Abstract

Several applications of optical tunneling (frustrated total reflection) are briefly discussed. There are several classes of optical bandpass filters which use optical tunneling: the Fabry-Perot filter (alias the FTR filter), the single tunnel layer filter, and the multiple tunnel layer filter. The properties of these filters are examined. The multiple tunnel layer filter shows promise as an ir long-wave pass filter.

© 1967 Optical Society of America

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References

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  1. Paul Drude, The Theory of Optics (reprinted by Dover, New York, 1959), p. 299.
  2. G. Laski, in Handbuch der Physik, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1928), Vol. 19, p. 815.
  3. M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959), 1st ed., p. 65.
  4. D. Bohm, Quantum Theory (Prentice-Hall, New York, 1951), p. 240.
  5. L. I. Schiff, Am. J. Phys. 25, 207A (1957).
  6. Reference 3, p. 54.
  7. L. I. Epstein, J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]
  8. P. Kard, Opt. i Spektroskopiya 6, 389 (1959); Opt. Spectry 6, 244 (1959).
  9. Reference 3, p. 59.
  10. E. E. Hall, Phys. Rev. 15, 99 (1902).
  11. R. W. Astheimer, G. Falbel, S. Minkowitz, Appl. Opt. 5, 87 (1966).
    [CrossRef] [PubMed]
  12. Reference 3, p. 616.
  13. Reference 3, p. 33.
  14. D. Gabor, U. S. Patent2,281,280 (1942).
  15. I. N. Court, F. K. von Willisen, Appl. Opt. 3, 719 (1964).
    [CrossRef]
  16. E. Land, U. S. Patent2,106,752 (1934).
  17. A. F. Turner, R. B. Horsfall, U.S. Patent2,422, 376 (1947).
  18. L. Bergstein, C. Shulman, Proc. Inst. Radio Engrs. 50, 1833 (1962).
  19. E. L. Steele, W. C. Davis, R. L. Treuthart, Appl. Opt. 5, 5 (1966).
    [CrossRef] [PubMed]
  20. A. F. Turner, P. J. Leurgans, J. Opt. Soc. Am. 37, 983A (1957).
  21. A. F. Turner, U. S. Patent2,601,806 (1952).
  22. A. F. Turner, J. Phys. Radium 11, 458 (1950).
    [CrossRef]
  23. L. N. Hadley, D. M. Dennison, J. Opt. Soc. Am. 37, 462 (1947).
    [CrossRef]
  24. Reference 21, column 5, line 31.
  25. A. Gee, H. D. Polster, J. Opt. Soc. Am. 39, 1044 (1949).
    [CrossRef]
  26. A. E. Gee, Thesis, Institute of Optics, University of Rochester, Rochester, New York, 1949.
  27. L. V. Iogansen, Opt. i Spektroskopiya 11, 542 (1961);Opt. Spectry. 11, 292 (1961).
  28. L. Bergstein, C. Shulman, Appl. Opt. 5, 20 (1966).
    [CrossRef]
  29. N. J. Harrick, Appl. Opt. 5, 1 (1966). See the bibliography for references to earlier papers.
    [CrossRef] [PubMed]
  30. W. N. Hansen, Spectrochim. Acta 21, 209 (1965). See the references to earlier papers.
    [CrossRef]
  31. B. H. Billings, J. Opt. Soc. Am. 40, 471 (1950).
    [CrossRef]
  32. P. G. Kard, Izv. Akad. Nauk. Est. SSR, Ser. Tekh. i Fiz.-Mat. Nauk 6, 344 (1957).
  33. G. R. Noyes, P. W. Baumeister, Appl. Opt. 6,(1957).
  34. P. H. Berning, A. F. Turner, J. Opt. Soc. Am. 47, 230 (1957).
    [CrossRef]
  35. P. W. Baumeister, V. R. Costich, S. C. Pieper, Appl. Opt. 4, 911 (1965).
    [CrossRef]
  36. S. M. MacNeille, U. S. Patent2,403,731 (1946).
  37. W. Wettling, L. Genzel, Infrared Phys. 4, 253 (1964).
    [CrossRef]
  38. R. Pohl, Optik und Atomphysik(Springer, Berlin, 1963), 11th ed., p. 148.
  39. J. S. Seeley, S. D. Smith, Appl. Opt. 5, 81 (1966).
    [CrossRef] [PubMed]
  40. P. J. Leurgans, J. Opt. Soc. Am. 41, 714 (1951).
    [CrossRef]
  41. G. L. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 9.
  42. Reference 41, Sec. 9.03.
  43. P. W. Baumeister, J. Opt. Soc. Am. 48, 955 (1958).
    [CrossRef]
  44. Frederick Seitz, The Modern Theory of Solids (McGraw-Hill, New York, 1940), p. 281.
  45. Reference 41, p. 531.
  46. Reference 41, Chap. 6.
  47. N. J. Harrick, Appl. Opt. 2, 1203 (1963).
    [CrossRef]
  48. C. C. Aleksoff, N. J. Harrick, Proc. IEEE 53, 1636 (1965).
    [CrossRef]
  49. ASTM publication designation E131-66T (1966).

