Abstract

The response of a vacuum photoemissive photodiode to a light beam has been investigated as a function of the angle of incidence in order to check whether the response is always proportional to the absorbed number of photons. By working mainly in the region of total internal reflection and measuring the reflected beam with an auxiliary detector at near-normal incidence, we were able to determine the absorptivity and to compare it with the measured photoelectric current. We found that the ratio of the two quantities is constant and independent of the angle of incidence for TE waves but not for TM waves. The results suggest that there exists an extra loss mechanism for TM waves, which may be connected with plasmon generation. Because of this extra loss, the response of the detector to TM waves is not a direct measure of the number of absorbed photons.

© 1988 Optical Society of America

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References

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  1. J. Durnin, C. Reece, L. Mandel, J. Opt. Soc. Am. 71, 115 (1981).
    [CrossRef]
  2. J. Geist, W. K. Gladden, E. F. Zalewski, J. Opt. Soc. Am. 72, 1068 (1982).
    [CrossRef]
  3. E. G. Ramberg, Appl. Opt. 6, 2163 (1967).
    [CrossRef] [PubMed]
  4. H. Hora, Phys. Status Solidi A 5, 159 (1971).
    [CrossRef]
  5. W. Greschat, H. Heinrich, P. Römer, in Advances in Electronics and Electron Physics, B. L. Morgan, R. W. Airey, K. D. McMullan, eds. (Academic, New York, 1976), Vol. 40A, p. 397.
    [CrossRef]
  6. A. Otto, Z. Phys. 216, 398 (1968);Z. Phys. 219, 227 (1969).
    [CrossRef]
  7. E. Kretschmann, H. Raether, Z. Naturforsch. A 23, 2135 (1968);E. Kretschmann, Z. Phys. 241, 313 (1971).
    [CrossRef]
  8. G. S. Agarwal, Phys. Rev. B 8, 4768 (1973).
    [CrossRef]
  9. T. A. Callcott, E. T. Arakawa, Phys. Rev. B 11, 2750 (1975).
    [CrossRef]
  10. H. J. Simon, D. E. Mitchell, J. G. Watson, Am. J. Phys. 43, 630 (1975),
    [CrossRef]
  11. J. E. Sipe, J. Becher, J. Opt. Soc. Am. 71, 1286 (1981).
    [CrossRef]
  12. L. Mandel, E. C. G. Sudarshan, E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
    [CrossRef]
  13. P. L. Kelley, W. H. Kleiner, Phys. Rev. 136, A316 (1964).
    [CrossRef]
  14. R. H. Lehmberg, Phys. Rev. 167, 1152 (1967).
    [CrossRef]
  15. B. R. Mollow, Phys. Rev. 168, 1896 (1968).
    [CrossRef]
  16. L. Mandel, D. Meltzer, Phys. Rev. 188, 198 (1969).
    [CrossRef]
  17. R. J. Cook, Phys. Rev. A 25, 2164;Phys. Rev. A 26, 2754 (1982).
  18. H. J. Kimble, L. Mandel, Phys. Rev. A 30, 844 (1984).
    [CrossRef]
  19. The angular distribution of the photoelectrons and its dependence on polarization was treated in some detail by K.-N. Huang, Phys. Rev. A 22, 223 (1980).
    [CrossRef]
  20. W. H. McCarroll, R. J. Paff, A. H. Sommer, J. Appl. Phys. 42, 569 (1971).
    [CrossRef]
  21. See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chaps. 1 and 13.
  22. V. E. Kondrashov, A. S. Shepov, Bull. Acad. Sci. USSR, Phys. Ser. 28, 1349 (1964).
  23. C. Ghosh, Phys. Rev. B 22, 1972 (1980).
    [CrossRef]
  24. R. W. Engstrom, Photomultiplier Handbook (RCA Corporation, Lancaster, Pa., 1980), p. 18.

1984

H. J. Kimble, L. Mandel, Phys. Rev. A 30, 844 (1984).
[CrossRef]

1982

1981

1980

The angular distribution of the photoelectrons and its dependence on polarization was treated in some detail by K.-N. Huang, Phys. Rev. A 22, 223 (1980).
[CrossRef]

