P. Vincent and M. Neviere, "The reciprocity theorm for corrugated surfaces used in conical diffraction mountings," Opt. Acta 26, 889–898 (1979).

P. Vincent, "Singularity expansions for cylinders of finite conductivity," Appl. Phys. 17, 239–248 (1978).

J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a non-periodic obstacle," Opt. Commun. 20, 360 (1977).

J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a locally deformed plane waveguide," Opt. Commun. 22, 221 (1977).

M. C. Hutley *et al.*, "Presentation and verification of a differential formulation for the diffraction by conducting gratings," Nouv. Rev. Opt. 6, 87–95 (1975).

J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a locally deformed plane waveguide," Opt. Commun. 22, 221 (1977).

J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a non-periodic obstacle," Opt. Commun. 20, 360 (1977).

J. P. Hugonin, "On the numerical study of the deformed dielectric waveguide," presented at the international Union Radio Scientifique Internationale Symposium, Munich, 1980.

M. C. Hutley *et al.*, "Presentation and verification of a differential formulation for the diffraction by conducting gratings," Nouv. Rev. Opt. 6, 87–95 (1975).

P. Vincent and M. Neviere, "The reciprocity theorm for corrugated surfaces used in conical diffraction mountings," Opt. Acta 26, 889–898 (1979).

J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a locally deformed plane waveguide," Opt. Commun. 22, 221 (1977).

J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a non-periodic obstacle," Opt. Commun. 20, 360 (1977).

R. Petit, Electromagnetic Theory of Gratings, Petit, ed. (Springer-Verlag, Berlin, 1980).

J. Van Bladel, Electromagnetic Fields (McGraw-Hill, New York, 1964), p. 252.

P. Vincent and M. Neviere, "The reciprocity theorm for corrugated surfaces used in conical diffraction mountings," Opt. Acta 26, 889–898 (1979).

P. Vincent, "Singularity expansions for cylinders of finite conductivity," Appl. Phys. 17, 239–248 (1978).

P. Vincent, "Singularity expansions for cylinders of finite conductivity," Appl. Phys. 17, 239–248 (1978).

M. C. Hutley *et al.*, "Presentation and verification of a differential formulation for the diffraction by conducting gratings," Nouv. Rev. Opt. 6, 87–95 (1975).

P. Vincent and M. Neviere, "The reciprocity theorm for corrugated surfaces used in conical diffraction mountings," Opt. Acta 26, 889–898 (1979).

J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a non-periodic obstacle," Opt. Commun. 20, 360 (1977).

J. P. Hugonin and R. Petit, "A numerical study of the problem of diffraction at a locally deformed plane waveguide," Opt. Commun. 22, 221 (1977).

J. P. Hugonin, "On the numerical study of the deformed dielectric waveguide," presented at the international Union Radio Scientifique Internationale Symposium, Munich, 1980.

More generally, the use of an approximation of L^{-1} is likely to increase the speed of convergence of the process.

We do not set in boldface letters that, like C, represent elements of an abstract vector space.

There is no possible confusion between the operator D and the rectangular domain that appears in Fig. 1.

The letters topped by the inverted-wedge sign are used for data (functions or constants) related to a given practical problem.

J. Van Bladel, Electromagnetic Fields (McGraw-Hill, New York, 1964), p. 252.

R. Petit, Electromagnetic Theory of Gratings, Petit, ed. (Springer-Verlag, Berlin, 1980).

Throughout the paper, when a is real and negative, √a means *i*√-a.

Since Fourier transforms are defined as in distribution theory, the integral notation is purely formal.

If, for example, the incident field is a plane wave in normal incidence [*E*^{i} = exp (-*iy*)], *E*_{DI}(ζ)contains a term in δ(ζ).

Let us recall that ζ*T* = 1 implies that *T* = *P*(1/ζ) + *a*δ(ζ), where *a* is an arbitrary constant.

*P*[*i*_{u}/*g* (ζ)] is the distribution that, to any test function ø (ζ) assigns (equations) where *I*_{Epislon;} is the set defined by (equations).

The Fourier transform of (equations), where P(1/ζ) is the principal value distribution.