Abstract

A procedure is described for calculating the power coupled between collimated, partially coherent vector fields that are in different states of coherence. This topic is of considerable importance in designing submillimeter-wave optical systems for astronomy. It is shown that if the incoming field S has coherence matrix A, and the outgoing field D has coherence matrix B, then the power coupled is simply Ps=Tr(ATBT), where the elements of T project the basis functions of B onto those of A. A similar technique can be used to calculate the power coupled from the background of S to D. The scheme is illustrated by calculating the power coupled between two scalar, Gaussian Schell-model beams. The procedure can be incorporated into optical design software.

© 2001 Optical Society of America

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References

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  1. P. F. Goldsmith, Quasioptical Systems (IEEE Press, New York, 1998), Chap. 6.
  2. R. Blundell, E. Tong, “Submillimetre receivers for radio astronomy,” Proc. IEEE 80, 1702–1720 (1992).
    [CrossRef]
  3. P. L. Richards, “Bolometers for infrared and millimeter waves,” J. Appl. Phys. 76, 1–24 (1994).
    [CrossRef]
  4. D. J. Benford, E. Serabyn, T. G. Phillips, S. H. Moseley, “Development of a broadband submillimeter grating spectrometer,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 278–288 (1998).
    [CrossRef]
  5. J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
    [CrossRef]
  6. W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
    [CrossRef]
  7. J. A. Murphy, “Radiation patterns of few-moded horns and condensing lightpipes,” Infrared Phys. 31, 291–299 (1991).
    [CrossRef]
  8. D. T. Emerson, J. M. Payne, “Multi-feed systems for radio telescopes,” Vol. 75 of Astronomical Society of the Pacific Conference Series (Astronomical Society of the Pacific, San Francisco, Calif., 1994).
  9. J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
    [CrossRef]
  10. S. Withington, J. A. Murphy, “Modal analysis of partially coherent submillimetre-wave quasioptical systems,” IEEE Trans. Antennas Propag. 46, 1651–1659 (1998).
    [CrossRef]
  11. J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimetre and submillimetre-wave optical systems,” IEEE Trans. Microwave Theory Tech. 41, 1700–1702 (1993).
    [CrossRef]
  12. S. Withington, J. A. Murphy, K. G. Isaak, “On the representation of mirrors in beam waveguides as inclined phase transforming surfaces,” Infrared Phys. Technol. 36, 723–734 (1995).
    [CrossRef]
  13. P. F. Goldsmith, “Quasioptical techniques at millimetre and submillimetre wavelengths,” in Infrared and Millimeter Waves, K. J. Button, ed. (Academic, New York, 1982), Vol. 6, Chap. 5.
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  15. R. H. Clarke, J. Brown, Diffraction Theory and Antennas (Ellis Horwood Ltd., Chichester UK, 1980), Chap. 3.
  16. T. Rozzi, M. Mongiardo, Open Electromagnetic Waveguides (The Institution of Electrical Engineers, Vol. 43 of Electromagnetic Wave Series 4, London, 1997).
  17. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, UK, 1995), Chap. 3.
  18. S. Withington, G. Yassin, J. A. Murphy, “Dyadic analysis of partially coherent submillimeter-wave antenna systems,” IEEE Trans. Antennas Propag. 49, 1226–1234 (2001).
    [CrossRef]
  19. 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. Am. 72, 343–351 (1982).
    [CrossRef]
  20. Y. Kano, E. Wolf, “Temporal coherence of black body radiation,” Proc. Phys. Soc. London 80, 1273–1276 (1962).
    [CrossRef]
  21. A. Starikov, E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields,” J. Opt. Soc. Am. 72, 923–928 (1982).
    [CrossRef]

2001 (1)

S. Withington, G. Yassin, J. A. Murphy, “Dyadic analysis of partially coherent submillimeter-wave antenna systems,” IEEE Trans. Antennas Propag. 49, 1226–1234 (2001).
[CrossRef]

1999 (2)

