Diffraction of Electromagnetic Waves from a Round Hole Located between Vacuum and Matter with a Refraction Index Differe
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raction of Electromagnetic Waves from a Round Hole Located between Vacuum and Matter with a Refraction Index Different from One A. R. Mkrtchyana, A. A. Lalayanb, *, H. S. Yeritsyana, b, A. L. Margaryana, Sh. K. Yeritsyanb, and Zh. B. Khachatryana,b aInstitute
of Applied Problems of Physics, NAS of Armenia, Yerevan, Armenia b Yerevan State University, Yerevan, Armenia *e-mail: [email protected]
Received December 25, 2019; revised February 9, 2020; accepted April 10, 2020
Abstract—The diffraction of an electromagnetic wave from a round hole on an opaque screen is studied when there is no vacuum on the opposite sides of the screen, as is usually considered, but on one side there is a refractive medium and on the other—vacuum. The diffraction peculiarities due to the fact that the medium into which the wave penetrates from the vacuum have a refractive index different from one are revealed. The case of diffraction in an anisotropic medium with the property of birefringence is also considered. Keywords: diffraction of electromagnetic waves, refraction index DOI: 10.3103/S1068337220040118
1. INTRODUCTION As is known, the diffraction of an electromagnetic wave on an infinite screen with a slit or a round hole is considered in optics when the vacuum is located in front of the screen, as well as after the it [1, 2]. As for diffraction in material media, in this case, it is usually considered caused not by the limitation of the wavefront (diffraction from the edges of slits or holes), but, mainly, by the periodicity of the inhomogeneities of the medium itself, where this wave propagates [3–5]. In [6], the Fraunhofer diffraction of a plane wave by an infinite slit is considered, when on both sides of the screen with a slit there is not the vacuum, but media with different values of the refractive index (one of which may be also the vacuum). It is shown, in particular, that in such a situation the nonreciprocity of the passage of the electromagnetic wave through the slit takes place. Taking this phenomenon into account is of great practical importance when creating optical systems in which there is a nonequivalence of mutually opposite directions of propagation of electromagnetic waves. [7, 8]. In this work, we consider diffraction by a circular hole in a material medium, while considering also the cases when the vacuum borders through the hole both with the isotropic and anisotropic homogeneous medium. 2. THE COMPUTATION OF THE INTENSITY OF A DIFFRACTED ELECTROMAGNETIC WAVE The basis for calculating the influence of the refractive index of the medium, where diffracted radiation penetrates, on the diffraction pattern at a round hole is based on the well-known formula [9]
J12(ak θ) (1) d θ, 2 θ where I0 is the radiation intensity of the wave incident on a circular hole of radius a, θ is the angle of dI = I 0
deflection of the diffracted wave from the normal direction to the screen (see Fig. 1), J12 is the first-order Bessel function, the solid angle in which the rays propagate is in the range of directions (θ, θ + dθ). 314
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