Abstract

This article provides experimental verification of the existence of discrete power distributions for a broadband frequency domain in a cross section of a dielectric antenna. The dielectric antenna used was chosen such that the directionally dependent acceptance of power was approximately the same as the psychophysically determined directional sensitivity to light of the foveal receptors (Stiles-Crawford I effect). Power summation in a cross section shows wavelength dependence on the directionally dependent acceptance of power, which is in good agreement with the p(λ) data of Stiles. Polarization dependence of the discrete power distribution occurs if power is dissipated in the antenna. Irradiation with electromagnetic energy waves from a broad wavelength band domain results in a discrete power distribution with minimum-maximum differences that are the same as those for a single wavelength from the domain, provided this wavelength gives rise to the same number of modes in the antenna. If the cross section of the antenna is elliptical the power distribution will not be influenced by the direction of polarization of the incident electromagnetic field. A small-diameter rod with a conical part attached in front shows a more pronounced directionally dependent acceptance of power than a small-diameter rod alone. The results obtained in this millimeter-wave experiment are compared with a model based on psychophysically determined effects such as the Stiles-Crawford I effect, transient Stiles-Crawford effect, and transient polarization adaptation. A discussion of these data leads us to conclude that the foveal receptors are dielectric antennas with a υ value of 2.31/λ, with λ in μm.

