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  1. M. H. A. KramersCollected Scientific Papers (North-Holland Publishing Company, Amsterdam, 1956), p. 333.
  2. R. de Laer-Krönig, J. Opt. Soc. Am. 12, 547 (1926).
    [Crossref]
  3. G. R. Screaton, Dispersion Relations (Oliver and Boyd, Edinburgh, London; Interscience Publishers Inc., New York, 1960) Chap. 1.
  4. H. Bode, Network Analysis and Feedback Amplifier Design, (D. Van Nostrand Company, Inc., New York, 1945).
  5. T. S. Moss, Optical Properties of Semiconductors (Academic Press Inc., New York, 1959).

1926 (1)

Bode, H.

H. Bode, Network Analysis and Feedback Amplifier Design, (D. Van Nostrand Company, Inc., New York, 1945).

de Laer-Krönig, R.

Kramers, M. H. A.

M. H. A. KramersCollected Scientific Papers (North-Holland Publishing Company, Amsterdam, 1956), p. 333.

Moss, T. S.

T. S. Moss, Optical Properties of Semiconductors (Academic Press Inc., New York, 1959).

Screaton, G. R.

G. R. Screaton, Dispersion Relations (Oliver and Boyd, Edinburgh, London; Interscience Publishers Inc., New York, 1960) Chap. 1.

J. Opt. Soc. Am. (1)

Other (4)

G. R. Screaton, Dispersion Relations (Oliver and Boyd, Edinburgh, London; Interscience Publishers Inc., New York, 1960) Chap. 1.

H. Bode, Network Analysis and Feedback Amplifier Design, (D. Van Nostrand Company, Inc., New York, 1945).

T. S. Moss, Optical Properties of Semiconductors (Academic Press Inc., New York, 1959).

M. H. A. KramersCollected Scientific Papers (North-Holland Publishing Company, Amsterdam, 1956), p. 333.

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Figures (1)

Fig. 1
Fig. 1

Grid of intervals defined by Eq. (7) for Kramers–Krönig inversion.

Equations (9)

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Φ a = - a π 0 ln R ( ν ) ν 2 - a 2 d ν ,
k a = 2 R a 1 2 sin Φ a ( 1 + R a - 2 R 1 2 cos Φ a ) - 1 ,
n a = ( 1 - R a ) ( 1 + R a - 2 R 1 2 cos Φ a ) - 1 .
R ( ν ) = R 0             for             ν < a / N ,
R ( ν ) = R             for             ν > N a ,
0 ln R ( ν ) ν 2 - a 2 d ν = - 0 a - ln R ( ν ) a 2 - ν 2 d ν + a + ln R ( ν ) ν 2 - a 2 d ν ;
Φ a = 1 π { ln R 0 tanh - 1 ( 1 N ) + a / N a - [ tanh - 1 ( ν a ) ] ( 1 / a ) ( ν i - Δ ν i / 2 ) ( 1 / a ) ( ν i + Δ ν i / 2 ) ln R ( ν i ) + a - N a [ coth - 1 ( ν a ) ] ( 1 / a ) ( ν j - Δ ν j / 2 ) ( 1 / a ) ( ν j + Δ ν j / 2 ) ln R ( ν j ) - ln R coth - 1 ( N ) } .
tanh - 1 ( 1 / N ) = coth - 1 ( N ) = tanh - 1 [ ( 1 / a ) ( ν i + Δ ν i / 2 ) ] - tanh - 1 [ ( 1 / a ) ( ν i - Δ ν i / 2 ) ] = coth - 1 [ ( 1 / a ) ( ν j - Δ ν j / 2 ) ] - coth - 1 [ ( 1 / a ) ( ν j + Δ ν j / 2 ) ] = C , a constant .
Φ a = C π [ a / N a - ln R ( ν i ) + ln R 0 - a + N a ln R ( ν j ) - ln R ] .