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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).
  2. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice Hall, Englewood Cliffs, N.J., 1973), p. 594.
  3. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 18, Eq. (1.6–14).
  4. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974), p. 5, Eq. (1.2–7).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Felsen, L. B.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice Hall, Englewood Cliffs, N.J., 1973), p. 594.

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 18, Eq. (1.6–14).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974), p. 5, Eq. (1.2–7).

Marcuvitz, N.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice Hall, Englewood Cliffs, N.J., 1973), p. 594.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice Hall, Englewood Cliffs, N.J., 1973), p. 594.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 18, Eq. (1.6–14).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974), p. 5, Eq. (1.2–7).

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Figures (3)

Fig. 1
Fig. 1

The caustic is defined as the tangent to all the rays.

Fig. 2
Fig. 2

The continuous refractive index distribution n(y) can conceptually be considered as the limit of a staircase curve.

Fig. 3
Fig. 3

This figure defines the parameters κ and β.

Equations (10)

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ϕ = - 2 arctan [ ( β 2 - n 2 2 k 2 ) 1 / 2 ( n 1 2 k 2 - β 2 ) 1 / 2 ] .
n ( y ) y = t = β / k ,
γ = ( β 2 - n 2 2 k 2 ) 1 / 2 ,
κ = ( n 1 2 k 2 - β 2 ) 1 / 2 .
( y 1 - t ) γ t y 1 [ β 2 - n 2 ( y ) k 2 ] 1 / 2 d y ,
( t - y 2 ) κ y 2 t [ n 2 ( y ) k 2 - β 2 ] 1 / 2 d y .
γ κ = lim 0 0 { β 2 - [ n ( t + u ) k ] 2 } 1 / 2 d u 0 { [ n ( t - u ) k ] 2 - β 2 } 1 / 2 d u .
n ( t + u ) = n ( t ) + u ( d n d y ) y = t
γ / κ = 1.
ϕ = - 2 arctan 1 = - ( π / 2 ) .

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