© 1980 Optical Society of America

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  1. W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
    [Crossref]
  2. W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. London Ser. B 123, 91–118 (1937).
    [Crossref]
  3. F. Flamant and W. S. Stiles, “The directional and spectral sensitivities of the retinal rods to adapting fields of different wavelengths,” J. Physiol. 107, 187–202 (1948).
  4. W. D. Wright and J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
    [Crossref]
  5. E. Brücke, “Ueber die physiologische Bedeutung der stabförmigen Körper und der Swillingszapfen in den Augen der Wirbeltiere,” Arch. Anat. Physiol. Anat. 11, 444–483 (1844).
  6. B. O’Brien, “The Stiles and Crawford effect in polarized light,” J. Opt. Soc. Am. 37, 275–278 (1947).
    [Crossref]
  7. G. Toraldo di Francia, “Retinal cones as dielectric antennae,” J. Opt. Soc. Am. 39, 324 (1948).
    [Crossref]
  8. B. O’Brien, “Vision and resolution in the central retina,” J. Opt. Soc. Am. 41, 882–894 (1951).
    [Crossref]
  9. J. M. Enoch and G. A. Fry, “Characteristics of a model retinal receptor studied at microwave frequencies,” J. Opt. Soc. Am. 48, 899–911 (1958).
    [Crossref] [PubMed]
  10. J. M. Enoch, “Response of a model retinal receptor as a function of wavelength,” J. Opt. Soc. Am. 50, 315–320 (1960).
    [Crossref] [PubMed]
  11. R. L. Sidman, “The structure and concentration of solids in photoreceptor cells studied by refractometry and interference microscopy,” J. Biophys. Biochem. Cytol. 3, 15–31 (1957).
  12. R. Barer, “Refractometry and interferometry of living cells,” J. Opt. Soc. Am. 47, 545–556 (1957).
    [Crossref] [PubMed]
  13. N. S. Kapany, “Fiber optics. Part I. Optical properties of certain dielectric cylinders,” J. Opt. Soc. Am. 47, 413–422 (1957).
    [Crossref]
  14. E. Snitzer, “Cylindrical dielectric waveguide modes,” J. Opt. Soc. Am. 51, 491–498 (1961).
    [Crossref]
  15. A. W. Snyder, “Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide,” IEEE Trans. Microwave Theory Tech. MIT-17, 1130–1138 (1969).
    [Crossref]
  16. A. W. Snyder, “Excitation and scattering of modes on a dielectric or optical fiber,” IEEE Trans. Microwave Theory Tech. MIT-17, 1138–1144 (1969).
    [Crossref]
  17. W. Wijngaard, “Mode interference patterns in retinal receptor outer segments,” Vision Res. 14, 889–893 (1974).
    [Crossref] [PubMed]
  18. J. M. Enoch, “Optical properties of the retinal receptors,” J. Opt. Soc. Am. 53, 71–85 (1963).
    [Crossref]
  19. A. W. Snyder and C. Pask, “The Stiles-Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
    [Crossref] [PubMed]
  20. A. W. Snyder, C. Pask, and D. J. Mitchell, “Light-acceptance property of an optical fiber,” J. Opt. Soc. Am. 63, 59–64 (1973).
    [Crossref] [PubMed]
  21. A. W. Snyder, “Coupling of modes on a tapered dielectric cylinder,” IEEE Trans. Microwave Theory Tech. MIT-18, 383–392 (1970).
    [Crossref]
  22. A. W. Snyder, “Mode propagation in a nonuniform cylindrical medium,” IEEE Trans. Microwave Theory Tech. MIT-19, 402–403 (1971).
    [Crossref]
  23. A. W. Snyder, “Power loss on optical fibers,” Proc. IEEE 60, 757–758 (1972).
    [Crossref]
  24. W. L. Makous, “A transient Stiles-Crawford effect,” Vision Res. 8, 1272–1284 (1968).
    [Crossref]
  25. R. Sansbury, J. Zacks, and J. Nachmias, “The Stiles-Crawford effect: two models evaluated,” Vision Res. 14, 803–812 (1974).
    [Crossref] [PubMed]
  26. P. J. de Groot and E. de Pender, “A transient effect contingent on the direction of polarization of light incident on the cornea,” Vision Res. 19, 1065–1066 (1979).
    [Crossref] [PubMed]
  27. P. J. de Groot, “Transient threshold increase due to combined changes in direction of propagation and plane of polarization,” Vision Res. 19, 1253–1259 (1979).
    [Crossref] [PubMed]
  28. W. A. H. Rushton, “Cone pigment kinetics in the protanope,” J. Physiol. 168, 374–388 (1963).
  29. A mechanism for describing the TSCE based upon the different types of synaptic transmissions is thought by us to be inadequate. If one assumes that the differences between synaptic transmissions make it possible to determine where the pigment molecules are bleached, then it follows that the TSCE does not depend on the retinal illuminance. In this paper we limit ourselves to the two mechanisms mentioned.
  30. C. Pask and A. W. Snyder, “Power of modes propagating inside a dielectric rod,” J. Opt. Soc. Am. 64, 393–395 (1974).
    [Crossref]
  31. A. F. Harvey, Microwave Engineering (Academic, London, 1963).
  32. S. J. Starr, Thesis, University of Chicago, 1977 (unpublished).
  33. Mm. Poo and R. A. Cone, “Lateral diffusion of rhodopsin in the photoreceptor membrane,” Nature 247, 438–441 (1974).
    [Crossref] [PubMed]
  34. S. Asano and G. Yamamoto, “Light scattering by a spherical particle,” Appl. Opt. 14, 29–49 (1975).
    [Crossref] [PubMed]
  35. C. Yeh, “Elliptical dielectric waveguides,” J. Appl. Phys. 33, 3235–3243 (1962).
    [Crossref]
  36. C. Yeh, “Scattering of obliquely incident light waves by elliptical fibers,” J. Opt. Soc. Am. 54, 1227–1231 (1964).
    [Crossref]
  37. C. Yeh, “Backscattering cross section of a dielectric elliptical cylinder,” J. Opt. Soc. Am. 55, 309–315 (1965).
    [Crossref]
  38. A. Duxbury, “A mathematical model of a retinal rod,” Proc. R. Soc. Edinburgh Sec. A,  LXVIII Part IV, 322–342 (1969).
  39. J. Bach Andersen, Thesis, Technical University of Denmark, Lyngby, Polyteknisk Forlag, 1971, ISBN 87502 0200 6.
  40. W. Wijngaard and J. van Kruysbergen, “The function of the nonguided light in some explanations of the Stiles-Crawford effects,” in Photoreceptor Optics, edited by A. W. Snyder and R. Menzel, (Springer-Verlag, Berlin, 1975).
    [Crossref]
  41. I. C. Goyal, A. Kumar, A. Sharma, and A. K. Ghatak, “Stiles Crawford effect, an inhomogeneous waveguide model for human cone-receptor,” Optik 49, 39–49 (1977).
  42. W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13, 2185–2194 (1973).
    [Crossref] [PubMed]
  43. A. W. Snyder and W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. 68, 297–309 (1978).
    [Crossref]
  44. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

1979 (2)

P. J. de Groot and E. de Pender, “A transient effect contingent on the direction of polarization of light incident on the cornea,” Vision Res. 19, 1065–1066 (1979).
[Crossref] [PubMed]

P. J. de Groot, “Transient threshold increase due to combined changes in direction of propagation and plane of polarization,” Vision Res. 19, 1253–1259 (1979).
[Crossref] [PubMed]

1978 (1)

1977 (1)

I. C. Goyal, A. Kumar, A. Sharma, and A. K. Ghatak, “Stiles Crawford effect, an inhomogeneous waveguide model for human cone-receptor,” Optik 49, 39–49 (1977).