1966

1965

C. C. Aleksoff, N. J. Harrick, Proc. IEEE 53, 1636 (1965).
[CrossRef]

P. W. Baumeister, V. R. Costich, S. C. Pieper, Appl. Opt. 4, 911 (1965).
[CrossRef]

W. N. Hansen, Spectrochim. Acta 21, 209 (1965). See the references to earlier papers.
[CrossRef]

1964

I. N. Court, F. K. von Willisen, Appl. Opt. 3, 719 (1964).
[CrossRef]

W. Wettling, L. Genzel, Infrared Phys. 4, 253 (1964).
[CrossRef]

1963

1962

L. Bergstein, C. Shulman, Proc. Inst. Radio Engrs. 50, 1833 (1962).

1961

L. V. Iogansen, Opt. i Spektroskopiya 11, 542 (1961);Opt. Spectry. 11, 292 (1961).

1959

P. Kard, Opt. i Spektroskopiya 6, 389 (1959); Opt. Spectry 6, 244 (1959).

1958

1957

P. H. Berning, A. F. Turner, J. Opt. Soc. Am. 47, 230 (1957).
[CrossRef]

A. F. Turner, P. J. Leurgans, J. Opt. Soc. Am. 37, 983A (1957).

P. G. Kard, Izv. Akad. Nauk. Est. SSR, Ser. Tekh. i Fiz.-Mat. Nauk 6, 344 (1957).

G. R. Noyes, P. W. Baumeister, Appl. Opt. 6,(1957).

L. I. Schiff, Am. J. Phys. 25, 207A (1957).

1952

1951

1950

B. H. Billings, J. Opt. Soc. Am. 40, 471 (1950).
[CrossRef]

A. F. Turner, J. Phys. Radium 11, 458 (1950).
[CrossRef]

1949

1947

L. N. Hadley, D. M. Dennison, J. Opt. Soc. Am. 37, 462 (1947).
[CrossRef]

1902

E. E. Hall, Phys. Rev. 15, 99 (1902).

Aleksoff, C. C.

C. C. Aleksoff, N. J. Harrick, Proc. IEEE 53, 1636 (1965).
[CrossRef]

Astheimer, R. W.

Baumeister, P. W.

Bergstein, L.

L. Bergstein, C. Shulman, Appl. Opt. 5, 20 (1966).
[CrossRef]

L. Bergstein, C. Shulman, Proc. Inst. Radio Engrs. 50, 1833 (1962).

Berning, P. H.

Billings, B. H.

Bohm, D.

D. Bohm, Quantum Theory (Prentice-Hall, New York, 1951), p. 240.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959), 1st ed., p. 65.