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
[CrossRef]

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

1998 (1)

S. Withington, J. A. Murphy, “Modal analysis of partially coherent submillimetre-wave quasioptical systems,” IEEE Trans. Antennas Propag. 46, 1651–1659 (1998).
[CrossRef]

1995 (1)

S. Withington, J. A. Murphy, K. G. Isaak, “On the representation of mirrors in beam waveguides as inclined phase transforming surfaces,” Infrared Phys. Technol. 36, 723–734 (1995).
[CrossRef]

1994 (1)

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. Appl. Phys. 76, 1–24 (1994).
[CrossRef]

1993 (1)

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimetre and submillimetre-wave optical systems,” IEEE Trans. Microwave Theory Tech. 41, 1700–1702 (1993).
[CrossRef]

1992 (1)

R. Blundell, E. Tong, “Submillimetre receivers for radio astronomy,” Proc. IEEE 80, 1702–1720 (1992).
[CrossRef]

1991 (1)

J. A. Murphy, “Radiation patterns of few-moded horns and condensing lightpipes,” Infrared Phys. 31, 291–299 (1991).
[CrossRef]

1982 (2)

1962 (1)

Y. Kano, E. Wolf, “Temporal coherence of black body radiation,” Proc. Phys. Soc. London 80, 1273–1276 (1962).
[CrossRef]

Ade, P. A. R.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Benford, D. J.

D. J. Benford, E. Serabyn, T. G. Phillips, S. H. Moseley, “Development of a broadband submillimeter grating spectrometer,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 278–288 (1998).
[CrossRef]

Blundell, R.

R. Blundell, E. Tong, “Submillimetre receivers for radio astronomy,” Proc. IEEE 80, 1702–1720 (1992).
[CrossRef]

Bock, J. J.

J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
[CrossRef]

Brown, J.

R. H. Clarke, J. Brown, Diffraction Theory and Antennas (Ellis Horwood Ltd., Chichester UK, 1980), Chap. 3.

Clarke, R. H.

R. H. Clarke, J. Brown, Diffraction Theory and Antennas (Ellis Horwood Ltd., Chichester UK, 1980), Chap. 3.

Colgan, R.

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
[CrossRef]

Cunningham, C. R.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Duncan, W. D.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Egan, A.

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimetre and submillimetre-wave optical systems,” IEEE Trans. Microwave Theory Tech. 41, 1700–1702 (1993).
[CrossRef]

Emerson, D. T.

D. T. Emerson, J. M. Payne, “Multi-feed systems for radio telescopes,” Vol. 75 of Astronomical Society of the Pacific Conference Series (Astronomical Society of the Pacific, San Francisco, Calif., 1994).

Gear, W. K.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Glenn, J.

J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
[CrossRef]

Goldsmith, P. F.

P. F. Goldsmith, Quasioptical Systems (IEEE Press, New York, 1998), Chap. 6.

P. F. Goldsmith, “Quasioptical techniques at millimetre and submillimetre wavelengths,” in Infrared and Millimeter Waves, K. J. Button, ed. (Academic, New York, 1982), Vol. 6, Chap. 5.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Grannan, S. M.

J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
[CrossRef]

Griffin, M. J.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Holland, W. S.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Irwin, K. D.

J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
[CrossRef]

Isaak, K. G.

S. Withington, J. A. Murphy, K. G. Isaak, “On the representation of mirrors in beam waveguides as inclined phase transforming surfaces,” Infrared Phys. Technol. 36, 723–734 (1995).
[CrossRef]

Ivison, R. J.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Jenness, T.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Kano, Y.

Y. Kano, E. Wolf, “Temporal coherence of black body radiation,” Proc. Phys. Soc. London 80, 1273–1276 (1962).
[CrossRef]

Lange, A. E.

J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
[CrossRef]

Lanigan, W.

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
[CrossRef]

LeDuc, H. G.

J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
[CrossRef]

Lightfoot, J. F.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, UK, 1995), Chap. 3.

