Parabasal field decomposition and its application to non-paraxial propagation |
Optics Express, Vol. 20, Issue 21, pp. 23502-23517 (2012)
http://dx.doi.org/10.1364/OE.20.023502
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Abstract
The fast and accurate propagation of general optical fields in free space is still a challenging task. Most of the standard algorithms are either fast or accurate. In the paper we introduce a new algorithm for the fast propagation of non-paraxial vectorial optical fields without further physical approximations. The method is based on decomposing highly divergent (non-paraxial) fields into subfields with small divergence. These subfields can then be propagated by a new semi-analytical spectrum of plane waves (SPW) operator using fast Fourier transformations. In the target plane, all propagated subfields are added coherently. Compared to the standard SPW operator, the numerical effort is reduced drastically due to the analytical handling of linear phase terms arising after the decomposition of the fields. Numerical results are presented for two examples demonstrating the efficiency and the accuracy of the new method.
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1. Introduction
1. F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58(5–6), 449–466 (2011). [CrossRef]
1. F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58(5–6), 449–466 (2011). [CrossRef]
3. A. Wuttig, M. Kanka, H. J. Kreuzer, and R. Riesenberg, “Packed domain Rayleigh-Sommerfeld wavefield propagation for large targets,” Opt. Express 18(26), 27036–27047 (2010). [CrossRef]
4. J. A. C. Veerman, J. J. Rusch, and H. P. Urbach, “Calculation of the Rayleigh–Sommerfeld diffraction integral by exact integration of the fast oscillating factor,” J. Opt. Soc. Am. A 22(4), 636–646 (2005). [CrossRef]
5. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6(5), 786–805 (1989). [CrossRef]
6. J. Braat, P. Dirksen, and A. J. E. M. Janssen, “Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A 19(5), 858–870 (2002). [CrossRef]
9. LightTrans GmbH, LightTrans VirtualLab Advanced^{TM}, www.lighttrans.com (2012).
2. Fundamentals of parabasal fields
3. Semi-analytical SPW propagation operator
4. Parabasal field decomposition technique
- The field is very divergent because of small features in the field function but it can be sampled without problems in the space domain. In this case the FFT algorithm can transform the field into the spatial frequency domain, where the PDT described above can be applied. A Gaussian beam with small waist or a strongly scattered field are examples of such fields of first kind.
- The field possesses a smooth but strong phase function, which does not allow its sampling in space domain. Here a FFT algorithm cannot be applied, meaning that the spectrum in the spatial frequency domain is not accessible. In this case the PDT must be performed in the space domain. Such fields, e.g. a spherical or cylindrical wave usually are given in an analytical form. In what follows we will refer to such fields as fields of second kind.
5. Examples for non-paraxial field propagation
5.1. Example I: convergent spherical wave
5.2. Example II: astigmatic Gaussian beam
6. Conclusion
References and links
1. | F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58(5–6), 449–466 (2011). [CrossRef] |
2. | L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995). |
3. | A. Wuttig, M. Kanka, H. J. Kreuzer, and R. Riesenberg, “Packed domain Rayleigh-Sommerfeld wavefield propagation for large targets,” Opt. Express 18(26), 27036–27047 (2010). [CrossRef] |
4. | J. A. C. Veerman, J. J. Rusch, and H. P. Urbach, “Calculation of the Rayleigh–Sommerfeld diffraction integral by exact integration of the fast oscillating factor,” J. Opt. Soc. Am. A 22(4), 636–646 (2005). [CrossRef] |
5. | M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6(5), 786–805 (1989). [CrossRef] |
6. | J. Braat, P. Dirksen, and A. J. E. M. Janssen, “Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A 19(5), 858–870 (2002). [CrossRef] |
7. | P. Valtr and P. Pechac, “Domain decomposition algorithm for complex boundary modeling using the Fourier split-step parabolic equation,” IEEE Trans. Antennas Propag. 6, 152–155 (2007). |
8. | W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968). |
9. | LightTrans GmbH, LightTrans VirtualLab Advanced^{TM}, www.lighttrans.com (2012). |
10. | E. O. Brigham, The Fast Fourier Transform and its Applications (Prentice Hall, 1988). |
OCIS Codes
(220.2560) Optical design and fabrication : Propagating methods
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
ToC Category:
Physical Optics
History
Original Manuscript: July 24, 2012
Revised Manuscript: August 30, 2012
Manuscript Accepted: August 31, 2012
Published: September 28, 2012
Citation
Daniel Asoubar, Site Zhang, Frank Wyrowski, and Michael Kuhn, "Parabasal field decomposition and its application to non-paraxial propagation," Opt. Express 20, 23502-23517 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23502
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References
- F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt.58(5–6), 449–466 (2011). [CrossRef]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
- A. Wuttig, M. Kanka, H. J. Kreuzer, and R. Riesenberg, “Packed domain Rayleigh-Sommerfeld wavefield propagation for large targets,” Opt. Express18(26), 27036–27047 (2010). [CrossRef]
- J. A. C. Veerman, J. J. Rusch, and H. P. Urbach, “Calculation of the Rayleigh–Sommerfeld diffraction integral by exact integration of the fast oscillating factor,” J. Opt. Soc. Am. A22(4), 636–646 (2005). [CrossRef]
- M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A6(5), 786–805 (1989). [CrossRef]
- J. Braat, P. Dirksen, and A. J. E. M. Janssen, “Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A19(5), 858–870 (2002). [CrossRef]
- P. Valtr and P. Pechac, “Domain decomposition algorithm for complex boundary modeling using the Fourier split-step parabolic equation,” IEEE Trans. Antennas Propag.6, 152–155 (2007).
- W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
- LightTrans GmbH, LightTrans VirtualLab AdvancedTM, www.lighttrans.com (2012).
- E. O. Brigham, The Fast Fourier Transform and its Applications (Prentice Hall, 1988).
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