Abstract

Multiple half-wave filters can be detuned to provide a nonpolarizing edge at a specific angle of incidence. For the case of quarter-wave layers, an analytic expression for the necessary amount of detuning can be derived. For non-quarter-wave layers, a more empirical design approach is used. The resulting two-material producible designs improve current limitations in wavelength-division multiplex transmission over multimode optical fibers.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
    [Crossref]
  2. H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, London, 1969).
  3. K. Rabinovitch and A. Pagis, “Polarization effects in multilayer dielectric thin films,” Opt. Acta 21, 963–980 (1974).
    [Crossref]
  4. Z. Knittl, Optics of Thin Films (Wiley, London, 1976).
  5. I. M. Minkov, “Theory of dielectric mirrors in obliquely incident light,” Opt. Spektrosk. 33, 332–338 (1972).
  6. A. Thelen, “Nonpolarizing interference films inside a glass cube,” Appl. Opt. 15, 2983–2985 (1976).
    [Crossref] [PubMed]
  7. A. Thelen, “Avoidance or enhancement of polarization in multilayers,” J. Opt. Soc. Am. 70, 118–121 (1980).
    [Crossref]
  8. K. Nosu, H. Ishio, and K. Hashimoto, “Multireflection optical multi/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
    [Crossref]
  9. H. F. Mahlein, “Designing of edge interference filters for wavelength-division multiplex transmission over multimode optical fibers,” Siemens Forsch. Entwicklungsber. 9, 142–150 (1980).
  10. P. Baumeister, “Design of multilayer filters by successive approximations,” J. Opt. Soc. Am. 48, 955–958 (1958).
    [Crossref]
  11. L. I. Epstein, “The design of optical filters,” J. Opt. Soc. Am. 42, 806–810 (1952).
    [Crossref]
  12. A. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 56, 1533–1538 (1966).
    [Crossref]
  13. J. S. Seeley, “Resolving power of multilayer filters,” J. Opt. Soc. Am. 54, 342–346 (1964).
    [Crossref]

1980 (2)

H. F. Mahlein, “Designing of edge interference filters for wavelength-division multiplex transmission over multimode optical fibers,” Siemens Forsch. Entwicklungsber. 9, 142–150 (1980).

A. Thelen, “Avoidance or enhancement of polarization in multilayers,” J. Opt. Soc. Am. 70, 118–121 (1980).
[Crossref]

1979 (1)

K. Nosu, H. Ishio, and K. Hashimoto, “Multireflection optical multi/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[Crossref]

1976 (1)

1974 (1)

K. Rabinovitch and A. Pagis, “Polarization effects in multilayer dielectric thin films,” Opt. Acta 21, 963–980 (1974).
[Crossref]

1972 (1)

I. M. Minkov, “Theory of dielectric mirrors in obliquely incident light,” Opt. Spektrosk. 33, 332–338 (1972).

1966 (1)

1964 (1)

1961 (1)

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
[Crossref]

1958 (1)

1952 (1)

Baumeister, P.

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
[Crossref]

P. Baumeister, “Design of multilayer filters by successive approximations,” J. Opt. Soc. Am. 48, 955–958 (1958).
[Crossref]

Epstein, L. I.

Hashimoto, K.

K. Nosu, H. Ishio, and K. Hashimoto, “Multireflection optical multi/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[Crossref]

Ishio, H.

K. Nosu, H. Ishio, and K. Hashimoto, “Multireflection optical multi/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[Crossref]

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, London, 1976).

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, London, 1969).

Mahlein, H. F.

H. F. Mahlein, “Designing of edge interference filters for wavelength-division multiplex transmission over multimode optical fibers,” Siemens Forsch. Entwicklungsber. 9, 142–150 (1980).

Minkov, I. M.

I. M. Minkov, “Theory of dielectric mirrors in obliquely incident light,” Opt. Spektrosk. 33, 332–338 (1972).

Nosu, K.

K. Nosu, H. Ishio, and K. Hashimoto, “Multireflection optical multi/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[Crossref]

Pagis, A.