1975 (1)

1974 (4)

R. Sansbury, J. Zacks, and J. Nachmias, “The Stiles-Crawford effect: two models evaluated,” Vision Res. 14, 803–812 (1974).
[Crossref] [PubMed]

Mm. Poo and R. A. Cone, “Lateral diffusion of rhodopsin in the photoreceptor membrane,” Nature 247, 438–441 (1974).
[Crossref] [PubMed]

W. Wijngaard, “Mode interference patterns in retinal receptor outer segments,” Vision Res. 14, 889–893 (1974).
[Crossref] [PubMed]

C. Pask and A. W. Snyder, “Power of modes propagating inside a dielectric rod,” J. Opt. Soc. Am. 64, 393–395 (1974).
[Crossref]

1973 (3)

A. W. Snyder, C. Pask, and D. J. Mitchell, “Light-acceptance property of an optical fiber,” J. Opt. Soc. Am. 63, 59–64 (1973).
[Crossref] [PubMed]

A. W. Snyder and C. Pask, “The Stiles-Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[Crossref] [PubMed]

W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13, 2185–2194 (1973).
[Crossref] [PubMed]

1972 (1)

A. W. Snyder, “Power loss on optical fibers,” Proc. IEEE 60, 757–758 (1972).
[Crossref]

1971 (1)

A. W. Snyder, “Mode propagation in a nonuniform cylindrical medium,” IEEE Trans. Microwave Theory Tech. MIT-19, 402–403 (1971).
[Crossref]

1970 (1)

A. W. Snyder, “Coupling of modes on a tapered dielectric cylinder,” IEEE Trans. Microwave Theory Tech. MIT-18, 383–392 (1970).
[Crossref]

1969 (3)

A. W. Snyder, “Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide,” IEEE Trans. Microwave Theory Tech. MIT-17, 1130–1138 (1969).
[Crossref]

A. W. Snyder, “Excitation and scattering of modes on a dielectric or optical fiber,” IEEE Trans. Microwave Theory Tech. MIT-17, 1138–1144 (1969).
[Crossref]

A. Duxbury, “A mathematical model of a retinal rod,” Proc. R. Soc. Edinburgh Sec. A,  LXVIII Part IV, 322–342 (1969).

1968 (1)

W. L. Makous, “A transient Stiles-Crawford effect,” Vision Res. 8, 1272–1284 (1968).
[Crossref]

1965 (1)

1964 (1)

1963 (2)

J. M. Enoch, “Optical properties of the retinal receptors,” J. Opt. Soc. Am. 53, 71–85 (1963).
[Crossref]

W. A. H. Rushton, “Cone pigment kinetics in the protanope,” J. Physiol. 168, 374–388 (1963).

1962 (1)

C. Yeh, “Elliptical dielectric waveguides,” J. Appl. Phys. 33, 3235–3243 (1962).
[Crossref]

1961 (1)

1960 (1)

1958 (1)

1957 (3)

N. S. Kapany, “Fiber optics. Part I. Optical properties of certain dielectric cylinders,” J. Opt. Soc. Am. 47, 413–422 (1957).
[Crossref]

R. Barer, “Refractometry and interferometry of living cells,” J. Opt. Soc. Am. 47, 545–556 (1957).
[Crossref] [PubMed]

R. L. Sidman, “The structure and concentration of solids in photoreceptor cells studied by refractometry and interference microscopy,” J. Biophys. Biochem. Cytol. 3, 15–31 (1957).

1951 (1)

1948 (2)

G. Toraldo di Francia, “Retinal cones as dielectric antennae,” J. Opt. Soc. Am. 39, 324 (1948).
[Crossref]

F. Flamant and W. S. Stiles, “The directional and spectral sensitivities of the retinal rods to adapting fields of different wavelengths,” J. Physiol. 107, 187–202 (1948).

1947 (1)

1937 (1)

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. London Ser. B 123, 91–118 (1937).
[Crossref]

1936 (1)

W. D. Wright and J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
[Crossref]

1933 (1)

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[Crossref]

1844 (1)

E. Brücke, “Ueber die physiologische Bedeutung der stabförmigen Körper und der Swillingszapfen in den Augen der Wirbeltiere,” Arch. Anat. Physiol. Anat. 11, 444–483 (1844).

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

Asano, S.

Bach Andersen, J.

J. Bach Andersen, Thesis, Technical University of Denmark, Lyngby, Polyteknisk Forlag, 1971, ISBN 87502 0200 6.

Barer, R.

Brücke, E.

E. Brücke, “Ueber die physiologische Bedeutung der stabförmigen Körper und der Swillingszapfen in den Augen der Wirbeltiere,” Arch. Anat. Physiol. Anat. 11, 444–483 (1844).

Cone, R. A.

