Abstract

Free-space power detectors often have energy absorbing structures comprising multilayer systems of patterned thin films. We show that for any system of interacting resistive films, the expectation value of the absorbed power is given by the contraction of two tensor fields: one describes the spatial state of coherence of the incoming radiation, the other the state of coherence to which the detector is sensitive. Equivalently, the natural modes of the optical field scatter power into the natural modes of the detector. We describe a procedure for determining the amplitude, phase, and polarization patterns of a detector’s optical modes and their relative responsivities. The procedure gives the state of coherence of the currents flowing in the system and leads to important conceptual insights into the way the pixels of an imaging array interact and extract information from an optical field.

© 2009 Optical Society of America

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  1. K. D. Irwin and G. C. Hilton, “Cryogenic particle detection,” Top. Appl. Phys. 99, 63-149, 2005.
  2. Millimeter and Submillimeter Detectors for Astronomy IV, W.M.Duncan, S.Holland, S.Withington, and J.Zmuidzinas, eds, Vol. 7020 (SPIE, 2008).
  3. Millimeter and Submillimeter Detectors for Astronomy III, W.M.Duncan, S.Holland, S.Withington, and J.Zmuidzinas, eds., Vol. 6275 (SPIE, 2006).
  4. D. T. Chuss, E. J. Wollack, S. H. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430-438 (2008).
    [CrossRef]
  5. S. Withington, C. Y. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for THz imaging systems,” Proc. SPIE 4855, 49-62 (2003).
    [CrossRef]
  6. C. N. Thomas and S. Withington, “A new experimental procedure for determining the response of bolometric detectors to fields in any state of spatial coherence,” Proc. SPIE 7020, 1Z1-1Z12 (2008).
  7. S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).
  8. P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature (London) 425, 817-821 (2003).
    [CrossRef]
  9. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, 1989).
  10. T. B. A. Senior, “Backscattering from resistive strips,” IEEE Trans. Antennas Propag. 27, 808-813 (1979).
    [CrossRef]
  11. R. C. Hall, R. Mittra, and K. M. Mitzner, “Scattering from finite thickness resistive strip gratings,” IEEE Trans. Antennas Propag. 36, 504-510 (1988).
    [CrossRef]
  12. W. P. Harokopus and L. P. B. Katehi, “Electromagnetic coupling and radiation loss considerations in microstrip MMIC design,” IEEE Trans. Microwave Theory Tech. 39, 413-421 (1991).
    [CrossRef]
  13. T. S. Horng, W. E. McKinzie, and N. G. Alexopoulos, “Full-wave spectral-domain analysis of compensation of microstrip discontinuities using triangular subdomain functions,” IEEE Trans. Microwave Theory Tech. 40, 2137-2145 (1992).
    [CrossRef]
  14. F. Tavakkol-Hamedani, A. Tavakoli, and L. Shafai, “Analysis of finite-microstrip structures using surface equivalence principle and multiple network theory (SEMN),” IEEE Trans. Antennas Propag. 50, 1128-1137 (2002).
    [CrossRef]
  15. S. Withington, G. Saklatvala, and M. P. Hobson, “Theoretical analysis of astronomical phased arrays,” J. Opt. A, Pure Appl. Opt. 10, 015304(10 pp) (2008).
    [CrossRef]
  16. G. Saklatvala, S. Withington, and M. P. Hobson, “Simulations of astronomical imaging phased arrays,” J. Opt. Soc. Am. A 25, 958-967 (2008).
    [CrossRef]
  17. S. Withington, M. P. Hobson, and E. S. Campbell, “Modal foundations of close-packed optical arrays with particular application to infrared and millimeter-wave astronomy,” J. Appl. Phys. 96, 1794-1802 (2004).
    [CrossRef]
  18. G. Saklatvala, S. Withington, and M. P. Hobson, “Coupled mode theory for infrared and submillimeter wave detectors,” J. Opt. Soc. Am. A 24, 764-775 (2007).
    [CrossRef]
  19. S. Withington and G. Saklatvala, “Characterizing the behaviour of partially coherent detectors through spatio-temporal modes,” J. Opt. A, Pure Appl. Opt. 9, 626-633 (2007).
    [CrossRef]
  20. D. A. B. Miller, “Communicating with waves between volumes: evaluating orthogonal spatial channels and limits on coupling strengths,” Appl. Opt. 39, 1681-1699 (2000).
    [CrossRef]
  21. M. D. Migliore, “On electromagnetics and information theory,” IEEE Trans. Antennas Propag. 56, 3188-3200 (2008).
    [CrossRef]
  22. T. Itoh and R. Mittra, “Spectral-domain approach for calculating the dispersion characteristics of microstrip lines,” IEEE Trans. Microwave Theory Tech. 21, 496-499 (1973).
    [CrossRef]
  23. P. G. Casazza, “The art of frame theory,” Taiwan. J. Math. 4, 129-201 (2002).
  24. S. Withington, M. P. Hobson, and R. H. Berry, “Representing the behavior of partially coherent optical systems by using overcomplete basis sets,” J. Opt. Soc. Am. A 21, 207-217 (2004).
    [CrossRef]
  25. R. H. Berry, M. P. Hobson, and S. Withington, “General approach for representing and propagating partially coherent terahertz fields with application to Gabor basis sets,” J. Opt. Soc. Am. A 21, 786-796 (2004).
    [CrossRef]
  26. J. D. Kraus, Radio Astronomy (McGraw-Hill, 1966).