C. Ghosh, Phys. Rev. B 22, 1972 (1980).
[CrossRef]

1975

T. A. Callcott, E. T. Arakawa, Phys. Rev. B 11, 2750 (1975).
[CrossRef]

H. J. Simon, D. E. Mitchell, J. G. Watson, Am. J. Phys. 43, 630 (1975),
[CrossRef]

1973

G. S. Agarwal, Phys. Rev. B 8, 4768 (1973).
[CrossRef]

1971

H. Hora, Phys. Status Solidi A 5, 159 (1971).
[CrossRef]

W. H. McCarroll, R. J. Paff, A. H. Sommer, J. Appl. Phys. 42, 569 (1971).
[CrossRef]

1969

L. Mandel, D. Meltzer, Phys. Rev. 188, 198 (1969).
[CrossRef]

1968

B. R. Mollow, Phys. Rev. 168, 1896 (1968).
[CrossRef]

A. Otto, Z. Phys. 216, 398 (1968);Z. Phys. 219, 227 (1969).
[CrossRef]

E. Kretschmann, H. Raether, Z. Naturforsch. A 23, 2135 (1968);E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

1967

1964

L. Mandel, E. C. G. Sudarshan, E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

P. L. Kelley, W. H. Kleiner, Phys. Rev. 136, A316 (1964).
[CrossRef]

V. E. Kondrashov, A. S. Shepov, Bull. Acad. Sci. USSR, Phys. Ser. 28, 1349 (1964).

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. B 8, 4768 (1973).
[CrossRef]

Arakawa, E. T.

T. A. Callcott, E. T. Arakawa, Phys. Rev. B 11, 2750 (1975).
[CrossRef]

Becher, J.

Born, M.

See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chaps. 1 and 13.

Callcott, T. A.

T. A. Callcott, E. T. Arakawa, Phys. Rev. B 11, 2750 (1975).
[CrossRef]

Cook, R. J.

R. J. Cook, Phys. Rev. A 25, 2164;Phys. Rev. A 26, 2754 (1982).

Durnin, J.

Engstrom, R. W.

R. W. Engstrom, Photomultiplier Handbook (RCA Corporation, Lancaster, Pa., 1980), p. 18.

Geist, J.

Ghosh, C.

C. Ghosh, Phys. Rev. B 22, 1972 (1980).
[CrossRef]

Gladden, W. K.

Greschat, W.

W. Greschat, H. Heinrich, P. Römer, in Advances in Electronics and Electron Physics, B. L. Morgan, R. W. Airey, K. D. McMullan, eds. (Academic, New York, 1976), Vol. 40A, p. 397.
[CrossRef]

Heinrich, H.

W. Greschat, H. Heinrich, P. Römer, in Advances in Electronics and Electron Physics, B. L. Morgan, R. W. Airey, K. D. McMullan, eds. (Academic, New York, 1976), Vol. 40A, p. 397.
[CrossRef]

Hora, H.

H. Hora, Phys. Status Solidi A 5, 159 (1971).
[CrossRef]

Huang, K.-N.

The angular distribution of the photoelectrons and its dependence on polarization was treated in some detail by K.-N. Huang, Phys. Rev. A 22, 223 (1980).
[CrossRef]

Kelley, P. L.

P. L. Kelley, W. H. Kleiner, Phys. Rev. 136, A316 (1964).
[CrossRef]

Kimble, H. J.

H. J. Kimble, L. Mandel, Phys. Rev. A 30, 844 (1984).
[CrossRef]

Kleiner, W. H.

P. L. Kelley, W. H. Kleiner, Phys. Rev. 136, A316 (1964).
[CrossRef]

Kondrashov, V. E.

V. E. Kondrashov, A. S. Shepov, Bull. Acad. Sci. USSR, Phys. Ser. 28, 1349 (1964).

Kretschmann, E.

E. Kretschmann, H. Raether, Z. Naturforsch. A 23, 2135 (1968);E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

Lehmberg, R. H.

R. H. Lehmberg, Phys. Rev. 167, 1152 (1967).
[CrossRef]

Mandel, L.

H. J. Kimble, L. Mandel, Phys. Rev. A 30, 844 (1984).
[CrossRef]

J. Durnin, C. Reece, L. Mandel, J. Opt. Soc. Am. 71, 115 (1981).
[CrossRef]

L. Mandel, D. Meltzer, Phys. Rev. 188, 198 (1969).
[CrossRef]

L. Mandel, E. C. G. Sudarshan, E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

McCarroll, W. H.

W. H. McCarroll, R. J. Paff, A. H. Sommer, J. Appl. Phys. 42, 569 (1971).
[CrossRef]

Meltzer, D.

L. Mandel, D. Meltzer, Phys. Rev. 188, 198 (1969).
[CrossRef]

Mitchell, D. E.

H. J. Simon, D. E. Mitchell, J. G. Watson, Am. J. Phys. 43, 630 (1975),
[CrossRef]

Mollow, B. R.

B. R. Mollow, Phys. Rev. 168, 1896 (1968).
[CrossRef]

Otto, A.

A. Otto, Z. Phys. 216, 398 (1968);Z. Phys. 219, 227 (1969).
[CrossRef]

Paff, R. J.

W. H. McCarroll, R. J. Paff, A. H. Sommer, J. Appl. Phys. 42, 569 (1971).
[CrossRef]

Raether, H.