Mm. Poo and R. A. Cone, “Lateral diffusion of rhodopsin in the photoreceptor membrane,” Nature 247, 438–441 (1974).
[Crossref] [PubMed]

Crawford, B. H.

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[Crossref]

de Groot, P. J.

P. J. de Groot, “Transient threshold increase due to combined changes in direction of propagation and plane of polarization,” Vision Res. 19, 1253–1259 (1979).
[Crossref] [PubMed]

P. J. de Groot and E. de Pender, “A transient effect contingent on the direction of polarization of light incident on the cornea,” Vision Res. 19, 1065–1066 (1979).
[Crossref] [PubMed]

de Pender, E.

P. J. de Groot and E. de Pender, “A transient effect contingent on the direction of polarization of light incident on the cornea,” Vision Res. 19, 1065–1066 (1979).
[Crossref] [PubMed]

Duxbury, A.

A. Duxbury, “A mathematical model of a retinal rod,” Proc. R. Soc. Edinburgh Sec. A,  LXVIII Part IV, 322–342 (1969).

Enoch, J. M.

Flamant, F.

F. Flamant and W. S. Stiles, “The directional and spectral sensitivities of the retinal rods to adapting fields of different wavelengths,” J. Physiol. 107, 187–202 (1948).

Fry, G. A.

Ghatak, A. K.

I. C. Goyal, A. Kumar, A. Sharma, and A. K. Ghatak, “Stiles Crawford effect, an inhomogeneous waveguide model for human cone-receptor,” Optik 49, 39–49 (1977).

Goyal, I. C.

I. C. Goyal, A. Kumar, A. Sharma, and A. K. Ghatak, “Stiles Crawford effect, an inhomogeneous waveguide model for human cone-receptor,” Optik 49, 39–49 (1977).

Harvey, A. F.

A. F. Harvey, Microwave Engineering (Academic, London, 1963).

Kapany, N. S.

Kumar, A.

I. C. Goyal, A. Kumar, A. Sharma, and A. K. Ghatak, “Stiles Crawford effect, an inhomogeneous waveguide model for human cone-receptor,” Optik 49, 39–49 (1977).

Makous, W. L.

W. L. Makous, “A transient Stiles-Crawford effect,” Vision Res. 8, 1272–1284 (1968).
[Crossref]

Miller, W. H.

W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13, 2185–2194 (1973).
[Crossref] [PubMed]

Mitchell, D. J.

Nachmias, J.

R. Sansbury, J. Zacks, and J. Nachmias, “The Stiles-Crawford effect: two models evaluated,” Vision Res. 14, 803–812 (1974).
[Crossref] [PubMed]

Nelson, J. H.

W. D. Wright and J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
[Crossref]

O’Brien, B.

Pask, C.

Poo, Mm.

Mm. Poo and R. A. Cone, “Lateral diffusion of rhodopsin in the photoreceptor membrane,” Nature 247, 438–441 (1974).
[Crossref] [PubMed]

Rushton, W. A. H.

W. A. H. Rushton, “Cone pigment kinetics in the protanope,” J. Physiol. 168, 374–388 (1963).

Sansbury, R.

R. Sansbury, J. Zacks, and J. Nachmias, “The Stiles-Crawford effect: two models evaluated,” Vision Res. 14, 803–812 (1974).
[Crossref] [PubMed]

Sharma, A.

I. C. Goyal, A. Kumar, A. Sharma, and A. K. Ghatak, “Stiles Crawford effect, an inhomogeneous waveguide model for human cone-receptor,” Optik 49, 39–49 (1977).

Sidman, R. L.

R. L. Sidman, “The structure and concentration of solids in photoreceptor cells studied by refractometry and interference microscopy,” J. Biophys. Biochem. Cytol. 3, 15–31 (1957).

Snitzer, E.

Snyder, A. W.

A. W. Snyder and W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. 68, 297–309 (1978).
[Crossref]

C. Pask and A. W. Snyder, “Power of modes propagating inside a dielectric rod,” J. Opt. Soc. Am. 64, 393–395 (1974).
[Crossref]

A. W. Snyder, C. Pask, and D. J. Mitchell, “Light-acceptance property of an optical fiber,” J. Opt. Soc. Am. 63, 59–64 (1973).
[Crossref] [PubMed]

A. W. Snyder and C. Pask, “The Stiles-Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[Crossref] [PubMed]

W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13, 2185–2194 (1973).
[Crossref] [PubMed]

A. W. Snyder, “Power loss on optical fibers,” Proc. IEEE 60, 757–758 (1972).
[Crossref]

A. W. Snyder, “Mode propagation in a nonuniform cylindrical medium,” IEEE Trans. Microwave Theory Tech. MIT-19, 402–403 (1971).
[Crossref]

A. W. Snyder, “Coupling of modes on a tapered dielectric cylinder,” IEEE Trans. Microwave Theory Tech. MIT-18, 383–392 (1970).
[Crossref]

A. W. Snyder, “Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide,” IEEE Trans. Microwave Theory Tech. MIT-17, 1130–1138 (1969).
[Crossref]

A. W. Snyder, “Excitation and scattering of modes on a dielectric or optical fiber,” IEEE Trans. Microwave Theory Tech. MIT-17, 1138–1144 (1969).
[Crossref]

Starr, S. J.

