Alejandro Aceves | Southern Methodist University (original) (raw)

Papers by Alejandro Aceves

HAL (Le Centre pour la Communication Scientifique Directe), Jun 21, 2021

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

It is not uncommon that the mathematics that describes the phenomena of light propagation in opti... more It is not uncommon that the mathematics that describes the phenomena of light propagation in optical media has strong similarities with the modeling of other physical systems. In this talk as a way of motivation, I will briefly discuss some classical examples followed by a discussion of the current research topics of nonlinear optics in PT-symmetric systems .

Journal of Physics A, Nov 16, 2017

In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a ... more In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a binary waveguide array model. We approach the problem both from a near-continuum perspective as well as from a highly discrete one. Starting from the former, we see that the continuum Dirac solitons can be continued for all values of the discretization (coupling) parameter, down to the uncoupled (so-called anti-continuum) limit where they result in a 9-site configuration. We also consider configurations with 1-or 2-sites at the anti-continuum limit and continue them to large couplings, finding that they also persist. For all the obtained solutions, we examine not only the existence, but also the spectral stability through a linearization analysis and finally consider prototypical examples of the dynamics for a selected number of cases for which the solutions are found to be unstable.

HAL (Le Centre pour la Communication Scientifique Directe), Jun 21, 2021

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Partial Differential Equations in Applied Mathematics

Journal of Evolution Equations, Mar 30, 2023

We prove that the solutions to the discrete nonlinear Schrödinger equation with non-local algebra... more We prove that the solutions to the discrete nonlinear Schrödinger equation with non-local algebraically decaying coupling converge strongly in L 2 (R 2) to those of the continuum fractional nonlinear Schrödinger equation, as the discretization parameter tends to zero. The proof relies on sharp dispersive estimates that yield the Strichartz estimates that are uniform in the discretization parameter. An explicit computation of the leading term of the oscillatory integral asymptotics is used to show that the best constants of a family of dispersive estimates blow up as the non-locality parameter α ∈ (1, 2) approaches the boundaries.

Birkhäuser Boston eBooks, 1993

Nonlinear optical physics, the study of the interaction of matter and intense electromagnetic fie... more Nonlinear optical physics, the study of the interaction of matter and intense electromagnetic fields in the visible spectrum, has become a very exciting and fruitful research topic for the applied scientist. This area, which started some 30 years ago, has already produced important applications in laser technology, optical communications and data storage to name some, and has potential applications such as all optical logic devices. It is also a continuous source of current theoretical research in the area of integrable and near integrable equations. It is well known, for example, that the nonlinear Schrödinger (NLS) equation and variations thereof, governs the dynamics of pulses in nonlinear dielectrics. The robustness of the known soliton solutions of the NLS equation [1], has been verified experimentally as optical pulses have been shown to propagate undistorted for thousands of kilometers in optical fibers [2].

arXiv (Cornell University), Jan 18, 2023

2020 Fourteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials)

Recent work have shown light confinement can occur during propagation through a twisted coreless ... more Recent work have shown light confinement can occur during propagation through a twisted coreless photonic crystal fiber (a chiral fiber). In the absence of a twist, the modal profile is assumed known from Bloch theory and assumed not to be confined. By use of asymptotic techniques applied to the field propagation equation, we provide a theoretical framework in support of observed confinement. While we do this for a particular periodic index profile, recent experiments suggest this to be a robust effect. In this work, we also explore the problem both in the linear and the nonlinear regime. We show that an increase in twist rate will result in more confined modes and indications that nonlinearity plays a secondary role on confinement.

OSA Advanced Photonics Congress (AP) 2020 (IPR, NP, NOMA, Networks, PVLED, PSC, SPPCom, SOF), 2020

Inspired by work on fractional Quantum Mechanics and Levy path integrals, recently we have seen i... more Inspired by work on fractional Quantum Mechanics and Levy path integrals, recently we have seen increased interest in extending this concept in optical settings. Here we present our first results in the spatio-temporal regime

