Abstract

We present an analytical solution to the problem of finding a diffractive surface relief that generates a specific optical amplitude and phase spectral reflection in a particular direction. We show that any discrete finite impulse response filter can be generated to within a multiplicative constant at nonzero frequencies. We propose an implementation of such a filter that works in the visible and the near infrared, based on a two-dimensional array of dual-state tiltable mirrors. A 1024×1024 array results in a 1024-tap filter with 10-bit quantization of the impulse response. The applications of such a device include spectroscopy and wavelength-division multiplex switching.

© 2003 Optical Society of America

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Corrections

Ruslan Belikov and Olav Solgaard, "Optical wavelength filtering by diffraction from a surface relief: erratum," Opt. Lett. 28, 1055-1055 (2003)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-28-12-1055

References

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  1. M. B. Sinclair, M. A. Butler, A. J. Ricco, and S. D. Senturia, Appl. Opt. 36, 3342 (1997).
    [CrossRef] [PubMed]
  2. G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.
  3. M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.
  4. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 4.

1997 (1)

Butler, M.

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Butler, M. A.

M. B. Sinclair, M. A. Butler, A. J. Ricco, and S. D. Senturia, Appl. Opt. 36, 3342 (1997).
[CrossRef] [PubMed]

M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.

Deutsch, E.

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Deutsch, E. R.

M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 4.

Hocker, G. B.

M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Plowman, T.

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Ricco, A. J.

M. B. Sinclair, M. A. Butler, A. J. Ricco, and S. D. Senturia, Appl. Opt. 36, 3342 (1997).
[CrossRef] [PubMed]

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Senturia, S.

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Senturia, S. D.

M. B. Sinclair, M. A. Butler, A. J. Ricco, and S. D. Senturia, Appl. Opt. 36, 3342 (1997).
[CrossRef] [PubMed]

M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.

Sinclair, M.

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Sinclair, M. B.

M. B. Sinclair, M. A. Butler, A. J. Ricco, and S. D. Senturia, Appl. Opt. 36, 3342 (1997).
[CrossRef] [PubMed]

M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.

Sweatt, W. C.

M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.

Volpicelli, A.

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Youngner, D.

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

Youngner, D. W.

M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.

Appl. Opt. (1)

Other (3)

G. B. Hocker, D. Youngner, M. Butler, M. Sinclair, T. Plowman, E. Deutsch, A. Volpicelli, S. Senturia, and A. J. Ricco, presented at the Solid State Sensor and Actuator Workshop, Hilton Head Island, S.C., June 4–8, 2000.

M. A. Butler, E. R. Deutsch, S. D. Senturia, M. B. Sinclair, W. C. Sweatt, D. W. Youngner, and G. B. Hocker, presented at the International Electron Devices Meeting, Washington, D.C., December 2–5, 2001.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 4.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of optical filtering by use of a diffractive surface.

Fig. 2
Fig. 2

Simulation of a synthesized spectrum of 10 randomly placed peaks with random amplitudes. N=1024. The total energy of the filter is 0.11, consistent with expression (11) in text. Inset, the relative mirror area at each distance h.

Fig. 3
Fig. 3

Illustration of an optical filter setup with a DMD array.

Equations (11)

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TΩ,δΩk=Ik,ΩδΩPk=AΩk2δΩΔΩk,ΔφΩk=AΩk,
AΩk=1SSexp-j2khrexp-jkΩ·rdr.
TΩk=AΩk2k2/kmax2.
Ak=A0k=1SSexp-j2khrdr,
Ak=-Δh/2Δh/2shexp-j2khdh,
hx,y=f-1x,    fh=-hshdh.
Δk=πδh    or Δλλλ2δh,δk=πΔh    or δλλλ2Δh.
n=0N-1snRsn=1sn0AN=AN-N,AN=AN-N,AN1.
sn=sˆn-sminC,
An=AˆnCn01n=0,
CM lnN/5,

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