Negative uniaxial

Fig. 47. Left positive uniaxial indicatrix. Right negative uniaxial indicatrix.

Figure 4.6 A principal section of the negative uniaxial indicatrix...

The direction of the principal axes of the index of refraction tensor n can be described by the indicatrix. For isotropic crystals the indicatrix is a sphere. For positive uniaxial crystals it is a prolate spheroid (ns > n0j) for negative uniaxial crystals it is an oblate spheroid (nol > n,). For orientations away from the principal axis orientations, the extraordinary ray will have a refractive index h - intermediate between nm and ne. 

IR or UV reflecting cholesterics are colorless in the visible region of the spectrum. Therefore, retardation plates can be realized for STN displays using a long pitch material. Also UV reflecting LC siloxanes are of interest for retardation plates because they exhibit behavior like an optical negative uniaxial material. 

Figure 4.2. Principal sections of the wave surfaces, o is the point source, o.a. is the optic axis, (a) positive uniaxial liquid crystal, (b) negative uniaxial liquid crystal.

Cholesteric-nematic phase transition change from negative uniaxiality to positive uniaxiality The electric field is parallel to the helix axis. ... 

Periodic structures of deep narrow grooves with vertical walls were prepared by liquid anisotropic etching of silicon. It was shown experimentally that the obtained media possesses the properties of a negative uniaxial crystal with its optical axis lying in the wafer plane. These structures display a large optical anisotropy in the middle IR range of spectrum. The difference in the effective refractive indices of the ordinary and the extraordinary rays An 1.5. 

Besides, both s tructures posses an optical anisotropy in the spectral range of X a where a i s the "lattice" constant. This is the so called anisotropy of shape described in [4]. Studies of birefringence in 2D PC from macroporous silicon [5] shows it is a positive uniaxial crystal with its optical axis oriented along the pores. The present work is focused on the studies of ID PC from grooved Si. It is expected to be a negative uniaxial crystal whose axis is perpendicular to the Si ribs. 

The cholesteric liquid, which is a spontaneously twisted nematic, behaves like a negative uniaxial crystal, so that light vibrating perpendicular to the molecular layers shows maximum velocity. Linearly polarized light transmitted perpendicular to the molecular layers shows rotation of its electrical vector along a helical path. 

This fourth-order equation represents two distinct surfaces which intersect in the biradials. For a negative uniaxial crystal v = v, these surfaces are a sphere and... 

In the present case 0jjj = 74 . Finally, the efficiency of 243 nm light generated at this phase-matched angle varies with (j) as can be seen from the equation (18) it maximises for = 0 or tt/2 and is zero for < ) = ir/4. (It is interesting to note here that the converse is true for negative uniaxial crystals such as ADA, ADP and its isomorphs.)... 

Temperature dependence of CT of the LC-elastomer i/ith the spacer length m=3 (x=60) (see Table 1) in the isotropic state (T>T ) NR=natural rubber optical negative, uniaxial... 

In the subwavelength region, a rectangular grating layer such as that in Fig. 1, may be approximately modeled as a homogeneous negative uniaxial layer with ordinary and extraordinary indices of refraction given by... 

Both a film and c film can be further divided into positive or negative films depending on the relative values of the extraordinary refractive index tie and the ordinary refractive index Table 8.1 lists aU the types of compensation films and their refractive index relationship. In our analyses, we focus on the uniaxial films. As a general rale, a positive uniaxial film means Tie > no, otherwise, rig < tig for a negative uniaxial film. 

X. Zhu and S. T. Wu, Super wide view in-plane switching LCD with positive and negative uniaxial a-films compensation, SID Digest Tech. Papers, 34, 1164 (2005). 

One distinguishes between type-I and type-II phase-matching depending on which of the three waves with coi, C02, C03 = coi C02 propagates as an ordinary or as an extraordinary wave. Type 1 corresponds to (1 e, 2 e, 3- 0) in positive uniaxial crystals and to (1 o, 2 o, 3 e) in negative uniaxial crystals, whereas type II is characterized by (1 o, 2 e, 3 o) for positive and (1 e, 2 o, 3 e) for negative uniaxial crystals [5.220]. Let us now illustrate these general considerations with some specific examples. 

Limitations of the SH output power generated by pulsed lasers are mainly set by the damage threshold of available nonlinear crystals. Very promising new crystals are the negative uniaxial BBO (beta-barium borate) [5.225-5.228] and lithium borate LiBO, which have high damage thresholds and which allow SHG from 205 nm to above 3000 nm. 

For biaxial crystals, the optical indicatrix is a bilayer surface with four points of interlayer contact, which correspond to the directions of the two optical axes. In the simple case of light propagation in the principal planes XY, YZ, and XZ, the dependences of the refractive indices on the direction of light propagation are represented by a combination of an ellipse and a circle. Thus, in the principal planes, a biaxial crystal can be considered as a uniaxial crystal for example, a biaxial crystal with nz > ny > nx in the XY plane is similar to a negative uniaxial crystal with Ho=nz... 

FIGURE 2 Index surfaces for (a) a positive uniaxial crystal and (b) a negative uniaxial crystal [29]. 

The nonchiral nematic is optically a positive uniaxial medium. A cholesteric is a nematic with twist. The local structure of a cholesteric is believed to be the same as that of the nematic except that it lacks reflection symmetry. This means that the director and therefore the local extraordinary optic axis is rotating around the helix axis making the cholesteric a negative uniaxial medium with the optic axis coinciding with the twist axis. The question has been asked as to why the nematic with twist could not be biaxial, and attempts have been made to measure a slight biaxiality of the cholesteric phase. In other words, why could the twist not be realized in such a way that the long molecular axis is inclined to the twist axis Why does it have to be perpendicular ... 

Bos et al. proposed an LC cell that is sandwiched between two negative uniaxial polarizers [60]. In this case, rather than compensating the retardation vertical to the cell, the compensation is satisfied in the oblique direction, for which a high voltage of 32 V was necessary to achieve the black state. 

Usually the z axis, sometimes also referred to as the crystal axis, is chosen as an axis of symmetry. For light propagating along this axis of symmetry, since hght is a transverse electromagnetic wave, its polarization vector (defined by the direction of its electric field E) is perpendicular to the z axis, that is, E lies on the x-y plane. If U] and 2 are unequal, such crystal is usually called biaxial. On the other hand, if = 2 (for all intents and purposes), the crystal is called uniaxial. Conventionally, if n > n, 2, the crystal is referred to as positive uniaxial or biaxial, whereas if n is < i, 2, the crystal is referred to as negative uniaxial or biaxial. 

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