I received my Ph. D. in Optics in September of 2002 from the CIO in Mexico, working with the distinguish professor Orestes Stavroudis. My research was to provide formulas for the ray tracing in uniaxial crystals based in the Huygens’s Principle. Additionally, considering those formulas for ray tracing in birefringent media, made possible several contributions in the field of uniaxial crystals. Subsequently as a result of my Postdoctoral Fellowship within the Optics and Microwaves Department at CCADET-UNAM in May 2006, and later as an Associate Researcher, we have developed a quantitative test for off-axis parabolic mirrors based in the null screens method. Since May 2010, I have been a full professor and I have established a new laboratory for testing single optical components associated within Optical Systems Group. My principal accomplishments research has been finding better ways to describe the propagation of wavefronts and the formation of caustic surfaces through arbitrary systems, providing analytical formulas to either reduce or increase the amount of spherical aberration, with potential applications such as single lenses without spherical aberration, diffusers of light, concentrators or collimators for solar cells. Recently we have implemented a method to design Hartmann type null screens to test either qualitatively or quantitatively fast aspheric lenses placing a CCD sensor inside the caustic surface. My research has resulted in 24 peer-reviewed journal articles and 27 international conference proceedings in the field of classical optics. I am active in promoting several topics in the field of Optics in particular Geometrical and Physical Optics in México, teaching at Faculty of Sciences and Faculty of Engineering of UNAM since 2006. Additionally I have been a regular reviewer of several journals such as JOSA-A, Appl. Opt., Opt. Exp., Opt. Lett., Am. J. of Phys., Opt. Comm., Proc. A Royal Soc., Journal of Modern Optics, Journal of Optics and Review of Scientific Instruments since 2007. Finally I become a Senior Member of the Optical Society of America in May 2017.

• Design, construction and evaluation of optical surfaces with arbitrary shape.

• Light phase modulators applied to optical tests.

• Measurement of parameters of Isotropic and birefringent optical components using optical modulators.

• Exact ray tracing in isotropic and birefringent media.

• Caustic surfaces and exact wavefront propagation.

• Polarization of light

• Estudio de las cáusticas para la evaluación de superficies ópticas, DGAPA-PAPIIT IN116420. Fecha, Enero 2020-Diciembre 2021
• Diseño y Evaluación de Superficies Ópticas Tradicionales, Arbitrarias No Convencionales y del Tipo Fresnel, CONACyT, CB2017-2018, #A1-S-44220, Fecha, Agosto 2019-Agosto 2022.
• Laboratorio Nacional de Óptica de la Visión, LANOV-CONACYT, 2018-2020.
• Diseño, construcción y evaluación de tres prototipos de concentradores solares (Canal cilíndrico parabólico, Canal Parabólico Compuesto y tipo Fresnel) sin movimiento con orientación E-W para aplicaciones fototérmicas y fotoquímicas, DGAPA-PAPIIT IT100619, Fecha, Enero 2019-Diciembre 2021, Vigente, (Participante).

UNDERGRADUATE

• Professor of the course: Optics, plan 2001. Semesters: 2021-I, 2020-II, 2020-I, 2019-II, 2019-I, 2018-II, 2018-I, 2017-II, 2017-I, 2016-II, 2016-I, 2015-II, 2015-I, 2014-II, 2014-I, 2013-II, 2013-I, 2012-2, 2012-I, 2011-2, 2011-I, Faculty of Science, National Autonomous University of Mexico.

GRADUATE

• Professor of the course: Applied Mathematics. Graduate Engineering Program. Semesters: 2021-I, 2020-I, 2018-I, 2017-I, 2013-I, 2012-I, 2011-I, 2010-I, 2008-I, FI-UNAM
• Professor of the course: Electromagnetic Theory, 2019-I.
• Professor of the course: Polarization of Light. Graduate Engineering Program. Semesters: 2020-II, 2019-II, 2018-II, 2017-II, 2016-2, 2014-II, 2013-II, 2013-I, 2012-II, 2011-II, 2010-II, FI-UNAM
• Professor of the course: Physics of Continuous Media. Electromagnetism. Graduate Engineering Program. Semestre. 2015-I, FI-UNAM

• Dr. Iván Moreno-Hernández (Faculty of Science, UAZ)
• Dr. Luis Castañeda-Aviña (Higher School of Medicine, IPN)
• Dr. Fermín Granados-Agustín (INAOE)
• Dr. Edwin Román-Hernández (University of Istmo, Oax.)
• Dr. Víctor Iván Moreno-Oliva (University of Istmo, Oax.)

