Abstract

The principles of microwave bandpass filter design are applied to design optical multilayer bandpass filters. The examples include several bandpass filters for wavelength division multiplexing.

© 2003 Optical Society of America

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References

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  1. A. J. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 56, 1533–1538 (1966).
    [CrossRef]
  2. G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.
  3. S. A. Schelkunoff, “The impedance concept and its application to problems of reflexion, refraction, shielding and power absorption,” Bell Syst. Tech. J. 17, 24 (1938).
    [CrossRef]
  4. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publishing, Bristol, UK, 2001), p. 60.
  5. Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), Chap. 9.
  6. A. Thelen, Design of Optical Interference Coatings (McGraw Hill, New York, 1989), p. 66.
  7. R. B. Muchmore, “Optimum bandwidth for two layer antireflection films,” J. Opt. Soc. Am. 38, 20–26 (1948).
    [CrossRef]
  8. P. Leurgans, “Impedance concept in thin film optics,” J. Opt. Soc. Am. 41, 714–717 (1951).
    [CrossRef]
  9. H. Dorgelo, C. Dosten, R. Kronig, F. Stieltjes, J. Brinkman, “Electrical, acoustic and optical impedance,” Ned. Tijdschr. Natuurkd. 14, 290 (1948).
  10. K. Altenburg, “Propagation of waves at normal incidence in a stratified medium and the application to circuit theory, electrical waves, optics, acoustics, wave mechanics, as well as mechanics and electrical four-pole networks,” Ann. Phys. (Leipzig) 13, 1 (1953).
    [CrossRef]
  11. M. Iwata, “On the interference filter,” Sci. Light (Tokyo) 2, 116–127 (1953).
  12. J. Seeley, “Synthesis of interference filters,” Proc. Phys. Soc. London 78, 998–1008 (1961).
    [CrossRef]
  13. L. Young, “Synthesis of multiple antireflection films over a prescribed frequency bandwidth,” J. Opt. Soc. Am. 51, 967–974 (1961).
    [CrossRef]
  14. T. Chen, “Optimized design of odd order optical lowpass and highpass multilayer filters by method of coefficient matching,” IEE Proc. J. 135, 166–177 (1988).
  15. Ref. 2, Fig. 9.07-1.
  16. P. Baumeister, “Design of a coarse WDM bandpass filter using the Thelen bandpass design method,” Opt. Express 9, 652–657 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  17. P. Baumeister, “Design of a wavelength-division multiplexing bandpass with quasi-Chebyshev spectral shape,” Appl. Opt. 40, 1132–1137 (2001).
    [CrossRef]
  18. Ref. 2, Eq. (6.09-4).
  19. Ref. 5, Section 3.2.3.
  20. Ref. 6, Section 3.1.
  21. J. Minowa, Y. Fujii, “High performance bandpass filter for WDM transmission,” Appl. Opt. 23, 193–194 (1984).
    [CrossRef]
  22. P. Baumeister, “Bandpass filters for wavelength division multiplexing—modification of the spectral bandwidth,” Appl. Opt. 37, 6609–6614 (1998).
    [CrossRef]
  23. Computer code TFCalc marketed by Software Spectra, 14025 N.W. Harvest Lane, Portland, Oreg. 97229.
  24. A. D. Noe, Software Spectra, 14025 N.W. Harvest Lane, Portland, Oreg. 97229 (personal communication, 2002).

2001 (2)

1998 (1)

1988 (1)

T. Chen, “Optimized design of odd order optical lowpass and highpass multilayer filters by method of coefficient matching,” IEE Proc. J. 135, 166–177 (1988).

1984 (1)

1966 (1)

1961 (2)

1953 (2)

K. Altenburg, “Propagation of waves at normal incidence in a stratified medium and the application to circuit theory, electrical waves, optics, acoustics, wave mechanics, as well as mechanics and electrical four-pole networks,” Ann. Phys. (Leipzig) 13, 1 (1953).
[CrossRef]

M. Iwata, “On the interference filter,” Sci. Light (Tokyo) 2, 116–127 (1953).

1951 (1)

1948 (2)

H. Dorgelo, C. Dosten, R. Kronig, F. Stieltjes, J. Brinkman, “Electrical, acoustic and optical impedance,” Ned. Tijdschr. Natuurkd. 14, 290 (1948).

