## 1. Introduction

[2] The problem of diffraction by an isorefractive wedge was solved by *Osipov* [1993], who applied the Kontorovich-Lebedev (KL) transform to the diffraction of a cylindrical wave by a dielectric wedge and reduced that problem to the solution of two coupled integral equations of the second kind, whose integral operators vanish in the isorefractive case and therefore yield an explicit solution to the boundary-value problem. Unaware of Osipov's work, *Knockaert et al.* [1997] rediscovered the same solution a few years later.

[3] The solution obtained by *Osipov* [1993] and by *Knockaert et al.* [1997] is in the spectral domain of KL transforms. In order to express the electromagnetic field in the physical domain, an inverse KL transform resulting in integrals that are difficult to evaluate by saddle point must be performed. On the other hand, the saddle point method is easily applicable to Sommerfeld-type integrals. In order to obtain the wedge diffraction coefficients, one should then proceed from the algebraic solutions in KL domain to Sommerfeld solutions using a method developed by Malyushinetz, then evaluate the Sommerfeld integrals by saddle point. An easier approach in the case of plane-wave incidence is provided by the method of rotating waves developed by *Daniele* [2003], which allows for the direct determination of Sommerfeld integrals.

[4] It should be pointed out that exact results for specific isorefractive wedge structures and incident fields have been obtained by a variety of methods. The special case of four right-angle wedges isorefractive to one another and with a common edge was solved by Wiener-Hopf technique [*Daniele and Uslenghi*, 2002]; in particular, it yielded the exact result obtained previously by *Uslenghi* [2000] via geometrical optics when the intrinsic impedances of the media in the four quadrants satisfy a certain relationship. Some other wedge structures were also solved exactly by geometrical optics [*Uslenghi*, 1997, 2004a, 2004b]. The radiation by a line source located at the edge of an isorefractive wedge was obtained in closed form by separation of variables [*Daniele and Uslenghi*, 1999].

[5] An alternative approach valid for all wedge angles was introduced by *Uslenghi* [2001]. It is based on a straightforward solution of the boundary-value problem by separation of variables in the physical domain, as done by *Macdonald* [1902] for the perfectly conducting wedge. The dispersion relation is identical to that obtained for circular cylindrical waveguides containing an isorefractive sector [*Uslenghi and Roy*, 1997], and may be solved explicitly in some cases when the wedge angle is commensurable to *π* radians, i.e. the ratio of the wedge angle to *π* equals the ratio of two integers. However, the expansion coefficients in the infinite series of eigenfunctions for the electromagnetic field components cannot be found as easily as in the case of a metallic wedge [see, e.g., *Harrington*, 1961] because now the fields occupy two angular regions of space filled with different materials. This difficulty is overcome by the approach illustrated in this paper, wherein the modal expansion coefficients are determined by utilizing properties of meromorphic functions.

[6] In this paper, the solution by separation of variables is given in section 2, and the explicit solution of the dispersion relation is detailed in section 3 for several wedge angles. The determination of the modal expansion coefficients is performed in section 4. The time-dependence factor exp(+*jωt*) is omitted throughout.