• O. Huerta Carranza***, R. Díaz-Uribe, M. Avendaño-Alejo, “Exact equations to measure highly aberrated wavefronts with the Hartmann test,” Opt. Exp., Vol 28, No. 21, pp. 30928-30942, (2020). https://doi.org/10.1364/OE.405363
• Iván Moreno, M. Avendaño-Alejo, C. P. Castañeda-Almanza, “Nonimaging metaoptics,” Opt. Lett., Vol. 45, Issue 10, pp. 2744-2747 (2020), https://doi.org/10.1364/OL.391357
• M. Avendaño-Alejo, Edwin Román-Hernández, Gabriel Castillo-Santiago, Jesús DelOlmo-Márquez, Luis Castañeda, “Sagittal and tangential foci produced by tilted plane wavefronts refracted through simple lenses,” Appl. Opt., Vol 58, No. 22, pp. 5959-5967, (2019), https://doi.org/10.1364/AO.58.005959, ISSN:1559-128X (print).
• M. Avendaño-Alejo, M. Carmen López Bautista, L. Castañeda and S. Maca-García, “Huygens’s Principle: Exact and approximate wavefronts propagated through conic lenses,” Appl. Opt., Vol 58, No. 4, pp. 939-947, (2019). doi.org/101364/AO.58.000939, ISSN:1559-128X (print), ISSN: 4542-4550 (online).
• M. Carmen López Bautista, M. Avendaño-Alejo, Luis Castañeda, J. A. Peralta-Ángeles and J. A. Reyes-Esqueda, “Study of nonlinear properties of N-(2-hydroxyphenyl)-2-propylpentanamide in polymeric solution,” Optik, International Journal for Light and Electron Optics, Vol. 180, 724-732, (2109). doi.org/10.1016/j.ijleo.2018.11.037
• M. Avendaño-Alejo, E. Román-Hernández, L. Castañeda and V. I. Moreno-Oliva “Analytic conic constants to reduce the spherical aberration of single lens used in collimated light,” Appl. Opt., Vol. 56, Issue 22, 6244-6254, doi.org/10.1364/AO.56.006244, ISSN:1559-128X (print), ISSN: 2155-3165 (online) (2017).
• M. Jiménez-Rodríguez***, M. Avendaño-Alejo, L. E. Verduzco-Grajeda, A. I. Martínez-Enríquez, R. García-Díaz and R. Díaz-Uribe, “Design of a solar concentrator considering arbitrary surfaces,” Proc. of SPIE Vol. 10448, Optifab 2017, Paper Number 104482J, doi: 10.1117/12.2279876.
• G. Castillo-Santiago***, D. Castán-Ricaño, M. Avendaño-Alejo, L. Castañeda and R. Díaz-Uribe, “Design of Hartmann type null screens for testing a plano-convex aspheric lens with a CCD sensor inside the caustic,” Opt. Exp., Vol. 24, No. 17, 19405-19416, #268375, ISSN 1094-4087, DOI: http://dx.doi.org/10.1364/OE.24.019405, (2016).
• M. Avendaño-Alejo, “Design of Fresnel Lenses using arbitrary surfaces,” Latin American Optics and Photonics Conference (LAOP), OSA 2016, Article Number LTh3C.1, ISBN: 978-1-943580-16-3, doi:10.1364/LAOP.2016.LTh3C.1, (2016).
• M. Avendaño-Alejo, L. Castañeda, I. Moreno, “Exact wavefronts and caustic surfaces produced by planar ripple lenses,” Opt. Exp., Vol. 23, No. 17, 21637-21649, ISSN: 1094-4087, DOI: 10.1364/OE.23.021637, (2015).
• *** Students developing their thesis respectively associated along with me

• Distinction of Senior Member OSA-2017.