R. B. Muchmore, “Optimum bandwidth for two layer antireflection films,” J. Opt. Soc. Am. 38, 20–26 (1948).
[CrossRef]

1938 (1)

S. A. Schelkunoff, “The impedance concept and its application to problems of reflexion, refraction, shielding and power absorption,” Bell Syst. Tech. J. 17, 24 (1938).
[CrossRef]

Altenburg, K.

K. Altenburg, “Propagation of waves at normal incidence in a stratified medium and the application to circuit theory, electrical waves, optics, acoustics, wave mechanics, as well as mechanics and electrical four-pole networks,” Ann. Phys. (Leipzig) 13, 1 (1953).
[CrossRef]

Baumeister, P.

Brinkman, J.

H. Dorgelo, C. Dosten, R. Kronig, F. Stieltjes, J. Brinkman, “Electrical, acoustic and optical impedance,” Ned. Tijdschr. Natuurkd. 14, 290 (1948).

Chen, T.

T. Chen, “Optimized design of odd order optical lowpass and highpass multilayer filters by method of coefficient matching,” IEE Proc. J. 135, 166–177 (1988).

Dorgelo, H.

H. Dorgelo, C. Dosten, R. Kronig, F. Stieltjes, J. Brinkman, “Electrical, acoustic and optical impedance,” Ned. Tijdschr. Natuurkd. 14, 290 (1948).

Dosten, C.

H. Dorgelo, C. Dosten, R. Kronig, F. Stieltjes, J. Brinkman, “Electrical, acoustic and optical impedance,” Ned. Tijdschr. Natuurkd. 14, 290 (1948).

Fujii, Y.

Iwata, M.

M. Iwata, “On the interference filter,” Sci. Light (Tokyo) 2, 116–127 (1953).

Jones, E. M. T.

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), Chap. 9.

Kronig, R.

H. Dorgelo, C. Dosten, R. Kronig, F. Stieltjes, J. Brinkman, “Electrical, acoustic and optical impedance,” Ned. Tijdschr. Natuurkd. 14, 290 (1948).

Leurgans, P.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publishing, Bristol, UK, 2001), p. 60.

Matthaei, G.

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

Minowa, J.

Muchmore, R. B.

Noe, A. D.

A. D. Noe, Software Spectra, 14025 N.W. Harvest Lane, Portland, Oreg. 97229 (personal communication, 2002).

Schelkunoff, S. A.

S. A. Schelkunoff, “The impedance concept and its application to problems of reflexion, refraction, shielding and power absorption,” Bell Syst. Tech. J. 17, 24 (1938).
[CrossRef]

Seeley, J.

J. Seeley, “Synthesis of interference filters,” Proc. Phys. Soc. London 78, 998–1008 (1961).
[CrossRef]

Stieltjes, F.

H. Dorgelo, C. Dosten, R. Kronig, F. Stieltjes, J. Brinkman, “Electrical, acoustic and optical impedance,” Ned. Tijdschr. Natuurkd. 14, 290 (1948).

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw Hill, New York, 1989), p. 66.

Thelen, A. J.

Young, L.

L. Young, “Synthesis of multiple antireflection films over a prescribed frequency bandwidth,” J. Opt. Soc. Am. 51, 967–974 (1961).
[CrossRef]

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

Ann. Phys. (Leipzig) (1)

K. Altenburg, “Propagation of waves at normal incidence in a stratified medium and the application to circuit theory, electrical waves, optics, acoustics, wave mechanics, as well as mechanics and electrical four-pole networks,” Ann. Phys. (Leipzig) 13, 1 (1953).
[CrossRef]

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

S. A. Schelkunoff, “The impedance concept and its application to problems of reflexion, refraction, shielding and power absorption,” Bell Syst. Tech. J. 17, 24 (1938).
[CrossRef]

IEE Proc. J. (1)

T. Chen, “Optimized design of odd order optical lowpass and highpass multilayer filters by method of coefficient matching,” IEE Proc. J. 135, 166–177 (1988).