Mongiardo, M.

T. Rozzi, M. Mongiardo, Open Electromagnetic Waveguides (The Institution of Electrical Engineers, Vol. 43 of Electromagnetic Wave Series 4, London, 1997).

Moseley, S. H.

D. J. Benford, E. Serabyn, T. G. Phillips, S. H. Moseley, “Development of a broadband submillimeter grating spectrometer,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 278–288 (1998).
[CrossRef]

Murphy, J. A.

S. Withington, G. Yassin, J. A. Murphy, “Dyadic analysis of partially coherent submillimeter-wave antenna systems,” IEEE Trans. Antennas Propag. 49, 1226–1234 (2001).
[CrossRef]

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
[CrossRef]

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

S. Withington, J. A. Murphy, “Modal analysis of partially coherent submillimetre-wave quasioptical systems,” IEEE Trans. Antennas Propag. 46, 1651–1659 (1998).
[CrossRef]

S. Withington, J. A. Murphy, K. G. Isaak, “On the representation of mirrors in beam waveguides as inclined phase transforming surfaces,” Infrared Phys. Technol. 36, 723–734 (1995).
[CrossRef]

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimetre and submillimetre-wave optical systems,” IEEE Trans. Microwave Theory Tech. 41, 1700–1702 (1993).
[CrossRef]

J. A. Murphy, “Radiation patterns of few-moded horns and condensing lightpipes,” Infrared Phys. 31, 291–299 (1991).
[CrossRef]

Naylor, D. A.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

O’Sullivan, C.

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
[CrossRef]

Payne, J. M.

D. T. Emerson, J. M. Payne, “Multi-feed systems for radio telescopes,” Vol. 75 of Astronomical Society of the Pacific Conference Series (Astronomical Society of the Pacific, San Francisco, Calif., 1994).

Phillips, T. G.

D. J. Benford, E. Serabyn, T. G. Phillips, S. H. Moseley, “Development of a broadband submillimeter grating spectrometer,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 278–288 (1998).
[CrossRef]

Richards, P. L.

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. Appl. Phys. 76, 1–24 (1994).
[CrossRef]

Robson, E. I.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Rozzi, T.

T. Rozzi, M. Mongiardo, Open Electromagnetic Waveguides (The Institution of Electrical Engineers, Vol. 43 of Electromagnetic Wave Series 4, London, 1997).

Serabyn, E.

D. J. Benford, E. Serabyn, T. G. Phillips, S. H. Moseley, “Development of a broadband submillimeter grating spectrometer,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 278–288 (1998).
[CrossRef]

Starikov, A.

Stevens, J. A.

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Tong, E.

R. Blundell, E. Tong, “Submillimetre receivers for radio astronomy,” Proc. IEEE 80, 1702–1720 (1992).
[CrossRef]

Trappe, N.

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
[CrossRef]

Turner, A. D.

J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
[CrossRef]

Withington, S.

S. Withington, G. Yassin, J. A. Murphy, “Dyadic analysis of partially coherent submillimeter-wave antenna systems,” IEEE Trans. Antennas Propag. 49, 1226–1234 (2001).
[CrossRef]

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
[CrossRef]

S. Withington, J. A. Murphy, “Modal analysis of partially coherent submillimetre-wave quasioptical systems,” IEEE Trans. Antennas Propag. 46, 1651–1659 (1998).
[CrossRef]

S. Withington, J. A. Murphy, K. G. Isaak, “On the representation of mirrors in beam waveguides as inclined phase transforming surfaces,” Infrared Phys. Technol. 36, 723–734 (1995).
[CrossRef]

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimetre and submillimetre-wave optical systems,” IEEE Trans. Microwave Theory Tech. 41, 1700–1702 (1993).
[CrossRef]

Wolf, E.

Yassin, G.