• Associated Editor SPIE Newsroom, for Optical Design and Engineering 2014-2016.
• Coauthor of the Chapter: O. Stavroudis and M. Avendaño-Alejo (2017), “Basic Ray Optics,” Handbook of Optical Engineering, Second Edition, Ed. CRC Press, Taylor & Francis Group, Chap. 1, pp. 21-69, EE.UU, (In press).
• 3rd Placed, Photo Contest 2011, granted by Optics and Photonics News, de la Optical Society of America.
• Miembro del comité Editorial del Boletín de la Revista Mexicana de Física, (2005-2006).
• Regular Reviewer of JOSA-A, Appl. Opt., Opt. Exp., Opt. Lett., Am. J. of Phys., Opt. Comm., Proc. A Royal Soc., Journal of Modern Optics, Journal of Optics and Review of Scientific Instruments.
• Distinction: “Design of a solar concentrator considering arbitrary surfaces,” fue distinguido Runner-Up Best Student Paper Award, otorgado por la SPIE, en el congreso OptiFab, Rochester New, York , EE. UU. (2018).
• Distinction: “Behavior of the centroids within the caustic of a fast lens,” fue distinguido Certificate of Excellence, for Second Place Student Presentation, otorgado por la SPIE, presentado en el Mexican Optics and Photonics Meeting (MOPM 2017).
• Distinction: “Design of a solar concentrator considering linear Fresnel reflectors”, granted by Best Student Presentation Award, for Second Place Student Presentation, Optical Society of America, and Mexican Optics and Photonics Meeting (MOPM 2017).

Doctorado

• Diana Nallely Castán Ricaño, Titulo de Tesis: “Diseño y evaluación de lentes plano-curvas arbitrarias,” ICAT-INAOE Instituto Nacional de Astrofísica Óptica y Electrónica, (Doctorado En Co-tutoría con el Dr. Fermín Granados Agustín INAOE).

• Oliver Huerta Carranza, Titulo de Tesis: Desarrollo de un sistema de evaluación para superficies con forma libre, Posgrado en Ingeniería Eléctrica – UNAM. (Doctorado en Co-tutoría con el Dr. Rufino Díaz Uribe)

• Jesús Alberto Del Olmo Márquez, Titulo de Tesis de Doctorado: Reconfiguración del frente de onda para evaluación de superficies plano-curvas arbitrarias suaves. Posgrado en Ingeniería Eléctrica– UNAM

• Martín Jiménez Rodríguez, Titulo de Tesis Maestría: “Diseño y evaluación de concentradores solares de plato tipo Fresnel,” Posgrado en Ingeniería Eléctrica, UNAM

• Osvaldo Ponce Hernández, Titulo de Tesis de Maestría: “Estudio de la superficie cáustica y el frente de onda refractado de una lente simple colocando una fuente puntual en una posición arbitraria a lo largo del eje óptico,” Posgrado en Ingeniería Eléctrica, UNAM.

• Adriana Rosalía Sánchez Montes, Titulo de Tesis de Maestría: “Diseño de dobletes acromáticos separados utilizando lentes simples y lentes de tipo Fresnel” Posgrado en Ingeniería Eléctrica – UNAM.

• Ismael Velázquez Gómez, Titulo de Tesis de Maestría: “Estudio del frente de onda y superficies cáusticas considerando un frente de onda inclinado a través de dobletes cementados,” Posgrado en Ingeniería Eléctrica – UNAM.

POSTDOCTORAL FELLOWSHIPS

• Postdoctoral fellowship: Dr. María del Carmen López-Bautista, Period: 1/IX/2019 – 30/VIII/2021, DGAPA-UNAM
• Postdoctoral fellowship: Dr. Gabriel Castillo-Santiago. Period: 1/I/2021 – 31/V/2021. CONACYT