Abstract

A standing wave Fourier transform spectrometer is realized. The spectrometer consists of an ultra thin and partially transparent photodetector and a tunable mirror. The incident light forms a standing wave in front of the mirror, which is sampled by the ultra thin optical detector. The thickness of the photodetector is significantly smaller than the wavelength of the incident light. The spectral information of the incident light is determined by the Fourier transform of the detector signal. The linear arrangement of the optical detector and the mirror enables the realization of spectrometer arrays and optical cameras with high spectral resolution. For the first time a complete optical model of the standing wave spectrometer is presented and compared with experimental results. The influence of the design of the optical detector on the performance of the spectrometer is discussed.

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References

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  1. R. F. Wolffenbuttel, “State-of-the-Art in Integrated Optical Microspectrometers,” IEEE Tr, IM, Vol. 53(1), 197 (2004).
  2. P. M. Zavracky, K. L. Denis, H. K. Xie, T. Wester, and P. Kelley, “A micromachined scanning Fabry–Pérot interferometer,” Proc. SPIE (3514), 179–187 (1998).
  3. G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biochemical analysis,” Sens. Act. A-Phys. 58(1), 61–66 (1997).
    [CrossRef]
  4. O. Manzardo, H. P. Herzig, C. R. Marxer, and N. F. de Rooij, “Miniaturized time-scanning Fourier transform spectrometer based on silicon technology,” Opt. Lett. 24(23), 1705–1707 (1999).
    [CrossRef]
  5. D. A. B. Miller, “Laser Tuners and Wavelength-sensitive Detectors based on absorbers in Standing Waves,” IEEE J. Quantum Electron. 30(3732), (1994).
    [CrossRef]
  6. M. Sasaki, X. Y. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Applied Physics Letters,Vol. 75(14), 2008–2010 (1999).
    [CrossRef]
  7. H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE Sel. Top. Quantum Electron. 8(1), 98–105 (2002).
    [CrossRef]
  8. D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
    [CrossRef]
  9. E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
    [CrossRef]
  10. W. Luft, and Y. Tuso, “Hydrogenated amorphous silicon alloy deposition processes”, Marcel Dekker, Inc., 1993.
  11. J. Kauppinen, and J. Partanen, “Fourier Transforms in Spectroscopy”, Wiley-VCH, 2001.
  12. Z. Knittl, “Optics of Thin Films”, New York: Wiley, 1976.
  13. P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetrical Characterization of novel multiple-channel sensors for imaging and metrology,” J. Electron. Imaging 8(4), 342–353 (1999).
    [CrossRef]
  14. O. Kluth, and A. Löffl, S. Wieder, C. Beneking, L. Houben, B. Rech, H. Wagner, S. Waser, J.A. Selvan, H. Keppner, “Texture etched Al-doped ZnO: A new material for enhanced light trapping in thin film solar cells”, Proc. 26th IEEE PVSEC, pp. 715–718 (1997).
  15. “Technology and Applications of Amorphous Silicon”, Springer Series in Material Science, 37. edited by R. A. Street, Berlin, Germany: Springer-Verlag, 2000.
  16. H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
    [CrossRef]
  17. H. Stiebig, D. Knipp, S. R. Bhalotra, H. L. Kung, and D. A. B. Miller, “Interferometric Sensors for Spectral Imaging”, Sens. Act. A: Phys. 120, 110–114 (2005).
    [CrossRef]

2007 (1)

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

2005 (2)

H. Stiebig, D. Knipp, S. R. Bhalotra, H. L. Kung, and D. A. B. Miller, “Interferometric Sensors for Spectral Imaging”, Sens. Act. A: Phys. 120, 110–114 (2005).
[CrossRef]

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
[CrossRef]

2004 (1)

R. F. Wolffenbuttel, “State-of-the-Art in Integrated Optical Microspectrometers,” IEEE Tr, IM, Vol. 53(1), 197 (2004).

2003 (1)

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
[CrossRef]

2002 (1)

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE Sel. Top. Quantum Electron. 8(1), 98–105 (2002).
[CrossRef]

1999 (3)

M. Sasaki, X. Y. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Applied Physics Letters,Vol. 75(14), 2008–2010 (1999).
[CrossRef]