S. Withington, G. Yassin, J. A. Murphy, “Dyadic analysis of partially coherent submillimeter-wave antenna systems,” IEEE Trans. Antennas Propag. 49, 1226–1234 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

S. Withington, J. A. Murphy, “Modal analysis of partially coherent submillimetre-wave quasioptical systems,” IEEE Trans. Antennas Propag. 46, 1651–1659 (1998).
[CrossRef]

S. Withington, G. Yassin, J. A. Murphy, “Dyadic analysis of partially coherent submillimeter-wave antenna systems,” IEEE Trans. Antennas Propag. 49, 1226–1234 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimetre and submillimetre-wave optical systems,” IEEE Trans. Microwave Theory Tech. 41, 1700–1702 (1993).
[CrossRef]

Infrared Phys. (1)

J. A. Murphy, “Radiation patterns of few-moded horns and condensing lightpipes,” Infrared Phys. 31, 291–299 (1991).
[CrossRef]

Infrared Phys. Technol. (1)

S. Withington, J. A. Murphy, K. G. Isaak, “On the representation of mirrors in beam waveguides as inclined phase transforming surfaces,” Infrared Phys. Technol. 36, 723–734 (1995).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

J. A. Murphy, C. O’Sullivan, N. Trappe, W. Lanigan, R. Colgan, S. Withington, “Modal analysis of the quasioptical performance of phase gratings,” Int. J. Infrared Millim. Waves 20, 1469–1486 (1999).
[CrossRef]

J. Appl. Phys. (1)

P. L. Richards, “Bolometers for infrared and millimeter waves,” J. Appl. Phys. 76, 1–24 (1994).
[CrossRef]

J. Opt. Soc. Am. (2)

Mon. Not. R. Astron. Soc. (1)

W. S. Holland, E. I. Robson, W. K. Gear, C. R. Cunningham, J. F. Lightfoot, T. Jenness, R. J. Ivison, J. A. Stevens, P. A. R. Ade, M. J. Griffin, W. D. Duncan, J. A. Murphy, D. A. Naylor, “SCUBA: a common-user submillimetre camera operating on the James Clerk Maxwell Telescope,” Mon. Not. R. Astron. Soc. 303, 659–672 (1999).
[CrossRef]

Proc. IEEE (1)

R. Blundell, E. Tong, “Submillimetre receivers for radio astronomy,” Proc. IEEE 80, 1702–1720 (1992).
[CrossRef]

Proc. Phys. Soc. London (1)

Y. Kano, E. Wolf, “Temporal coherence of black body radiation,” Proc. Phys. Soc. London 80, 1273–1276 (1962).
[CrossRef]

Other (9)

P. F. Goldsmith, Quasioptical Systems (IEEE Press, New York, 1998), Chap. 6.

D. J. Benford, E. Serabyn, T. G. Phillips, S. H. Moseley, “Development of a broadband submillimeter grating spectrometer,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 278–288 (1998).
[CrossRef]

J. J. Bock, J. Glenn, S. M. Grannan, K. D. Irwin, A. E. Lange, H. G. LeDuc, A. D. Turner, “Silicon nitride micromesh bolometer arrays for SPIRE,” in Advanced Technology MMW, Radio, and THz Telescopes, T. G. Phillips, ed., Proc. SPIE3357, 297–304 (1998).
[CrossRef]

D. T. Emerson, J. M. Payne, “Multi-feed systems for radio telescopes,” Vol. 75 of Astronomical Society of the Pacific Conference Series (Astronomical Society of the Pacific, San Francisco, Calif., 1994).

P. F. Goldsmith, “Quasioptical techniques at millimetre and submillimetre wavelengths,” in Infrared and Millimeter Waves, K. J. Button, ed. (Academic, New York, 1982), Vol. 6, Chap. 5.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

R. H. Clarke, J. Brown, Diffraction Theory and Antennas (Ellis Horwood Ltd., Chichester UK, 1980), Chap. 3.

T. Rozzi, M. Mongiardo, Open Electromagnetic Waveguides (The Institution of Electrical Engineers, Vol. 43 of Electromagnetic Wave Series 4, London, 1997).