2008 (6)

C. N. Thomas and S. Withington, “A new experimental procedure for determining the response of bolometric detectors to fields in any state of spatial coherence,” Proc. SPIE 7020, 1Z1-1Z12 (2008).

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

D. T. Chuss, E. J. Wollack, S. H. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430-438 (2008).
[CrossRef]

S. Withington, G. Saklatvala, and M. P. Hobson, “Theoretical analysis of astronomical phased arrays,” J. Opt. A, Pure Appl. Opt. 10, 015304(10 pp) (2008).
[CrossRef]

M. D. Migliore, “On electromagnetics and information theory,” IEEE Trans. Antennas Propag. 56, 3188-3200 (2008).
[CrossRef]

G. Saklatvala, S. Withington, and M. P. Hobson, “Simulations of astronomical imaging phased arrays,” J. Opt. Soc. Am. A 25, 958-967 (2008).
[CrossRef]

2007 (2)

G. Saklatvala, S. Withington, and M. P. Hobson, “Coupled mode theory for infrared and submillimeter wave detectors,” J. Opt. Soc. Am. A 24, 764-775 (2007).
[CrossRef]

S. Withington and G. Saklatvala, “Characterizing the behaviour of partially coherent detectors through spatio-temporal modes,” J. Opt. A, Pure Appl. Opt. 9, 626-633 (2007).
[CrossRef]

2005 (1)

K. D. Irwin and G. C. Hilton, “Cryogenic particle detection,” Top. Appl. Phys. 99, 63-149, 2005.

2004 (3)

2003 (2)

S. Withington, C. Y. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for THz imaging systems,” Proc. SPIE 4855, 49-62 (2003).
[CrossRef]

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature (London) 425, 817-821 (2003).
[CrossRef]

2002 (2)

F. Tavakkol-Hamedani, A. Tavakoli, and L. Shafai, “Analysis of finite-microstrip structures using surface equivalence principle and multiple network theory (SEMN),” IEEE Trans. Antennas Propag. 50, 1128-1137 (2002).
[CrossRef]

P. G. Casazza, “The art of frame theory,” Taiwan. J. Math. 4, 129-201 (2002).

2000 (1)

1992 (1)

T. S. Horng, W. E. McKinzie, and N. G. Alexopoulos, “Full-wave spectral-domain analysis of compensation of microstrip discontinuities using triangular subdomain functions,” IEEE Trans. Microwave Theory Tech. 40, 2137-2145 (1992).
[CrossRef]

1991 (1)

W. P. Harokopus and L. P. B. Katehi, “Electromagnetic coupling and radiation loss considerations in microstrip MMIC design,” IEEE Trans. Microwave Theory Tech. 39, 413-421 (1991).
[CrossRef]

1988 (1)

R. C. Hall, R. Mittra, and K. M. Mitzner, “Scattering from finite thickness resistive strip gratings,” IEEE Trans. Antennas Propag. 36, 504-510 (1988).
[CrossRef]

1979 (1)

T. B. A. Senior, “Backscattering from resistive strips,” IEEE Trans. Antennas Propag. 27, 808-813 (1979).
[CrossRef]

1973 (1)

T. Itoh and R. Mittra, “Spectral-domain approach for calculating the dispersion characteristics of microstrip lines,” IEEE Trans. Microwave Theory Tech. 21, 496-499 (1973).
[CrossRef]

Alexopoulos, N. G.

