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Diffraction of large-number whispering gallery mode by boundary straightening with jump of curvature

E. A. Zlobina

Abstract

Diffraction of a high-frequency large-number whispering gallery mode is studied, which runs along a concave curve turning to a straight line. At the point of straitening, the curvature of the boundary suffers a jump. The parabolic equation method is developed in the problem, and asymptotic formulas are presented for all waves arising in the vicinity of the non-smoothness point of the boundary. The ``ray skeleton'' of the wavefield is investigated in detail.

Diffraction of large-number whispering gallery mode by boundary straightening with jump of curvature

Abstract

Diffraction of a high-frequency large-number whispering gallery mode is studied, which runs along a concave curve turning to a straight line. At the point of straitening, the curvature of the boundary suffers a jump. The parabolic equation method is developed in the problem, and asymptotic formulas are presented for all waves arising in the vicinity of the non-smoothness point of the boundary. The ``ray skeleton'' of the wavefield is investigated in detail.
Paper Structure (13 sections, 113 equations, 5 figures)

This paper contains 13 sections, 113 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Geometrical considerations
  4. Qualitative discussion of ray structure of wavefield
  5. Rays of families $\ell_1$ and $\ell_2$
  6. Eikonals of waves $u_1$ and $u_2$
  7. Problem for parabolic equation and its exact solution
  8. Asymptotic investigation of attenuation factor
  9. Investigation of integral $I_1$
  10. Integral $I_1^{--}$
  11. Integrals $I^{++}$, $I^{+-}$ и $I^{-+}$
  12. Investigation of integral $I_2$
  13. Conclusions

Figures (5)

  • Figure 1: Geometry of the problem
  • Figure 2: Ray structure of wavefield (diffracted wave is omitted)
  • Figure 3: Rays of families $\ell_1$ and $\ell_2$, limit ray $l_O$ and horizontal ray $l_B$
  • Figure 4: Calculation of eikonals
  • Figure 5: Sketch of rays and boundary layers (diffracted wave is omitted)