Computer modeling wave propagation with a variation of the Helmholtz-Kirchhoff relation

Paul G. Rudolf; Jeffrey J. Tollett; Rebecca R. McGowan

doi:10.1364/AO.29.000998

Applied Optics
Vol. 29,
Issue 7,
pp. 998-1003
(1990)
•https://doi.org/10.1364/AO.29.000998

Computer modeling wave propagation with a variation of the Helmholtz-Kirchhoff relation

Paul G. Rudolf, Jeffrey J. Tollett, and Rebecca R. McGowan

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Paul G. Rudolf, Jeffrey J. Tollett, and Rebecca R. McGowan, "Computer modeling wave propagation with a variation of the Helmholtz-Kirchhoff relation," Appl. Opt. 29, 998-1003 (1990)

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Abstract

We have employed a variation of the Helmholtz-Kirchhoff equation to computer model a wide range of diffracting systems. The equation leads to a straightforward, easily understood and implemented simulation. It is shown to work as well in the Fresnel as in the Fraunhofer limits and is used to model a wide variety of aperture shapes and incident wavefronts.

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	Analytical	Computed
sin(θ)	(normalized intensity)
0.0000	1.000000	1.000000
0.0032	0.872174	0.872177
0.0047	0.731029	0.731044
0.0063	0.564337	0.564365
0.0079	0.395228	0.395262
0.0095	0.244454	0.244485
0.0111	0.126755	0.126776
0.0127	0.048836	0.048846
0.0142	0.009267	0.009268
0.0158	0.000149	0.000149
0.0174	0.009966	0.009975
0.0190	0.026791	0.026816
0.0206	0.041032	0.041074
0.0221	0.047109	0.047162
0.0253	0.033444	0.033491
0.0269	0.020256	0.020288
0.0285	0.008616	0.008631
0.0300	0.001579	0.001581
0.0316	0.000140	0.000140

		Analytical	Calculated
X (10³ λ)	Y (10³ λ)	(normalized intensity)
0	0	1.000000	1.000000
500	0	0.810569	0.811839
1000	0	0.405285	0.408625
1500	0	0.090063	0.092950
2000	0	0.000000	0.000025
2500	0	0.032423	0.032047
3000	0	0.045032	0.048307
3500	0	0.016542	0.021251
4000	0	0.000000	0.000427
4500	0	0.010007	0.007783
5000	0	0.016211	0.018683
500	500	0.657023	0.659257
1000	1000	0.164256	0.167798
1500	1500	0.008111	0.008962
2000	2000	0.000000	0.000000
2500	2500	0.001051	0.000929
3000	3000	0.002028	0.002393
3500	3500	0.000274	0.000610
4000	4000	0.000000	0.000003
4500	4500	0.000100	0.000022
5000	5000	0.000263	0.000283

	Analytical	Computed
sin(θ)	(normalized intensity)
0.0000	1.000000	1.000000
0.0032	0.872174	0.872177
0.0047	0.731029	0.731044
0.0063	0.564337	0.564365
0.0079	0.395228	0.395262
0.0095	0.244454	0.244485
0.0111	0.126755	0.126776
0.0127	0.048836	0.048846
0.0142	0.009267	0.009268
0.0158	0.000149	0.000149
0.0174	0.009966	0.009975
0.0190	0.026791	0.026816
0.0206	0.041032	0.041074
0.0221	0.047109	0.047162
0.0253	0.033444	0.033491
0.0269	0.020256	0.020288
0.0285	0.008616	0.008631
0.0300	0.001579	0.001581
0.0316	0.000140	0.000140

		Analytical	Calculated
X (10³ λ)	Y (10³ λ)	(normalized intensity)
0	0	1.000000	1.000000
500	0	0.810569	0.811839
1000	0	0.405285	0.408625
1500	0	0.090063	0.092950
2000	0	0.000000	0.000025
2500	0	0.032423	0.032047
3000	0	0.045032	0.048307
3500	0	0.016542	0.021251
4000	0	0.000000	0.000427
4500	0	0.010007	0.007783
5000	0	0.016211	0.018683
500	500	0.657023	0.659257
1000	1000	0.164256	0.167798
1500	1500	0.008111	0.008962
2000	2000	0.000000	0.000000
2500	2500	0.001051	0.000929
3000	3000	0.002028	0.002393
3500	3500	0.000274	0.000610
4000	4000	0.000000	0.000003
4500	4500	0.000100	0.000022
5000	5000	0.000263	0.000283

Abstract

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Figures (8)

Tables (2)

Equations (15)

Applied Optics