Abstract

A general formula that gives the absorption of a dielectric substrate with two metallic films is derived. The variation of the absorption as a function of the relevant parameters (refractive index of substrate, thickness of metallic films, and angle of incidence) is analyzed in order to identify the criteria for the optimization of this substrate as an absorber for composite bolometers.

© 1981 Optical Society of America

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References

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  1. N. Coron, G. Dambier, and J. Leblanc, in Infrared Detection Techniques for Space Research, V. Manno and J. Ring, eds. (Reidel, Dordrecht, The Netherlands, 1971), pp. 121–131.
  2. M. W. Werner and et al., “Observation of 1-millimeter continuum radiation from the DR 21 region,” Astrophys J. 199, L185–L187 (1975).
    [CrossRef]
  3. N. S. Nishioka, P. L. Richards, and D. P. Woody, “Composite bolometers for submillimeter wavelengths,” Appl. Opt. 17, 1562–1567 (1978).
    [CrossRef] [PubMed]
  4. L. N. Hadley and D. M. Dennison, “Reflection and transmission interference filters,” J. Opt. Soc. Am. 37, 451–465 (1947).
    [CrossRef] [PubMed]
  5. M. E. Golay, “A pneumatic infrared detector,” Rev. Sci. Instrum. 18, 357–362 (1947).
    [CrossRef] [PubMed]
  6. B. Carli, “Design of a blackbody reference standard for the submillimeter region,” IEEE Trans. Microwave Theory Tech. MTT-22, 1094–1099 (1975).
  7. J. Clarke and et al., “Superconductive bolometers for submillimeter wavelengths,” J. Appl. Phys. 48, 4865–4879 (1977).
    [CrossRef]
  8. S. A. El-Atawy and P. A. R. Ade, “Far-infrared composite bolometers using surface ion implanted Ge as an absorbing surface,” Infrared Phys. 18, 683–690 (1978).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.

1978 (2)

S. A. El-Atawy and P. A. R. Ade, “Far-infrared composite bolometers using surface ion implanted Ge as an absorbing surface,” Infrared Phys. 18, 683–690 (1978).
[CrossRef]

N. S. Nishioka, P. L. Richards, and D. P. Woody, “Composite bolometers for submillimeter wavelengths,” Appl. Opt. 17, 1562–1567 (1978).
[CrossRef] [PubMed]

1977 (1)

J. Clarke and et al., “Superconductive bolometers for submillimeter wavelengths,” J. Appl. Phys. 48, 4865–4879 (1977).
[CrossRef]

1975 (2)

M. W. Werner and et al., “Observation of 1-millimeter continuum radiation from the DR 21 region,” Astrophys J. 199, L185–L187 (1975).
[CrossRef]

B. Carli, “Design of a blackbody reference standard for the submillimeter region,” IEEE Trans. Microwave Theory Tech. MTT-22, 1094–1099 (1975).

1947 (2)

Ade, P. A. R.

S. A. El-Atawy and P. A. R. Ade, “Far-infrared composite bolometers using surface ion implanted Ge as an absorbing surface,” Infrared Phys. 18, 683–690 (1978).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.

Carli, B.

B. Carli, “Design of a blackbody reference standard for the submillimeter region,” IEEE Trans. Microwave Theory Tech. MTT-22, 1094–1099 (1975).

Clarke, J.

J. Clarke and et al., “Superconductive bolometers for submillimeter wavelengths,” J. Appl. Phys. 48, 4865–4879 (1977).
[CrossRef]

Coron, N.

N. Coron, G. Dambier, and J. Leblanc, in Infrared Detection Techniques for Space Research, V. Manno and J. Ring, eds. (Reidel, Dordrecht, The Netherlands, 1971), pp. 121–131.

Dambier, G.

N. Coron, G. Dambier, and J. Leblanc, in Infrared Detection Techniques for Space Research, V. Manno and J. Ring, eds. (Reidel, Dordrecht, The Netherlands, 1971), pp. 121–131.

Dennison, D. M.

El-Atawy, S. A.

S. A. El-Atawy and P. A. R. Ade, “Far-infrared composite bolometers using surface ion implanted Ge as an absorbing surface,” Infrared Phys. 18, 683–690 (1978).
[CrossRef]

Golay, M. E.

M. E. Golay, “A pneumatic infrared detector,” Rev. Sci. Instrum. 18, 357–362 (1947).
[CrossRef] [PubMed]

Hadley, L. N.

Leblanc, J.

N. Coron, G. Dambier, and J. Leblanc, in Infrared Detection Techniques for Space Research, V. Manno and J. Ring, eds. (Reidel, Dordrecht, The Netherlands, 1971), pp. 121–131.

Nishioka, N. S.

Richards, P. L.

Werner, M. W.

M. W. Werner and et al., “Observation of 1-millimeter continuum radiation from the DR 21 region,” Astrophys J. 199, L185–L187 (1975).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.

Woody, D. P.

Appl. Opt. (1)

Astrophys J. (1)

M. W. Werner and et al., “Observation of 1-millimeter continuum radiation from the DR 21 region,” Astrophys J. 199, L185–L187 (1975).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

B. Carli, “Design of a blackbody reference standard for the submillimeter region,” IEEE Trans. Microwave Theory Tech. MTT-22, 1094–1099 (1975).

Infrared Phys. (1)

S. A. El-Atawy and P. A. R. Ade, “Far-infrared composite bolometers using surface ion implanted Ge as an absorbing surface,” Infrared Phys. 18, 683–690 (1978).
[CrossRef]

J. Appl. Phys. (1)

J. Clarke and et al., “Superconductive bolometers for submillimeter wavelengths,” J. Appl. Phys. 48, 4865–4879 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

Rev. Sci. Instrum. (1)

M. E. Golay, “A pneumatic infrared detector,” Rev. Sci. Instrum. 18, 357–362 (1947).
[CrossRef] [PubMed]

Other (2)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.