Costich, V. R.

Court, I. N.

Davis, W. C.

Dennison, D. M.

L. N. Hadley, D. M. Dennison, J. Opt. Soc. Am. 37, 462 (1947).
[CrossRef]

Drude, Paul

Paul Drude, The Theory of Optics (reprinted by Dover, New York, 1959), p. 299.

Epstein, L. I.

Falbel, G.

Gabor, D.

D. Gabor, U. S. Patent2,281,280 (1942).

Gee, A.

Gee, A. E.

A. E. Gee, Thesis, Institute of Optics, University of Rochester, Rochester, New York, 1949.

Genzel, L.

W. Wettling, L. Genzel, Infrared Phys. 4, 253 (1964).
[CrossRef]

Hadley, L. N.

L. N. Hadley, D. M. Dennison, J. Opt. Soc. Am. 37, 462 (1947).
[CrossRef]

Hall, E. E.

E. E. Hall, Phys. Rev. 15, 99 (1902).

Hansen, W. N.

W. N. Hansen, Spectrochim. Acta 21, 209 (1965). See the references to earlier papers.
[CrossRef]

Harrick, N. J.

Horsfall, R. B.

A. F. Turner, R. B. Horsfall, U.S. Patent2,422, 376 (1947).

Iogansen, L. V.

L. V. Iogansen, Opt. i Spektroskopiya 11, 542 (1961);Opt. Spectry. 11, 292 (1961).

Jones, E. M. T.

G. L. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 9.

Kard, P.

P. Kard, Opt. i Spektroskopiya 6, 389 (1959); Opt. Spectry 6, 244 (1959).

Kard, P. G.

P. G. Kard, Izv. Akad. Nauk. Est. SSR, Ser. Tekh. i Fiz.-Mat. Nauk 6, 344 (1957).

Land, E.

E. Land, U. S. Patent2,106,752 (1934).

Laski, G.

G. Laski, in Handbuch der Physik, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1928), Vol. 19, p. 815.

Leurgans, P. J.

A. F. Turner, P. J. Leurgans, J. Opt. Soc. Am. 37, 983A (1957).

P. J. Leurgans, J. Opt. Soc. Am. 41, 714 (1951).
[CrossRef]

MacNeille, S. M.

S. M. MacNeille, U. S. Patent2,403,731 (1946).

Matthaei, G. L.

G. L. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 9.

Minkowitz, S.

Noyes, G. R.

G. R. Noyes, P. W. Baumeister, Appl. Opt. 6,(1957).

Pieper, S. C.

Pohl, R.

R. Pohl, Optik und Atomphysik(Springer, Berlin, 1963), 11th ed., p. 148.

Polster, H. D.

Schiff, L. I.

L. I. Schiff, Am. J. Phys. 25, 207A (1957).

Seeley, J. S.

Seitz, Frederick

Frederick Seitz, The Modern Theory of Solids (McGraw-Hill, New York, 1940), p. 281.

Shulman, C.

L. Bergstein, C. Shulman, Appl. Opt. 5, 20 (1966).
[CrossRef]

L. Bergstein, C. Shulman, Proc. Inst. Radio Engrs. 50, 1833 (1962).

Smith, S. D.

Steele, E. L.

Treuthart, R. L.

Turner, A. F.

P. H. Berning, A. F. Turner, J. Opt. Soc. Am. 47, 230 (1957).
[CrossRef]

A. F. Turner, P. J. Leurgans, J. Opt. Soc. Am. 37, 983A (1957).

A. F. Turner, J. Phys. Radium 11, 458 (1950).
[CrossRef]

A. F. Turner, R. B. Horsfall, U.S. Patent2,422, 376 (1947).

A. F. Turner, U. S. Patent2,601,806 (1952).

von Willisen, F. K.

Wettling, W.