E. Kretschmann, H. Raether, Z. Naturforsch. A 23, 2135 (1968);E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

Ramberg, E. G.

Reece, C.

Römer, P.

W. Greschat, H. Heinrich, P. Römer, in Advances in Electronics and Electron Physics, B. L. Morgan, R. W. Airey, K. D. McMullan, eds. (Academic, New York, 1976), Vol. 40A, p. 397.
[CrossRef]

Shepov, A. S.

V. E. Kondrashov, A. S. Shepov, Bull. Acad. Sci. USSR, Phys. Ser. 28, 1349 (1964).

Simon, H. J.

H. J. Simon, D. E. Mitchell, J. G. Watson, Am. J. Phys. 43, 630 (1975),
[CrossRef]

Sipe, J. E.

Sommer, A. H.

W. H. McCarroll, R. J. Paff, A. H. Sommer, J. Appl. Phys. 42, 569 (1971).
[CrossRef]

Sudarshan, E. C. G.

L. Mandel, E. C. G. Sudarshan, E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

Watson, J. G.

H. J. Simon, D. E. Mitchell, J. G. Watson, Am. J. Phys. 43, 630 (1975),
[CrossRef]

Wolf, E.

L. Mandel, E. C. G. Sudarshan, E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chaps. 1 and 13.

Zalewski, E. F.

Am. J. Phys.

H. J. Simon, D. E. Mitchell, J. G. Watson, Am. J. Phys. 43, 630 (1975),
[CrossRef]

Appl. Opt.

Bull. Acad. Sci. USSR, Phys. Ser.

V. E. Kondrashov, A. S. Shepov, Bull. Acad. Sci. USSR, Phys. Ser. 28, 1349 (1964).

J. Appl. Phys.

W. H. McCarroll, R. J. Paff, A. H. Sommer, J. Appl. Phys. 42, 569 (1971).
[CrossRef]

J. Opt. Soc. Am.

Phys. Rev.

P. L. Kelley, W. H. Kleiner, Phys. Rev. 136, A316 (1964).
[CrossRef]

R. H. Lehmberg, Phys. Rev. 167, 1152 (1967).
[CrossRef]

B. R. Mollow, Phys. Rev. 168, 1896 (1968).
[CrossRef]

L. Mandel, D. Meltzer, Phys. Rev. 188, 198 (1969).
[CrossRef]

Phys. Rev. A

R. J. Cook, Phys. Rev. A 25, 2164;Phys. Rev. A 26, 2754 (1982).

H. J. Kimble, L. Mandel, Phys. Rev. A 30, 844 (1984).
[CrossRef]

The angular distribution of the photoelectrons and its dependence on polarization was treated in some detail by K.-N. Huang, Phys. Rev. A 22, 223 (1980).
[CrossRef]

Phys. Rev. B

G. S. Agarwal, Phys. Rev. B 8, 4768 (1973).
[CrossRef]

T. A. Callcott, E. T. Arakawa, Phys. Rev. B 11, 2750 (1975).
[CrossRef]

C. Ghosh, Phys. Rev. B 22, 1972 (1980).
[CrossRef]

Phys. Status Solidi A

H. Hora, Phys. Status Solidi A 5, 159 (1971).
[CrossRef]

Proc. Phys. Soc. (London)

L. Mandel, E. C. G. Sudarshan, E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).
[CrossRef]

Z. Naturforsch. A

E. Kretschmann, H. Raether, Z. Naturforsch. A 23, 2135 (1968);E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

Z. Phys.

A. Otto, Z. Phys. 216, 398 (1968);Z. Phys. 219, 227 (1969).
[CrossRef]

Other

W. Greschat, H. Heinrich, P. Römer, in Advances in Electronics and Electron Physics, B. L. Morgan, R. W. Airey, K. D. McMullan, eds. (Academic, New York, 1976), Vol. 40A, p. 397.
[CrossRef]

See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chaps. 1 and 13.

R. W. Engstrom, Photomultiplier Handbook (RCA Corporation, Lancaster, Pa., 1980), p. 18.

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Figures (8)

Fig. 1
Fig. 1

Light beam striking a photodetector at an angle of incidence θ.

Fig. 2
Fig. 2

Outline of the detector geometry.

Fig. 3
Fig. 3

The absorptivity A ( θ ) for TE and TM waves as a function of the angle of incidence θ calculated from Eqs. (3) and (8) (solid curve) and modified by Eqs. (10) and (11) (dashed curve). The chosen parameter values are nL = 1.535, nG = 1.515, lG = 0.1 mm, nwindow = 1.53, nphotocath. = 2.6 (1 + i0.135),lphotocath. = 270 Å.

Fig. 4
Fig. 4

(a) Outline of the phototube and (b) outline of the experimental setup. See text for further discussion.

