#### This work consists of analytic models for describing monochromatic fields focused beyond the paraxial regime, including aspects such as fundamental relations related to focal properties, the effects of polarization, closed-form complete orthonormal basis expansions (nonparaxial generalizations of Laguerre-Gaussian beams), and generalizations of Mie theory describing the interaction of these fields with spherical scatterers.

**Effects of nonparaxiality on polarization**

### Book chapter

Journal articles

- R. Gutiérrez-Cuevas and M.A. Alonso, “Analytic treatment of nonparaxial full-Poincaré fields: singularity structure and trapping properties,” J. Opt.
**23**, 024005 (2021). - J.S. Eismann, L.H. Nicholls, D.J. Roth, M.A. Alonso, P. Banzer, F.J. Rodr’guez-Fortuño, A.V. Zayats, F. Nori and K.Y. Bliokh, “Transverse spinning of unpolarized light,” Nature Phot. (2020).
- K.Y. Bliokh, M.A. Alonso and M.R. Dennis, “Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects,” Rep. Prog. Phys.
**82**, 122401 (2019). - M.A. Alonso, “The effect of orbital angular momentum and helicity in the uncertainty-type relations between focal spot size and angular spread,” J. Opt.
**13**, 064016 (2011). - K.Y. Bliokh, E.A. Ostrovskaya, M.A. Alonso, O.G. Rodriguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express
**19**, 26132-26149 (2011). - K.Y. Bliokh, M.A. Alonso, E.A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction for nonparaxial light in free space,” Phys. Rev. A
**82**, 036825 (2010). - R. Borghi, M. Santarsiero, and M.A. Alonso, “Highly focused spirally polarized beams,” J. Opt. Soc. Am. A
**22**, 1420-1431 (2005).

Conference proceedings

- M.A. Alonso and K.Y. Bliokh, “Angular momenta and spin-orbit interaction for nonparaxial beams,” 22nd Congress of the International Commission for Optics: Light for the Development of the World, SPIE Proceedings
**8011**, 80116H (2011). - K.Y. Bliokh, M.A. Alonso, and E.A. Ostrovskaya, “Angular momentum of light revisited: Spin-orbit interactions in free space,” Complex Light and Optical Forces V, SPIE Proceedings
**7950**, 1-8 (2011).

**Interaction of strongly focused beams and spherical particles**

Journal articles

- R. Gutiérrez-Cuevas, N.J. Moore, and M.A. Alonso, “Lorenz-Mie scattering of focused light via complex focus fields: An analytic treatment,” Phys. Rev. A
**97**, 053848 (2018). - N.J. Moore and M.A. Alonso, “Mie scattering of highly focused, scalar fields: an analytic approach,” J. Opt. Soc. Am. A
**33**, 1236-1243 (2016). - K. Lombardo and M.A. Alonso, “Two-dimensional directional basis for nonparaxial focused fields and its application to scattering,” Am. J. Phys.
**80**, 82-93 (2012). - N.J. Moore and M.A. Alonso, “Closed form formula for Mie scattering of nonparaxial analogues of Gaussian beams,” Opt. Express
**16**, 5926-5933 (2008).

Conference proceedings

- M.A. Alonso, “Analytical techniques for the study of focused beams,” Proceedings of the Complex Light and Optical Forces VII conference, Photonics West, SPIE proceeding
**8637**, 863716 (2013). - N.J. Moore and M.A. Alonso, “Mie scattering for high numerical aperture fields,” 22nd Congress of the International Commission for Optics: Light for the Development of the World, SPIE Proceedings
**8011**, 801162 (2011).

**Basis expansions for nonparaxial fields**

### Book chapter

Journal articles

R. Gutiérrez-Cuevas and M.A. Alonso, ”Complete confined bases for beam propagation in Cartesian coordinates” J. Opt. Soc. Am. A **34**, 1697-1702 (2017).

R. Gutiérrez-Cuevas and M.A. Alonso, ”Scalar and electromagnetic nonparaxial bases composed as superpositions of simple vortex fields with complex foci,” Opt. Express **25**, 14856-14870 (2017).

R. Gutiérrez-Cuevas and M.A. Alonso, ”Polynomials of Gaussians and vortex-Gaussian beams as complete, transversely confined bases,” Opt. Lett. **42**, 2205-2208 (2017).

K. Lombardo and M.A. Alonso, “Two-dimensional directional basis for nonparaxial focused fields and its application to scattering,” Am. J. Phys. **80**, 82-93 (2012).

N.J. Moore and M.A. Alonso, “Closed-form bases for the description of monochromatic, strongly focused, electromagnetic fields,” J. Opt. Soc. Am. A **26**, 2211-2218 (2009).

N.J. Moore and M.A. Alonso, “Bases for the description of monochromatic, strongly focused, scalar fields,” J. Opt. Soc. Am. A **26**, 1754-1761 (2009).

M.A. Alonso, R. Borghi, and M. Santarsiero, “New basis for rotationally-symmetric nonparaxial fields in terms of spherical waves with complex foci” Opt. Exp. **14**, 6894-6905 (2006).

**Series expansions for paraxial and nonparaxial fields**

Journal articles

- M.R. Dennis, J.B. Götte, R.P. King, M.A. Morgan and M.A. Alonso, “Paraxial and nonparaxial polynomial beams and the analytic approach to propagation,” Opt. Lett.
**36**, 4452-4454 (2011). - R. Borghi and M.A. Alonso, “Free-space asymptotic far-field series,” J. Opt. Soc. Am. A
**26**, 2410-2417 (2009). - M.A. Alonso and R. Borghi, “Complete far-field asymptotic series for free fields,” Opt. Lett.
**31**, 3028-3030 (2006). - M.A. Alonso, A.A. Asatryan, and G.W. Forbes, “Beyond the Fresnel approximation for focused waves,” J. Opt. Soc. Am. A
**16**, 1958-1969 (1999).

Conference proceedings

**Uncertainty relations for focused beams**

Journal articles

- M.A. Alonso, “The effect of orbital angular momentum and helicity in the uncertainty-type relations between focal spot size and angular spread,” J. Opt.
**13**, 064016 (2011). - C.J.R. Sheppard, M.A. Alonso, and N.J. Moore, “Localization measures for high-aperture wavefields based on moments of the pupil,” J. Opt. A
**10**, 033001 (2008). - N.J. Moore, M.A. Alonso, and C.J.R. Sheppard, “Monochromatic electromagnetic fields with maximum focal energy density,” J. Opt. Soc. Am. A
**24**, 3115-3122 (2007). - N.J. Moore, M.A. Alonso, and C.J.R. Sheppard, “Monochromatic scalar fields with maximum focal irradiance,” J. Opt. Soc. Am. A
**24**, 2057-2064 (2007). - M.A. Alonso, R. Borghi, and M. Santarsiero, “Joint spatial-directional features for fields focused at a complex point,” J. Opt. Soc. Am. A
**23**, 933-939 (2006). - M.A. Alonso, R. Borghi, and M. Santarsiero, “Nonparaxial fields with maximum joint spatial-directional localization. II. Vectorial case,” J. Opt. Soc. Am. A
**23**, 701-712 (2006). - M.A. Alonso, R. Borghi, and M. Santarsiero, “Nonparaxial fields with maximum joint spatial-directional localization. I. Scalar case,” J. Opt. Soc. Am. A
**23**, 691-700 (2006). - M.A. Alonso and G.W. Forbes, “Uncertainty products for nonparaxial fields,” J. Opt. Soc. Am. A
**17**, 2391-2402 (2000).

**Other topics**

Journal articles