Due to analytical and numerical difficulties, the propagation of optical fields in any state of spatial coherence is traditionally computed under severe approximations. The paraxial approach in the Fresnel–Fraunhofer domain is one of the most widely used. These approximations provide a rough knowledge of the actual light behavior as it propagates, which is not enough for supporting applications, such as light propagation under a high numerical aperture (NA). In this paper, a non-approximated model for the propagation of optical fields in any state of spatial coherence is presented. The method is applicable in very practical cases, as high-NA propagations, because of its simplicity of implementation. This approach allows for studying unaware behaviors of light as it propagates. The light behavior close to the diffracting transmittances can also be analyzed with the aid of the proposed tool.

© 2011 OSA

1. F. Zernike, “The concept of Degree of Coherence and its application to optical problems,” Physica5(8), 785–795 (1938). [CrossRef]
2. M. Born and E. Wolf, Principles of Optics, 6th. ed. (Pergamon Press, 1993), Chap. 10.
3. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995), Chap. 4.
4. Z. Jaroszewicz, Axicons: Design and Propagation Properties (Research and development treatises, SPIE Polish chapter) (SPIE, 1997), Vol. 5.
5. D. C. Alvarez-Palacio and J. Garcia-Sucerquia, “Lensless microscopy technique for static and dynamic colloidal systems,” J. Colloid Interface Sci.349(2), 637–640 (2010). [CrossRef] [PubMed]
6. K. Jahn and N. Bokor, “Intensity control of the focal spot by vectorial beam shaping,” Opt. Commun.283(24), 4859–4865 (2010). [CrossRef]
7. R. Castañeda, “The optics of spatial coherence wavelets, in Advances in Imaging and Electron Physics, P. Hawkes, ed. (Academic Press, 2010), Vol. 164.
8. R. Castañeda, G. Cañas-Cardona, and J. Garcia-Sucerquia, “Radiant, virtual, and dual sources of optical fields in any state of spatial coherence,” J. Opt. Soc. Am. A27(6), 1322–1330 (2010). [CrossRef] [PubMed]
9. R. Castañeda, H. Muñoz-Ossa, and J. Garcia-Sucerquia, “Efficient numerical calculation of interference and diffraction of optical fields in any state of spatial coherence in the phase-space representation,” Appl. Opt.49(31), 6063–6071 (2010). [CrossRef]
10. R. Castañeda, H. Muñoz, and G. Cañas-Cardona, “The structured spatial coherence support,” J. Mod. Opt. , 58(11) (2011), doi: . [CrossRef]
11. K. Iizuka, Engineering Optics (Springer Verlag, 1985).
12. R. Castañeda and J. García, “Classes of source pairs in interference and diffraction,” Opt. Commun.226(1-6), 45–55 (2003). [CrossRef]

Appl. Opt.

• R. Castañeda, H. Muñoz-Ossa, and J. Garcia-Sucerquia, “Efficient numerical calculation of interference and diffraction of optical fields in any state of spatial coherence in the phase-space representation,” Appl. Opt.49(31), 6063–6071 (2010). [CrossRef]

J. Colloid Interface Sci.

• D. C. Alvarez-Palacio and J. Garcia-Sucerquia, “Lensless microscopy technique for static and dynamic colloidal systems,” J. Colloid Interface Sci.349(2), 637–640 (2010). [CrossRef] [PubMed]

J. Mod. Opt.

• R. Castañeda, H. Muñoz, and G. Cañas-Cardona, “The structured spatial coherence support,” J. Mod. Opt. , 58(11) (2011), doi: . [CrossRef]

J. Opt. Soc. Am. A

• R. Castañeda, G. Cañas-Cardona, and J. Garcia-Sucerquia, “Radiant, virtual, and dual sources of optical fields in any state of spatial coherence,” J. Opt. Soc. Am. A27(6), 1322–1330 (2010). [CrossRef] [PubMed]

Opt. Commun.

• R. Castañeda and J. García, “Classes of source pairs in interference and diffraction,” Opt. Commun.226(1-6), 45–55 (2003). [CrossRef]
• K. Jahn and N. Bokor, “Intensity control of the focal spot by vectorial beam shaping,” Opt. Commun.283(24), 4859–4865 (2010). [CrossRef]

Physica

• F. Zernike, “The concept of Degree of Coherence and its application to optical problems,” Physica5(8), 785–795 (1938). [CrossRef]

Other

• M. Born and E. Wolf, Principles of Optics, 6th. ed. (Pergamon Press, 1993), Chap. 10.
• L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995), Chap. 4.
• Z. Jaroszewicz, Axicons: Design and Propagation Properties (Research and development treatises, SPIE Polish chapter) (SPIE, 1997), Vol. 5.
• R. Castañeda, “The optics of spatial coherence wavelets, in Advances in Imaging and Electron Physics, P. Hawkes, ed. (Academic Press, 2010), Vol. 164.
• K. Iizuka, Engineering Optics (Springer Verlag, 1985).

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