N. Coron, G. Dambier, and J. Leblanc, in Infrared Detection Techniques for Space Research, V. Manno and J. Ring, eds. (Reidel, Dordrecht, The Netherlands, 1971), pp. 121–131.

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Figures (12)

Fig. 1
Fig. 1

Structure of a composite bolometer.

Fig. 2
Fig. 2

Geometrical and optical parameters of the absorber.

Fig. 3
Fig. 3

Residual absorption periodicity under conditions (10) and (11) as a function of θ. Dashed line and solid line are extreme values of absorption for TE waves. Dash–dot line and solid line are extreme values of absorption for TM waves.

Fig. 4
Fig. 4

Absorption as a function of β for those values of f and f′ that maximize the monochromatic absorption at normal incidence. Dashed line, n = 1; dash–dot line, n = 2; solid line, n = 3.

Fig. 5
Fig. 5

Absorption as a function of the angle of incidence θ for those values of f and f′ that maximize the monochromatic absorption at normal incidence. The two curves refer to the two planes of polarization and are calculated at the wavelength that corresponds to the first-order maximum of A (see Fig. 4).

Fig. 6
Fig. 6

Absorption as a function of β in the case of configuration A and for the value of f′ that maximizes the monochromatic absorption at normal incidence. Dashed line, n = 1; dash–dot line, n = 2; solid line, n = 3.

Fig. 7
Fig. 7

Maximum value of the average absorption A ¯ at normal incidence as a function of n for general case, solid line; configuration A, long-dashed line; configuration B, short-dashed line; and configuration C, dash–dot line. Circles mark the points corresponding to the cases studied in Figs. 9,11, and 12.

Fig. 8
Fig. 8

Contour lines of the average absorption A ¯ in terms of f and f′ at normal incidence and n = 2.

Fig. 9
Fig. 9

Maximum and minimum values of the absorption (sin2β = 1, upper curves; sin2β = 0, lower curves), calculated for n = 2 in the two planes of polarization (dashed line, TE waves; dash–dot line, TM waves) as a function of the angle of incidence. f and f′ are those values that maximize the average absorption A ¯ for normal incidence.

Fig. 10
Fig. 10

Average adsorption A ¯ at normal incidence as a function of f in the case of configuration A. Dashed line, n = 1; dash–dot line, n = 2; solid line, n = 3.

Fig. 11
Fig. 11

Maximum and minimum values of the absorption (sin2β = 1, upper curves; sin2β = 0, lower curves) in the case of configuration A, calculated for n = 2 in the two planes of polarization (dashed line, TE waves; dash–dot line, TM waves) as a function of the angle of incidence. f′ is the term that maximizes the average absorption for normal incidence.

Fig. 12
Fig. 12

Maximum and minimum values of the absorption, as in Fig. 11, calculated for n = 3.

Tables (2)

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Table 1 Reflection and Transmission Coefficients

Tables Icon

Table 2 Maximum Average Absorption

Equations (21)

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= r 12 2 + g 2 r 23 2 - 2 r 12 r 23 g cos ( 2 β ) 1 + r 23 2 r 21 2 - 2 r 23 r 21 cos ( 2 β ) ,
T = t 12 2 t 23 2 1 + r 23 2 r 21 2 - 2 r 23 r 21 cos ( 2 β ) ,
A = 1 - - T ,
n ¯ k 1.
s λ 0 n ¯
A = 4 p q 2 ( f + f ) + 4 p f ( p + f - q ) ( p + f + q ) sin 2 β q 2 ( 2 p + f + f ) 2 + ( p + f - q ) ( p + f + q ) ( p + f - q ) ( p + f + q ) sin 2 β ,
A = 4 p q 2 [ n 4 p 2 ( f + f ) - f ( n 2 p + q + f p q ) ( n 2 p - q - f p q ) sin 2 β ] n 4 p 2 q 2 [ 2 + p ( f + f ) ] 2 + ( n 2 p - q - f p q ) ( n 2 p - q - f p q ) ( n 2 p + q + f p q ) ( n 2 p + q + f p q ) sin 2 β ,
f = 0 and f 0             ( configuration A ) , f 0 and f = 0             ( configuration B ) , f 0 and f =             ( configuration C ) .
f = q - p .
A ( f = q - p ) = 4 p ( f + q - p ) ( f + q + p ) 2 .
f = 3 p - q
f = n - 1
f = 3 - n ,
( A f ) β = π / 2 = 0 ,             ( A f ) β = π / 2 = 0 ,
A ( f = 1 , f = ) = 4 p sin 2 β q 2 + ( 1 + p - q ) ( 1 + p + q ) sin 2 β .
A θ = 0 ( f = 1 , n = 2 , f = ) = sin 2 β = 1 / 2 ( 1 - cos β ) , θ = 0 ( f = 1 , n = 2 , f = ) = 1 / 2 ( 1 + cos β ) .
A ¯ = 2 π 0 π / 2 A ( β ) d β = 4 p q ( f + f ) ( f + p + q ) + f ( f + p - q ) ( 2 p + f + f ) ( 2 p + f + f ) ( f + p + q ) [ ( f + p ) ( f + p ) + q 2 ] .
A ¯ = 4 p q f ( 2 p + f ) [ p ( f + p ) + q 2 ] .
A ¯ ( f max ) = 8 p q { 2 p + [ 2 ( p 2 + q 2 ) ] 1 / 2 } 2
A ¯ = 4 p f ( f + p + q ) ( f + q ) .
A ¯ ( f max ) = 2 p p + [ p ( p + q ) ] 1 / 2 .