1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 46 Number 11, November 1998

Table of Contents for this issue

Complete paper in PDF format

Modal Analysis of Partially Coherent Submillimeter-Wave Quasi-Optical Systems

Stafford Withington, Member, IEEE, and J. Anthony Murphy, Member, IEEE

Page 1651.

Abstract:

We consider the modal analysis of partially coherent submillimeter-wave quasi-optical systems. According to our scheme the cross-spectral density at a plane is expanded as a sum of partially coherent propagating free-space modes. The coherence matrix, the elements of which are determined by evaluating bimodal overlap integrals, completely describes the state of the field at a plane. The coherence matrix can be traced through an optical system to another plane by means of a scattering matrix. Whereas diagonalizing the scattering matrix gives the natural modes of the optical system, diagonalizing the coherence matrix gives the natural modes of the field. We demonstrate the technique by studying the behavior of Gaussian beam telescopes when the field at the source plane is completely incoherent.

References

  1. P. F. Goldsmith, "Quasioptical techniques at millimeter and submillimeter wavelengths," in Infrared and Millimeter Waves, K. J. Button, Ed.New York: Academic, 1982, vol. 6, ch. 5.
  2. S. Withington and J. A. Murphy, "Multimode Gaussian optics," in Proc. 3rd Int. Workshop Terahertz Electron., Zermatt, Switzerland, Aug. 1995, pp. 1676-1690.
  3. D. H. Martin and J. W. Bowen, "Long-wave optics," IEEE Trans. Microwave Theory Tech., vol. 41, pp. 1678-1690, Oct. 1993.
  4. R. Padman, J. A. Murphy, and R. E Hills, "Gaussian mode analysis of Cassegrain antenna efficiency," IEEE Trans. Antennas Propagat., vol. AP-35, pp. 1093-1103, Oct. 1987.
  5. J. A. Murphy, "Aperture efficiencies of large axisymmetric reflector antennas fed by conical horns," IEEE Trans. Antennas Propagat., vol. AP-36, pp. 570-575, Apr. 1988.
  6. J. W. Goodman, Introduction to Fourier Optics.New York: McGraw-Hill, 1968.
  7. S. Withington and K. G. Isaak, "Phase retrieval at submillimeter wavelengths using Gaussian Hermite modes," in Proc. 4th Int. Symp. Space Terahertz Technol., Los Angeles, CA, Apr. 1993, pp. 199-210.
  8. A. Cutolo, A. Esposito, T. Isernia, R. Pierri, and L. Zeni, "Characterization of the transverse modes in a laser beam: Analysis and application to a Q-switched Nd:YAG laser," Appl. Opt., vol. 31, pp. 2723-2733, 1992.
  9. R. Blundell and C.-Y. E. Tong, "Submillimeter receivers for radio astronomy," in Proc. IEEE, vol. 80, pp. 1702-1720, Nov. 1992.
  10. P. F. Goldsmith, "Quasioptical techniques," in Proc. IEEE, vol. 80, pp. 1729-1747, Nov. 1992.
  11. J. A. Murphy and A. Egan, "Examples of Fresnel diffraction using Gaussian modes," Eur. J. Phys., vol. 14, pp. 121-127, 1993.
  12. E. Wolf, "New theory of partial coherence in the space-frequency domain. Part I: Spectra and cross spectra of steady-state sources," J. Opt. Soc. Amer., vol. 72, pp. 343-351, 1982.
  13. E. Wolf, "New theory of partial coherence in the space-frequency domain--Part II: Steady-state fields and high-order correlations," J. Opt. Soc. Amer. A., vol. 3, pp. 76-85, 1986.
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics.Cambridge, U.K.: Cambridge Univ. Press, 1995.
  15. F. Roddier, "The problematic of adaptive optics design," in Adaptive Optics for Astronomy, D. M. Alloin and J.-M. Mariotti, Eds.Amsterdam, The Netherlands: Kluwer, 1994, pp. 89-112.
  16. D. T. Emerson and J. M. Payne, "Multifeed systems for radio telescopes," Astronom. Soc. Pacific Conf. Ser., Tucson, AZ, May 1994, vol. 75.
  17. G. T. D. Francia, "Degrees of freedom of an image," J. Opt. Soc. Amer., vol. 59, pp. 799-804, 1969.
  18. M. Bendinelli, A. Consortini, L. Ronchi, and B. R. Frieden, "Degrees of freedom, and eigenfunctions for the noisy image," J. Opt. Soc. Amer., vol. 64, pp. 1498-1502, 1974.
  19. S. Withington, J. A. Murphy, and K. G. Isaak, "Representation of mirrors in beam waveguides as inclined phase-transforming surfaces," Infrared Phys. Technol., vol. 36, no. 3, pp. 723-734, 1995.
  20. J. A. Murphy, A. Egan, and S. Withington, "Truncation in beam waveguides," IEEE Trans. Antennas Propagat., vol. 41, pp. 1408-1413, Oct. 1993.
  21. J. A. Murphy, S. Withington, and A. Egan, "Mode conversion at diffracting apertures in millimeter and submillimeter-wave optical systems," IEEE Trans. Microwave Theory Tech., vol. 41, pp. 1700-1702, Oct. 1993.
  22. E. Wolf, "Spatial coherence in resonant modes in a maser interferometer," Phys. Lett., vol. 3, pp. 166-168, 1963.
  23. D. C. W. Morley, D. G. Schofield, L. Allen, and D. G. C. Jones, "Spatial coherence and mode structure in the He-Ne laser," Brit. J. Appl. Phys., vol. 18, pp. 1419-1422, 1967.
  24. W. Streifer, "Spatial coherence in periodic systems," J. Opt. Soc. Amer., vol. 56, pp. 1481-1489, 1966.
  25. H. Bosma, "On the theory of linear noisy systems," Philips Res. Rep. Suppl., no. 10, 1967.
  26. S. Withington, "Scattered noise waves in millimeter wave networks," Microwave J., vol. 32, pp. 169-178, 1989.
  27. S. Withington and J. A. Murphy, "Analysis of diagonal horns through Gaussian-Hermite modes," IEEE Trans. Antennas Propagat., vol. 40, pp. 198-206, Feb. 1992.
  28. R. J. Wylde, "Millimeter-wave Gaussian beam-mode optics and corrugated feed horns," Proc. Inst. Elect. Eng., vol. 131, pt. H, pp. 258-262, 1984.