Abstract

A three-dimensional model for beam propagation through optical interference filters is presented. The model predicts a wavelength-dependent lateral beam displacement of tens or hundreds of micrometers in narrowband filters at an angle of incidence of only 3° to 5°. The effects of filter bandwidth, wavelength offset, angle of incidence, and beam size are investigated. The effect is experimentally confirmed for a 100  GHz filter at a 3.5° angle of incidence.

© 2006 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Physik 1, 333-345 (1947).
    [CrossRef]
  2. M. McGuirk and C. K. Carniglia, "An angular spectrum representation approach to the Goos Hänchen shift," J. Opt. Soc. Am. 67, 103-107 (1977).
    [CrossRef]
  3. C. W. Hsue and T. Tamir, "Lateral displacement and distortion of beams incident upon a transmitting-layer configuration," J. Opt. Soc. Am. A 2, 978-988 (1985).
    [CrossRef]
  4. C. K. Carniglia, "Diffraction effects in interference filters," in OSA Annual Meeting Technical Digest (Optical Society of America, 1988), paper WS2.
  5. M. Gerken and D. A. B. Miller, "Multilayer thin-film structures with high spatial dispersion," Appl. Opt. 42, 1330-1345 (2003).
    [CrossRef] [PubMed]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  7. H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Physics Publishing, 2001).
    [CrossRef]
  8. J. J. Pan, F. Q. Zhou, and M. Zhou, "High-performance filters for dense wavelength-division-multiplex fiber optic communication," in Proceedings of the 41st Society of Vacuum Coaters Annual Conference (Society of Vacuum Coaters, 1998), pp. 217-219.
  9. C. A. Hulse, R. Klinger, and R. B. Sargent, "Optical coupler device for dense wavelength division multiplexing," U.S. patent 6,215,924 (10 April 2001).

2003

1985

1977

1947

F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Physik 1, 333-345 (1947).
[CrossRef]

Carniglia, C. K.

M. McGuirk and C. K. Carniglia, "An angular spectrum representation approach to the Goos Hänchen shift," J. Opt. Soc. Am. 67, 103-107 (1977).
[CrossRef]

C. K. Carniglia, "Diffraction effects in interference filters," in OSA Annual Meeting Technical Digest (Optical Society of America, 1988), paper WS2.

Gerken, M.

Goodman, J. W.

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

Goos, F.

F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Physik 1, 333-345 (1947).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Physik 1, 333-345 (1947).
[CrossRef]

Hsue, C. W.

Hulse, C. A.

C. A. Hulse, R. Klinger, and R. B. Sargent, "Optical coupler device for dense wavelength division multiplexing," U.S. patent 6,215,924 (10 April 2001).

Klinger, R.

C. A. Hulse, R. Klinger, and R. B. Sargent, "Optical coupler device for dense wavelength division multiplexing," U.S. patent 6,215,924 (10 April 2001).

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Physics Publishing, 2001).
[CrossRef]

McGuirk, M.

Miller, D. A. B.

Pan, J. J.

J. J. Pan, F. Q. Zhou, and M. Zhou, "High-performance filters for dense wavelength-division-multiplex fiber optic communication," in Proceedings of the 41st Society of Vacuum Coaters Annual Conference (Society of Vacuum Coaters, 1998), pp. 217-219.

Sargent, R. B.

C. A. Hulse, R. Klinger, and R. B. Sargent, "Optical coupler device for dense wavelength division multiplexing," U.S. patent 6,215,924 (10 April 2001).

Tamir, T.

Zhou, F. Q.

J. J. Pan, F. Q. Zhou, and M. Zhou, "High-performance filters for dense wavelength-division-multiplex fiber optic communication," in Proceedings of the 41st Society of Vacuum Coaters Annual Conference (Society of Vacuum Coaters, 1998), pp. 217-219.

Zhou, M.

J. J. Pan, F. Q. Zhou, and M. Zhou, "High-performance filters for dense wavelength-division-multiplex fiber optic communication," in Proceedings of the 41st Society of Vacuum Coaters Annual Conference (Society of Vacuum Coaters, 1998), pp. 217-219.

Ann. Physik

F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Physik 1, 333-345 (1947).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Other

C. K. Carniglia, "Diffraction effects in interference filters," in OSA Annual Meeting Technical Digest (Optical Society of America, 1988), paper WS2.

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

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Physics Publishing, 2001).
[CrossRef]

J. J. Pan, F. Q. Zhou, and M. Zhou, "High-performance filters for dense wavelength-division-multiplex fiber optic communication," in Proceedings of the 41st Society of Vacuum Coaters Annual Conference (Society of Vacuum Coaters, 1998), pp. 217-219.

C. A. Hulse, R. Klinger, and R. B. Sargent, "Optical coupler device for dense wavelength division multiplexing," U.S. patent 6,215,924 (10 April 2001).

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Figures (7)

Fig. 1
Fig. 1

Plane-wave transmission spectrum of a 200 GHz filter.

Fig. 2
Fig. 2

Results of beam model calculation of the output intensity profile for the 200 GHz filter at three angles and two beam sizes, as indicated. Each box is 1 mm square.

Fig. 3
Fig. 3

(Color online) Model predictions of transmission response and beam displacement of 0.15 and 0.75 mm beams as well as the CBL for the 200 GHz filter at a 5° angle of incidence.

Fig. 4
Fig. 4

Plane-wave transmission spectrum of a 100 GHz filter.

Fig. 5
Fig. 5

Results of beam model calculation of the output intensity profile for the 100 GHz filter at three angles and two beam sizes, as indicated. Note that the angles indicated are the equivalent air-matched angles; the filter was designed for use in an immersed medium. Each box is 1 mm square.

Fig. 6
Fig. 6

(Color online) Model predictions of the transmission response and beam displacement of 0.15 and 0.75 mm beams as well as the CBL for the 100 GHz filter at 5° air-equivalent angle of incidence.

Fig. 7
Fig. 7

(Color online) (a) Schematic diagram of the experimental system used to verify the model predictions. The filter sample is shown tilted to a small positive angle, and the direction of a positive beam shift is shown at the lower right. (b) Left, beam measurement at a 0° angle of incidence; right, beam measurement at a 3.5° angle of incidence, shifted ∼170 μm.

Equations (9)

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

A ( k x , k y ) = 1 2 π E ( x , y , 0 ) exp [ i ( k x x + k y y ) ] d x d y .
k | k | = ( k x 2 + k y 2 + k z 2 ) 1 / 2 = n ω c = 2 π n λ ,
E ( x , y , z , t ) = A ( k x , k y ) exp [ i ( ω t k x x k y y k z z ) ] d k x d k y ,    z 0.
E ( x , y , z , t ) = t ( k x , k y ) A ( k x , k y ) exp { i [ ω t k x x k y y k z ( z d ) ] } d k x d k y ,
z d .
φ ( k x ) = φ ( k x 0 ) + φ ( k x 0 ) ( k x k x 0 ) + .
E ( x , t ) = t ( k x 0 ) exp { i [ φ ( k x 0 ) k x 0 φ ( k x 0 ) ] } × A ( k x ) exp ( i { ω t k x [ x φ ( k x 0 ) ] } ) d k x
= t ( k x 0 ) exp ( j Φ 0 ) E [ x φ ( k x 0 ) , t ] .
Substrate   | ( H L ) 6 H   6 L H ( L H ) 6 L ( H L ) 7 H   4 L H ( L H ) 7 L ( H L ) 7 H   6 L H ( L H ) 7 L ( H L ) 6 H   8 L H ( L H ) 7 L | Air,

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