Journal of Epidemiology and Global Health, 2021

The novel Coronavirus Disease 2019 (COVID-19) recently gained attention as the virus continues to... more The novel Coronavirus Disease 2019 (COVID-19) recently gained attention as the virus continues to claim more lives globally. The disease hastily spread from Wuhan to further China provinces and other nations worldwide. Currently (as of August 10, 2020), more than 19.8 million cases have been confirmed with about 12.1 million recovered and 732,000 related deaths across the globe, as stated by the Johns Hopkins virus dashboard. At the beginning of the epidemic, elderly people were more susceptible to COVID-19 [1]. As the epidemic progressed, an increase in the number of cases among people between 45 and 64 years was recorded, as well as an upsurge in the number of cases among individuals, especially individuals between 18 and 44 years [2]. Reports also show that the cases are 2.6 times higher on Black/African American and 2.8 times higher on Hispanic/Latino individuals. Furthermore, COVID-19 induced death is nine times lower on 0-4 years old children and 630 times higher on 85+ years old adults [3]. The various signs associated with COVID-19 are fever, dry cough, short breath, and breathing difficulties. COVID-19 poses a severe threat to the health of individuals worldwide; on January 30, 2020, the World Health Organization declared a universal health emergence on COVID-19 [4,5]. On January 21, 2020, the COVID-19 index case was confirmed in the USA. Roughly a month after that (February 29, 2020), the first death was reported in Washington state. As of August 10, 2020, the USA has confirmed about 4.9 million cases and over 161,284 related deaths. At least 229,073 of those cases occurred in New York City, 184,

Journal of Optics, 2014

Light propagation in nonlinear waveguide arrays displays rich phenomena with multiple application... more Light propagation in nonlinear waveguide arrays displays rich phenomena with multiple applications. Technological advances present opportunities to study distinct dynamical features for a wide range of one-dimensional and two-dimensional arrays. The traditional research on arrays considers the individual elements to be identical. Here we study coupled arrays of non-identical waveguides in geometries that account for nonuniform coupling strengths. The model is now a generalized nonlinear Schr?dinger equation where the usual Laplacian is replaced by the graph Laplacian. We show that since this matrix is symmetric, the dynamics is naturally described using its eigenvectors as a basis. When the eigenvalues are all distinct, we show that there is no resonant transfer of energy between the different eigenmodes. We illustrate this on a simple graph.

Physical Review A, 2017

In this work, we study optical self-focusing that leads to collapse events for the time-independe... more In this work, we study optical self-focusing that leads to collapse events for the time-independent model of co-propagating beams with different wavelengths. We show that collapse events depend on the combined critical power of two beams for both fundamental, vortex and mixed configurations as well as on the ratio of their individual powers.

HAL (Le Centre pour la Communication Scientifique Directe), Sep 1, 2014

Solitons propagating along a fiber when perturbed by higher-order dispersion terms transfer energ... more Solitons propagating along a fiber when perturbed by higher-order dispersion terms transfer energy into linear dispersive waves. We consider the situation when solitons traveling at different speeds collide and analytically explain the dramatic enhancement of the dispersive wave power due to this soliton-soliton interaction; numerical simulations confirm the predictions of our theory

Physical review, Feb 1, 1989

The theory presented in the preceding paper is extended to account for incident optical beam brea... more The theory presented in the preceding paper is extended to account for incident optical beam breakup into multiple self-focused channels and to deal with multiple reflection and transmission at multiple interfaces. Beam breakup is explained by examining the decomposition of the channel in one medium, into its soliton and radiation components after it has crossed into the new medium. A formula is derived which gives the criterion for the number of channels appearing as a consequence of breakup. This formula also provides analytic expressions for the individual self-focused channel powers and the amount of radiation generated. An important observation here is that the amount of radiation generated at the interface shrinks rapidly as a function of increasing channel number N. Each new component generated can be treated as a separate equivalent particle moving in its own equivalent potential. The theory of the preceding paper [Aceves, Moloney, and Newell, Phys. Rev. A 39, 1809 (1989)] can therefore be applied directly to show that low-power channels generated in the breakup will suffer reflection while higher-power channels will undergo transmission. An added ingredient to allow for mutual-channel interaction is the soliton-collision formula. The multipleinterface extension of the single-interface problem results from patching individual single-interface equivalent potentials together. The theory is illustrated with two applications: (i) a nonlinear version of a directional coupler requiring just two interfaces and (iij trapping of a channel at an interface by a ramped linear refractive index.