S. J. Starr, Thesis, University of Chicago, 1977 (unpublished).

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

Stiles, W. S.

F. Flamant and W. S. Stiles, “The directional and spectral sensitivities of the retinal rods to adapting fields of different wavelengths,” J. Physiol. 107, 187–202 (1948).

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. London Ser. B 123, 91–118 (1937).
[Crossref]

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[Crossref]

Toraldo di Francia, G.

van Kruysbergen, J.

W. Wijngaard and J. van Kruysbergen, “The function of the nonguided light in some explanations of the Stiles-Crawford effects,” in Photoreceptor Optics, edited by A. W. Snyder and R. Menzel, (Springer-Verlag, Berlin, 1975).
[Crossref]

Wijngaard, W.

W. Wijngaard, “Mode interference patterns in retinal receptor outer segments,” Vision Res. 14, 889–893 (1974).
[Crossref] [PubMed]

W. Wijngaard and J. van Kruysbergen, “The function of the nonguided light in some explanations of the Stiles-Crawford effects,” in Photoreceptor Optics, edited by A. W. Snyder and R. Menzel, (Springer-Verlag, Berlin, 1975).
[Crossref]

Wright, W. D.

W. D. Wright and J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
[Crossref]

Yamamoto, G.

Yeh, C.

Young, W. R.

Zacks, J.

R. Sansbury, J. Zacks, and J. Nachmias, “The Stiles-Crawford effect: two models evaluated,” Vision Res. 14, 803–812 (1974).
[Crossref] [PubMed]

Appl. Opt. (1)

Arch. Anat. Physiol. Anat. (1)

E. Brücke, “Ueber die physiologische Bedeutung der stabförmigen Körper und der Swillingszapfen in den Augen der Wirbeltiere,” Arch. Anat. Physiol. Anat. 11, 444–483 (1844).

IEEE Trans. Microwave Theory Tech. (4)

A. W. Snyder, “Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide,” IEEE Trans. Microwave Theory Tech. MIT-17, 1130–1138 (1969).
[Crossref]

A. W. Snyder, “Excitation and scattering of modes on a dielectric or optical fiber,” IEEE Trans. Microwave Theory Tech. MIT-17, 1138–1144 (1969).
[Crossref]

A. W. Snyder, “Coupling of modes on a tapered dielectric cylinder,” IEEE Trans. Microwave Theory Tech. MIT-18, 383–392 (1970).
[Crossref]

A. W. Snyder, “Mode propagation in a nonuniform cylindrical medium,” IEEE Trans. Microwave Theory Tech. MIT-19, 402–403 (1971).
[Crossref]

J. Appl. Phys. (1)

C. Yeh, “Elliptical dielectric waveguides,” J. Appl. Phys. 33, 3235–3243 (1962).
[Crossref]

J. Biophys. Biochem. Cytol. (1)

R. L. Sidman, “The structure and concentration of solids in photoreceptor cells studied by refractometry and interference microscopy,” J. Biophys. Biochem. Cytol. 3, 15–31 (1957).

J. Opt. Soc. Am. (14)

R. Barer, “Refractometry and interferometry of living cells,” J. Opt. Soc. Am. 47, 545–556 (1957).
[Crossref] [PubMed]

N. S. Kapany, “Fiber optics. Part I. Optical properties of certain dielectric cylinders,” J. Opt. Soc. Am. 47, 413–422 (1957).
[Crossref]

E. Snitzer, “Cylindrical dielectric waveguide modes,” J. Opt. Soc. Am. 51, 491–498 (1961).
[Crossref]

J. M. Enoch, “Optical properties of the retinal receptors,” J. Opt. Soc. Am. 53, 71–85 (1963).
[Crossref]

B. O’Brien, “The Stiles and Crawford effect in polarized light,” J. Opt. Soc. Am. 37, 275–278 (1947).
[Crossref]

G. Toraldo di Francia, “Retinal cones as dielectric antennae,” J. Opt. Soc. Am. 39, 324 (1948).
[Crossref]

B. O’Brien, “Vision and resolution in the central retina,” J. Opt. Soc. Am. 41, 882–894 (1951).
[Crossref]

J. M. Enoch and G. A. Fry, “Characteristics of a model retinal receptor studied at microwave frequencies,” J. Opt. Soc. Am. 48, 899–911 (1958).
[Crossref] [PubMed]

