By Alexander Vasil'evich Khomchenko
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Extra resources for Waveguide Spectroscopy of Thin Films
K 0 n 0 Fig. 5. Dependencies of n and k on frequency near to the fundamental frequency o0 of optical transitions. 26a) 0 ðoÞ À 1 ¼ vp p o02 À o2 0 Z 1 0 0 4ps 2o ðo Þ À 1 ¼ vp 00 ðoÞ À do0 . 26a). 26b) are regarded as their principal values. The dispersion relation relating to the refractive index and the absorption coefﬁcient is written as Z 1 0 2 o kðo0 Þ do. 28) where the singularity area is extracted. Note that at o ¼ o0 , lim o0 kðo0 Þ À okðoÞ kðoÞ 1 dk þ . ¼ 2o 2 do ðo0 Þ2 À o2 In the calculation of the refractive index the region of integration is split into four ranges: from 1 to o1 , where kðoÞ is described by the Drude model; from o1 to op, where the harmonic oscillator model is used; in the frequency range from op to oh the approach based on the pol- ynomial approximation of the values kðoÞ, which are measured experimentally, is used; and in the range from o ¼ oh to o ¼ 1, the asymptotic interpolation of ðoÞ is used for determining the k.
3. Input of Radiation into Waveguide by the Prism Coupler For the excitation of guided modes, directed by the ﬁlm, the experimental techniques that use a prism coupler or a prism device of a tunnel excitation of modes are employed. This device provides the selective excitation of a certain mode. 1). 1) where gm is the incidence angle of radiation on the prism base and np the refractive index of the prism. The similar scheme depicted in Ref. . The light beam with radius aw is directed onto the prism base.
1 mm. 01 mm. Hence, the role of losses caused by the scattering becomes less signiﬁcant. In semiconductor waveguides, the losses caused by light absorption are usually quite signiﬁcant and scattering is not so important. The absorption losses are related to the absorption near the band edge and to the absorption on the impurity or surface state levels. Such losses in waveguide are $10–200 dB/cm (or 2–50 cmÀ1) approximately. In case of ﬁlm thickness less than 1 mm it is quite difﬁcult to measure such great attenuation of light by non-waveguide methods.