T. S. Horng, W. E. McKinzie, and N. G. Alexopoulos, “Full-wave spectral-domain analysis of compensation of microstrip discontinuities using triangular subdomain functions,” IEEE Trans. Microwave Theory Tech. 40, 2137-2145 (1992).
[CrossRef]

Baselmans, J. J. A.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Berry, R. H.

Campbell, E. S.

S. Withington, M. P. Hobson, and E. S. Campbell, “Modal foundations of close-packed optical arrays with particular application to infrared and millimeter-wave astronomy,” J. Appl. Phys. 96, 1794-1802 (2004).
[CrossRef]

Casazza, P. G.

P. G. Casazza, “The art of frame theory,” Taiwan. J. Math. 4, 129-201 (2002).

Chuss, D. T.

D. T. Chuss, E. J. Wollack, S. H. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430-438 (2008).
[CrossRef]

Courant, R.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, 1989).

Day, P. K.

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature (London) 425, 817-821 (2003).
[CrossRef]

Doyle, S.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Glowacka, D.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Goldie, D.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Hall, R. C.

R. C. Hall, R. Mittra, and K. M. Mitzner, “Scattering from finite thickness resistive strip gratings,” IEEE Trans. Antennas Propag. 36, 504-510 (1988).
[CrossRef]

Harokopus, W. P.

W. P. Harokopus and L. P. B. Katehi, “Electromagnetic coupling and radiation loss considerations in microstrip MMIC design,” IEEE Trans. Microwave Theory Tech. 39, 413-421 (1991).
[CrossRef]

Hilbert, D.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, 1989).

Hilton, G. C.

K. D. Irwin and G. C. Hilton, “Cryogenic particle detection,” Top. Appl. Phys. 99, 63-149, 2005.

Hobson, M. P.

Hoevers, H. F. C.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Horng, T. S.

T. S. Horng, W. E. McKinzie, and N. G. Alexopoulos, “Full-wave spectral-domain analysis of compensation of microstrip discontinuities using triangular subdomain functions,” IEEE Trans. Microwave Theory Tech. 40, 2137-2145 (1992).
[CrossRef]

Irwin, K. D.

K. D. Irwin and G. C. Hilton, “Cryogenic particle detection,” Top. Appl. Phys. 99, 63-149, 2005.

Itoh, T.

T. Itoh and R. Mittra, “Spectral-domain approach for calculating the dispersion characteristics of microstrip lines,” IEEE Trans. Microwave Theory Tech. 21, 496-499 (1973).
[CrossRef]

Katehi, L. P. B.

W. P. Harokopus and L. P. B. Katehi, “Electromagnetic coupling and radiation loss considerations in microstrip MMIC design,” IEEE Trans. Microwave Theory Tech. 39, 413-421 (1991).
[CrossRef]

Kraus, J. D.

J. D. Kraus, Radio Astronomy (McGraw-Hill, 1966).

LeDuc, H. G.

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature (London) 425, 817-821 (2003).
[CrossRef]

Mauskopf, P. D.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Mazin, B. A.

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature (London) 425, 817-821 (2003).
[CrossRef]

McKinzie, W. E.

T. S. Horng, W. E. McKinzie, and N. G. Alexopoulos, “Full-wave spectral-domain analysis of compensation of microstrip discontinuities using triangular subdomain functions,” IEEE Trans. Microwave Theory Tech. 40, 2137-2145 (1992).
[CrossRef]

Migliore, M. D.

M. D. Migliore, “On electromagnetics and information theory,” IEEE Trans. Antennas Propag. 56, 3188-3200 (2008).
[CrossRef]

Miller, D. A. B.

Mittra, R.