J. Opt. Soc. Am. (4)

Ned. Tijdschr. Natuurkd. (1)

H. Dorgelo, C. Dosten, R. Kronig, F. Stieltjes, J. Brinkman, “Electrical, acoustic and optical impedance,” Ned. Tijdschr. Natuurkd. 14, 290 (1948).

Opt. Express (1)

Proc. Phys. Soc. London (1)

J. Seeley, “Synthesis of interference filters,” Proc. Phys. Soc. London 78, 998–1008 (1961).
[CrossRef]

Sci. Light (Tokyo) (1)

M. Iwata, “On the interference filter,” Sci. Light (Tokyo) 2, 116–127 (1953).

Other (10)

Ref. 2, Eq. (6.09-4).

Ref. 5, Section 3.2.3.

Ref. 6, Section 3.1.

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics Publishing, Bristol, UK, 2001), p. 60.

Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), Chap. 9.

A. Thelen, Design of Optical Interference Coatings (McGraw Hill, New York, 1989), p. 66.

Ref. 2, Fig. 9.07-1.

Computer code TFCalc marketed by Software Spectra, 14025 N.W. Harvest Lane, Portland, Oreg. 97229.

A. D. Noe, Software Spectra, 14025 N.W. Harvest Lane, Portland, Oreg. 97229 (personal communication, 2002).

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Figures (13)

Fig. 1
Fig. 1

Wavelength versus transmittance of the bandpass whose design is cement 0.222L 0.519H 0.222L L H 2L H L H 0.167H 0.632L 0.167H H L H 2L H L H L 0.270L 0.425H 0.270L L H L H 2L H L H L 0.213L 0.538H 0.213L L H L H 2L H L H L 0.270L 0.425H 0.270L L H L H 2L H L H 0.167H 0.632L 0.167H H L H 2L H L 0.222L 0.519H 0.222L glass, where the refractive indices of cement, glass, L, and H are 1.52, 1.52, 1.38, and 2.25, respectively. H and L represent layers of optical thickness λ0/4 at λ0 of 633 nm. The scale of the ordinate changes from linear to log at 0.9. The scale of the abscissa changes at 620 and 650 nm.

Fig. 2
Fig. 2

Optical thickness (in waves) versus refractive indices of the layers in a six-cavity prototype bandpass that is the basis for the bandpass in Fig. 1. The standing-wave ratio at each interface is shown.

Fig. 3
Fig. 3

Top, construction of a six-cavity bandpass in which reflectors (symbol R) are interdispersed between spacer layers (symbol S). Bottom, reflector 5 is extracted from the stack and thus isolated.

Fig. 4
Fig. 4

Microwave bandpass filter that consists of iris diaphragm reflectors interdispersed between cavity spacers.

Fig. 5
Fig. 5

In the optical bandpass simulation of the microwave bandpass, each iris diaphragm reflector is replaced with a quarter-wave stack consisting of high-index layers H, low-index layers L, and equivalent layers E.

Fig. 6
Fig. 6

Radiant reflectance (in units of standing-wave ratio SWR) versus relative frequency of the multilayer bandpass in Fig. 1 (solid curve) and the measured data of a microwave bandpass (dashed curve) from Fig. 9.07-2 of Ref. 2.

Fig. 7
Fig. 7

Transmittance (in decibels) versus wavelength of a 13-cavity bandpass of the design air 0.241L 2.499H 1.241L H (L H)3 2L (H L)5 1.3257H 0.3329L 1.3257H (L H)5 2L (H L)5 H 1.2077L 0.5671H 1.2077L H (L H)5 2L (H L)6 1.4654H 0.0654L 1.4654H (L H)6 2L (H L)6 1.4251H 0.1419L 1.4251H (L H)6 2L (H L)6 1.4072H 0.1759L 1.4072H (L H)6 2L (H L)6 1.4001H 0.1894L 1.4001H (L H)6 2L (H L)6 1.4001H 0.1894L 1.4001H (L H)6 2L (H L)6 1.4072H 0.1759L 1.4072H (L H)6 2L (H L)6 1.4251H 0.1419L 1.4251H (L H)6 2L (H L)6 1.4654H 0.0654L 1.4654H (L H)6 2L (H L)5 H 1.2077L 0.5671H 1.2077L H (L H)5 2L (H L)5 1.3257H 0.3329L 1.3257H (L H)5 2L (H L)4 H 2.628L 1.818H glass, where glass, L, and H represent materials of refractive indices 1.50, 1.47, and 2.065, respectively. The optical thickness of layers L and H is λ0/4 at λ0 of 1550 nm. The ordinate changes scale at -0.04 dB.

