#### This work includes the definition of measures of spread for periodic distributions (e.g., over a circle or a sphere), the uncertainty relations these measures satisfy, and applications to nonparaxial fields and short pulses.

**Uncertainty relations for periodic distributions (Fourier series and discrete Fourier transforms)**

Journal articles

- M.A. Alonso and M.J. Bastiaans, “Mapping-based width measures and uncertainty relations for periodic functions,” Signal Proc.
**84**, 2425-2435 (2004). - G.W. Forbes, M.A. Alonso, and A.E. Siegman, “Uncertainty relations and minimum uncertainty states for the discrete Fourier transform and the Fourier series,” J. Phys. A: Math. Gen.
**36**, 7027-7047 (2003). - G.W. Forbes and M.A. Alonso, “Consistent analogues of the Fourier uncertainty relation,” Am. J. Phys.
**69**, 1091-1095 (2001). - G.W. Forbes and M.A. Alonso, “Measures of spread for periodic distributions and the associated uncertainty relations,” Am. J. Phys.
**69**, 340-347 (2001).

Conference proceedings

- M.A. Alonso and G.W. Forbes, “Periodic minimum uncertainty states,” Proceedings of the 8th International Conference on Squeezed States and Uncertainty Relations, H. Moya-Cessa et al., Eds. (Rinton, Princeton, 2003), pp. 1-6.
- M.A. Alonso and M.J. Bastiaans, “Mapping-based width measures and uncertainty relations for periodic functions,” Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology, 2003. ISSPIT (2003), pp. 625-628.

**Uncertainty relations for wave fields and pulses**

Journal articles

- M.A. Alonso, T. Setälä, and A.T. Friberg, “Minimum uncertainty solutions for partially coherent fields and quantum mixed states,” N. J. Phys.
**16**, 123023 (2014). - M.A. Alonso, T. Setälä, and A.T. Friberg, “Optimal pulses for arbitrary dispersive media,” J. Eur. Opt. Soc. R.P.
**6**, 11035 (2011). - 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).