Abstract

A precision, double prism attenuator for CO2 lasers, calibrated by its gap capacitance, was constructed to evaluate its possible use as a standard for attenuation measurements. It was found that the accuracy was about 0.1 dB with a dynamic range of about 40 dB.

© 1971 Optical Society of America

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References

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  1. E. R. Schineller, in Quasi-Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), pp. 517–531.
  2. S. Minkowitz, Appl. Opt. 5, 87 (1966).
    [CrossRef] [PubMed]
  3. J. Hamasaki, unpublished.
  4. W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962).

1966 (1)

Hamasaki, J.

J. Hamasaki, unpublished.

Minkowitz, S.

Panofsky, W. K. H.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962).

Phillips, M.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962).

Schineller, E. R.

E. R. Schineller, in Quasi-Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), pp. 517–531.

Appl. Opt. (1)

Other (3)

J. Hamasaki, unpublished.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962).

E. R. Schineller, in Quasi-Optics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), pp. 517–531.

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Figures (14)

Fig. 1
Fig. 1

The basic configuration of the VDPA for CO2 lasers.

Fig. 2
Fig. 2

Propagation characteristics of a hermitian–gaussian beam through the VDPA.

Fig. 3
Fig. 3

Variation of F1 (ϕ0, λ, n, d) with the gap spacing where ϕ0 = 45°, λ = 10.6 μm, and n = 4.0.

Fig. 4
Fig. 4

Attenuation error Δ(ATT) θ due to the tilted angle of the interfaces.

Fig. 5
Fig. 5

Attenuation error Δ(ATT)ϕ0 due to misalignment of incident radiation.

Fig. 6
Fig. 6

A model for the gap capacitance calculation.

Fig. 7
Fig. 7

Attenuation error Δ(ATT)Δ θ due to variation of the tilted angle of the electrodes.

Fig. 8
Fig. 8

Sketch of the VDPA.

Fig. 9
Fig. 9

Photograph of the VDPA.

Fig. 10
Fig. 10

Experimental setup of the VDPA for CO2 lasers.

Fig. 11
Fig. 11

Variation of the attenuation of the VDPA with its gap capacitance.

Fig. 12
Fig. 12

Dependency of the transmission coefficient and gap spacing on the incident power.

Fig. 13
Fig. 13

Resettability of the VDPA.

Fig. 14
Fig. 14

Variation of the attenuation of the VDPA with its gap spacing determined by the gap capacitance.

Equations (27)