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetrical Characterization of novel multiple-channel sensors for imaging and metrology,” J. Electron. Imaging 8(4), 342–353 (1999).
[CrossRef]

O. Manzardo, H. P. Herzig, C. R. Marxer, and N. F. de Rooij, “Miniaturized time-scanning Fourier transform spectrometer based on silicon technology,” Opt. Lett. 24(23), 1705–1707 (1999).
[CrossRef]

1997 (1)

G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biochemical analysis,” Sens. Act. A-Phys. 58(1), 61–66 (1997).
[CrossRef]

1994 (1)

D. A. B. Miller, “Laser Tuners and Wavelength-sensitive Detectors based on absorbers in Standing Waves,” IEEE J. Quantum Electron. 30(3732), (1994).
[CrossRef]

Albin, M.

G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biochemical analysis,” Sens. Act. A-Phys. 58(1), 61–66 (1997).
[CrossRef]

Benech, P.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Bhalotra, S. R.

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
[CrossRef]

H. Stiebig, D. Knipp, S. R. Bhalotra, H. L. Kung, and D. A. B. Miller, “Interferometric Sensors for Spectral Imaging”, Sens. Act. A: Phys. 120, 110–114 (2005).
[CrossRef]

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE Sel. Top. Quantum Electron. 8(1), 98–105 (2002).
[CrossRef]

Blaize, S.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Büchner, H.-J.

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
[CrossRef]

Bunte, E.

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
[CrossRef]

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
[CrossRef]

de Rooij, N. F.

Fedeli, J. M.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Hane, K.

M. Sasaki, X. Y. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Applied Physics Letters,Vol. 75(14), 2008–2010 (1999).
[CrossRef]

Harris, J. S.

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE Sel. Top. Quantum Electron. 8(1), 98–105 (2002).
[CrossRef]

Herzig, H. P.

Herzog, P. G.

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetrical Characterization of novel multiple-channel sensors for imaging and metrology,” J. Electron. Imaging 8(4), 342–353 (1999).
[CrossRef]

Hing, P. A.

G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biochemical analysis,” Sens. Act. A-Phys. 58(1), 61–66 (1997).
[CrossRef]

Jäger, G.

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
[CrossRef]

Kern, P.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Knipp, D.

H. Stiebig, D. Knipp, S. R. Bhalotra, H. L. Kung, and D. A. B. Miller, “Interferometric Sensors for Spectral Imaging”, Sens. Act. A: Phys. 120, 110–114 (2005).
[CrossRef]

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
[CrossRef]

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
[CrossRef]

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetrical Characterization of novel multiple-channel sensors for imaging and metrology,” J. Electron. Imaging 8(4), 342–353 (1999).
[CrossRef]

König, F.

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetrical Characterization of novel multiple-channel sensors for imaging and metrology,” J. Electron. Imaging 8(4), 342–353 (1999).
[CrossRef]

Kovacs, G. T. A.

G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biochemical analysis,” Sens. Act. A-Phys. 58(1), 61–66 (1997).
[CrossRef]

Kung, H. L.

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
[CrossRef]

H. Stiebig, D. Knipp, S. R. Bhalotra, H. L. Kung, and D. A. B. Miller, “Interferometric Sensors for Spectral Imaging”, Sens. Act. A: Phys. 120, 110–114 (2005).
[CrossRef]

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE Sel. Top. Quantum Electron. 8(1), 98–105 (2002).
[CrossRef]

le Coarer, E.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Leblond, G.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Lérondel, G.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Maluf, N. I.

G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biochemical analysis,” Sens. Act. A-Phys. 58(1), 61–66 (1997).
[CrossRef]

Mandryka, V.

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
[CrossRef]

Mansell, J. D.

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE Sel. Top. Quantum Electron. 8(1), 98–105 (2002).
[CrossRef]

Manzardo, O.

Marxer, C. R.

Mi, X. Y.

M. Sasaki, X. Y. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Applied Physics Letters,Vol. 75(14), 2008–2010 (1999).
[CrossRef]

Miller, D. A. B.

