Oblique incidence

The theory of propagation inclined to the optic axis is, of course, very much more complicated, and analytical solutions have not so far been found. The first attempt at solving the problem numerically was by Taupin, but the most complete calculations are those of Berreman and Scheffer who also carried out a precise experimental study of reflexion from monodomain samples at oblique incidence. Fig. 4.1.15 presents their observed reflexion spectra for two polarizations. 

Berreman used a 4x4 matrix multiplication method. Assuming the incident and reflected wavevectors to be in the xz plane, z being along the helical axis of the cholesteric, the dependence on the y coordinate may be ignored altogether. Writing exp [i( ut—etc., it is easily verified 

The results of their computations are shown in fig. 4.1.15. The agreement with the experimental spectra can be seen to be good. There is a difference in the intensities, which may conceivably be due to thin regions near the surface with anomalous dielectric properties or due to the neglect of absorption. 

An important fact that emerged from this study is that the observed features were best reproduced when the local dielectric ellipsoid was taken to be a prolate spheroid, with the principal axis Oc parallel to z and e = e—(x. Thus the assumption that is generally made that the local dielectric ellipsoid is uniaxial would appear to be valid to a very good approximation as far as optical calculations are concerned (see, however, 4.10). 

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Fig. 15. Oblique-incidence evaporation (a) and a possible columnar stmcture (b).

Picardi, G., Nguyen, Q., Ossikovski, R. and Schreiber, J. (2007) Polarization properties of oblique incidence scanning tunneling microscopy — tip-enhanced Raman... 

Fig. 13 shows an example where data for an irregular struetured multilayer thin-film-filter (TFF) are imported into a waveguide design. A FDTD-simulation earned out in order to check the influence of the internal resonator-like strueture of the TFF onto the waveguide deviee shows a signifieant transversal shift for oblique incidence. This hinders symmetrical multi-port designs, but may be used for specific WDM functionality. ... 

Figure 2.5 Reflection and transmission of obliquely incident light for electric vector parallel (a) and perpendicular (b) to the plane of incidence.

Equations (2.67)-(2.70) are the Fresnel formulas for reflection and transmission of light obliquely incident on a plane boundary. 

In addition to irradiance and frequency, a monochromatic (i.e., time-harmonic) electromagnetic wave has a property called its state of polarization, a property that was briefly touched on in Section 2.7, where it was shown that the reflectance of obliquely incident light depends on the polarization of the electric field. In fact, polarization would be an uninteresting property were it not for the fact that two waves with identical frequency and irradiance, but different polarization, can behave quite differently. Before we leave the subject of plane waves it is desirable to present polarization in a systematic way, which will prove to be useful when we discuss the polarization of scattered light. 

Extinction calculations for obliquely incident light, also taken from Asano (1979), are shown in Fig. 11.16. The symmetry axis is parallel to the z axis and the direction of the incident beam, which makes an angle with the symmetry axis, lies in the xz plane, the plane of incidence. The incident light is polarized cither with its electric field or its magnetic field perpendicular to the plane of incidence these two polarization states are denoted by TE (transverse electric) and TM (transverse magnetic). 

Figure 11.16 Calculated extinction of obliquely incident light by spheroids. From Asano (1979).

Figure 11.17 Calculated extinction by infinite cylinders for obliquely incident light = 90° corresponds to normally incident light. TE and TM denote light with the electric and magnetic vectors, respectively, perpendicular to the xz plane. From Lind and Greenberg (1966).

Tsukahara, Y., Nakaso, N., and Ohira, K. (1991). Angular spectral approach to reflection of focussed beams with oblique incidence in spherical-planar-pair lenses. IEEE Trans. UFFC 38, 468-80. [149]... 

When the microdensitometer data have been corrected for oblique incidence, they are in a form suitable for substitution into equation 18 for the specimen intensity transform. In practice, the correction is made as the integration is performed (see section 10.2). 

Specular reflection, light that is elastically scattered without penetrating the tissue, is also undesirable. Strategies such as oblique incidence,26 90° collection geometry,3 and a hole in the collection mirror have been realized to reduce its effect.27... 

Transmission through Homogeneous Materials at Oblique Incidence... 

Oblique incidence of light through a shear flow. The axes defining the components n j and n2 lie in the (JC, y) plane. 

With interference lithography (IL) a resist layer is exposed by an interference pattern generated by two obliquely incident laser beams, which is used to expose a photoresist layer without the use of a mask (see section... 

Table III Adhesion and structural properties of perpendicular and oblique incidence evaporated aluminum onto non treated polymer...

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