R. C. Hall, R. Mittra, and K. M. Mitzner, “Scattering from finite thickness resistive strip gratings,” IEEE Trans. Antennas Propag. 36, 504-510 (1988).
[CrossRef]

T. Itoh and R. Mittra, “Spectral-domain approach for calculating the dispersion characteristics of microstrip lines,” IEEE Trans. Microwave Theory Tech. 21, 496-499 (1973).
[CrossRef]

Mitzner, K. M.

R. C. Hall, R. Mittra, and K. M. Mitzner, “Scattering from finite thickness resistive strip gratings,” IEEE Trans. Antennas Propag. 36, 504-510 (1988).
[CrossRef]

Moseley, S. H.

D. T. Chuss, E. J. Wollack, S. H. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430-438 (2008).
[CrossRef]

Naylon, J.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Porch, A.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Saklatvala, G.

D. T. Chuss, E. J. Wollack, S. H. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430-438 (2008).
[CrossRef]

G. Saklatvala, S. Withington, and M. P. Hobson, “Simulations of astronomical imaging phased arrays,” J. Opt. Soc. Am. A 25, 958-967 (2008).
[CrossRef]

S. Withington, G. Saklatvala, and M. P. Hobson, “Theoretical analysis of astronomical phased arrays,” J. Opt. A, Pure Appl. Opt. 10, 015304(10 pp) (2008).
[CrossRef]

S. Withington and G. Saklatvala, “Characterizing the behaviour of partially coherent detectors through spatio-temporal modes,” J. Opt. A, Pure Appl. Opt. 9, 626-633 (2007).
[CrossRef]

G. Saklatvala, S. Withington, and M. P. Hobson, “Coupled mode theory for infrared and submillimeter wave detectors,” J. Opt. Soc. Am. A 24, 764-775 (2007).
[CrossRef]

Senior, T. B. A.

T. B. A. Senior, “Backscattering from resistive strips,” IEEE Trans. Antennas Propag. 27, 808-813 (1979).
[CrossRef]

Shafai, L.

F. Tavakkol-Hamedani, A. Tavakoli, and L. Shafai, “Analysis of finite-microstrip structures using surface equivalence principle and multiple network theory (SEMN),” IEEE Trans. Antennas Propag. 50, 1128-1137 (2002).
[CrossRef]

Tavakkol-Hamedani, F.

F. Tavakkol-Hamedani, A. Tavakoli, and L. Shafai, “Analysis of finite-microstrip structures using surface equivalence principle and multiple network theory (SEMN),” IEEE Trans. Antennas Propag. 50, 1128-1137 (2002).
[CrossRef]

Tavakoli, A.

F. Tavakkol-Hamedani, A. Tavakoli, and L. Shafai, “Analysis of finite-microstrip structures using surface equivalence principle and multiple network theory (SEMN),” IEEE Trans. Antennas Propag. 50, 1128-1137 (2002).
[CrossRef]

Tham, C. Y.

S. Withington, C. Y. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for THz imaging systems,” Proc. SPIE 4855, 49-62 (2003).
[CrossRef]

Thomas, C. N.

C. N. Thomas and S. Withington, “A new experimental procedure for determining the response of bolometric detectors to fields in any state of spatial coherence,” Proc. SPIE 7020, 1Z1-1Z12 (2008).

Vayonakis, A.

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature (London) 425, 817-821 (2003).
[CrossRef]

Withington, S.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

D. T. Chuss, E. J. Wollack, S. H. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430-438 (2008).
[CrossRef]

G. Saklatvala, S. Withington, and M. P. Hobson, “Simulations of astronomical imaging phased arrays,” J. Opt. Soc. Am. A 25, 958-967 (2008).
[CrossRef]

C. N. Thomas and S. Withington, “A new experimental procedure for determining the response of bolometric detectors to fields in any state of spatial coherence,” Proc. SPIE 7020, 1Z1-1Z12 (2008).

