Abstract

A method for exploiting nonuniform ultrahigh spatial-frequency relief gratings as space-variant polarization elements is presented. In this method the local direction of the gratings determines the polarization angles, while the period of the gratings is controlled to ensure continuity of the grating function for any desired polarization operation. We illustrate the method with a specific space-variant half-wave plate for laser radiation of 10.6 μm.

© 1992 Optical Society of America

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References

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  1. R. C. Enger, S. K. Case, Appl. Opt. 22, 3220 (1983).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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1992 (1)

1991 (2)

1990 (1)

1989 (1)

1987 (1)

1983 (2)

1974 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985), p. 707.

Case, S. K.

Cescato, L. H.

Davidson, N.

Enger, R. C.

Flanders, D. C.

D. C. Flanders, Appl. Phys. Lett. 42, 492 (1983).
[CrossRef]

Friesem, A. A.

Gila, O.

Gluch, E.

Hasman, E.

Kimura, Y.

Lee, W. H.

Nishida, N.

Ohta, Y.

Ono, Y.

Shariv, I.

Streibl, N.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985), p. 707.

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Figures (5)

Fig. 1
Fig. 1

Diagram illustrating the relationship among αin, αout, β and K.

Fig. 2
Fig. 2

Transformation from the input uniform polarization to the output nonuniform polarization. The polarization direction is indicated by the arrows.

Fig. 3
Fig. 3

Electron microscope picture of the relief pattern from a typical etched section of the polarization element.

Fig. 4
Fig. 4

Experimental setup for measuring the properties of the polarization element. P1, P2, polarizers; L1–L3, lenses; D, detector.

Fig. 5
Fig. 5

Experimental and predicted normalized light intensities as a function of the position of the slit.

Equations (12)

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Δ n = n n = [ q + ( 1 q ) / n 2 ] 1 / 2 [ q + ( 1 q ) n 2 ] 1 / 2 ,
Φ = ( 2 π / λ ) Δ n t .
K = K 0 sin ( β ) y ^ K 0 cos ( β ) x ^ ,
β ( x , y ) = [ α in ( x , y ) + α out ( x , y ) ] / 2 .
K ( x , y ) = K 0 ( x , y ) sin [ β ( x , y ) ] y ^ K 0 ( x , y ) cos [ β ( x , y ) ] x ^ ,
× K = K x y K y x = 0 .
K 0 ( cos β β x sin β β y ) + sin β K 0 x + cos β K 0 y = 0 .
ϕ ( x , y ) = λ 2 π 0 x K x ( x , y = 0 ) d x + λ 2 π 0 y K y ( x , y ) d y .
K ( x , y ) = K 0 ( y ) sin ( a x ) y ^ K 0 ( y ) cos ( a x ) x ^ .
d K 0 ( y ) d y = a K 0 ( y ) .
K 0 ( y ) = 2 π 0 exp ( a y ) ,
ϕ ( x , y ) = λ 0 a sin ( a x ) exp ( a y ) .

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