medium the plane wave can be polarized in any direction, but in the anisotropic medium there are only two polarizations, characterized... 

Comparison of these two polarizations shows that P2 Pi- Hence, in an isotropic medium such as a gas or a liquid x " = 0 and second order phenomena are not observable. Thus, only anisotropic media such as certain crystals are suitable for three-wave mixing processes. A consequence of a crystal being anisotropic is that it exhibits birefringence. However, the crystal birefringence enables phase matching to be achieved resulting in efficient generation of the new wave. 

Finally, at the mesoscopic level, we reported the birefringence observed by microscopy in polarized light of these xerogels that demonstrates unambiguously the anisotropic organization of the medium as exemplified by Fig. 1 [73, 76-78]. 

The birefringence in external electric and magnetic fields (the Kerr and Cotton-Mouton effects) can be explained by the anisotropy of the properties of the medium that is due to either the orientation of anisotropic molecules in the external field (the Langevin-Bom mechanism) or the deformation of the electric or magnetic susceptibilities by this field, i.e., to hyperpolarizabilities (Voight mechanism). The former mechanism is effective for molecules that are anisotropic in the absence of the field and... 

The ability of anisotropic and anisometric particles to assume some co-orientation in external force fields is not only responsible for significant changes in scattering properties but also causes birefringence (double refraction), i.e., the average refractive indexes of two beams polarized in perpendicular planes happen to be different. The specific orientation of particles and birefringecne may be caused by the action of electric field (Kerr effect), magnetic field (Cotton-Mouton effect), or in the case of anisotropic particles by flow of medium (Maxwell effect) [25]. 

Birefridgence may be observed with optically anisotropic particles of dispersed phase as well as with optically isotropic but anisometric particles, whose refractive index, n, is different from the refractive index of the medium, n0. One can reveal these two components of birefringence by varying the refractive index of dispersion medium. The own double refraction of particles, characterized by the difference in the refractive indexes of extraordinary, nE, and ordinary, nm, beams, is independent of the refractive index of medium and is maintained when particles are placed into the medium with the same refractive index. For optically isotropic but anisometric particles undergoing co-orientation in the flow, the double refraction, nE - nm, is proportional to (n2 - n20)2. The proportionality constant is positive for rod-like particles and negative for plate-like ones. In the case of particles that are both optically anisotropic and anisometric these effects are additive. 

Basically, birefringence is the contribution to the total birefringence of two-phase materials, due to deformation of the electric field associated with a propagating ray of light at anisotropically shaped phase boundaries. The effect may also occur with isotropic particles in an isotropic medium if they dispersed with a preferred orientation. The magnitude of the effect depends on the refractive index difference between the two phases and the shape of the dispersed particles. In thermoplastic systems the two phases may be crystalline and amorphous regions, plastic matrix and microvoids, or plastic and filler. See amorphous plastic coefficient of optical stress compact disc crystalline plastic directional property, anisotropic ... 

Birefringence (or double refraction) is an optical property of structurally anisotropic crystals. Such materials transform an incident light beam into two perpendicularly linearly polarized rays, the ordinary and extraordinary (e) rays, which propagate at different velocities in the medium. Unless the direction of incidence coincides with that of the optical axis of the (uniaxial) crystal, the e ray emerging from the crystal is displaced parallel to the o ray in the plane of the particular principal section of the crystal (see, for example. Ref 2). The well-known double images that appear when an object is viewed through a polished calcite crystal are a manifestation of the phenomenon. 

An optically isotropic liquid crystal (LC) refers to a composite material system whose refractive index is isotropic macroscopically, yet its dielectric constant remains anisotropic microscopically [1]. When such a material is subject to an external electric field, induced birefringence takes place along the electric field direction if the employed LC host has a positive dielectric anisotropy (Ae). This optically isotropic medium is different from a polar Uquid crystal in an isotropic state, such as 5CB (clearing point = 35.4°C) at 50 C. The latter is not switchable because its dielectric anisotropy and optical anisotropy (birefringence) both vanish in the isotropic phase. Blue phase, which exists between cholesteric and isotropic phases, is an example of optically isotropic media. 

A well-known nonlinear process taking place in the liquid state of anisotropic molecules is the optical-field induced birefringence (optical Kerr effect ). This nonlinearity results from the reorientation of the molecules in the electric field of a light beam. In the isotropic phase the optical field perturbs the orientational distribution of the molecules. In the perturbed state more molecules are aligned parallel to the electric field than perpendicularly to it and as a consequence the medium becomes birefringent. On the other hand in liquid crystals the orientational distribution of the molecules is inherently anisotropic. The optical field, just as a d.c. electric or magnetic field, induces a collective rotation of the molecules. This process can be described as a reorientation of the director. 

The speed of sound through a medium is a function of applied strain. The relationship is governed by the acoustoelastic coefficient. Stress states with unequal principle stresses (i.e., nonhydrostatic) have the effect of introducing anisotropic acoustic behavior to otherwise isotropic materials. This effect is similar to strain-induced optical birefringence (covered in the next section). The advantage is that ultrasonic birefringence can be measured in optically opaque materials. 

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