Final Report Summary - NOLACOME (Nonlinear Optics and Lasing in Complex Media)
In this overview we summarize the project’s context and its objectives for both the outgoing phase carried out at Princeton University and the reintegration phase carried out at TU-Wien. In this fellowship, there are four aims-objectives corresponding to four different topics-subprojects, which we aimed to accomplish in a total period of 36 months. In general terms these objectives are related to the understanding of the role of a spatially non-uniform pump on laser characteristics (topic 1), to the lasing and scattering in Parity-Time (PT) symmetric cavities (topic 2), to the role of Anderson localization in random lasing media (topic 3) and finally to high harmonic generation due to collective-multimode effects in nonlinear optics (topic 4). The work on these four general topics in the area of nonlinear optics and complex lasers during both phases is best reflected in the main results that have been achieved so far and that will be now summarized.
Regarding the first topic of the fellowship, the fellow was trained to use and acquire the required background for performing simulations in the context of semi-classsical laser theory. In particular during the first three months the fellow got familiar with the SALT (Self-consistent Ab-initio Laser Theory) formalism and the associated software package (training period), as planned. Based on this knowledge the fellow studied and investigated the laser characteristics of gain-induced cavities in periodic media, and specifically in one-dimensional photonic crystals (in collaboration with both institutions). The effect of partial pump on the lasing modes was systematically understood (based on SALT simulations) and a corresponding manuscript is under preparation. Another direction the fellow pursued during the outgoing phase (in collaboration with TU-Wien) which is directly related to the first topic of the proposal, was a scalable numerical approach for the SALT framework. In cooperation also with other groups from Yale, MIT and CUNY an efficient and flexible method for solving the non-linear lasing equations could be successfully demonstrated. Unlike previous techniques, we solved the underlying system of partial differential equations directly, without the need of setting up a parametrized basis of so-called constant flux states that were used up to this point. We validated our approach in one-dimensional as well as in cylindrical systems, and demonstrated its scalability to full-vector three-dimensional calculations in photonic-crystal slabs. A corresponding manuscript has meanwhile been published in Physical Review A.
Regarding the second topic of the fellowship, the fellow examined (in collaboration with the host institution TU-Wien) scattering in PT-symmetric cavities, constant-intensity waves and singular amplification in non-hermitian media. More specifically, the scattering properties of a PT-cavity are crucial for the understanding of a PT-laser and its relation to the anti-laser. In this spirit, the fellow (in collaboration with the Vienna group as well as with groups at Yale, Singapore and Princeton) examined the relation of the PT-symmetry breaking point of an open system (based on scattering matrix eigenvalues) with that of the corresponding bounded system (based on an effective Hamiltonian approach). A corresponding manuscript has been published in Physical Review X, and a second one related to symmetry breaking in PT-cavities by scanning the incidence angle is about to be submitted in a special issue of IEEE Quantum Electronics journal. Furthermore, the fellow examined (in collaboration with the host institution at Princeton) the use of overall lossy potentials as power amplifiers. This study was based on the effect of anomalous transient amplification in non-normal photonic media. We studied the unexpected characteristics of such non-normal photonic structures (with distributed gain and loss that are on average lossy) to amplify light. Such lossy power amplifiers may play a critical role in mitigating losses in active plasmonic structures. A corresponding manuscript has been published in Physical Review X, and a second one about singular amplification in coupled systems is ready to be submitted to a special issue on non-hermitian photonics in the New Journal of Physics. In collaboration with the return host institution (TU-Wien), the fellow also worked on constant intensity waves (CI-waves) and their modulation instability in inhomogeneous environments. These unidirectional waves are a generalization of the concept of plane waves in free space to non-hermitian media. A paper introducing this new idea and examining the diffraction as well as the stability properties of such waves in nonlinear media has meanwhile been published in Nature Communications. As a follow-up of these projects, the fellow collaborated with the host institution (TU-Wien) on studying a novel class of periodic potentials that contain gain and loss with a “shifted PT-symmetry”. Specifically, the optical potential is PT-symmetric not around zero but around a different spatial point, which is not on the center of symmetry of the potential. A manuscript is currently made ready for submission to Physical Review E.