S. Withington, G. Saklatvala, and M. P. Hobson, “Theoretical analysis of astronomical phased arrays,” J. Opt. A, Pure Appl. Opt. 10, 015304(10 pp) (2008).
[CrossRef]

S. Withington and G. Saklatvala, “Characterizing the behaviour of partially coherent detectors through spatio-temporal modes,” J. Opt. A, Pure Appl. Opt. 9, 626-633 (2007).
[CrossRef]

G. Saklatvala, S. Withington, and M. P. Hobson, “Coupled mode theory for infrared and submillimeter wave detectors,” J. Opt. Soc. Am. A 24, 764-775 (2007).
[CrossRef]

R. H. Berry, M. P. Hobson, and S. Withington, “General approach for representing and propagating partially coherent terahertz fields with application to Gabor basis sets,” J. Opt. Soc. Am. A 21, 786-796 (2004).
[CrossRef]

S. Withington, M. P. Hobson, and E. S. Campbell, “Modal foundations of close-packed optical arrays with particular application to infrared and millimeter-wave astronomy,” J. Appl. Phys. 96, 1794-1802 (2004).
[CrossRef]

S. Withington, M. P. Hobson, and R. H. Berry, “Representing the behavior of partially coherent optical systems by using overcomplete basis sets,” J. Opt. Soc. Am. A 21, 207-217 (2004).
[CrossRef]

S. Withington, C. Y. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for THz imaging systems,” Proc. SPIE 4855, 49-62 (2003).
[CrossRef]

Wollack, E. J.

D. T. Chuss, E. J. Wollack, S. H. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430-438 (2008).
[CrossRef]

Yassin, G.

S. Withington, C. Y. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for THz imaging systems,” Proc. SPIE 4855, 49-62 (2003).
[CrossRef]

Yates, S. J. C.

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Zmuidzinas, J.

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature (London) 425, 817-821 (2003).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (4)

T. B. A. Senior, “Backscattering from resistive strips,” IEEE Trans. Antennas Propag. 27, 808-813 (1979).
[CrossRef]

R. C. Hall, R. Mittra, and K. M. Mitzner, “Scattering from finite thickness resistive strip gratings,” IEEE Trans. Antennas Propag. 36, 504-510 (1988).
[CrossRef]

F. Tavakkol-Hamedani, A. Tavakoli, and L. Shafai, “Analysis of finite-microstrip structures using surface equivalence principle and multiple network theory (SEMN),” IEEE Trans. Antennas Propag. 50, 1128-1137 (2002).
[CrossRef]

M. D. Migliore, “On electromagnetics and information theory,” IEEE Trans. Antennas Propag. 56, 3188-3200 (2008).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

T. Itoh and R. Mittra, “Spectral-domain approach for calculating the dispersion characteristics of microstrip lines,” IEEE Trans. Microwave Theory Tech. 21, 496-499 (1973).
[CrossRef]

W. P. Harokopus and L. P. B. Katehi, “Electromagnetic coupling and radiation loss considerations in microstrip MMIC design,” IEEE Trans. Microwave Theory Tech. 39, 413-421 (1991).
[CrossRef]

T. S. Horng, W. E. McKinzie, and N. G. Alexopoulos, “Full-wave spectral-domain analysis of compensation of microstrip discontinuities using triangular subdomain functions,” IEEE Trans. Microwave Theory Tech. 40, 2137-2145 (1992).
[CrossRef]

J. Appl. Phys. (1)

S. Withington, M. P. Hobson, and E. S. Campbell, “Modal foundations of close-packed optical arrays with particular application to infrared and millimeter-wave astronomy,” J. Appl. Phys. 96, 1794-1802 (2004).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

S. Withington and G. Saklatvala, “Characterizing the behaviour of partially coherent detectors through spatio-temporal modes,” J. Opt. A, Pure Appl. Opt. 9, 626-633 (2007).
[CrossRef]

S. Withington, G. Saklatvala, and M. P. Hobson, “Theoretical analysis of astronomical phased arrays,” J. Opt. A, Pure Appl. Opt. 10, 015304(10 pp) (2008).
[CrossRef]

J. Opt. Soc. Am. A (4)

Nature (London) (1)

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature (London) 425, 817-821 (2003).
[CrossRef]

Proc. SPIE (3)

S. Withington, C. Y. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for THz imaging systems,” Proc. SPIE 4855, 49-62 (2003).
[CrossRef]

C. N. Thomas and S. Withington, “A new experimental procedure for determining the response of bolometric detectors to fields in any state of spatial coherence,” Proc. SPIE 7020, 1Z1-1Z12 (2008).