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, UK, 1995), Chap. 3.

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Figures (9)

Fig. 1
Fig. 1

Generic optical system comprising an incoherent source, S, a sequence of optical components, S and S, and a multimode detector, D. H is a general surface in the system at which we wish to calculate the coupled power.

Fig. 2
Fig. 2

Flow diagram showing the way in which power is scattered from the natural modes of the source field to the natural modes of the detector. αn are the eigenvalues of the source coherence matrix, and βn the eigenvalues of the detector coherence matrix. Tmn are the elements of the projection matrix between the two basis sets.

Fig. 3
Fig. 3

Power coupled through each of the natural modes of the output field. The source field has a total of 30 natural modes. Curves a, b, c, d, e, and f correspond to different degrees of coherence: q=q=0.01, 0.025, 0.05, 0.1, 0.25, and 0.5, respectively. The input and output fields have the same scale size, r=1.0.

Fig. 4
Fig. 4

Background power coupled through each of the natural modes of the output field. The source field has a total of 30 natural modes. Curves a, b, c, d, e, and f correspond to different degrees of coherence: q=q=0.01, 0.025, 0.05, 0.1, 0.25, and 0.5, respectively. The input and output fields have the same scale size, r=1.0.

Fig. 5
Fig. 5

Power coupled between two identical Gaussian Schell-model beams, r=1 and q=q, as a function of the degree of coherence. The input and output beams are each limited to having no more than 30 natural modes at most. The solid curve shows the power coupled between the two beams, and the dashed curve shows the power coupled from the background.

Fig. 6
Fig. 6

Power coupled between two Gaussian Schell-model beams of equal size, r=1. The output beam is fully coherent, q=20, and the coherence of the input beam q is varied. The input and output beams are each limited to having no more than 30 natural modes at most. The solid curve shows the power coupled between the two beams, and the dashed curve shows the power coupled from the background.

Fig. 7
Fig. 7

Power coupled between two Gaussian Schell-model beams. The input beam is four times larger than the output beam, r=0.25, and the output beam is fully coherent, q=20; the coherence of the input beam q is varied. The input and output beams are each limited to having no more than 30 natural modes at most. The solid curve shows the power coupled between the two beams, and the dashed curve shows the power coupled from the background.

Fig. 8
Fig. 8

Power coupled between two Gaussian Schell-model beams of equal size, r=1. The output beam is essentially fully incoherent, q=0.1, and the coherence of the input beam q is varied. The input and output beams are each limited to having no more than 30 natural modes at most. The solid curve shows the power coupled between the two beams, and the dashed curve shows the power coupled from the background.

Fig. 9
Fig. 9

Power coupled between two Gaussian Schell-model beams. The output beam is four times larger than the input beam, r=4, and the output beam is essentially fully incoherent, q=0.1; the coherence of the input beam q is varied. The input and output beams are each limited to having no more than 30 natural modes at most. The solid curve shows the power coupled between the two beams, and the dashed curve shows the power coupled from the background.

Equations (67)