W. Wettling, L. Genzel, Infrared Phys. 4, 253 (1964).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959), 1st ed., p. 65.

Young, L.

G. L. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 9.

Am. J. Phys.

L. I. Schiff, Am. J. Phys. 25, 207A (1957).

Appl. Opt.

ASTM publication designation E131-66T

ASTM publication designation E131-66T (1966).

Infrared Phys.

W. Wettling, L. Genzel, Infrared Phys. 4, 253 (1964).
[CrossRef]

Izv. Akad. Nauk. Est. SSR, Ser. Tekh. i Fiz.-Mat. Nauk

P. G. Kard, Izv. Akad. Nauk. Est. SSR, Ser. Tekh. i Fiz.-Mat. Nauk 6, 344 (1957).

J. Opt. Soc. Am.

J. Phys. Radium

A. F. Turner, J. Phys. Radium 11, 458 (1950).
[CrossRef]

Opt. i Spektroskopiya

P. Kard, Opt. i Spektroskopiya 6, 389 (1959); Opt. Spectry 6, 244 (1959).

L. V. Iogansen, Opt. i Spektroskopiya 11, 542 (1961);Opt. Spectry. 11, 292 (1961).

Phys. Rev.

E. E. Hall, Phys. Rev. 15, 99 (1902).

Proc. IEEE

C. C. Aleksoff, N. J. Harrick, Proc. IEEE 53, 1636 (1965).
[CrossRef]

Proc. Inst. Radio Engrs.

L. Bergstein, C. Shulman, Proc. Inst. Radio Engrs. 50, 1833 (1962).

Spectrochim. Acta

W. N. Hansen, Spectrochim. Acta 21, 209 (1965). See the references to earlier papers.
[CrossRef]

Other

Reference 21, column 5, line 31.

A. E. Gee, Thesis, Institute of Optics, University of Rochester, Rochester, New York, 1949.

S. M. MacNeille, U. S. Patent2,403,731 (1946).

A. F. Turner, U. S. Patent2,601,806 (1952).

Reference 3, p. 616.

Reference 3, p. 33.

D. Gabor, U. S. Patent2,281,280 (1942).

E. Land, U. S. Patent2,106,752 (1934).

A. F. Turner, R. B. Horsfall, U.S. Patent2,422, 376 (1947).

Reference 3, p. 59.

Reference 3, p. 54.

Paul Drude, The Theory of Optics (reprinted by Dover, New York, 1959), p. 299.

G. Laski, in Handbuch der Physik, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1928), Vol. 19, p. 815.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959), 1st ed., p. 65.

D. Bohm, Quantum Theory (Prentice-Hall, New York, 1951), p. 240.

R. Pohl, Optik und Atomphysik(Springer, Berlin, 1963), 11th ed., p. 148.

Frederick Seitz, The Modern Theory of Solids (McGraw-Hill, New York, 1940), p. 281.

Reference 41, p. 531.

Reference 41, Chap. 6.

G. L. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 9.

Reference 41, Sec. 9.03.

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Figures (19)

Fig. 1
Fig. 1

The apparatus for observing the tunneling through the air gap between two prisms.

Fig. 2
Fig. 2

Nomenclature used to specify the design of a multilayer. For the sake of clarity, the multiple reflections are not shown.

Fig. 3
Fig. 3

The reflectance and transmittance of a single tunnel layer at 60° incidence. The design is enumerated in Table I.

Fig. 4
Fig. 4

The reflectance of a single tunnel layer 0.2 waves in physical thickness, as a function of the angle of incidence. The critical angle (θcrit) is shown; p, s designate the polarization. The design is listed in Table I.

Fig. 5
Fig. 5

The types of bandpass filters that contain tunnel layers. The tunnel layers are shaded. These filters are: a, the single tunnel layer filter; b, the Fabry-Perot tunnel layer filter; and c, the multiple tunnel layer filter.