Optica, Dec 16, 2015

We demonstrate that monochromatic infrared laser pulses can generate polychromatic light in nonce... more We demonstrate that monochromatic infrared laser pulses can generate polychromatic light in noncentrosymmetric crystals simultaneously covering the ultraviolet, visible, and infrared domains. The spatial shape of the beam and its energy can influence this multicolor frequency conversion, unveiling complex and interesting dynamics. We performed our experiments in a bulk crystal of periodically poled lithium niobate, working close to the optimal condition for second-harmonic generation. We used an input laser beam wide enough that, at very low intensities, the diffraction leaves its diameter unchanged along the propagation in the crystal. At high intensities instead, as we show in this work, such a spatially wide laser beam can be reshaped into a beam of much smaller diameter and guiding multispectral components. We also show how this outcome may permit exploitation of other parameters, like the crystal temperature, for tuning the spectrum of the generated multicolor light.

Physical Review A, Aug 1, 1990

An earlier equivalent-particle theory, describing the propagation of a self-focused light channel... more An earlier equivalent-particle theory, describing the propagation of a self-focused light channel at an oblique angle of incidence to the interface separating two nonlinear dielectric media [A. B.

arXiv (Cornell University), Jun 26, 2015

We describe the generation of powerful dispersive waves that are observed when pumping a dual con... more We describe the generation of powerful dispersive waves that are observed when pumping a dual concentric core microstructured fiber by means of a sub-nanosecond laser emitting at the wavelength of 1064 nm. The presence of three zeros in the dispersion curve, their spectral separation from the pump wavelength, and the complex dynamics of solitons originated by the pump pulse break-up, all contribute to boost the amplitude of the dispersive wave on the long-wavelength side of the pump. The measured conversion efficiency towards the dispersive wave at 1548 nm is as high as 50%. Our experimental analysis of the output spectra is completed by the acquisition of the time delays of the different spectral components. Numerical simulations and an analytical perturbative analysis identify the central wavelength of the red-shifted pump solitons and the dispersion profile of the fiber as the key parameters for determining the efficiency of the dispersive wave generation process.

We overview theoretical and experimental advances in the field of rogue wave solutions of multi-c... more We overview theoretical and experimental advances in the field of rogue wave solutions of multi-component optical wave systems. In these systems, the transfer of energy among the coupled waves may lead to novel and complex extreme wave phenomena. We focus our attention on the case of vector field co-propagation in randomly birefringent optical fibers, and on the coupling among counter-propagating waves in a periodic nonlinear waveguide.

HAL (Le Centre pour la Communication Scientifique Directe), Jun 21, 2021

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

It is not uncommon that the mathematics that describes the phenomena of light propagation in opti... more It is not uncommon that the mathematics that describes the phenomena of light propagation in optical media has strong similarities with the modeling of other physical systems. In this talk as a way of motivation, I will briefly discuss some classical examples followed by a discussion of the current research topics of nonlinear optics in PT-symmetric systems .

Journal of Physics A, Nov 16, 2017

In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a ... more In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a binary waveguide array model. We approach the problem both from a near-continuum perspective as well as from a highly discrete one. Starting from the former, we see that the continuum Dirac solitons can be continued for all values of the discretization (coupling) parameter, down to the uncoupled (so-called anti-continuum) limit where they result in a 9-site configuration. We also consider configurations with 1-or 2-sites at the anti-continuum limit and continue them to large couplings, finding that they also persist. For all the obtained solutions, we examine not only the existence, but also the spectral stability through a linearization analysis and finally consider prototypical examples of the dynamics for a selected number of cases for which the solutions are found to be unstable.

HAL (Le Centre pour la Communication Scientifique Directe), Jun 21, 2021

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Partial Differential Equations in Applied Mathematics

Journal of Evolution Equations, Mar 30, 2023

We prove that the solutions to the discrete nonlinear Schrödinger equation with non-local algebra... more We prove that the solutions to the discrete nonlinear Schrödinger equation with non-local algebraically decaying coupling converge strongly in L 2 (R 2) to those of the continuum fractional nonlinear Schrödinger equation, as the discretization parameter tends to zero. The proof relies on sharp dispersive estimates that yield the Strichartz estimates that are uniform in the discretization parameter. An explicit computation of the leading term of the oscillatory integral asymptotics is used to show that the best constants of a family of dispersive estimates blow up as the non-locality parameter α ∈ (1, 2) approaches the boundaries.