J. M. Enoch, “Response of a model retinal receptor as a function of wavelength,” J. Opt. Soc. Am. 50, 315–320 (1960).
[Crossref] [PubMed]

C. Yeh, “Scattering of obliquely incident light waves by elliptical fibers,” J. Opt. Soc. Am. 54, 1227–1231 (1964).
[Crossref]

C. Yeh, “Backscattering cross section of a dielectric elliptical cylinder,” J. Opt. Soc. Am. 55, 309–315 (1965).
[Crossref]

A. W. Snyder, C. Pask, and D. J. Mitchell, “Light-acceptance property of an optical fiber,” J. Opt. Soc. Am. 63, 59–64 (1973).
[Crossref] [PubMed]

C. Pask and A. W. Snyder, “Power of modes propagating inside a dielectric rod,” J. Opt. Soc. Am. 64, 393–395 (1974).
[Crossref]

A. W. Snyder and W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am. 68, 297–309 (1978).
[Crossref]

J. Physiol. (2)

W. A. H. Rushton, “Cone pigment kinetics in the protanope,” J. Physiol. 168, 374–388 (1963).

F. Flamant and W. S. Stiles, “The directional and spectral sensitivities of the retinal rods to adapting fields of different wavelengths,” J. Physiol. 107, 187–202 (1948).

Nature (1)

Mm. Poo and R. A. Cone, “Lateral diffusion of rhodopsin in the photoreceptor membrane,” Nature 247, 438–441 (1974).
[Crossref] [PubMed]

Optik (1)

I. C. Goyal, A. Kumar, A. Sharma, and A. K. Ghatak, “Stiles Crawford effect, an inhomogeneous waveguide model for human cone-receptor,” Optik 49, 39–49 (1977).

Proc. IEEE (1)

A. W. Snyder, “Power loss on optical fibers,” Proc. IEEE 60, 757–758 (1972).
[Crossref]

Proc. Phys. Soc. London (1)

W. D. Wright and J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
[Crossref]

Proc. R. Soc. Edinburgh Sec. A (1)

A. Duxbury, “A mathematical model of a retinal rod,” Proc. R. Soc. Edinburgh Sec. A,  LXVIII Part IV, 322–342 (1969).

Proc. R. Soc. London Ser. B (2)

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[Crossref]

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. London Ser. B 123, 91–118 (1937).
[Crossref]

Vision Res. (7)

A. W. Snyder and C. Pask, “The Stiles-Crawford effect—explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[Crossref] [PubMed]

W. Wijngaard, “Mode interference patterns in retinal receptor outer segments,” Vision Res. 14, 889–893 (1974).
[Crossref] [PubMed]

W. H. Miller and A. W. Snyder, “Optical function of human peripheral cones,” Vision Res. 13, 2185–2194 (1973).
[Crossref] [PubMed]

W. L. Makous, “A transient Stiles-Crawford effect,” Vision Res. 8, 1272–1284 (1968).
[Crossref]

R. Sansbury, J. Zacks, and J. Nachmias, “The Stiles-Crawford effect: two models evaluated,” Vision Res. 14, 803–812 (1974).
[Crossref] [PubMed]

P. J. de Groot and E. de Pender, “A transient effect contingent on the direction of polarization of light incident on the cornea,” Vision Res. 19, 1065–1066 (1979).
[Crossref] [PubMed]

P. J. de Groot, “Transient threshold increase due to combined changes in direction of propagation and plane of polarization,” Vision Res. 19, 1253–1259 (1979).
[Crossref] [PubMed]

Other (6)

A mechanism for describing the TSCE based upon the different types of synaptic transmissions is thought by us to be inadequate. If one assumes that the differences between synaptic transmissions make it possible to determine where the pigment molecules are bleached, then it follows that the TSCE does not depend on the retinal illuminance. In this paper we limit ourselves to the two mechanisms mentioned.

A. F. Harvey, Microwave Engineering (Academic, London, 1963).

S. J. Starr, Thesis, University of Chicago, 1977 (unpublished).

J. Bach Andersen, Thesis, Technical University of Denmark, Lyngby, Polyteknisk Forlag, 1971, ISBN 87502 0200 6.

W. Wijngaard and J. van Kruysbergen, “The function of the nonguided light in some explanations of the Stiles-Crawford effects,” in Photoreceptor Optics, edited by A. W. Snyder and R. Menzel, (Springer-Verlag, Berlin, 1975).
[Crossref]

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

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Figures (13)

FIG. 1
FIG. 1

Half-infinite homogeneous dielectric antenna, diameter 2ρ, dielectric constant 1 imbedded in a homogeneous medium, dielectric constant 2 < 1. In front of the antenna (z < 0) there is a homogeneous medium with dielectric constant 0 < 1. Overall magnetic permeability μ0 is constant. Electromagnetic power is incident in the x-z plane at an angle θ with respect to the z axis.