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
[CrossRef]

H. Stiebig, D. Knipp, S. R. Bhalotra, H. L. Kung, and D. A. B. Miller, “Interferometric Sensors for Spectral Imaging”, Sens. Act. A: Phys. 120, 110–114 (2005).
[CrossRef]

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE Sel. Top. Quantum Electron. 8(1), 98–105 (2002).
[CrossRef]

D. A. B. Miller, “Laser Tuners and Wavelength-sensitive Detectors based on absorbers in Standing Waves,” IEEE J. Quantum Electron. 30(3732), (1994).
[CrossRef]

Morand, A.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Royer, P.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Sasaki, M.

M. Sasaki, X. Y. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Applied Physics Letters,Vol. 75(14), 2008–2010 (1999).
[CrossRef]

Stefanon, I.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Stiebig, H.

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
[CrossRef]

H. Stiebig, D. Knipp, S. R. Bhalotra, H. L. Kung, and D. A. B. Miller, “Interferometric Sensors for Spectral Imaging”, Sens. Act. A: Phys. 120, 110–114 (2005).
[CrossRef]

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
[CrossRef]

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetrical Characterization of novel multiple-channel sensors for imaging and metrology,” J. Electron. Imaging 8(4), 342–353 (1999).
[CrossRef]

Wolffenbuttel, R. F.

R. F. Wolffenbuttel, “State-of-the-Art in Integrated Optical Microspectrometers,” IEEE Tr, IM, Vol. 53(1), 197 (2004).

Yee, G. M.

G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biochemical analysis,” Sens. Act. A-Phys. 58(1), 61–66 (1997).
[CrossRef]

Applied Physics Letters,Vol. (1)

M. Sasaki, X. Y. Mi, and K. Hane, “Standing wave detection and interferometer application using a photodiode thinner than optical wavelength,” Applied Physics Letters,Vol. 75(14), 2008–2010 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. A. B. Miller, “Laser Tuners and Wavelength-sensitive Detectors based on absorbers in Standing Waves,” IEEE J. Quantum Electron. 30(3732), (1994).
[CrossRef]

IEEE Sel. Top. Quantum Electron. (1)

H. L. Kung, S. R. Bhalotra, J. D. Mansell, D. A. B. Miller, and J. S. Harris., “Standing-wave transform spectrometer based on integrated MEMS mirror and thin-film photodetector,” IEEE Sel. Top. Quantum Electron. 8(1), 98–105 (2002).
[CrossRef]

IEEE Tr, IM, Vol. (1)

R. F. Wolffenbuttel, “State-of-the-Art in Integrated Optical Microspectrometers,” IEEE Tr, IM, Vol. 53(1), 197 (2004).

IEEE Trans. Electron Dev. (1)

D. Knipp, H. Stiebig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon based Micro-Fourier spectrometer,” IEEE Trans. Electron Dev. 52(3), 419–426 (2005).
[CrossRef]

J. Electron. Imaging (1)

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetrical Characterization of novel multiple-channel sensors for imaging and metrology,” J. Electron. Imaging 8(4), 342–353 (1999).
[CrossRef]

Nat. Photonics (1)

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, “Wavelength-scale stationary-wave integrated Fourier-transform spectrometry,” Nat. Photonics 1(8), 473–478 (2007).
[CrossRef]

Opt. Lett. (1)

Sens. Act. A-Phys. (1)

G. M. Yee, N. I. Maluf, P. A. Hing, M. Albin, and G. T. A. Kovacs, “Miniature spectrometers for biochemical analysis,” Sens. Act. A-Phys. 58(1), 61–66 (1997).
[CrossRef]

Sens. Act. A: Phys. (1)

H. Stiebig, D. Knipp, S. R. Bhalotra, H. L. Kung, and D. A. B. Miller, “Interferometric Sensors for Spectral Imaging”, Sens. Act. A: Phys. 120, 110–114 (2005).
[CrossRef]

Thin Solid Films (1)

H. Stiebig, H.-J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n–i–p diodes of amorphous silicon,” Thin Solid Films 427(1-2), 152–156 (2003).
[CrossRef]

Other (6)

O. Kluth, and A. Löffl, S. Wieder, C. Beneking, L. Houben, B. Rech, H. Wagner, S. Waser, J.A. Selvan, H. Keppner, “Texture etched Al-doped ZnO: A new material for enhanced light trapping in thin film solar cells”, Proc. 26th IEEE PVSEC, pp. 715–718 (1997).

“Technology and Applications of Amorphous Silicon”, Springer Series in Material Science, 37. edited by R. A. Street, Berlin, Germany: Springer-Verlag, 2000.

