Effect of multiple reflections of light on the optical characteristics of crystals

Temperature dependence of optical activity and circular dichroism in α‐ZnP2 crystals

“…The experimental values derived from Hence, the oscillatory temperature behaviour of both the azimuth and the ellipticity of light passed through the crystal is well explained in frame of the multiple reflections hypothesis. As far as we know this is one of the first examples of quantitative description of the manifestations of multiple reflections in the optical anisotropy parameters of crystals (see also [21,16]). Let us also mention that the observation of temperature oscillations due to the multiple reflections in the gyration along the optical axis in a-ZnP 2 contradicts the theoretical results [29] which predict the absence of the phenomenon in case of a normal light incidence upon a uniaxial crystal.…”

“…Firstly, semiconducting a-ZnP 2 exhibits high enough refractive indices (n o ' 3:2 [2]) and therefore large reflectivities, making important the multiple internal reflections of light between the interfaces of a crystal plate. It should be stressed (see the analysis [16]) that, up to date, the latter effect has been usually accounted for such that the optical anisotropy of crystal is completely disregarded. An apt example is the wellknown formulae [17] for the optical transmittance coefficients of semiconducting crystals.…”

“…We have solved the two problems in a manner very similar to that used in the works [13,16], and the refined formulae are as follows: tan 2ðc À dcÞ % sin 2ðq þ qdÞ À 2r cos 2j½2 sin 2q þ sin 2qd cos 2ðq þ qdÞ þ 2r cos 2j½sin 2q tan ðq þ qdÞ À cos 2q À cos 2qd…”

“…Here r ¼ bR e Àad , R ¼ ½ð n n À 1Þ=ð n n þ 1Þ 2 is the mean one-surface reflectance, a ¼ 2pðj e þ j o Þ=l the mean absorption coefficient (with j o and j e the extinctions for the ordinary and extraordinary waves, respectively), j ¼ pd n n=l the mean phase shift of the waves upon a single pass through the plate, 0 b 1 the parameter that accounts for the reduction of the multiple reflections due to light scattering and non-parallelity of the entrance and exit surfaces [16], and dc and de the effective imperfection parameters of the optical equipment, which may be dependent on q and c angles in case if the latter are large enough. It is worth noticing that formula (5) in fact suggests a purely polarimetric method for determining the circular dichroism, which does not require any dichrographic apparatus.…”

“…For this reason we do not represent the e 0 ðTÞ dependence which is rather unmonotonous as a result of temperature variations of the last term in the righthand side of formula (1). It should be also reminded that we disregard a possible influence of the multiple reflections on our e 0 data, since it is known [16] that, in the HAUP-type experimental geometry, the mentioned influence concerns mainly the phase retardation (i.e., the linear birefringence) but not the optical activity.…”