FIG. 2
FIG. 2

(a) Portion ηi of the power Pi(θ) in a mode guided in the antenna for different modes. (b) Fraction of power in each mode.

FIG. 3
FIG. 3

Apparatus; for explanation see text.

FIG. 4
FIG. 4

Directionally dependent acceptance of electromagnetic power by a single rod (ρ = 20.0 mm, 1 = 1.06, 0 = 2 = 1.00, z/ρ = 20.5) with end inserted into a receiving horn for different v values. ●: measurements; □: theoretically determined by means of Eq. (5).

FIG. 5
FIG. 5

Power distributions at a cross section of a nondissipative rod (ρ = 35.0 mm, 1 = 1.06, 0 = 2 = 1.00, z/ρ = 8.3). The values denoted as “MIN. POWER” and “MAX. POWER” indicate the increase in dB value with respect to an arbitrary 0.0 dB (decrease in power). Horizontal direction: dependence on λ [equivalent to v by Eq. (4)]; vertical direction: dependence on the angle of incidence θ [equivalent to α by Eq. (3)]. Large circle: boundary of the dielectric antenna. 21 locations are indicated in their correct position by a single circle. dB differences are denoted by a corresponding number of circles in the position indicator. On the far right of the figure the theoretically determined power distributions are given for v = 4.7 and α = 0.0, 0.4, 0.6, and 1.0.

FIG. 6
FIG. 6

Power distribution for a cross section of a dielectric rod (ρ = 35.0 mm, 1 = 1.06, 0 = 2 = 1.00, z/ρ = 8.3) with broadband-wavelength irradiation. Domain 3.3 < v < 4.7 for different angles of incidence.

FIG. 7
FIG. 7

Directionally dependent acceptance of electromagnetic power of a conical-shaped dielectric antenna (shown at the top) for ν = 18.0, 22.0, and 26.0 GHz.

FIG. 8
FIG. 8

✫ ◯ ★: data of Stiles2 for p(λ), which are represented according to the lower wavelength axis. ● and continuous line: theoretically determined p(λ) of a dielectric antenna with parameters ρ = 35.0 mm, 1 = 1.06, 0 = 2 = 1.00; these data are related to the upper wavelength axis, which also corresponds to the v axis at the top. The way in which the wavelength and p(λ) axes of the millimeter-wave domain are scaled to those of the light domain is explained in the text. □: power summation over the cross section of the antenna; the data are shown in Fig. 5.

FIG. 9
FIG. 9

Power distribution at a cross section for elliptically cross sectioned dielectric antenna (1 = 1.06, 0 = 2 = 1.00; the long axis is 105.0 mm, the short axis is 70.0 mm; ellipticity is 1:1.5, z = 0.3 m) for λ = 11.5 and 16.6 mm (vertical direction) and α = 0.0 and 0.8 (horizontal direction). Upper figure E parallel to the plane of incidence, lower figure E orthogonal to the plane of incidence.

FIG. 10
FIG. 10

Directionally dependent acceptance of electromagnetic power by a dissipative dielectric antenna (ρ = 35.0 mm, 1 = 1.06, 0 = 2 = 1.00, z/ρ = 7.7) for 3 different frequencies: ν = 18.0, 22.0, and 26.0 GHz. ●: E parallel to the plane of incidence; ★: E orthogonal to the plane of incidence. At the top of the figure there is the representation of the geometrical circumstances under which the measurements with a dissipative antenna were made. Dissipative material (Morganite resistance sheet 100 Ω/□) was inserted at cross section C as indicated on the left. Cross section B shows results given in this figure, cross section A shows results given in Figs. 11 and 12.

FIG. 11
FIG. 11

Power distribution at a cross section of a rod which dissipates electromagnetic power, (ρ = 35.0 mm, = 1.06, 0 = 2 = 1.00, z/ρ = 7.7) (represented in the top of Fig. 10: plane A). E is parallel to the plane of incidence. For explanation of the set of data, see legend to Fig. 5.

FIG. 12
FIG. 12

The same as in Fig. 11, but E is orthogonal to the plane of incidence (see legend to Fig. 5).

