Abstract

A variable-length reflection cell is employed in the free-space determination of the complex index of refraction of liquids at mm wavelengths. Explicit expressions are obtained for both the ordinary index of refraction η and the extinction coefficient κ.

The results of measurements on toluene, dioxane, and cyclohexane are reported for wavelengths of 4.2 mm, 3.2 mm, 2.5 mm, and 1.8 mm.

© 1959 Optical Society of America

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References

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  1. J. Ph. Poley, Appl. Sci. Research B4, 337 (1955).
    [CrossRef]
  2. F. W. Heineken and F. Bruin, Physica 23, 57 (1957).
    [CrossRef]
  3. A. G. Mungall and John Hart, Can. J. Phys. 35, 995 (1957).
    [CrossRef]
  4. Rampolla, Miller, and Smyth, J. Chem. Phys. 30, 566 (1959).
    [CrossRef]
  5. Brooks, Greig, Pine, Zoellner, and Rohrbaugh, J. Opt. Soc. Am. 43, 1191 (1953).
    [CrossRef]
  6. Rohrbaugh, Pine, Zoellner, and Hatcher, J. Opt. Soc. Am. 48, 710 (1958).
    [CrossRef]
  7. J. H. Greig and W. F. C. Ferguson, J. Opt. Soc. Am. 40, 504 (1950).
    [CrossRef]
  8. A. R. von Hippel, editor, Dielectric Materials and Applications (Technology Press, Cambridge, Massachusetts, and John Wiley & Sons, Inc., New York, 1954), p. 331.
  9. J. G. Powles, Trans. Faraday Soc. 42A, 157 (1946).

1959 (1)

Rampolla, Miller, and Smyth, J. Chem. Phys. 30, 566 (1959).
[CrossRef]

1958 (1)

1957 (2)

F. W. Heineken and F. Bruin, Physica 23, 57 (1957).
[CrossRef]

A. G. Mungall and John Hart, Can. J. Phys. 35, 995 (1957).
[CrossRef]

1955 (1)

J. Ph. Poley, Appl. Sci. Research B4, 337 (1955).
[CrossRef]

1953 (1)

1950 (1)

1946 (1)

J. G. Powles, Trans. Faraday Soc. 42A, 157 (1946).

Brooks,

Bruin, F.

F. W. Heineken and F. Bruin, Physica 23, 57 (1957).
[CrossRef]

Ferguson, W. F. C.

Greig,

Greig, J. H.

Hart, John

A. G. Mungall and John Hart, Can. J. Phys. 35, 995 (1957).
[CrossRef]

Hatcher,

Heineken, F. W.

F. W. Heineken and F. Bruin, Physica 23, 57 (1957).
[CrossRef]

Miller,

Rampolla, Miller, and Smyth, J. Chem. Phys. 30, 566 (1959).
[CrossRef]

Mungall, A. G.

A. G. Mungall and John Hart, Can. J. Phys. 35, 995 (1957).
[CrossRef]

Pine,

Poley, J. Ph.

J. Ph. Poley, Appl. Sci. Research B4, 337 (1955).
[CrossRef]

Powles, J. G.

J. G. Powles, Trans. Faraday Soc. 42A, 157 (1946).

Rampolla,

Rampolla, Miller, and Smyth, J. Chem. Phys. 30, 566 (1959).
[CrossRef]

Rohrbaugh,

Smyth,

Rampolla, Miller, and Smyth, J. Chem. Phys. 30, 566 (1959).
[CrossRef]

Zoellner,

Appl. Sci. Research (1)

J. Ph. Poley, Appl. Sci. Research B4, 337 (1955).
[CrossRef]

Can. J. Phys. (1)

A. G. Mungall and John Hart, Can. J. Phys. 35, 995 (1957).
[CrossRef]

J. Chem. Phys. (1)

Rampolla, Miller, and Smyth, J. Chem. Phys. 30, 566 (1959).
[CrossRef]

J. Opt. Soc. Am. (3)

Physica (1)

F. W. Heineken and F. Bruin, Physica 23, 57 (1957).
[CrossRef]

Trans. Faraday Soc. (1)

J. G. Powles, Trans. Faraday Soc. 42A, 157 (1946).

Other (1)

A. R. von Hippel, editor, Dielectric Materials and Applications (Technology Press, Cambridge, Massachusetts, and John Wiley & Sons, Inc., New York, 1954), p. 331.

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Figures (1)

F. 1
F. 1

Source, monochromator, transmission bolometer, and cell arrangement for measuring the complex index of refraction of liquids in the mm wavelength range.

Tables (2)

Tables Icon

Table I Measured values of η and κ.

Tables Icon

Table II Values of Φ, Φ, , and the percentage error in η for various values of κ and x1.