W. Luft, and Y. Tuso, “Hydrogenated amorphous silicon alloy deposition processes”, Marcel Dekker, Inc., 1993.

J. Kauppinen, and J. Partanen, “Fourier Transforms in Spectroscopy”, Wiley-VCH, 2001.

Z. Knittl, “Optics of Thin Films”, New York: Wiley, 1976.

P. M. Zavracky, K. L. Denis, H. K. Xie, T. Wester, and P. Kelley, “A micromachined scanning Fabry–Pérot interferometer,” Proc. SPIE (3514), 179–187 (1998).

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Figures (8)

Fig. 1
Fig. 1

Schematic sketch of a) Michelson spectrometer and b) standing wave spectrometer.

Fig. 2
Fig. 2

Schematic setup of a standing wave spectrometer consisting of a partially transparent photodetector, represented by an absorbing layer, and a tunable mirror.

Fig. 3
Fig. 3

Absorption coefficient of amorphous silicon and crystalline silicon.

Fig. 4
Fig. 4

Instrument profile of the standing wave spectrometer for different scanning lengths.

Fig. 5
Fig. 5

Schematic setup of the real standing wave spectrometer.

Fig. 6
Fig. 6

(a) Normalized electric filed intensity and (b) power loss in the standing wave spectrometer.

Fig. 7
Fig. 7

The AC component of the photocurrent as a function of the mirror displacement (a) experiment and model of the ideal spectrometer, (b) experiment and model of the real spectrometer.

Fig. 8
Fig. 8

Instrument profile (a) for model of the ideal spectrometer, (b) for model of the real spectrometer and (c) experimentally obtained.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

E s = E 1 + E 2 ,
I = c ε 0 η 2 | E | 2 ,
I s = c ε 0 η 2 | E 1 | 2 + | E 2 | 2 + E 1 * E 2 + E 1 E 2 * ,
I s = I 1 + I 2 + 2 I 1 I 2 cos φ ,
φ = 2 k 0 x m + ϕ m ,
I s = 2 I 0 1 cos 2 k 0 x m = 4 I 0 sin 2 k 0 x m .
I s A C x m = 2 I 0 cos 2 k 0 x m .
| I s A C k | = π I 0 δ k k 0 .
E j x = E 0 exp ( i 2 π λ n j x ) + E 0 exp i φ exp ( i 2 π λ n j 2 d j x ) ,
I j x , x m = I 0 η j ( exp ( 4 π λ κ j x ) + exp ( 4 π λ κ j 2 d j x ) 2 exp ( 4 π λ κ j d j ) cos ( 4 π λ η j d j x + 4 π λ x m ) ) .
Q j x , x m = α j I j x , x m ,
I p h x m = A q λ h c 0 d j Q j x , x m d x ,
I p h x m = A q η j λ h c I 0 1 exp 2 α j d j + + α j λ η j π exp α j d j sin ( 2 π λ η j d j ) cos ( 2 π λ η j d j + 4 π λ x m ) ) .
I p h A C x m = 4 π A q α j h c k 0 2 I 0 exp α j d j sin k 0 η j d j cos ( 2 k 0 ( x m + η j d j 2 ) ) r e c t [ x m L s ] n = + δ x m n Δ x ,
| I p h A C k | = 2 π A q α j h c k 0 2 I 0 N exp α j d j | sin k 0 η j d j | | sin k k 0 L s | k k 0 L s ,
Δ k = π L S .
Δ λ = λ 2 2 L S .
E j x = E 0 t c exp ( i 2 π λ n j x ) + E 0 t c r c exp ( i 2 π λ n j 2 d j x ) .
I j x , x m = I 0 t 2 x m η j ( exp ( 4 π λ κ j x ) + r 2 x m exp ( 4 π λ κ j 2 d j x ) + 2 r x m exp ( 4 π λ κ j d j ) cos ( 4 π λ η j d j x θ x m ) ) ,
I p h x m = A q η j λ h c I 0 t 2 x m 1 exp α j d j 1 r 2 x m r 2 x m exp 2 α j d j α j λ η j π r x m exp α j d j sin ( 2 π λ η j d j ) cos ( 2 π λ η j d j θ x m ) ) .

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