K. Rabinovitch and A. Pagis, “Polarization effects in multilayer dielectric thin films,” Opt. Acta 21, 963–980 (1974).
[Crossref]

Rabinovitch, K.

K. Rabinovitch and A. Pagis, “Polarization effects in multilayer dielectric thin films,” Opt. Acta 21, 963–980 (1974).
[Crossref]

Seeley, J. S.

Thelen, A.

Appl. Opt. (1)

Electron. Lett. (1)

K. Nosu, H. Ishio, and K. Hashimoto, “Multireflection optical multi/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[Crossref]

J. Opt. Soc. Am. (5)

Opt. Acta (2)

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
[Crossref]

K. Rabinovitch and A. Pagis, “Polarization effects in multilayer dielectric thin films,” Opt. Acta 21, 963–980 (1974).
[Crossref]

Opt. Spektrosk. (1)

I. M. Minkov, “Theory of dielectric mirrors in obliquely incident light,” Opt. Spektrosk. 33, 332–338 (1972).

Siemens Forsch. Entwicklungsber. (1)

H. F. Mahlein, “Designing of edge interference filters for wavelength-division multiplex transmission over multimode optical fibers,” Siemens Forsch. Entwicklungsber. 9, 142–150 (1980).

Other (2)

Z. Knittl, Optics of Thin Films (Wiley, London, 1976).

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, London, 1969).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

Reflectance of the single-spacer all-dielectric narrow-bandpass filter 1.0 | HLHLHLHLLHLHLHLH | 1.52 with nH = 2.28, nL = 1.45, and 45° light incidence in both planes of polarization. λ0 is the wavelength in which the H and L layers are one-quarter-wave thick.

Fig. 2
Fig. 2

Construction of a single-spacer narrow-bandpass filter and the formulas governing its performance. T is the transmittance, R is the reflectance, and Φ is the phase on reflection.

Fig. 3
Fig. 3

Difference between the phases on reflection in the two planes of polarization for the configuration 1.45 | HLHLHLH | 1.52 with nH = 2.28, nL = 1.45, and 45° light incidence.

Fig. 4
Fig. 4

Reflectance of the design shown in Fig. 1 with a detuned cavity. The design is now 1.0 | HLHLHLH 1.8L HLHLHLH | 1.52 with nH = 2.28, nL = 1.45, and 45° light incidence.

Fig. 5
Fig. 5

Schematic of the reflectances in the two planes of polarization for a multiple half-wave filter with detuned half waves. λC and λC|| are the centers of the pass bands and λe and λe|| the edges.

Fig. 6
Fig. 6

Reflectances in the two planes of polarization of the low-wave-number pass filter 1.0 | H 0.8L(0.8L HLHLHLH 0.8L)40.8L HLH | 1.52 with nH = 2.28, nL = 1.45, and 45° light incidence. The design went through an extensive refining procedure.10 The deviations from the configuration given above are listed in Table 1.

Fig. 7
Fig. 7

Average reflectance 1/2(R + R||) of the design given in Fig. 6.

Fig. 8
Fig. 8

Reflectances in the two planes of polarization of the high-wave-number pass filter 1.0 | H 1.2L(1.2L HLHLHLH 1.2L)41.2L HLH | 1.52 with nH = 2.28, nL = 1.45, and 45° light incidence. The design went also through an extensive refining procedure.10 The deviations from the configuration given above are listed in Table 1.

Fig. 9
Fig. 9

Average reflectance 1/2(R + R||) of the design given in Fig. 8.

Fig. 10
Fig. 10

Reflectances in the two planes of polarization of the low-wave-number pass design 1.52 | HLH 0.8L(0.8L HLHLHLH 0.8L)40.8L HLH | 1.52 with nH = 2.28, nL = 1.45, and 45° light incidence. No refining was done.

Fig. 11
Fig. 11

Average reflectance 1/2(R + R||) of the design given in Fig. 10.

