Abstract

The transmittance of skew rays through metal light pipes is examined with ray tracing. The transmittance with respect to pipe length is compared with analytical approximations and with experimental data. The effects of pipe material, pipe shape, wavelength of the incident light, distribution of the incident light, and maximum angle of incidence on transmittance are examined. The transmittance is shown, in general, not to be exponential with respect to pipe length. Additionally, the effect on transmittance of elbows and gaps in a pipe is investigated.

© 1999 Optical Society of America

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References

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  1. R. C. Ohlmann, P. L. Richards, M. Tinkham, “Far infrared transmission through metal light pipes,” J. Opt. Soc. Am. 48, 531–533 (1958).
    [CrossRef]
  2. E. Fu, “Transmission of submillimeter waves through metal light pipes,” J. Opt. Soc. Am. B 13, 702–705 (1996).
    [CrossRef]
  3. R. E. Harris, R. L. Cappelletti, D. M. Ginsberg, “Far infrared transmission through metal light pipes with low thermal conductance,” Appl. Opt. 5, 1083–1084 (1966).
    [CrossRef] [PubMed]
  4. E. V. Loewenstein, D. C. Newell, “Ray traces through hollow metal light-pipe elements,” J. Opt. Soc. Am. 59, 407–414 (1969).
    [CrossRef]
  5. For the square pipes Cartesian coordinates were used in place of the polar coordinates, r and α.
  6. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, New York, 1992), pp. 26–34.
  7. A Gaussian distribution is accomplished by weighting the uniform distribution by wr=exp-r22σ2, where σ is the standard deviation of the distribution.
  8. H. E. Bennett, J. M. Bennett, “Validity of the Drude theory,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed. (North-Holland, Amsterdam, 1966), pp. 175–175.
  9. L. Muldawer, H. J. Goldman, “Optical constants of beta-brass alloys,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed., (North-Holland, Amsterdam, 1966), pp. 574–574.
  10. G. K. White, Experimental Techniques in Low-Temperature Physics (Oxford U. Press, Toronto, 1959), pp. 298–298.

1996 (1)

1969 (1)

1966 (1)

1958 (1)

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, New York, 1992), pp. 26–34.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, New York, 1992), pp. 26–34.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed. (North-Holland, Amsterdam, 1966), pp. 175–175.

Bennett, J. M.

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed. (North-Holland, Amsterdam, 1966), pp. 175–175.

Cappelletti, R. L.

Fu, E.

Ginsberg, D. M.

Goldman, H. J.

L. Muldawer, H. J. Goldman, “Optical constants of beta-brass alloys,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed., (North-Holland, Amsterdam, 1966), pp. 574–574.

Harris, R. E.

Loewenstein, E. V.

Muldawer, L.

L. Muldawer, H. J. Goldman, “Optical constants of beta-brass alloys,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed., (North-Holland, Amsterdam, 1966), pp. 574–574.

Newell, D. C.

Ohlmann, R. C.

Richards, P. L.

Tinkham, M.

White, G. K.

G. K. White, Experimental Techniques in Low-Temperature Physics (Oxford U. Press, Toronto, 1959), pp. 298–298.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (1)

Other (6)

For the square pipes Cartesian coordinates were used in place of the polar coordinates, r and α.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, New York, 1992), pp. 26–34.

A Gaussian distribution is accomplished by weighting the uniform distribution by wr=exp-r22σ2, where σ is the standard deviation of the distribution.

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed. (North-Holland, Amsterdam, 1966), pp. 175–175.

L. Muldawer, H. J. Goldman, “Optical constants of beta-brass alloys,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed., (North-Holland, Amsterdam, 1966), pp. 574–574.

G. K. White, Experimental Techniques in Low-Temperature Physics (Oxford U. Press, Toronto, 1959), pp. 298–298.

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Figures (11)

Fig. 1
Fig. 1

Initial position, defined by position coordinates r and α, and initial wave vector, defined by the spherical coordinates θ and ϕ, of an incident light ray.