Fig. 5
Fig. 5

Measured photocurrent of the vacuum phototube as a function of the laser intensity, as monitored by photodiode DM, for θ = 60°.

Fig. 6
Fig. 6

Results of the photocurrent P(θ) (triangles) and absorptivity A ( θ ) (circles) measurements as a function of the angle of incidence θ superimposed upon the calculated curves A theor . ( θ ) for TE and for TM waves. The P(θ) data points overlap below θ = 15° for TE and TM waves. The refractive index and thickness parameters were adjusted within the allowed ranges for best agreement between A theor . ( θ ) and measured, A ( θ ) namely, nL = 1.535, nG = 1.515, lG = 0.1 mm, nwindow = 1.53, nphotocath. = 2.6(1 + i0.135), lphotocath. = 270 Å.

Fig. 7
Fig. 7

The ratio of the measured photocurrent P(θ) to the measured absorptivity A ( θ ) as a function of the angle of incidence θ for TE and TM waves. The ratio was made equal to unity for TE waves at θ = 70°.

Fig. 8
Fig. 8

Results of the photocurrent P(θ) (triangles) and absorptivity A ( θ ) (circles) measurements as a function of the angle of incidence θ, superimposed upon the calculated curves A theor . ( θ ) for TE and TM waves. The P(θ) data points overlap below θ = 15° for TE and TM waves. The refractive index and thickness parameters were adjusted within the allowed ranges for best agreement between A theor . ( θ ) and measured P(θ), namely, nL = 1.535, nG = 1.515, lG = 0.1 mm, nwindow = 1.52, nphotocath. = 2.8(1 + i0.13), lphotocath. = 200 Å.

Equations (13)

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P ( t ) = ϕ | e m t t + Δ t d t ϕ | p ̂ ( t ) . A ( r 0 , t ) | ϕ 0 | 2 .
P ( t ) = ϕ g ( ϕ ) | e m t t + Δ t d t ϕ | p ̂ ( t ) A ( r 0 , t ) | ϕ 0 | 2 .
A ( θ ) + R ( θ ) + T ( θ ) = 1 ,
r ( θ 1 ) = | z 1 | 2 e 2 η υ + | z 2 | 2 e 2 η υ + 2 | z 1 | | z 2 | cos ( arg z 2 arg z 1 + 2 u η ) e 2 η υ + | z 1 | 2 | z 2 | 2 e 2 η υ + 2 | z 1 | | z 2 | cos ( arg z 2 arg z 1 + 2 u η )
t ( θ 1 ) = ( 1 n 1 2 sin 2 θ 1 ) 1 / 2 16 n 1 2 cos 2 θ 1 ( u 2 + υ 2 ) G n 1 cos θ 1 [ e 2 η υ + | z 1 | 2 | z 2 | 2 e 2 η υ + 2 | z 1 | | z 2 | cos ( arg z 2 + arg z 1 + 2 u η ) ] ,
z 1 n 1 cos θ 1 u i υ n 1 cos θ 1 + u + i υ , z 2 ( 1 n 1 2 sin 2 θ 1 ) 1 / 2 + u + i υ ( 1 n 1 2 sin 2 θ 1 ) 1 / 2 + u + i υ , G 1 | n 1 cos θ 1 + u + i υ | 2 | ( 1 n 1 2 sin 2 θ 1 ) 1 / 2 + u + i υ | 2
z 1 ñ 2 2 cos θ 1 n 1 ( u + i υ ) ñ 2 2 cos θ 1 + n 1 ( u + i υ ) , z 2 ñ 2 2 ( 1 n 1 2 sin 2 θ 1 ) 1 / 2 + u + i υ ñ 2 2 ( 1 n 1 2 sin 2 θ 1 ) 1 / 2 + u + i υ , G | ñ 2 | 4 | ñ 2 2 cos θ 1 + n 1 ( u + i υ ) | 2 ñ 2 2 | ( 1 n 1 2 sin 2 θ 1 ) 1 / 2 + u + i υ | 2 .
u + i υ = n 2 cos θ 2 ,
n 1 sin θ 1 = n 2 sin θ 2 .
R ( θ ) = r ( θ ) + t 2 ( θ ) r ( θ ) [ 1 + r ( θ ) r ( θ ) + r 2 ( θ ) r 2 ( θ ) + ] = r ( θ ) + t 2 ( θ ) r ( θ ) 1 r ( θ ) r ( θ )
T ( θ ) = t ( θ ) + t ( θ ) [ 1 + r ( θ ) r ( θ ) + r 2 ( θ ) r 2 ( θ ) + ] = t ( θ ) t ( θ ) 1 r ( θ ) r ( θ ) ,
n 1 sin θ = n 1 sin θ
A = ( 1 V R / V 0 t V T / V 0 ) .

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