S. Doyle, J. Naylon, P. D. Mauskopf, A. Porch, S. Withington, D. Goldie, D. Glowacka, J. J. A. Baselmans, S. J. C. Yates, H. F. C. Hoevers, “Lumped kinetic inductance detectors for far infrared astronomy,” Proc. SPIE 7020, 0T1-0T10 (2008).

Publ. Astron. Soc. Pac. (1)

D. T. Chuss, E. J. Wollack, S. H. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430-438 (2008).
[CrossRef]

Taiwan. J. Math. (1)

P. G. Casazza, “The art of frame theory,” Taiwan. J. Math. 4, 129-201 (2002).

Top. Appl. Phys. (1)

K. D. Irwin and G. C. Hilton, “Cryogenic particle detection,” Top. Appl. Phys. 99, 63-149, 2005.

Other (4)

Millimeter and Submillimeter Detectors for Astronomy IV, W.M.Duncan, S.Holland, S.Withington, and J.Zmuidzinas, eds, Vol. 7020 (SPIE, 2008).

Millimeter and Submillimeter Detectors for Astronomy III, W.M.Duncan, S.Holland, S.Withington, and J.Zmuidzinas, eds., Vol. 6275 (SPIE, 2006).

J. D. Kraus, Radio Astronomy (McGraw-Hill, 1966).

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, 1989).

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Fig. 1
Fig. 1

Resistive films on three planes.

Equations (71)

