Quadratic phase of tightly focused wavefronts

In an aplanatic optical system, where the entrance pupil is not located at the front focal plane, a corresponding quadratic phase is expected at the back focal plane. However, tightly focused optical fields evaluated by methods based on the traditional Richards-Wolf approach, lacks this quadratic phase. In the current work we calculate the focused field, for both high and medium numerical apertures, based on the Stratton-Chu diffraction integral in a 2D system. We find that the quadratic phase factor depends on the numerical aperture, and it approaches the corresponding paraxial value for lower numerical apertures. References and links 1. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II Structure of the image field in an optical system,” Proc. R. Soc. Lond. A. 253, 358-379 (1959). 2. A. Normatov, B. Spektor, and J. Shamir, “Tight Focusing of Wavefronts with Piecewise Constant Phase,” CCIT Report #681, Electrical Engineering Faculty, Technion, January 2008. 3. J. A. Stratton and L. J. Chu, “Diffraction Theory of Electromagnetic Waves”, Phys. Rev. 56, 99-107 (1939). 4. E. Wolf and Y. Li, “Conditions for the validity of the Debye integral representation of focused fields,” Opt. Comm. 39, 205-210 (1981). 5. E. Wolf, “Electromagnetic diffraction in optical systems, I An integral representation of the image field,” Proc. R. Soc. Lond. A. 253, 349-357 (1959). 6. M. Born and E. Wolf, Principles of Optics (Cambridge University Press 2003). 7. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill 1968). 8. P. Torok, P.R.T. Munro and E.E. Kriezis “Rigorous nearto far-field transformation for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A. 23, 713-722 (2006). 9. P. Varga and P. Torok, “Focusing of electromagnetic waves by paraboloid mirrors. I. Theory,” J. Opt. Soc. Am. A. 17, 2081-2089 (2000). 10. J. W. Goodman, Introduction To Fourier Optics (McGraw-Hill 1968). 11. J. Shamir, Optical Systems and Processes (SPIE, 1999).