Birkhäuser Boston eBooks, 1993

Nonlinear optical physics, the study of the interaction of matter and intense electromagnetic fie... more Nonlinear optical physics, the study of the interaction of matter and intense electromagnetic fields in the visible spectrum, has become a very exciting and fruitful research topic for the applied scientist. This area, which started some 30 years ago, has already produced important applications in laser technology, optical communications and data storage to name some, and has potential applications such as all optical logic devices. It is also a continuous source of current theoretical research in the area of integrable and near integrable equations. It is well known, for example, that the nonlinear Schrödinger (NLS) equation and variations thereof, governs the dynamics of pulses in nonlinear dielectrics. The robustness of the known soliton solutions of the NLS equation [1], has been verified experimentally as optical pulses have been shown to propagate undistorted for thousands of kilometers in optical fibers [2].

arXiv (Cornell University), Jan 18, 2023

2020 Fourteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials)

Recent work have shown light confinement can occur during propagation through a twisted coreless ... more Recent work have shown light confinement can occur during propagation through a twisted coreless photonic crystal fiber (a chiral fiber). In the absence of a twist, the modal profile is assumed known from Bloch theory and assumed not to be confined. By use of asymptotic techniques applied to the field propagation equation, we provide a theoretical framework in support of observed confinement. While we do this for a particular periodic index profile, recent experiments suggest this to be a robust effect. In this work, we also explore the problem both in the linear and the nonlinear regime. We show that an increase in twist rate will result in more confined modes and indications that nonlinearity plays a secondary role on confinement.

OSA Advanced Photonics Congress (AP) 2020 (IPR, NP, NOMA, Networks, PVLED, PSC, SPPCom, SOF), 2020

Inspired by work on fractional Quantum Mechanics and Levy path integrals, recently we have seen i... more Inspired by work on fractional Quantum Mechanics and Levy path integrals, recently we have seen increased interest in extending this concept in optical settings. Here we present our first results in the spatio-temporal regime

Journal of Epidemiology and Global Health, 2021

The novel Coronavirus Disease 2019 (COVID-19) recently gained attention as the virus continues to... more The novel Coronavirus Disease 2019 (COVID-19) recently gained attention as the virus continues to claim more lives globally. The disease hastily spread from Wuhan to further China provinces and other nations worldwide. Currently (as of August 10, 2020), more than 19.8 million cases have been confirmed with about 12.1 million recovered and 732,000 related deaths across the globe, as stated by the Johns Hopkins virus dashboard. At the beginning of the epidemic, elderly people were more susceptible to COVID-19 [1]. As the epidemic progressed, an increase in the number of cases among people between 45 and 64 years was recorded, as well as an upsurge in the number of cases among individuals, especially individuals between 18 and 44 years [2]. Reports also show that the cases are 2.6 times higher on Black/African American and 2.8 times higher on Hispanic/Latino individuals. Furthermore, COVID-19 induced death is nine times lower on 0-4 years old children and 630 times higher on 85+ years old adults [3]. The various signs associated with COVID-19 are fever, dry cough, short breath, and breathing difficulties. COVID-19 poses a severe threat to the health of individuals worldwide; on January 30, 2020, the World Health Organization declared a universal health emergence on COVID-19 [4,5]. On January 21, 2020, the COVID-19 index case was confirmed in the USA. Roughly a month after that (February 29, 2020), the first death was reported in Washington state. As of August 10, 2020, the USA has confirmed about 4.9 million cases and over 161,284 related deaths. At least 229,073 of those cases occurred in New York City, 184,

Journal of Optics, 2014

Light propagation in nonlinear waveguide arrays displays rich phenomena with multiple application... more Light propagation in nonlinear waveguide arrays displays rich phenomena with multiple applications. Technological advances present opportunities to study distinct dynamical features for a wide range of one-dimensional and two-dimensional arrays. The traditional research on arrays considers the individual elements to be identical. Here we study coupled arrays of non-identical waveguides in geometries that account for nonuniform coupling strengths. The model is now a generalized nonlinear Schr?dinger equation where the usual Laplacian is replaced by the graph Laplacian. We show that since this matrix is symmetric, the dynamics is naturally described using its eigenvectors as a basis. When the eigenvalues are all distinct, we show that there is no resonant transfer of energy between the different eigenmodes. We illustrate this on a simple graph.

Physical Review A, 2017

In this work, we study optical self-focusing that leads to collapse events for the time-independe... more In this work, we study optical self-focusing that leads to collapse events for the time-independent model of co-propagating beams with different wavelengths. We show that collapse events depend on the combined critical power of two beams for both fundamental, vortex and mixed configurations as well as on the ratio of their individual powers.