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[ E k ( r t ) + E k s ( r t ) ] tang = Z ̿ k s ( r t ) J k s ( r t ) ,
[ I ̿ z ̂ z ̂ ] E k ( r t ) = Z ̿ k s ( r t ) J k s ( r t ) k S k G ̿ k k t ( r t r t ) J k s ( r t ) d 2 r t ,
G ̿ k k t ( r t r t ) = [ I ̿ z ̂ z ̂ ] G ̿ k k ( r t r t ) .
[ I ̿ z ̂ z ̂ ] E k ( r t ) = k S k L ̿ k k ( r t r t ) J k s ( r t ) d 2 r t ,
L ̿ k k ( r t r t ) = [ Z ̿ k s ( r t ) δ k k δ ( r t r t ) G ̿ k k t ( r t r t ) ]
L ̿ k k ( r t r t ) = n σ n f k n ( r t ) g k n * ( r t ) ,
k S k f k n ( r t ) f k n * ( r t ) d 2 r t = δ n n ,
k S k g k n ( r t ) g k n * ( r t ) d 2 r t = δ n n .
[ I ̿ z ̂ z ̂ ] E k ( r t ) = n σ n f k n ( r t ) k S k g k n * ( r t ) J k s ( r t ) d 2 r t .
J k s ( r t ) = n 1 σ n g k n ( r t ) k S k f k n * ( r t ) [ I ̿ z ̂ z ̂ ] E k ( r t ) d 2 r t ,
M ̿ k k ( r t r t ) = n 1 σ n g k n ( r t ) f k n * ( r t ) [ I ̿ z ̂ z ̂ ]
J k s ( r t ) = k S k M ̿ k k ( r t r t ) E k ( r t ) d 2 r t .
P = 1 2 k S k J k s * ( r t ) R ̿ k s ( r t ) J k s ( r t ) d 2 r t = 1 2 k S k Tr [ R ̿ k s ( r t ) J ̿ k k s ( r t r t ) ] d 2 r t ,
P i = 1 2 k i S k i Tr [ R ̿ k s ( r t ) J ̿ k k s ( r t r t ) ] d 2 r t ,
P = 1 2 k r s S k d 2 r t S r d 2 r t 1 S s d 2 r t 2 Tr [ R ̿ k s ( r t ) M ̿ k r ( r t r t 1 ) E ̿ r s ( r t 1 r t 2 ) M ̿ s k ( r t 2 r t ) ] = 1 2 k r s S k d 2 r t S r d 2 r t 1 S s d 2 r t 2 Tr [ M ̿ s k ( r t 2 r t ) R ̿ k s ( r t ) M ̿ k r ( r t r t 1 ) E ̿ r s ( r t 1 r t 2 ) ] = r s S r d 2 r t 1 S s d 2 r t 2 Tr [ D ̿ s r ( r t 2 r t 1 ) E ̿ r s ( r t 1 r t 2 ) ] ,
D ̿ s r ( r t 2 r t 1 ) = 1 2 k S k M ̿ s k ( r t 2 r t ) R ̿ k s ( r t ) M ̿ k r ( r t r t 1 ) d 2 r t .
P = r s S r S s D ̿ s r ( r t 2 r t 1 ) E ̿ r s ( r t 1 r t 2 ) d 2 r t 1 d 2 r t 2 ,
P i = r s S r S s D ̿ s r i ( r t 2 r t 1 ) E ̿ r s ( r t 1 r t 2 ) d 2 r t 1 d 2 r t 2 ,
D ̿ s r i ( r t 2 r t 1 ) = 1 2 k i S k i M ̿ s k ( r t 2 r t ) R ̿ k s ( r t ) M ̿ k r ( r t r t 1 ) d 2 r t .
E ̿ r s ( r t 1 r t 2 ) = n α n e r n ( r t 1 ) e s n * ( r t 2 ) ,
D ̿ r s ( r t 1 r t 2 ) = n β n d r n ( r t 1 ) d s n * ( r t 2 ) .
P = n n β n T n n 2 α n ,
T n n = r S r d r n * ( r t 1 ) e r n ( r t 1 ) d 2 r t 1 .
M ̿ k r ( r t r t 1 ) = n 1 σ n g k n ( r t ) f r n * ( r t 1 ) [ I ̿ z ̂ z ̂ ] ,
M ̿ s k ( r t 2 r t ) = n 1 σ n [ I ̿ z ̂ z ̂ ] f s n ( r t 2 ) g k n * ( r t ) .
D ̿ s r ( r t 2 r t 1 ) = 1 2 n n 1 σ n σ n S n n f s n ( r t 2 ) f r n * ( r t 1 ) ,
S n n = k S k g k n * ( r t ) R ̿ k s ( r t ) g k n ( r t ) d 2 r t .
D ̿ s r ( r t 2 r t 1 ) = 1 2 R s k S k M ̿ s k ( r t 2 r t ) M ̿ k r ( r t r t 1 ) d 2 r t .
D ̿ s r ( r t 2 r t 1 ) = 1 2 R s n 1 ( σ n ) 2 f s n ( r t 2 ) f r n * ( r t 1 ) ,
L ̿ k k ( r t r t ) = [ Z ̿ k s ( r t ) δ k k δ ( r t r t ) G ̿ k k t ( r t r t ) ] .
E ( r ) = i ω μ o V G ̿ ( r r ) J ( r ) d 3 r ,
g ( r r ) = 1 4 π r r exp [ i k o r r ] ,