Regarding the third topic of the fellowship, the fellow (in collaboration with the return host institution at TU-Wien), examined the propagation of CI-waves in random media. In particular, it was shown that in a general class of non-hermitian scattering media such CI-waves can propagate without any reflection. The connection of such effects with the unidirectional invisibility was also analysed. A corresponding manuscript is ready to be submitted to Physical Review Letters. In the same direction the fellow pursued a project on the modulation instability of CI-waves in nonlinear disordered systems (again in collaboration with TU-Wien), which is directly related to the third and fourth topic of the proposal. Unlike previous attempts to understand the role of nonlinearity in localization and filament formation in random media, we can now solve this problem for the first time by considering media that support CI-waves and have gain and loss. A corresponding physical structure that realizes such a Manakov system, is that of a nonlinear optical fiber (or waveguide) with transverse disorder that contains gain and loss. The fundamental phenomenon of modulational instability can be examined by considering CI-waves (the structure supports them because of the existence of gain and loss). A corresponding manuscript is currently in preparation and will be submitted to Physical Review X.
Regarding the fourth topic of the fellowship, the fellow examined (in collaboration with the host institution Institute for Theoretical Physics, TU-Wien and the Atominstitut of TU-Wien) a topic that has to do with nonlinear effects in open photonic systems with gain and loss. In particular, the physical system of interest was that of coupled nonlinear PT-symmetric phonon lasers. By using a semiclassical approach, coupled nonlinear ordinary differential equations were derived to describe the time dynamics of such a system. The effect of nonlinear saturation on the symmetry breaking was systematically investigated by examining the steady state of the oscillators. The effect of noise was also an important component of this study. The counterintuitive main result was that of the existence of a new phase transition from a high thermal noise state to a low amplitude lasing state. A corresponding manuscript has meanwhile been submitted to Physical Review Letters. Another closely related theme (related to the fourth topic of the proposal) is that of a more detailed understanding of the role of openness in lasing in complex media. More specifically, the fellow in close collaboration with the outgoing institution at Princeton University, developed a novel spectral method for laser dynamics that is based on the open modes of the structure and in particular on the constant-flux states. This novel method (Constant Flux Time Dynamics, CFTD) is based on the semiclassical Maxwell-Bloch laser equations and can be applied to any laser system and treats the openeness of the structure exactly. The effect of the outcoupling and of nonlinearity in cooperative frequency locking between two laser modes was demonstrated numerically. A manuscript on this subject as well as a conference proceeding are already submitted.
In conclusion, results from these research activities are also expected to have potential impact both on basic research and on applied technology for the design of the next generation of synthetic photonic devices. The combination of gain and loss in an engineered way, can lead to new synthetic optical elements and lasers with unique and counterintuitive properties that are important for various photonic technologies.
Regarding the first topic of the fellowship, the fellow was trained to use and acquire the required background for performing simulations in the context of semi-classsical laser theory. In particular during the first three months the fellow got familiar with the SALT (Self-consistent Ab-initio Laser Theory) formalism and the associated software package (training period), as planned. Based on this knowledge the fellow studied and investigated the laser characteristics of gain-induced cavities in periodic media, and specifically in one-dimensional photonic crystals (in collaboration with both institutions). The effect of partial pump on the lasing modes was systematically understood (based on SALT simulations) and a corresponding manuscript is under preparation. Another direction the fellow pursued during the outgoing phase (in collaboration with TU-Wien) which is directly related to the first topic of the proposal, was a scalable numerical approach for the SALT framework. In cooperation also with other groups from Yale, MIT and CUNY an efficient and flexible method for solving the non-linear lasing equations could be successfully demonstrated. Unlike previous techniques, we solved the underlying system of partial differential equations directly, without the need of setting up a parametrized basis of so-called constant flux states that were used up to this point. We validated our approach in one-dimensional as well as in cylindrical systems, and demonstrated its scalability to full-vector three-dimensional calculations in photonic-crystal slabs. A corresponding manuscript has meanwhile been published in Physical Review A.
