Effect of the Goos–Hänchen shift on the geometrical-optics model for spherical-cavity mode spacing

In the geometrical-optics framework, the internal fields near morphology-dependent resonances (MDR) of dielectric spheres are represented by rays undergoing total internal reflection at the sphere surface. The round-trip path length of rays circumnavigating the sphere is used to compute the mode spacing of MDR’s. The Goos–Hanchen shift of the total internally reflected rays at the sphere surface is included in the ray picture to explain the qualitative behavior of the MDR frequency spacing in the Lorentz-Mie formalism for the entire size-parameter (circumference/wavelength) range. The MDR’s are characterized by a radial distance rm′. A connection between the ray picture and the Mie theory is established, based on rm′.

[1]  Chew Radiation and lifetimes of atoms inside dielectric particles. , 1988, Physical review. A, General physics.

[2]  V. Datsyuk Some characteristics of resonant electromagnetic modes in a dielectric sphere , 1992 .

[3]  H. M. Lai,et al.  Dielectric microspheres as optical cavities: thermal spectrum and density of states , 1987 .

[4]  A. Campillo,et al.  Some characteristics of a droplet whispering-gallery-mode laser. , 1986, Optics letters.

[5]  Richard K. Chang,et al.  Third-order sum-frequency generation in droplets: experimental results , 1993 .

[6]  R. Chang,et al.  Coherent Raman mixing and coherent anti-Stokes Raman scattering from individual micrometer-size droplets. , 1985, Optics letters.

[7]  S C Hill,et al.  Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics. , 1992, Applied optics.

[8]  R L Byer,et al.  High-resolution spectroscopy of whispering gallery modes in large dielectric spheres. , 1991, Optics letters.

[9]  S. Schiller Asymptotic expansion of morphological resonance frequencies in Mie scattering. , 1993, Applied optics.

[10]  C. C. Lam,et al.  Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering , 1992 .

[11]  C. Dobson,et al.  Survey of the Mie problem source function , 1989 .

[12]  J Z Zhang,et al.  Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers. , 1987, Applied optics.

[13]  P. Chylek,et al.  Resonance structure of Mie scattering: distance between resonances , 1990 .

[14]  J. Lock,et al.  Internal Caustic Structure of Illuminated Liquid Droplets , 1991 .

[15]  R. Chang,et al.  Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances. , 1984, Optics letters.

[16]  K. Young,et al.  Characterization of the internal energy density in Mie scattering , 1991 .

[17]  V. Srivastava,et al.  Electromagnetic field enhancement in small liquid droplets using geometric optics. , 1989, Applied optics.

[18]  H. Nussenzveig,et al.  Complex angular momentum theory of the rainbow and the glory , 1979 .

[19]  R. Chang,et al.  Third-order optical sum-frequency generation in micrometer-sized liquid droplets. , 1989, Optics letters.

[20]  Latifi,et al.  Double-resonance stimulated Raman scattering from optically levitated glycerol droplets. , 1989, Physical review. A, General physics.

[21]  H. Nussenzveig,et al.  Theory of the Glory , 1977 .

[22]  R. Chang,et al.  Phase-modulation-broadened line shapes from micrometer-size CS2 droplets. , 1986, Optics letters.

[23]  Critical angle light scattering from bubbles: an asymptotic series approximation. , 1991, Applied optics.

[24]  Nussenzveig,et al.  Theory of near-critical-angle scattering from a curved interface. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[25]  V. Srivastava,et al.  Laser-induced stimulated Raman scattering in the forward direction of a droplet: comparison of Mie theory with geometrical optics. , 1991, Optics letters.

[26]  H. M. Lai,et al.  Goos–Hänchen effect around and off the critical angle , 1986 .

[27]  H. M. Lai,et al.  Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift , 1987 .

[28]  H. Kogelnik,et al.  Rays, stored energy, and power flow in dielectric waveguides* , 1974 .

[29]  B. R. Johnson,et al.  Theory of morphology-dependent resonances : shape resonances and width formulas , 1993 .

[30]  J. Longwell,et al.  Photophoresis of irradiated spheres: absorption centers , 1985 .

[31]  R. Chang,et al.  Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances. , 1985, Optics letters.