Equations (34)

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E ( x ) = C exp [ i ( 2 π / λ 0 ) n x ] = C exp [ ( 2 π / λ 0 ) κ x ] exp [ i ( 2 π / λ 0 ) η x ] ,
E = E 0 [ 1 + ρ e i θ D 2 e a x e i ( b x + 2 α ) ]
I = c E 0 2 { D 4 e 2 a x + 1 + 2 ρ cos θ + ρ 2 2 D 2 e a x [ ( 1 + ρ cos θ ) cos ( b x + 2 α ) + ρ sin θ sin ( b x + 2 α ) ] } .
tan φ = ( ρ sin θ ) / ( 1 + ρ cos θ ) , β = + ( 1 + 2 ρ cos θ + ρ 2 ) 1 2 , ρ sin θ = β sin φ , 1 + ρ cos θ = β cos φ .
I = c E 0 2 [ D 4 e 2 a x + β 2 2 β D 2 e a x cos ( b x + 2 α φ ) ] .
I max = c E 0 2 [ D 4 e 2 a x + β 2 + 2 β D 2 e a x ]
I min = c E 0 2 [ D 4 e 2 a x + β 2 2 β D 2 e a x ] ,
I max I min = 4 c E 0 2 β D 2 exp ( a x ) .
( I max 1 I min 1 ) / ( I max 2 I min 2 ) = exp [ a ( x 1 x 2 ) ] ,
κ = [ λ 0 / 4 π ( x 2 x 1 ) ] × ln [ ( I max 1 I min 1 ) / ( I max 2 I min 2 ) ] .
κ = λ 0 4 π ( x 2 x 1 ) ln ( I max 1 I min 1 I max 2 I min 2 ) + λ 0 4 π ( x 2 x 1 ) ln S .
S = [ 1 R 2 exp ( 2 a x 1 ) 1 R 2 exp ( 2 a x 2 ) ] 2 × [ P 2 R Q exp ( 2 a x 2 ) R 2 Q exp ( 3 a x 2 ) P 2 R Q exp ( 2 a x 1 ) R 2 Q exp ( 3 a x 1 ) ]
R = ( η η ) / ( η + η ) ,
P = 2 ( 1 + R D 2 ) , and Q = D 2 + R 2 D 2 + 2 R .
[ λ 0 / 4 π ( x 2 x 1 ) ] ln S = 0.00004 ,
η β sin ( b x + 2 α φ ) + κ β cos ( b x + 2 α φ ) = κ D 2 e a x .
x m + 1 x m = ( λ 0 / 2 η ) +
x m + 1 x m = ( λ 0 / 2 η ) + , < 0 ,
( 1 / λ 0 2 ) = ( 1 / ( λ 0 ) 2 ) + ( 1 / λ c 2 ) .
( 1 / λ 2 ) = ( 1 / ( λ ) 2 ) + ( 1 / λ c 2 ) .
η = [ ( λ 0 / λ ) 2 + ( λ 0 / λ c ) 2 1 + ( λ 0 / λ c ) 2 ] 1 2 .
sin ( b x + ψ ) + ( κ / η ) cos ( b x + ψ ) = ( κ D 2 / η β ) e a x .
I = c E 0 2 ( D 4 + β 2 2 β D 2 cos m π ) .
sin Φ 1 + ( κ / η ) cos Φ 1 = ( κ D 2 / η β ) e a x 1 ,
x 2 = x 1 + ( λ 0 / 2 η ) + , > 0 ,
sin Φ 1 + ( κ / η ) cos Φ 1 = ( κ D 2 / η β ) e a x 1 .
sin Φ 2 + ( κ / η ) cos Φ 2 = ( κ D 2 / η β ) e a x 2 .
x r + 1 x r = ( λ 0 / 2 η ) + ,
x = x 2 = x 1 + ( λ 0 / 2 η ) +
sin Φ cos b + cos Φ sin b + ( κ / η ) + cos Φ cos b ( κ / η ) sin Φ sin b = ( κ D 2 / η β ) exp ( a ) × exp { a [ x 1 + ( λ 0 / 2 η ) ] } .
sin Φ + ( κ / η ) cos Φ + ( cos Φ ( κ / η ) sin Φ ) b = ( κ D 2 / η β ) ( 1 a ) exp { a [ x 1 + ( λ 0 / 2 η ) ] } ( a κ D 2 / η β ) exp { a [ x 1 + ( λ 0 / 2 η ) ] } .
= κ D 2 exp { a [ x 1 + ( λ 0 / 2 η ) ] } β ( η sin Φ + κ cos Φ ) β b ( η cos Φ κ sin Φ ) + κ D 2 a exp { a [ x 1 + ( λ 0 / 2 η ) ] } .
sin Φ + ( κ / η ) cos Φ = ( κ D 2 / η β ) e a x 1 .
sin Φ = η κ D 2 ( η 2 + κ 2 ) β e a x 1 ± κ ( η 2 + κ 2 ) β [ ( η 2 + κ 2 ) β 2 κ 2 D 4 e 2 a x 1 ] 1 2 .