Regarding the second topic of the fellowship, the fellow examined (in collaboration with the host institution TU-Wien) scattering in PT-symmetric cavities, constant-intensity waves and singular amplification in non-hermitian media. More specifically, the scattering properties of a PT-cavity are crucial for the understanding of a PT-laser and its relation to the anti-laser. In this spirit, the fellow (in collaboration with the Vienna group as well as with groups at Yale, Singapore and Princeton) examined the relation of the PT-symmetry breaking point of an open system (based on scattering matrix eigenvalues) with that of the corresponding bounded system (based on an effective Hamiltonian approach). A corresponding manuscript has been published in Physical Review X, and a second one related to symmetry breaking in PT-cavities by scanning the incidence angle is about to be submitted in a special issue of IEEE Quantum Electronics journal. Furthermore, the fellow examined (in collaboration with the host institution at Princeton) the use of overall lossy potentials as power amplifiers. This study was based on the effect of anomalous transient amplification in non-normal photonic media. We studied the unexpected characteristics of such non-normal photonic structures (with distributed gain and loss that are on average lossy) to amplify light. Such lossy power amplifiers may play a critical role in mitigating losses in active plasmonic structures. A corresponding manuscript has been published in Physical Review X, and a second one about singular amplification in coupled systems is ready to be submitted to a special issue on non-hermitian photonics in the New Journal of Physics. In collaboration with the return host institution (TU-Wien), the fellow also worked on constant intensity waves (CI-waves) and their modulation instability in inhomogeneous environments. These unidirectional waves are a generalization of the concept of plane waves in free space to non-hermitian media. A paper introducing this new idea and examining the diffraction as well as the stability properties of such waves in nonlinear media has meanwhile been published in Nature Communications. As a follow-up of these projects, the fellow collaborated with the host institution (TU-Wien) on studying a novel class of periodic potentials that contain gain and loss with a “shifted PT-symmetry”. Specifically, the optical potential is PT-symmetric not around zero but around a different spatial point, which is not on the center of symmetry of the potential. A manuscript is currently made ready for submission to Physical Review E.
Regarding the third topic of the fellowship, the fellow (in collaboration with the return host institution at TU-Wien), examined the propagation of CI-waves in random media. In particular, it was shown that in a general class of non-hermitian scattering media such CI-waves can propagate without any reflection. The connection of such effects with the unidirectional invisibility was also analysed. A corresponding manuscript is ready to be submitted to Physical Review Letters. In the same direction the fellow pursued a project on the modulation instability of CI-waves in nonlinear disordered systems (again in collaboration with TU-Wien), which is directly related to the third and fourth topic of the proposal. Unlike previous attempts to understand the role of nonlinearity in localization and filament formation in random media, we can now solve this problem for the first time by considering media that support CI-waves and have gain and loss. A corresponding physical structure that realizes such a Manakov system, is that of a nonlinear optical fiber (or waveguide) with transverse disorder that contains gain and loss. The fundamental phenomenon of modulational instability can be examined by considering CI-waves (the structure supports them because of the existence of gain and loss). A corresponding manuscript is currently in preparation and will be submitted to Physical Review X.
Regarding the fourth topic of the fellowship, the fellow examined (in collaboration with the host institution Institute for Theoretical Physics, TU-Wien and the Atominstitut of TU-Wien) a topic that has to do with nonlinear effects in open photonic systems with gain and loss. In particular, the physical system of interest was that of coupled nonlinear PT-symmetric phonon lasers. By using a semiclassical approach, coupled nonlinear ordinary differential equations were derived to describe the time dynamics of such a system. The effect of nonlinear saturation on the symmetry breaking was systematically investigated by examining the steady state of the oscillators. The effect of noise was also an important component of this study. The counterintuitive main result was that of the existence of a new phase transition from a high thermal noise state to a low amplitude lasing state. A corresponding manuscript has meanwhile been submitted to Physical Review Letters. Another closely related theme (related to the fourth topic of the proposal) is that of a more detailed understanding of the role of openness in lasing in complex media. More specifically, the fellow in close collaboration with the outgoing institution at Princeton University, developed a novel spectral method for laser dynamics that is based on the open modes of the structure and in particular on the constant-flux states. This novel method (Constant Flux Time Dynamics, CFTD) is based on the semiclassical Maxwell-Bloch laser equations and can be applied to any laser system and treats the openeness of the structure exactly. The effect of the outcoupling and of nonlinearity in cooperative frequency locking between two laser modes was demonstrated numerically. A manuscript on this subject as well as a conference proceeding are already submitted.
In conclusion, results from these research activities are also expected to have potential impact both on basic research and on applied technology for the design of the next generation of synthetic photonic devices. The combination of gain and loss in an engineered way, can lead to new synthetic optical elements and lasers with unique and counterintuitive properties that are important for various photonic technologies.