Fig. 2
Fig. 2

Calculated transmittance for various values of ϕ m . In this simulation a brass pipe was used with λ = 140 µm and a uniform input distribution.

Fig. 3
Fig. 3

s and p components of the electric-field vector for a nonskew ray with θ i = 1.5. The transmittance of this ray is also shown. In this simulation a brass pipe was used with λ = 140 µm.

Fig. 4
Fig. 4

Transmittance of a circular brass pipe for incident light of various wavelengths in the infrared region. In these simulations ϕ m = 0.125 rad, and a uniform distribution of incident light was used. Note that on the semilogarithmic scale the transmittance is clearly not exponential for small wavelengths.

Fig. 5
Fig. 5

Elliptically polarized electric-field vector defined by four parameters: phase angle δ, azimuth angle θ a , ellipticity ∊, and amplitude A. This representation is depicted by Eq. (10).

Fig. 6
Fig. 6

Comparison of Eqs. (5) and (6), experimental data provided by Ohlmann et al.,1 and the results of the simulation. Included are a simulation with a pretube of 10 cm and a simulation with no pretube. The incident light is of λ = 140 µm. The pipe is a brass pipe of radius R = 0.55 cm and ϕ m = 0.3398 rad. For the simulation, the light was considered to have uniform distribution.

Fig. 7
Fig. 7

Comparison of transmittance for light pipes with Gaussian and uniform input distributions. Also, a pipe test with a Gaussian distribution over angle ϕ is shown. In these simulations a circular brass pipe was used with λ = 140 µm and ϕ m = 0.125 rad.

Fig. 8
Fig. 8

Transmittance of silver, gold, aluminum, brass, and stainless-steel light pipes. The pipes are all circular pipes with uniform input distribution of light. All pipes are simulated at λ = 140 µm and ϕ m = 0.125 rad with the optical properties given in Table 1.

Fig. 9
Fig. 9

Comparison of circular, square, elliptical, and semicircular pipes with the same input area and uniform input distribution. The input area of each pipe is π. In these simulations brass pipes were used with λ = 140 µm and ϕ m = 0.125 rad. For the elliptical pipes a is the semimajor axis and b is the semiminor axis.

Fig. 10
Fig. 10

Effect on transmittance of a 90° elbow. To illustrate the effect of the mirror we have reflected the elbow in the mirror plane to yield an image (I′,II′) of the elbow (I,II) and removed the mirror. Transmitted rays reflect down pipe II′, and rays that strike the two dashed holes will either go back up in image pipe I′ or be highly attenuated in pipe II. The elbow loss is equivalent to that of the two circular holes.

Fig. 11
Fig. 11

Percentage loss in intensity to the gap as a function of gap length for ϕ m = 0.125 and ϕ m = 0.25 rad. For this simulation circular brass pipes of R = 1 were used with λ = 140 µm and a uniform input distribution. The gap was arbitrarily centered at z = 100 down the length of the pipe.

Tables (1)

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Table 1 Optical Properties of Various Metals

Equations (13)

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E=E0 expik·p,
rs=cos2 θi--sin2 θicos2 θi+-sin2 θi, rp= cos2 θi--sin2 θi cos2 θi+-sin2 θi,
θr=cos-1k1×n1·k1×n2|k1×n1|k1×n2|.
T= w|Ef|2 w|Ei|2,
T=½1+exp-2q-qF28,  q=0.09ρλLR.
T=exp-νσL2R,
T=rsmEs2+rpmEp2.
Es=rsEs cos θr+rpEp sin θr,
Ep=rpEp cos θr-rsEs sin θr.
EsEp=A expiδcos θa cos -i sin θa sin sin θa cos +i cos θa sin .
=1-ωp2ω2+γ2+i ωp2γωω2+γ2,
4πσ0=ωp2τ.
wr=exp-r22σ2,

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