One common approach is to resolve the non-paraxial (vector) field into plane waves, which then propagate through the optical train according to the Huygen-Fresnel principle. According to this principle, each point on every interface is illuminated by each of these plane waves and then acts as a point source of spherical waves. These outgoing spherical waves then may be decomposed into plane waves and allowed to propagate further. At the end, all of the contributions of all of the plane waves are recombined, in phase and with their full vector nature, along the surface of interest. Just as it sounds, this is very messy. Fortunately, Emil Wolf and his collaborators worked out formalism, and the result is manageable. The original reference is E. Wolf, Electromagnetic Diffraction in Optical Systems. I. An Integral Representation of the Image Field, Proc. R. Soc. Lond. A 253, 349-357 (1957). The technique is now is called the Debye-Wolf integral formulation.

With the outstanding developments in femtosecond and attosecond technologies, more appropriate tools are required to describe the propagation of non-paraxial ultrashort light pulses, sometimes called light bullets.

According to the formalism presented elsewhere in papers, the obtained solutions under the paraxial beam optics theory, can be extended to the case of tightly focused (non-paraxial) ultrashort (few-cycle) wave packets using the general formulation developed.

I suggest you to apply systematically Fresnel regime of propagation between the corresponding planes. It can work as in a cascade linear system. See for example: GENERAL TRANSFER-FUNCTION OF A COMPOUND OPTICAL-SYSTEM UNDER LINEARITY CONDITIONS IN THE FRESNEL REGIME

OPTICAL ENGINEERING 30 (10): 1503-1510 OCT 1991

For tightly focused incident laser beam, non-paraxial wave optics formalism is appropriate in predicting the EM-field profile as it pass thru different optical media. Otherwise, just use the ray optics or ray tracing approach. Indeed non-paraxial wave optics formalism of a tightly focused laser beam is a mathematical nightmare but this can address some of the more interesting issue in laser beam propagation profiling (i.e. diffraction).

Refer to the work of J.W. Wang et.al. in the characterization of the fifth-order Hermite-Gaussian (0,0) and (0,1) mode laser beam in Physical Review E published in November 20, 2001 for tightly-focused laser beam propagation.

Next issue to overcome is the nature of the optical medium where the laser beam is propagating (i.e. dispersion, induced polarization in the medium - is it linear or non-linear, absorption, orientation of the interface between media, multiple reflection, surface waves, and etc).

The exact analytic nonparaxial theory for initially phase-modulated by lens short optical pulse do not performed yet.

It must be done numerically by solving the corresponding nonparaxial amplitude equation.

Exact nonparaxial theory of an Gaussian light bullet with analytical expression was performed in my papers JOSA A, 25, 9, pp 2232-2243 (2008), and “Erratum” JOSA A 25, 12, pp3097 (2008).

The metaxial optics of George Bonnet, which recovers the condition of isoplanatism, when going from treating the field on planes to the spherical surfaces.

http://barrere.univ-tln.fr/metaxial.pdf

G. Bonnet, Ann. Télécommun. 33 (1978) 143.

G. Bonnet, Ann. Télécommun. 33 (1978) 225.

G. Bonnet, in: Septième colloque sur le traitement du signal et ses applications,

54/1-8, GRETSI-Actes de Colloques, 1979 ().

Rolf,

Rolf,

Even in the paraxial optics, if you use small initial aperture D=0.02 cm and lens F=15 cm, at 800 nm the "minimal spot" will appear at a shorter distance z=12.5 cm. The formula is Z^(spot)_(min)=F/{1+[F/(K_0D^2)]^2}, where K_0D^2 is the diffraction length and K_0= 2pi/lamda.