HAL (Le Centre pour la Communication Scientifique Directe), Sep 1, 2014

Solitons propagating along a fiber when perturbed by higher-order dispersion terms transfer energ... more Solitons propagating along a fiber when perturbed by higher-order dispersion terms transfer energy into linear dispersive waves. We consider the situation when solitons traveling at different speeds collide and analytically explain the dramatic enhancement of the dispersive wave power due to this soliton-soliton interaction; numerical simulations confirm the predictions of our theory

Physical review, Feb 1, 1989

The theory presented in the preceding paper is extended to account for incident optical beam brea... more The theory presented in the preceding paper is extended to account for incident optical beam breakup into multiple self-focused channels and to deal with multiple reflection and transmission at multiple interfaces. Beam breakup is explained by examining the decomposition of the channel in one medium, into its soliton and radiation components after it has crossed into the new medium. A formula is derived which gives the criterion for the number of channels appearing as a consequence of breakup. This formula also provides analytic expressions for the individual self-focused channel powers and the amount of radiation generated. An important observation here is that the amount of radiation generated at the interface shrinks rapidly as a function of increasing channel number N. Each new component generated can be treated as a separate equivalent particle moving in its own equivalent potential. The theory of the preceding paper [Aceves, Moloney, and Newell, Phys. Rev. A 39, 1809 (1989)] can therefore be applied directly to show that low-power channels generated in the breakup will suffer reflection while higher-power channels will undergo transmission. An added ingredient to allow for mutual-channel interaction is the soliton-collision formula. The multipleinterface extension of the single-interface problem results from patching individual single-interface equivalent potentials together. The theory is illustrated with two applications: (i) a nonlinear version of a directional coupler requiring just two interfaces and (iij trapping of a channel at an interface by a ramped linear refractive index.

Optica, Dec 16, 2015

We demonstrate that monochromatic infrared laser pulses can generate polychromatic light in nonce... more We demonstrate that monochromatic infrared laser pulses can generate polychromatic light in noncentrosymmetric crystals simultaneously covering the ultraviolet, visible, and infrared domains. The spatial shape of the beam and its energy can influence this multicolor frequency conversion, unveiling complex and interesting dynamics. We performed our experiments in a bulk crystal of periodically poled lithium niobate, working close to the optimal condition for second-harmonic generation. We used an input laser beam wide enough that, at very low intensities, the diffraction leaves its diameter unchanged along the propagation in the crystal. At high intensities instead, as we show in this work, such a spatially wide laser beam can be reshaped into a beam of much smaller diameter and guiding multispectral components. We also show how this outcome may permit exploitation of other parameters, like the crystal temperature, for tuning the spectrum of the generated multicolor light.

Physical Review A, Aug 1, 1990

An earlier equivalent-particle theory, describing the propagation of a self-focused light channel... more An earlier equivalent-particle theory, describing the propagation of a self-focused light channel at an oblique angle of incidence to the interface separating two nonlinear dielectric media [A. B.

arXiv (Cornell University), Jun 26, 2015

We describe the generation of powerful dispersive waves that are observed when pumping a dual con... more We describe the generation of powerful dispersive waves that are observed when pumping a dual concentric core microstructured fiber by means of a sub-nanosecond laser emitting at the wavelength of 1064 nm. The presence of three zeros in the dispersion curve, their spectral separation from the pump wavelength, and the complex dynamics of solitons originated by the pump pulse break-up, all contribute to boost the amplitude of the dispersive wave on the long-wavelength side of the pump. The measured conversion efficiency towards the dispersive wave at 1548 nm is as high as 50%. Our experimental analysis of the output spectra is completed by the acquisition of the time delays of the different spectral components. Numerical simulations and an analytical perturbative analysis identify the central wavelength of the red-shifted pump solitons and the dispersion profile of the fiber as the key parameters for determining the efficiency of the dispersive wave generation process.

We overview theoretical and experimental advances in the field of rogue wave solutions of multi-c... more We overview theoretical and experimental advances in the field of rogue wave solutions of multi-component optical wave systems. In these systems, the transfer of energy among the coupled waves may lead to novel and complex extreme wave phenomena. We focus our attention on the case of vector field co-propagation in randomly birefringent optical fibers, and on the coupling among counter-propagating waves in a periodic nonlinear waveguide.