FIG. 13
FIG. 13

Differences in the results presented in Figs. 11 and 12. Power distribution in dB values for E parallel to the plane of incidence minus the power distribution in dB values for E orthogonal to the plane of incidence (see also legend to Fig. 5).

Equations (43)

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η ( r ) = η ( 0 ) 10 p ( r r o ) 2 ,
δ = 1 2 / 1 ,
α = 0 sin ( θ ) / 1 2 ,
υ = ( 2 π ρ / λ ) / 1 2 / 0 ,
P ( θ ) = i η i P i ( θ )
P i ( θ ) = ( 2 u I υ ) 2 K i ± 1 2 ( w ) K i ( w ) K i ± 2 ( w ) ,
η i = ( u υ ) 2 [ ( w u ) 2 + K i ± 1 2 ( w ) K i ( w ) K i ± 2 ( w ) ] .
u Δ : I = ± 1 u 2 Δ 2 [ Δ J i ( Δ ) u J i ( u ) J i ± 1 ( Δ ) J i ± 1 ( u ) ]
u = Δ : I = 1 2 [ J i ± 1 ( u ) J i ( u ) J i ± 2 ( u ) J i ± 1 ( u ) ] ,
Δ = ( υ / δ ) sin ( θ ) .
Δ Φ i , j = ( u i 2 u j 2 ) ( δ / 2 υ ) z / ρ ,
| S ( x , y , z ) | E ( x , y , z ) E * ( x , y , z )
P = A S d a .
Δ ϕ = ( 2 π / λ ) ( T 2 / 2 T ) ,
λ ( mm ) λ ( nm ) = ρ 1 2 | antenna d n i 2 n o 2 | foveal receptor .
Stiles : log ( η ( r ) η ( 0 ) ) = p ( λ ) ( r r o ) 2 ,
Millimeter - waves : log ( power ( α ) power ( 0 ) ) = p ( λ ) α 2 .
p ( λ ) ( r r o ) 2 = p ( λ ) α 2 .
p ( λ ) = p ( λ ) / 0.06 T 2 .
σ = 5.5.10 11 ν k tan ( δ ) , ( 1 Ω m )
( h k o ) * L = π ,
h i = ( 2 π 1 / λ ) 1 ( u i / υ ) 2 δ
k o = 2 π / λ .
π ( 2 λ L { [ 1 ( u i υ ) 2 δ ] 1 } ) .
Φ ( 2 1 c 2 2 t 2 ) Φ = 0
Φ = Φ ( r ) e i ω t ,
( 2 + ω 2 / c 2 ) Φ = 0 .
E z = A n J n ( u r ρ ) cos ( n ϕ + α n ) exp [ i ( h z ω t ) ] H z = B n J n ( u r ρ ) cos ( n ϕ + β n ) exp [ i ( h z ω t ) ] } 0 < r < ρ ,
E z = C n K n ( w r ρ ) cos ( n ϕ + α n ) exp [ i ( h z ω t ) ] H z = D n K n ( w z ρ ) cos ( n ϕ + β n ) exp [ i ( h z ω t ) ] } r > ρ ,
( u / ρ ) 2 = k 1 2 h 2 ( w / ρ ) 2 = h 2 k 2 2 } k i 2 = ω 2 μ 0 i .
υ = ( u 2 + w 2 ) 1 / 2 = ( 2 π ρ / λ ) ( 1 2 ) / 0
E r = i ( h k i 2 h 2 ) [ ( E z r ) + μ ω 4 h ( H z θ ) ] ,
E θ = i ( h k i 2 h 2 ) [ 1 r ( E z θ ) μ ω h ( H z r ) ] ,
H r = i ( h k i 2 h 2 ) [ k i 2 μ ω h ( E z d θ ) + ( H z r ) ] ,
H θ = i ( h k i 2 h 2 ) [ k i 2 μ ω h ( E z r ) + 1 r ( H z d θ ) ] .
J 0 ( u ) u J 0 ( u ) = K 0 ( w ) w K 0 ( w ) ,
J 0 ( u ) u J 0 ( u ) = ( 1 δ ) K 0 ( w ) w K 0 ( w ) ,
J n + 1 ( u ) u J n ( u ) = K n + 1 ( w ) w K n ( w ) ,
J n 1 ( u ) u J n ( u ) = K n 1 ( w ) w K n ( w ) .
k 2 h 2 = ( π / a ) 2 ,
( 2 π n / λ vac ) 2 ( 2 π / λ g ) 2 = ( π / a ) 2 ,
ν = ( c / 2 n ) [ 1 / a 2 + ( m / b ) 2 ] 1 / 2 ,
n = ( c / 2 ν ) [ 1 / a 2 + ( m / b ) 2 ] 1 / 2 .