Abstract

We present a new method for the analysis of diffractive optical elements, which we refer to as field stitching. It is suitable for use with grating structures of arbitrarily large period, even when the local feature size is of the order of a wavelength. Furthermore, the concept is straightforwardly extendable to aperiodic structures. To assess its applicability, we have calculated the diffracted orders from a 1 × 81 fan-out grating with periods of 100λ and 10, 000λ. The field-stitched calculations agree very well with independent rigorous predictions for the small-period element and scalar-regime predictions for the large-period element. We believe that a variety of areas within the diffractive-optics field will benefit from this new analytical tool. It promises accurate analysis and, by facilitating component optimization, high-performance designs.

© 1996 Optical Society of America

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References

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  1. M. G. Moharam, T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981).
    [CrossRef]
  2. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, Opt. Acta 28, 413 (1981).
    [CrossRef]
  3. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  4. K. Knop, J. Opt. Soc. Am. 68, 1206 (1978).
    [CrossRef]
  5. J. T. Sheridan, C. J. R. Sheppard, J. Opt. Soc. Am. A 4, 614 (1993).
    [CrossRef]
  6. F. Montiel, M. Nevière, J. Opt. Soc. Am. A 12, 2672 (1995).
    [CrossRef]

1995

1993

1981

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

M. G. Moharam, T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981).
[CrossRef]

1978

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Gaylord, T. K.

Knop, K.

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Moharam, M. G.

Montiel, F.

Nevière, M.

Sheppard, C. J. R.

Sheridan, J. T.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Other

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic representation of a grating and associated parameters.

Fig. 2
Fig. 2

Analysis of a 1 × 81 fan-out grating with a period of 100 wavelengths. The dotted curve shows the diffracted-order efficiencies as calculated with the rigorous BKK method. The field-stitching curve is indistinguishable on this plot. The dashed curve represents the percentage difference of the field-stitched efficiency from the rigorous efficiency. Field-stitching parameters are w = 10, l = 201.

Fig. 3
Fig. 3

Analysis of a 1 × 81 fan-out grating with a period of 10,000 wavelengths. The dotted curve shows the diffracted-order efficiencies as calculated with paraxial scalar theory (with Fresnel reflection adjustment). The field-stitching curve is also plotted but is only distinguishable from the scalar curve in the zeroth order. The dashed curve represents the percentage difference of the field-stitched efficiency from the scalar efficiency. Field-stitching parameters are w = 20, l = 151.

Equations (4)

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U t = p = p = T p exp { i [ γ p x t p ( z h ) ] } ,
U b = m = m = T m ( n ) δ n exp [ i γ m ( x + x s ) ] , ( n 1 ) w x n w ,
T p = 1 d n = 1 N m = m ( ) m ( + ) T m ( n ) δ n exp { i γ m [ x s + ( 1 n ) w ] } × ( n 1 ) w n w exp [ i γ m x ] exp ( i γ p x ) d x .
m ( + ) = largest integer d l λ [ n t n 0 sin ( θ ) ] , m ( ) = smallest integer d l λ [ n t n 0 sin ( θ ) ] ,

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