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E¯(r¯t, z)=Ex(r¯t, z)xˆ+Ey(r¯t, z)yˆ,
W¯¯(r¯t, r¯t, z)=E¯(r¯t, z)E¯*(r¯t, z).
E¯(r¯t, z)=nanΨ¯n(r¯t, z),
Ψ¯n(r¯t, z)=ψn(r¯t, z)uˆ+ϕn(r¯t, z)vˆ
W¯¯(r¯t, r¯t, z)=nmCnmΨ¯n(r¯t, z)Ψ¯m*(r¯t, z),
Cnm=anam*.
Cnm=SSΨ¯n*(r¯t, z)·W¯¯(r¯t, r¯t, z)·Ψ¯m(r¯t, z)d2r¯td2r¯t,
W¯¯(r¯t, r¯t, z1)=I¯¯I(r¯t)δ(r¯t-r¯t),
Cnm=SI(r¯t)[ψn*(r¯t, z)ψm(r¯t, z)+ϕn*(r¯t, z)ϕm(r¯t, z)]d2r¯t,
an=SE¯(r¯t, z1)·Ψ¯n*(r¯t, z1)d2r¯t
C=aa,
W¯¯(r¯t, r¯t, z)=iW¯¯i(r¯t, r¯t, z).
C=iCi,
D=bb=SCS.
W¯¯(r¯t, r¯t, z)=iβiΨ¯iβ(r¯t, z)Ψ¯iβ*(r¯t, z),
βiΨ¯iβ(r¯t, z)=SW¯¯(r¯t, r¯t, z)·Ψ¯iβ(r¯t, z)d2r¯t,
Ψ¯iβ(r¯)=jUji[ϕj(r¯)uˆ+ϕj(r¯)vˆ].
Pt=SE¯(r¯t, z)·E¯*(r¯t, z)d2r¯t=nmCnmδnm=Tr C,
W¯¯(r¯t, r¯t, z1)=I¯¯hνexphνkTs(r¯t)-1s(r¯t)+hνexphνkTb-1[1-s(r¯t)]×δ(r¯t-r¯t),
Cnm=Shνs(r¯t)exphνkTs(r¯t)-1Ψ¯n*(r¯t, z1)·Ψ¯m(r¯t, z1)d2r¯t,
Dnm=Dηd(r¯t)Ψ¯n*(r¯t)·Ψ¯m(r¯t)d2r¯t,
E¯(r¯t, z)=n=0anΨ¯n(r¯t, z),
E¯(r¯t, z)=m=0amΦ¯m(r¯t, z),
am=SΦ¯m*(r¯t, z)·E¯(r¯t, z)d2r¯t.
a=Ta,
Tmn=SΦ¯m*(r¯t, z)·Ψ¯n(r¯t, z)d2r¯t
A=aa=TaaT=TAT.
A=TΛT,
Amm=n=0|Tmn|2αn,
Ps=m=0n=0|Tmn|2αnβm.
Pt=hνexp[(hν)/(kTs)]-1,
Ps=Tr(TΛTΥ).
UAU=Λ,
Ps=Tr(TATΥ),
VBV=Υ,
Ps=Tr(ATBT),
Ps=Tr(TATB).
Ps=Tr(AB).
Ps=nanbn*2.
Ps=HE¯A·E¯B*dH2.
Ps=nmanbm*SΨ¯n(r¯t, z)·Φ¯m(r¯t, z)*ds2,
Ib=hνexp[(hν)/(kTb)]I,
N=Ib-C.
UCU=Λ.
UNU=U(Ib-C)U=Ib-Λ.
ηn=1-αn,
Pn=Tr{(Ib-A)B},
Pn=Tr{(Ib-A)B}.
Pn=Tr{S(Ib-C)SB+(Io-SIoS)B},
Pn=Tr{(Io-SIoS)B}.
W(x1, x2)=[S(x1)]1/2[S(x2)]1/2g(x2-x1),
S(x)=exp-x22σs2,
g(x2-x1)=exp-(x2-x1)22σg2.
W(x1, x2)=n=0βnϕn*(x1)ϕn(x2),
ϕn(x)=2cπ1/41(2nn!)1/2Hn[x(2c)1/2]exp(-cx2),
c=(a2+2ab)1/2,
a=1/4σs2,
b=1/2σg2.
βmβ0=ba+b+cm.
Ps=m=0n=0|Tmn|2αnβm,
Tmn=-+ϕm(x)ψn(x)dx.
Tmn=ξ-+hm(ku)hn(u)du,
ξ=(c/c)1/2
hm(u)=Hm(u)exp(-u2/2)(π2mm!)1/2,
cc=1r2qq1+(q/2)21+(q/2)21/2,
αnα0=1q2/2+1+q[(q/2)2+1]1/2n,
βnβ0=1q2/2+1+q[(q/2)2+1]1/2n.

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