Fig. 8
Fig. 8

Transmittance (in decibels) versus wavelength of a bandpass containing 13 first-order spacers of the design air 0.244L 0.493H 1.244L H L H L H L H 2L H L H L H L H L M L M L H L H L H L H L H 2L H L H L H L H L M L M L M L M L H L H L H L H 2L H L H L H L M L M L M L M L M L H L H L H L H 2L H L H L H L H L H L H L M L H L H L H L H L H L H 2L H L H L H L M L M L M L M L M L M L H L H L H 2L H L H L H L M L M L M L M L M L M L H L H L H 2L H L H L H L M L M L M L M L M L M L H L H L H 2L H L H L H L M L M L M L M L M L M L H L H L H 2L H L H L H L H L H L H L M L H L H L H L H L H L H 2L H L H L H L H L M L M L M L M L M L H L H L H 2L H L H L H L H L M L M L M L M L H L H L H L H 2L H L H L H L H L H L M L M L H L H L H L H 2L H L H L M L H L H L glass, where glass, L, H, and M represent materials of refractive indices 1.50, 1.47, 2.065, and 2.23, respectively. The optical thickness of layers L, H, and M is λ0/4 at λ0 of 1550 nm. The ordinate changes scale at -0.1 dB.

Fig. 9
Fig. 9

For the solid curve, transmittance (in decibels) versus wavelength of a bandpass of the design glass E H L H L H L M 4L H L H L H L M L M L H L H L H L H 12L H L H L H L M L M L M L H L H L H L H 6L H L H L H L H L H L H L H L H L H L H L H 12L H L H L H L H L H L M L H L H L H L H L H 6L H L H L H L H L H L M L H L H L H L H L H 12L H L H L H L H L H L M L H L H L H L H L H 6L H L H L H L H L H L M L H L H L H L H L H 12L H L H L H L H L H L M L H L H L H L H L H 6L H L H L H L H L H L M L H L H L H L H L H 12L H L H L H L H L H L H L H L H L H L H L H 6L H L H L H L H L M L M L M L H L H L H 12L H L H L H L H L M L M L H L H L H 4L M L H L H L H E glass, where glass, L, H, M, and E represent materials of refractive indices 1.50, 1.47, 2.065, 2.23, and 1.375, respectively. The optical thickness of layers L, H, M, and E is λ0/4 at λ0 of 1550 nm. A detailed plot of the dashed curve appears in Fig. 10.

Fig. 10
Fig. 10

Transmittance (in decibels) versus wavelength of a bandpass of the design air 0.531L 1.723H H L H L H L M 4L 3H 3L H L H L M L M L H L H L H L H 12L H L H L H L M L M L M L H L H L H L H 6L H L H 3L H 3L H L 3H L H L H L H 3L H L H L H 12L H L H L H L H L H L M L H L 3H L H L H L H 6L H L H L H L H L H L M L H L H 3L 3H L H L H 12L H L H L H L H L H L M L H 3L H L H L H L H 6L H L H L H L H 3L H L M L H L H L H L H L H 12L H L H L 3H 3L H L H L M L H L H L H L H L H 6L H L H L H L 3H L H L M L H L H L H L H L H 12L H L H L H 3L H L H L H L 3H L H 3L H 3L H L H 6L H L H L H L H L M L M L M L H L H L H 12L H L H L H L H L M L M L H L H 3L 3H 4L M L H L H L H 0.618L 1.854H glass, where glass, L, H, and M represent materials of refractive indices 1.50, 1.47, 2.065, and 2.23, respectively. The optical thickness of layers L, H, and M is λ0/4 at λ0 of 1550 nm. The ordinate changes scale at -0.04 dB.

