Optics InfoBase > JOSA > Volume 69 > Issue 9 > Page 1218
Polarization and losses of whispering-gallery waves along twisted trajectories
M. E. Marhic »View Author Affiliations
Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois 60201
JOSA, Vol. 69, Issue 9, pp. 1218-1226 (1979)
http://dx.doi.org/10.1364/JOSA.69.001218
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Abstract
A geometrical optics treatment shows that whispering-gallery waves following twisted trajectories can be in eigenstates of polarization if σ = (radius of curvature × torsion) is a constant. The Jones vectors of these eigenpolarizations are calculated, along with their propagation constants and power attenuation constants. The curve representing the evolution of an arbitrary input polarization makes a constant angle with the circles passing through the points corresponding to the eigenpolarizations, on the Poincaré sphere or in any one of the equivalent complex-plane representations. Experiments carried out with a cylindrical glass tube give results in good agreement with theoretical conclusions. The theory predicts that the smallest attenuation constant for three-dimensional trajectories in infrared and far-infrared guides should be about (1 + σ^{2}) times larger than that for TE waves along two-dimensional trajectories of the same curvature, providing a practical criterion for the design of guides exhibiting twisted trajectories.
© 1979 Optical Society of America
Citation
M. E. Marhic, "Polarization and losses of whispering-gallery waves along twisted trajectories," J. Opt. Soc. Am. 69, 1218-1226 (1979)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-69-9-1218
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References
- E. Garmire, T. McMahon, and M. Bass, "Low-loss optical transmigsion through bent hollow metal waveguides," Appl. Phys. Lett. 31, 92–94 (1977).
- H. Krammer, "Light waves guided by a single curved metallic surface," Appl. Opt. 17, 316–319 (1978).
- M. E. Marhic, L. I. Kwan, and M. Epstein, "Optical surface waves along a toroidal metallic guide," Appl. Phys. Lett. 33, 609–611 (1078); "invariant properties of helical-circular metallic waveguides," Appl. Phys. Lett; 33, 874–876 (1978).
- E. Kreyszig, Introduction to Differential Geometry and Riemannian Geometry (University of Toronto, Toronto, 1968), p. 32.
- If n_{1} is complex, an appropriate attenuation term should be introduced in what follows. We omit this term, together with a phase term, since they have no bearing on the eigenpolarizations, and if needed can easily be taken into account in the expressions of the propagation and attenuation constants.
- Three-dimensional curves with σ = const make a constant angle γ = tan^{-1}σ with a fixed direction, and are called general helixes; Ref. 4, p. 46.
- R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 1.
- H. S. M. Coxeter, Introduction to Geometry (Wiley, New York, 1969), p. 88.
- Here, "to reach" should be understood in a physical rather than a mathematical sense, meaning to come so close to the eigenpolarization as to be practically indistinguishable from it.
- Another possibility is ω_{±} = 0, ∞, which can be viewed as a limiting form of the general statement, since the point at infinity in the w plane belongs, in particular, to the imaginary axis.
- R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 1.
- R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 1.
- E. Garmire, T. McMahon, and M. Bass, "Low-loss optical transmigsion through bent hollow metal waveguides," Appl. Phys. Lett. 31, 92–94 (1977).
- H. S. M. Coxeter, Introduction to Geometry (Wiley, New York, 1969), p. 88.
- M. E. Marhic, L. I. Kwan, and M. Epstein, "Optical surface waves along a toroidal metallic guide," Appl. Phys. Lett. 33, 609–611 (1078); "invariant properties of helical-circular metallic waveguides," Appl. Phys. Lett; 33, 874–876 (1978).
- E. Garmire, T. McMahon, and M. Bass, "Low-loss optical transmigsion through bent hollow metal waveguides," Appl. Phys. Lett. 31, 92–94 (1977).
- E. Kreyszig, Introduction to Differential Geometry and Riemannian Geometry (University of Toronto, Toronto, 1968), p. 32.
- M. E. Marhic, L. I. Kwan, and M. Epstein, "Optical surface waves along a toroidal metallic guide," Appl. Phys. Lett. 33, 609–611 (1078); "invariant properties of helical-circular metallic waveguides," Appl. Phys. Lett; 33, 874–876 (1978).
- M. E. Marhic, L. I. Kwan, and M. Epstein, "Optical surface waves along a toroidal metallic guide," Appl. Phys. Lett. 33, 609–611 (1078); "invariant properties of helical-circular metallic waveguides," Appl. Phys. Lett; 33, 874–876 (1978).
- E. Garmire, T. McMahon, and M. Bass, "Low-loss optical transmigsion through bent hollow metal waveguides," Appl. Phys. Lett. 31, 92–94 (1977).
Appl. Opt.
- H. Krammer, "Light waves guided by a single curved metallic surface," Appl. Opt. 17, 316–319 (1978).
Appl. Phys. Lett.
- E. Garmire, T. McMahon, and M. Bass, "Low-loss optical transmigsion through bent hollow metal waveguides," Appl. Phys. Lett. 31, 92–94 (1977).
- M. E. Marhic, L. I. Kwan, and M. Epstein, "Optical surface waves along a toroidal metallic guide," Appl. Phys. Lett. 33, 609–611 (1078); "invariant properties of helical-circular metallic waveguides," Appl. Phys. Lett; 33, 874–876 (1978).
Other
- E. Kreyszig, Introduction to Differential Geometry and Riemannian Geometry (University of Toronto, Toronto, 1968), p. 32.
- If n_{1} is complex, an appropriate attenuation term should be introduced in what follows. We omit this term, together with a phase term, since they have no bearing on the eigenpolarizations, and if needed can easily be taken into account in the expressions of the propagation and attenuation constants.
- Three-dimensional curves with σ = const make a constant angle γ = tan^{-1}σ with a fixed direction, and are called general helixes; Ref. 4, p. 46.
- R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 1.
- H. S. M. Coxeter, Introduction to Geometry (Wiley, New York, 1969), p. 88.
- Here, "to reach" should be understood in a physical rather than a mathematical sense, meaning to come so close to the eigenpolarization as to be practically indistinguishable from it.
- Another possibility is ω_{±} = 0, ∞, which can be viewed as a limiting form of the general statement, since the point at infinity in the w plane belongs, in particular, to the imaginary axis.
1978, Krammer, Appl. Opt.
- E. Garmire, T. McMahon, and M. Bass, "Low-loss optical transmigsion through bent hollow metal waveguides," Appl. Phys. Lett. 31, 92–94 (1977).
- M. E. Marhic, L. I. Kwan, and M. Epstein, "Optical surface waves along a toroidal metallic guide," Appl. Phys. Lett. 33, 609–611 (1078); "invariant properties of helical-circular metallic waveguides," Appl. Phys. Lett; 33, 874–876 (1978).
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