By Salvatore Solimeno

ISBN-10: 0121990702

ISBN-13: 9780121990701

ISBN-10: 0126543402

ISBN-13: 9780126543407

ISBN-10: 0126543410

ISBN-13: 9780126543414

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**Extra resources for Guiding, Diffraction, and Confinement of Optical Radiation**

**Sample text**

19b) where θ = Θ' — W" is the complex angle between k and z. The above relations imply the validity of E · k = 0 as well as Hx = Hz = 0 (TM wave). 20b) and by eliminating t between the above equations, we easily obtain £ 2 (sin 2 0' + sinh 2 0") + £ 2 (cos 2 0' + sinh 2 0") - £ x £ z sin20' = isinh 2 20". 21) Therefore, the vector Ex(t)x + Ey(t)y describes an ellipse whose major axis is inclined with respect to the x direction by an angle 0', the lengths of the two axes being proportional to cosh0" and |sinh0"|.

3) „2_ 2 = [ (FS) ]Eo = 0 Accordingly, the function S(r), known as the eikonal, must be chosen to satisfy the eikonal equation (VS)2 = n2(r). 4) Forfinitevalues of ω, we cannot neglect a priori the terms in l//c0 appearing in Eq. (II. 2), since we are not able to appreciate the error deriving from this approximation, once we accept as an ansatz the representation of the field given by Eq. (II. 1). An answer to this problem can be found by resorting to a more accurate representation of the field in terms of asymptotic series, the subject of the following section.

7), we can write dS/dc = -n(x)(dF/dc)/\VF\. 9) Thus, since S depends only c, the right-hand side of Eq. 9) must be a function of c only. In other words, Eq. 6) represents a family of wave 4 The Ray Equation 55 fronts if the right-hand side of Eq. 9) remains constant on each surface of the family. 4 The Ray Equation Let us consider a single-valued eikonal 5(r) and define the unit vector (see Fig. 1) where s(r) is perpendicular to the wave fronts and points in the propagation direction, and let us introduce the trajectories (rays) r(s) tangent to s(r) at each r.

### Guiding, Diffraction, and Confinement of Optical Radiation by Salvatore Solimeno

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