G ̿ ( r r ) = [ I ̿ + 1 k o 2 ] g ( r r ) .
G ̿ ( r r ) = [ I ̿ + 1 k o 2 ] g ( r r p ) + [ I ̿ i + 1 k o 2 ] g ( r r i ) .
J k s ( r t ) = m I m Ψ k m ( r t ) ,
k S k Ψ k m ( r t ) Ψ k m * ( r t ) d 2 r t δ m m ,
k S k Ψ k m ( r t ) Ψ ̃ k m * ( r t ) d 2 r t = δ m m ,
I m = k S k J k s ( r t ) Ψ ̃ k m * ( r t ) d 2 r t .
[ I ̿ z ̂ z ̂ ] E k ( r t ) = n E n Φ k n ( r t ) ,
k S k Φ k n ( r t ) Φ ̃ k n * ( r t ) d 2 r t = δ n n ,
E n = k S k E k ( r t ) Φ ̃ k n * ( r t ) d 2 r t .
E n = m I m k k S k S k Φ ̃ k n * ( r t ) L ̿ k k ( r t r t ) Ψ k m ( r t ) d 2 r t d 2 r t
E n = m I m L n m ,
L n m = k k S k S k Φ ̃ k n * ( r t ) L ̿ k k ( r t r t ) Ψ k m ( r t ) d 2 r t d 2 r t ,
L n m = i [ k S k Φ ̃ k n * ( r t ) f k i ( r t ) d 2 r t ] σ i [ k S k g k i * ( r t ) Ψ k m ( r t ) d 2 r t ] ,
L = U Σ V .
U n i = k S k Φ ̃ k n * ( r t ) f k i ( r t ) d 2 r t ,
V m i = k S k g k i ( r t ) Ψ k m * ( r t ) d 2 r t .
f k i ( r t ) = n U n i Φ k n ( r t ) ,
g k i ( r t ) = m V m i Ψ ̃ k m ( r t ) .
E n s ( r ) = i ω μ o k S k G ̿ r ( r r t , z k ) g k n ( r t ) d 2 r t ,
P i = r s S r S s D ̿ s r i ( r t 2 r t 1 ) E ̿ r s ( r t 1 r t 2 ) d 2 r t 1 d 2 r t 2 .
E r ( r t ) = i ω μ o V G ̿ ( r t , z r r ) J ( r ) d 3 r ,
E ̿ r s ( r t 1 r t 2 ) = ( ω μ o ) 2 V V G ̿ ( r t 1 , z 1 r r ) J ̿ ( r , r ) G ̿ ( r r t 2 , z 2 s ) d 3 r d 3 r ,
J ̿ ( r , r ) = J ( r ) J * ( r )
P i = V V W ̿ i ( r r ) J ̿ ( r , r ) d 3 r d 3 r ,
W ̿ i ( r r ) = ( ω μ o ) 2 r s S r S s G ̿ ( r r t 2 , z 2 s ) D ̿ s r i ( r t 2 r t 1 ) G ̿ ( r t 1 , z 1 r r ) d 2 r t 1 d 2 r t 2 .
E ( r ) = 1 2 π m a m ( k t ) s ̂ m ( k t ) exp [ i k t r t ] exp [ i k z z ] d 2 k t ,
E ̿ r s ( r t 1 r t 2 ) = 1 ( 2 π ) 2 A ̿ ( k t k t ) exp [ i k t r t 1 ] exp [ i k z z r ] × exp [ i k t r t 2 ] exp [ i k z z s ] d 2 k t d 2 k t ,
A ̿ ( k t k t ) = m m a m ( k t ) a m * ( k t ) s ̂ m ( k t ) s ̂ m ( k t )
P i = F ̿ i ( k t k t ) A ̿ ( k t k t ) d 2 k t d 2 k t ,
F ̿ i ( k t k t ) = r s exp [ i k z z s ] F ̿ s r i ( k t k t ) exp [ i k z z r ] ,
F ̿ s r i ( k t k t ) = 1 ( 2 π ) 2 S r S s exp [ i k t r t 2 ] D ̿ s r i ( r t 2 r t 1 ) exp [ i k t r t 1 ] d 2 r t 1 d 2 r t 2 .
F ̿ i ( k t k t ) = r r F ̿ r r i ( k t k t ) exp [ ( i ( k z k z ) z r ) ] .
E ( r ) e ( Ω ̂ ) exp [ i k r ] r as r ,
A ̿ ( k t k t ) = 1 ( k z k z ) e ( Ω ̂ ) e * ( Ω ̂ ) = 1 k z k z E ̿ ( Ω ̂ Ω ̂ ) ,
A ̿ ( k t k t ) d 2 k t d 2 k t = k 2 E ̿ ( Ω ̂ Ω ̂ ) d Ω d Ω .
P i = S S 2 Z o ( 2 π ) 2 F ̿ i ( Ω ̂ Ω ̂ ) 1 2 λ 2 Z o E ̿ ( Ω ̂ Ω ̂ ) d Ω d Ω = S S P ̿ i ( Ω ̂ Ω ̂ ) B ̿ ( Ω ̂ Ω ̂ ) d Ω d Ω .
P i = Tr [ P ̿ i ( Ω ̂ Ω ̂ ) ] B ( Ω ̂ ) d Ω P i ( Ω ̂ ) B ( Ω ̂ ) d Ω ,
F s i ( k t ) = 1 ( 2 π ) S s exp [ i k t r t 2 ] d s i n ( r t 2 ) d 2 r t 2
F i ( k t ) = s exp [ i k z z s ] F s i ( k t ) .

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