Fig. 11
Fig. 11

Transmittance (in decibels) versus wavelength of a bandpass of the design air 1.883L 1.059H L H L H L 3H 2L 3H L H L H L H L H L H L H L H L H L H 6L H L H L H L H L H L H L H L 3H L H L H L H 8L H L H L H L H L H L H L H L H L 3H L H L H L H 2L H L H L H L H L H L H L H L H 3L H L H L H L H 10L H L H L H L H L H L H L H L H L 3H 3L H L H L H 2L H L H L H L H L H 3L H L H L H 3L H L H L H L H 10L H L H L H L H 3L H L H L H 3L H L H L H L H L H 2L H L H L H 3L 3H L H L H L H L H L H L H L H L H 10L H L H L H L H 3L H L H L H L H L H L H L H L H 2L H L H L H L 3H L H L H L H L H L H L H L H L H 8L H L H L H L 3H L H L H L H L H L H L H L H 6L H L H L H L H L H L H L H L H L H L 3H 2L 3H L H L H L H 2.711L 1.622H glass, where glass, L, and H represent materials of refractive indices 1.50, 1.47, and 2.065, respectively. The optical thickness of layers L and H is λ0/4 at λ0 of 1550 nm. The ordinate changes scale at -0.04 dB.

Fig. 12
Fig. 12

The caption in Fig. 11 obtains with the exception that the design is air 1.501L 0.259H H L H L H L H 6L H L H L H L H L H L H L H 5L H L H L H 4L H L H L H L H L H L H L 5H L H L H L H L H 10L H L H L H L H L H L H L H L H L H L H L H 8L H L H L H L H L H L H L 3H L H L H L H L H 10L H L H 5L H L H L 5H 7L 5H 9L H L H L H L H L H 8L H L H L H L H L H L H L H L H L H L H L H 12L H L H L H L H L H L H L H L H L H L H L H 8L H L H L H L H L H 9L 5H 7L 5H L H L H 5L H L H 10L H L H L H L H L 3H L H L H L H L H L H L H 8L H L H L H L H L H L H L H L H L H L H L H 10L H L H L H L H L 5H L H L H L H L H L H L H 4L H L H L H 5L H L H L H L H L H L H L H 6L H L H L H L H 0.625L 1.828H glass.

Fig. 13
Fig. 13

Same as Fig. 11 except that the design is air 0.722L 0.605H L H L H L H L 3H 2L H L H 3L H L H L H L 3H L H L H L H L 3H L H 2L H L H L H L H 3L H L H 3L H L H L H L H 3L H L 3H 2L 3H L H L H L H 3L H L H 3L H L H L H 3L H L H L 3H 2L H 3L H L H L H L H 3L H 3L H L H L H L H L H 3L 3H 2L 3H L H 3L H L H L H L H 3L H L H L H 3L H L H L 3H 2L 3H L H L H L H L H L H 3L H L H 3L H L H L 3H L 3H 2L 3H L 3H L H L H 3L H L H 3L H L H L H L H L H L 3H 2L 3H L H L H 3L H L H L H 3L H L H L H L H 3L H L 3H 2L 3H 3L H L H L H L H L H 3L H 3L H L H L H L H 3L H 2L 3H L H L H 3L H L H L H 3L H L H 3L H L H L H L 3H 2L 3H L H 3L H L H L H L H 3L H L H 3L H L H L H L H 2L H L 3H L H L H L H L 3H L H L H L H 3L H L H 2L 3H L H L H L H L 1.964L 1.079H glass.

Tables (4)

Tables Icon

Table 1 Standing-Wave Ratios of the Reflectors of the Six-Cavity Bandpass of Fig. 1

Tables Icon

Table 2 Standing-Wave Ratios of the Reflectors of the 13-Cavity Bandpass in Fig. 7

Tables Icon

Table 3 Optical Properties of Bandpass Filters

Tables Icon

Table 4 Standing-Wave Ratios of the Reflectors of the Bandpass in Fig. 8

Equations (4)

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

Vi=1+Ri1/21-Ri1/2-1.
V0=Vq, V1=Vq-1, V2=Vq-2, V3=Vq-3,
V0=V6, V1=V5, V2=V4,
V6=nH2nL-3nE2ns-1=2.2521.38-31.98221.52-1=4.98,

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