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J 0 = J a / 1 + ( n 2 - 1 ) 2 sinh 2 μ 4 n 2 cos 2 ϕ 0 ( n 2 sin 2 ϕ 0 - 1 ) ,
μ = 2 π λ d ( n 2 sin 2 ϕ 0 - 1 ) 1 2
( ATT ) = - 10 log 10 J 0
40 π · log 10 e ( d / λ ) ( n 2 sin 2 ϕ 0 - 1 ) 1 2 ,
d = S / C ,
E I ( x 1 , z 1 ) = E 0 M m H m [ ( 2 ) 1 2 x 1 / ω 0 ] exp [ - j k x 1 2 2 q + j ( m + 1 2 ) arc tan ( 2 z k ω 0 2 ) ]
E I ( x 1 , z 1 ) = E 0 - N m H m ( 2 1 2 π ω 0 ξ 1 ) exp ( - π 2 ω 0 2 ξ 1 2 ) × exp ( - j 2 π ζ 1 z 0 ) exp [ - j 2 π ( ξ 1 x 1 + ζ 1 z 1 ) ] d ξ 1 ,
E III ( x 3 , z 3 ) = E 0 - N m T ( ξ 2 ) H m ( 2 1 2 π ω 0 ξ 1 ) exp ( - π 2 ω 0 2 ξ 1 2 ) × exp ( - j 2 π ξ 1 z 0 ) exp [ - j 2 π ( ξ 1 x 3 + ξ 1 z 3 ) ] d ξ 1 ,
T ( ξ 3 ) = { cosh [ 2 π d λ ( λ 2 ξ 2 2 - 1 ) 1 2 ] + j ( n 2 + 1 - 2 λ 2 ξ 2 2 ) 2 ( n 2 - λ 2 ξ 2 2 ) 1 2 ( λ 2 ξ 2 2 - 1 ) 1 2 sinh [ 2 π d λ ( λ 2 ξ 2 2 - 1 ) 1 2 ] } - 1 ,
T ( ξ 2 ) = T ( sin ϕ 0 / λ 1 ) + ( T / ξ 1 ) ξ 1 = 0 · ξ 1 ,
x H m ( x ) = H m + 1 ( x ) + m H m - 1 ( x ) ,
E III ( x 3 , z 3 ) = E 0 - + N m [ T ( sin ϕ 0 / λ 1 ) H m ( 2 1 2 π ξ 1 ω 0 ) + ( T / ξ 1 ) ξ 1 = 0 2 · 2 1 2 π ω 0 H m + 1 ( 2 1 2 π ξ 1 ω 0 ) + m ( T / ξ 1 ) ξ 1 = 0 2 1 2 π ω 0 H m - 1 ( 2 1 2 π ω 0 ξ 1 ) ] exp ( - j 2 π ζ 1 z 0 ) exp ( - π 2 ω 0 2 ξ 1 2 ) exp [ - j 2 π ( ξ 1 x 3 + ζ 1 z 3 ) ] d ξ 1 .
J = J 0 [ 1 + ϕ 2 F l ( n , ϕ 0 , λ , d ) ] ,
F 1 = sin 2 ϕ 0 4 ( n 2 sin 2 ϕ 0 - 1 ) [ 4 ( 1 - π n cos ϕ 0 d / λ ) 2 + ( n 2 cos 2 ϕ 0 + 1 ) 2 n 2 cos 2 ϕ 0 ( n 2 sin 2 ϕ 0 - 1 ) ] .
Δ ( ATT ) ϕ = - 41.8 ϕ 2 F 1 ( n , ϕ 0 , λ , d ) [ dB ] ( ϕ :             radian ) .
J ( ϕ 0 , θ , d ) = n 2 cos 2 ϕ 0 ( n 2 sin 2 ϕ 0 - 1 ) 4 ( n 2 - 1 ) 2 exp [ - 4 π d λ ( n 2 sin 2 ϕ 0 - 1 ) 1 2 ] × [ 1 + ϕ 0 2 F 1 ( ϕ 0 , n , λ , d ) + θ 2 F 2 ( ϕ 0 , λ , n , d ) ] F 3 ( θ , ω 0 , n , ϕ 0 ) ,
F 2 ( ϕ 0 , λ , n , d ) = [ ( n 2 - 1 ) 2 tan ϕ 0 2 n cos ϕ 0 ( n 2 sin 2 ϕ 0 - 1 ) 1 2 + π n d sin ϕ 0 λ ] 2 ,
F 3 ( θ , ω 0 , n , ϕ 0 ) = exp [ 2 π 2 ω 0 2 λ 2 cos 2 ϕ 0 ( n 2 sin 2 ϕ 0 - 1 ) ] ,
Δ ( ATT ) ϕ 0 = 4.3 Δ ϕ n [ sin 2 ϕ 0 ( n 2 - 1 ) 4 n 2 cos 2 ϕ 0 ( n 2 sin 2 ϕ 0 - 1 ) - d λ 2 π n 2 sin 2 ϕ 0 ( n 2 sin 2 ϕ 0 - 1 ) 1 2 ] ,
J = J 0 [ cos 2 γ + ( n 2 sin 2 ϕ 0 - cos 2 ϕ 0 ) - 2 sin 2 γ ] ,
C = electrode θ r d s ,
d ( θ L 2 / 2 ) coth ( θ C / 2 L 1 0 ) ,
Δ ( ATT ) Δ θ = μ ( d / θ ) c Δ θ ,
( d θ ) c 5 24 L 2 2 θ d .
θ x = Δ ( ATT ) x / μ Δ x ,
θ ( θ x 2 + θ y 2 ) 1 2 ,
α arctan ( θ y / θ x ) .

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