We predict the self-collimation phenomena (or equivalently, dynamical localization) in two-dimensional PT-symmetric complex potentials, where the complex modulation is considered in the transverse, longitudinal, or simultaneously in both directions. Nondiffractive propagation is analytically predicted and further confirmed by numerical integration of a paraxial model. The parameter space is explored to identify the self-collimation regime in crystals with different PT symmetries. In addition, we also analyze how the PT-symmetric potentials determine the energy distribution between spatial modes of the self-collimated beams.
We introduce a class of systems holding parity-time (PT) symmetry locally, whereas being globally P symmetric. The potential, U = U(vertical bar r vertical bar), fulfills PT symmetry with respect to periodically distributed points r(0) : U(vertical bar r(0) + r vertical bar) = U*(vertical bar r(0) - r vertical bar) being r(0) not equal 0. We show that such systems hold unusual properties arising from the merging of the two different symmetries, leading to a strong field localization and enhancement at the double-symmetry center, r = 0, when the coupling of outward to inward propagating waves is favored. We explore such general potentials in one and two dimensions, which could have actual realizations combining gain-loss and index modulations in nanophotonic structures. In particular, we show how to render a broad aperture vertical-cavity surface-emitting laser into a bright and narrow beam source, as a direct application.
PT-symmetric structures in photonic crystals, combining refractive index and gain-loss modulations is becoming a research field with increasing interest due to the light directionality induced by these particular potentials. Here, we consider PT-symmetric potentials with axial symmetry to direct light to the crystal central point obtaining a localization effect. The axial and PT-symmetric potential intrinsically generates an exceptional central point in the photonic crystal by the merge of both symmetries. This particular point in the crystal lattice causes field amplitude gradients with exponential slopes around the crystal center. The field localization strongly depends on the phase of the central point and on the complex amplitude of the PT-potential.
The presented work analyzes in a first stage 1D linear PT-axisymmetric crystals and the role of the central point phase that determines the defect character, i.e. refractive index defect, gain-loss defect or a combination of both. The interplay of the directional light effect induced by the PT-symmetry and the light localization around the central point through the axial symmetry enhances localization and allows higher field concentration for certain phases. The linearity of the studied crystals introduces an exponential growth of the field that mainly depends on the complex amplitude of the potential. The work is completed by the analysis of 2D PT-axisymmetric potentials showing different spatial slopes and growth rates caused by symmetry reasons.
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We propose a new class of systems holding PT-symmetry only locally; the potential fulfills: U(r-r0)=U*(-r+r0 ) in a small neighborhood of any point r0, whereas on a global scale the system is only Parity symmetric: U(r-r0)=U(-r+r0) for all r. We show that such systems lead to a strong field localization at r=0, arising from the merge of the two different
symmetries. We explore these new potentials in one- and two- dimensional complex nanophotonic structures, combining gain/loss and index modulations, which we expect to have direct applications
as turning broad aperture lasers into bright and narrow output beam sources.
Ahmed, W.; Botey, M.; Herrero, R.; Staliunas, K. International Conference on Transparent Optical Networks p. 1-6 DOI: 10.1109/ICTON.2016.7550396 Data de presentació: 2016-07 Presentació treball a congrés
Optical Parity-Time (PT-) symmetric systems support unusual properties. When the symmetric coupling between internal modes is broken the system becomes strongly unidirectional resulting in novel effects such as asymmetric reflections, invisibility or asymmetric mode coupling. Here, we propose a new class of nanophotonic PTaxisymmetric systems which lead to an extreme field enhancement and high localization at the P-symmetry center when the coupling of inward propagating waves is favored due to the asymmetric radial coupling. We expect the effect to have direct applications such as rendering broad aperture lasers into bright and narrow output beam sources.
We show that modulation instability (MI) can be suppressed in vertical external cavity surface emitting lasers (VECSELs) by introducing a periodic spatio-temporal modulation of the pump profile which in turn allows a simple flatmirror configuration. The stability analysis of such pump modulated flat-mirror VECSELs is performed by a modified Floquet method and results are confirmed by full numerical integration of the model equations. It is found that the amplitude of the modulation as well as its spatial and temporal frequencies are crucial parameters for high spatial beam quality emission. We identify regions of complete and partial stabilization in parameter space for VECSELs with different external cavity lengths. The proposed method is shown to efficiently stabilize VECSELs with cavity lengths ranging from millimetres up to centimetres. However, the applicability of this method becomes limited for micro-meterlong cavities due to strong intrinsic relaxation oscillations.
We propose the stabilization of the output beam of Broad Area Semiconductor (BAS) amplifiers through the introduction of a spatially periodic modulated potential. We show that a periodic modulation of the pump profile in transverse and longitudinal directions, under certain ‘resonance’ condition, can solve two serious problems of BAS amplifiers (and possibly lasers), which are (i) the lack of an intrinsic spatial mode selection mechanism in linear amplification regimes and (ii) the modulation instability (also called Bespalov-Talanov instability) in nonlinear regimes. The elimination of these two drawbacks can significantly improve the spatial quality of the emitted beam in BAS amplifiers.
We propose and demonstrate theoretically that vertical-external-cavity surface-emitting lasers (VECSELs) with external flat mirrors can be stabilized by applying a periodic spatiotemporal modulation of the pump current. Such pump modulation is shown to suppress the pattern-forming instabilities (modulation instabilities), which eventually results in stable beam emission. A modified Floquet linear stability analysis is used to characterize the dynamics of the modulated system and to evaluate its stabilization performance. Stability maps identify the regions in parameter space for complete and partial stabilization of VECSELs operating in different regimes depending on the external-cavity length. In particular, the stabilization method is shown to operate most efficiently in Class-A laser limit (for relatively long VECSEL resonators), while it becomes ineffective in Class-B laser limit (for relatively short resonators). The stabilization effect is further confirmed through direct integration of the dynamical equations.
Kumar, S.; Ahmed, W.; Radziunas, M.; Botey, M.; Herrero, R.; Staliunas, K. International Conference on Transparent Optical Networks p. 1-4 DOI: 10.1109/ICTON.2015.7193465 Data de presentació: 2015-07-07 Presentació treball a congrés
Semiconductor lasers are efficient light sources with an important drawback, the lack of an intrinsic mode selection mechanism which leads to spatio-temporal instabilities. The modulation instability that unstabilizes the homogeneous solution can be suppressed by the introduction of spatial modulations in the transverse and longitudinal directions. The present work applies this stabilization technique to two of the most popular semiconductor devices, the Broad Area Semiconductor (BAS) amplifier and the Vertical-Cavity Surface-Emitting Laser (VCSEL).