Fig. 6
Fig. 6

The spectral transmittance of a Fabry-Perot tunnel layer filter whose design is shown in Table I. The p and s polarized transmittance curves correspond to the TM and TE waves, respectively.

Fig. 7
Fig. 7

The internal angle of incidence ϕ at the face of a tunnel-layer filter and also the change in the external angle of incidence Δϕ. As shown, Δϕ is positive.

Fig. 8
Fig. 8

The spectral transmittance of a Fabry-Perot tunnel layer filter whose design is shown in Table I. The tunnel layers are slightly absorbing. The p and s polarized transmittance curves correspond to the TM and TE waves, respectively.

Fig. 9
Fig. 9

The spectral transmittance of a modified Fabry-Perot tunnel layer filter of Kard’s design. The design is shown in Table II, and the p and s polarized transmittance curves correspond to the TM and TE wave, respectively. Incident angle = 60°. nI = 1.550.

Fig. 10
Fig. 10

The design of a single tunnel layer filter. The admittance Y of the matching stack is measured at its surface.

Fig. 11
Fig. 11

Isotransmittance (in percent) curves, for the p polarization, for a tunnel layer 0.333 waves in physical thickness and refractive index 1.35. The angle of incidence is 60° and the incident medium index is 1.70. The curves are plotted on the admittance plane, which is mapped onto the r plane via the Smith chart. The dashed curve is a parametric plot of the admittance of the multilayer matching stack (at 60° incidence) 1.65L H(L H)4 substrate. L is 2.0 quarter-waves at λ0 and index 1.70. H is 1.3016 quarter-waves at λ0 and index 2.30.

Fig. 12
Fig. 12

The s polarization isotransmittance curves for the same tunnel layer described in the caption to Fig. 11. The transmittance is in percent.

Fig. 13
Fig. 13

The spectral transmittance of the single tunnel layer bandpass filter, whose design is given in Table III. The p and s transmittance curves are for the TM and TE waves, respectively.

Fig. 14
Fig. 14

The spectral transmittance (for the p polarization) at an external angle of incidence, Δϕ = −1.70° (curve a) and Δϕ + 1.70° (curve b). Same filter as in Fig. 13.

Fig. 15
Fig. 15

The spectral transmittance (for the p polarization) of a single tunnel layer filter in which the tunnel layer is slightly absorbing. The design is given in Table III.

Fig. 16
Fig. 16

An embodiment of a multiple tunnel layer ir filter. The tunnel layer filter is deposited on the hypotenuse of the 35° CdTe prism, and the auxiliary filter is deposited on the entrance face of the prism.

Fig. 17
Fig. 17

The design of a microwave filter, which consists of a waveguide with irises inserted at specified intervals.

Fig. 18
Fig. 18

The spectral transmittance of a multiple layer tunnel filter for the ir, whose design is shown in Table IV. The transmittance curves are for the p polarization (TM wave), s polarization (TE wave), and the average transmittance = 1 2 ( T s + T p ).

Fig. 19
Fig. 19

The average transmittance of the same filter described in the caption to Fig. 18, but at internal angles of incidence of 34° and 35°.

Tables (3)

Tables Icon

Table I The Design of Tunnel Layer Filters Whose Spectral Transmittance Curves Are Shown in Figs. 3, 4, 6, and 8a

Tables Icon

Table II The Design of Kard’s Fabry-Perot Tunnel Layer Filtera

Tables Icon

Table III The Design of the Multilayers Whose Transmittance Curves Are Shown in Figs. 1315, 18, and 19a

Equations (5)

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

β i = 2 π σ n i d i γ i ,
γ i = ( 1 - n 0 2 n i - 2 sin 2 ϕ ) ½
γ i j γ i ,
γ i = ( n 0 2 n i - 2 sin 2 ϕ - 1 ) ½ .
[ cosh β i j g i - 1 sinh β i j h i sinh β i cosh β i ] ,

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