Fig. 12
Fig. 12

Reflectances in the two planes of polarization of the high-wave-number pass design 1.52 | HLH 1.25L(1.25L HLHLHLH 1.25L)41.25L HLH | 1.52 with nH = 2.28, nL = 1.45, and 45° light incidence. No refining was done.

Fig. 13
Fig. 13

Average reflectance 1/2(R + R||) of the design given in Fig. 12.

Fig. 14
Fig. 14

Reflectances in the two planes of polarization of the non-quarter-wave high-wave-number pass design 1.0 | H 1.02Z Z4 1.02Z HLH | 1.52 with Z = 1.3H 0.6L 1.2H 0.6L 1.2H 0.6L 1.3H, nH = 2.28, nL = 1.45, and 45° light incidence. No refining was done.

Fig. 15
Fig. 15

Average reflectance 1/2(R + R||) of the design of Fig. 14.

Fig. 16
Fig. 16

Transmittance in the parallel plane of polarization of an actual filter based on the design of Fig. 14 with TiO2 as high-index material and SiO2 as low-index material. The back side of the substrate was not antireflection coated and the resulting reflection loss was not eliminated.

Fig. 17
Fig. 17

Transmittance in the perpendicular plane of polarization of the filter described in Fig 16.

Fig. 18
Fig. 18

Average transmittance 1/2(T|| + T) of the filter described in Fig. 16.

Tables (1)

Tables Icon

Table 1 Deviations in Percentages from the Starting Optical Thicknesses of the Designs in Fig. 8 (High-Wave-Number Pass) and Fig. 10 (Low-Wave-Number Pass)

Equations (18)

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

Medium matching layers spacer layer reflecting stack spacer layer ................ ............ ................ ............ ................ ............ reflecting stack spacer layer matching layers             substrate .
medium matching layers ( half spacer reflecting stack half spacer ) ν matching layers substrate .
ρ s B A B A A B A ρ s B ,
( M 11 j M 12 j M 21 M 22 ) = ( cos α j sin α n B j n B sin α cos α ) × ( C 11 j C 12 j C 21 C 22 ) × ( cos α j sin α n B j n B sin α cos α ) ,
C 11 = ( - 1 ) ( x - 1 ) 1 / 2 sin η [ ( n A / n B ) ( x - 1 ) + ( n A / n B ) ( x - 2 ) + + ( n A / n B ) ( 1 - x ) ] , C 12 = ( - 1 ) ( x - 1 ) / [ ( n A / n B ) x n B ] , C 21 = ( - 1 ) ( x - 1 ) ( n A / n B ) x n B , C 22 = C 11 ,
± 1 = D sin η cos 2 α - E sin 2 α , ± 1 = D sin η cos 2 α - E sin 2 α ,
D = 1 / 2 ( - 1 ) ( x - 1 ) [ ( n A / n B ) ( x - 1 ) + ( n A / n B ) ( x - 2 ) + + ( n A / n B ) ( 1 - x ) ] , E = 1 / 2 ( - 1 ) ( x - 1 ) [ ( n A / n B ) x + ( n B / n A ) x ] .
n A = n A / cos ψ A ,             n B = n B / cos ψ B ,
n A = n A cos ψ A ,             n B = n B cos ψ B ,
n medium sin ψ medium = n A sin ψ A = n B sin ψ B ,
sin 2 α = ± D - D D E - D E
sin η = ± 1 + E sin 2 α D cos 2 α ,
ρ s = λ s / λ 0 = 2 α / η .
ρ s = 1.14 and 0.86
ρ s = 1.20 and 0.80.
( half spacer - reflecting stack - half spacer ) = ( 1.2 H 0.6 L 1.2 H ) or ( 1.2 L 0.6 H 1.2 L ) .
Z = 1.2 H 0.6 L 1.2 H 0.6 L 1.2 H 0.6 L 1.2 H ,
Z = 1.3 H 0.6 L 1.2 H 0.6 L 1.2 H 0.6 L 1.3 H .