Diffraction transforms in homogeneous birefringent media

Moshe Nazarathy; J. W. Goodman

doi:10.1364/JOSAA.3.000523

Journal of the Optical Society of America A
Vol. 3,
Issue 4,
pp. 523-531
(1986)
•https://doi.org/10.1364/JOSAA.3.000523

Diffraction transforms in homogeneous birefringent media

Moshe Nazarathy and J. W. Goodman

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Moshe Nazarathy and J. W. Goodman, "Diffraction transforms in homogeneous birefringent media," J. Opt. Soc. Am. A 3, 523-531 (1986)

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Abstract

The Fresnel–Kirchhoff free-space diffraction transform is generalized to describe paraxial-beam propagation in homogeneous birefringent media, extending Fourier optics to anisotropic homogeneous media. Canonical operator formalism is used for the derivation. The method is applied to designing an optical Fourier transformer in a biaxial crystal.

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	V	F	Q	R	G	S
V	V[a₂]V[a₁] = V[a₂a₁]	V[a]F = FV[1/a]	V[a]Q[c] = Q[a²c]V[a]	V[a]R[d] = R[d/a²]V[a]	V[a]G[p] = G[pa]V[a]	V[a]S[m] = S[ma⁻¹]V[a]
F	FV[a] = V[1/a]F	FF = V[−1]	FQ[c] = R[−c]F	FR[d] = Q[−d]F	FG[p] = S[p]F	FS[m] = G[−m]F
Q	Q[c]V[a] = V[a]Q[c/a₂]	Q[c]F = FR[−c]	Q[c₂]Q[c1] = Q[c₂ + c₁]	Q[c]R[d] = R[(d⁻¹ + c)⁻¹1] V[1 + cdlQ[c⁻¹1 + d)⁻¹]	Q[c]G[p] = G[p]Q[c]	Q[c]S[m] = (Qm[−c]) G[mc]S[m]Q[c]
R	R[d]V[a] = V[a]R[a²d]	R[d]F = FQ [−d]	R[d]Q[c] = Q[(c⁻¹ + d)⁻¹] V[(1 + cd)⁻¹] R[d⁻¹ + c)⁻¹]	R[d₂]R[d₁] = R[d₂ + d₁]	R[d]G[p] = (Q_p[−d])	R[d]S[m] = S[m]R[d]
G	G [p]V[a] = V[a]G[pa⁻¹]	G[p]F = FS[−p]	G[p]Q[c] = Q[c]G[p]	G[p]R[d] = Qp[d]R[d]G[p]S[−pd]	G[p]S[pd]R[d] G[p₁]G[p₂] = G [p₂ + p₁]	G[p]S[m] = (Gm[p]) S[m]G[p]
S	S[m]V[a] = V[a]S[am]	S[m]F = FG[m]	S[m]Q[c] = (Q_m[c])Q[c] G[−mc]S[m]	S[m]R[d] = R[d]S[m]	S[m]G[p] = (Gm[−p]) G[p]S[m]	S[m₁]S[m₂] = S[m₂ + m₁]

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Journal of the Optical Society of America A