Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers

Radziunas, Mindaugas; Botey, Muriel; Herrero, R.; Staliūnas, Kęstutis

doi:10.1063/1.4821251

Cited by 39 publications

(28 citation statements)

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“…In optics, the refractive index corresponds to the real component of the potential whereas gain/loss stands for its imaginary part. Purely real or imaginary modulated systems being Photonic Crystals and Gain/Loss Modulated (GLM) systems, respectively [15][16][17][18]. Therefore, PT-symmetric optical potentials are expected to behave either as PhC-like systems or as GLM-like systems.…”

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confidence: 99%

Locally parity-time-symmetric and globally parity-symmetric systems

et al. 2016

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We introduce a new class of systems holding Parity Time (PT)-symmetry locally whereas being globally Psymmetric. The potential is globally symmetric, U=U(|r|), and fulfills PT-symmetry with respect to periodically distributed points r 0 : U(|r 0 +r|)=U*(|r 0 -r|) being r 0 ∫ 0. We show that such systems hold novel 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 1D and 2D, which could have actual realizations in different fields, in particular in optics, combining gain/loss and index modulations in nanophotonic structures. As a direct application, we show how to render a broad aperture VCSEL into a bright and narrow beam source.PACS numbers: 78.20. Bh, 42.25.Bs PT-symmetric systems, introduced as a curiosity in quantum mechanics [1,2], are recently being explored in the field of optics, acoustics, plasmonics or Bose-Einstein condensates [3][4][5][6][7][8]. A necessary condition for a system to be PT-symmetric is that the complex potential fulfills U(r)=U* (-r). Such complex systems with real spectra may support novel unexpected properties [9][10][11].Most PT-symmetric systems can be regarded as belonging to two limiting situations of complex periodic potentials. On one extreme, there are purely real-valued potentials holding real periodic modulations in space; which potential, in the simplest harmonic modulation case, reads: U(r) = n Re cos(qx), being q the spatial period of the modulation and n Re its amplitude. On the other extreme, we find purely imaginary potentials only exhibiting gain-loss modulations, which in the simplest harmonic case may be expressed as: U(r) = n Im cos(qx). Both limits lead to a symmetric coupling of resonant modes, i.e. the two counter-propagating modes with wavevector |k|, exp( ) ikx  and exp( ), ikx are coupled symmetrically at resonance, for 2 q k  . The most peculiar situation arises when both the real and imaginary parts of the potential are simultaneously modulated, with a / 2   phase shift: U(r) = n Re cos(qx) + n Im sin(qx). When both modulations are balanced, n Re = n Im , the complex potential can be simply expressed as: U(r) = n exp(±iqx), which evidences that the coupling becomes strongly unidirectional. E.g. for such a complex modulation the left-propagating mode exp(, is efficiently coupled to the right propagating mode, exp( ), ikx  but not vice versa. The point n Re = n Im is precisely the so-called phase transition, separating two extreme situations. Mathematically, the coupling between left/right propagating modes is conveniently described via linear coupling matrices, M = {{0,n Re +n Im },{n Re -n Im ,0}} which at the PT-phase transition point degenerate to M ={{0,2n},{0,0}}. Generally, in the presence of several modes (or mode continuum) the situation becomes more engaged, however the phase transition separating the two extreme limits of ...

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Locally parity-time-symmetric and globally parity-symmetric systems

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“…where q z = 2π/d z , q x = 2π/d x , and d x (d z ) denotes the transverse (longitudinal) modulation period [18]. The factor ρ determines the considered electrical contact configuration, such that ρ = 0 corresponds to the chessboard-type configuration [see Fig.…”

Section: Traveling Wave Modelmentioning

confidence: 99%

“…[18] to consider BA amplifiers of moderate length with a 2D, longitudinal and transverse, modulation of Our theoretical study is based on the analysis and simulations of the 1 (time) + 2 (space)-dimensional traveling wave (TW) model which takes into account the spatio-temporal dynamics of slowly varying complex amplitudes of the counter-propagating optical fields, in-duced polarizations and carrier densities [14,20,21]. This modeling approach was already used by us to demonstrate the principle of angular filtering of the moderate-intensity optical beams in BA amplifiers [18].…”

Section: Introductionmentioning

confidence: 99%

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Far-field narrowing in spatially modulated broad-area edge-emitting semiconductor amplifiers

et al. 2015

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UPCommonsPortal del coneixement obert de la UPC http://upcommons.upc.edu/e-prints Radziunas, M., Herrero, R., Botey, M., Staliunas, K. (2015) We perform a detailed theoretical analysis of the far field narrowing in broad-area edge-emitting semiconductor amplifiers that are electrically injected through the contacts periodically modulated in both, longitudinal and transverse, directions. The beam propagation properties within the semiconductor amplifier are explored by a (1+2)-dimensional traveling wave model and its coupled mode approximation. Assuming a weak field regime, we analyze the impact of different parameters and modulation geometry on the narrowing of the principal far field component. OCIS codes:(250.5980) Semiconductor optical amplifiers; (140.3300) Laser beam shaping; (220.2740) Geometric optical design; (130.5296) Photonic crystal waveguides.http://dx

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“…On the other hand, recent works on systems with gain-loss modulations in two dimensions [7,8], and also on complex two-dimensional 2D crystals [9,10] where the gain-loss and index are simultaneously modulated, have shown the micro-and nanophotonics to be a platform for developing synthetic materials with novel beam propagation effects. However, none of these cases [7][8][9][10] can be attributed to PT-symmetric systems because they do not meet the requirements of PT symmetry.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional complex parity-time-symmetric photonic structures

et al. 2015

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We propose a simple realistic two-dimensional complex parity-time-symmetric photonic structure that is described by a non-Hermitian potential but possesses real-valued eigenvalues. The concept is developed from basic physical considerations to provide asymmetric coupling between harmonic wave components of the electromagnetic field. The structure results in a nonreciprocal chirality and asymmetric transmission between in-and out-coupling channels into the structure. The analytical results are supported by a numerical study of the Bloch-like mode formations and calculations of a realistic planar semiconductor structure.

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Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers

Abstract: Postprint (published version

Cited by 39 publications

References 23 publications

Locally parity-time-symmetric and globally parity-symmetric systems

Locally parity-time-symmetric and globally parity-symmetric systems

Far-field narrowing in spatially modulated broad-area edge-emitting semiconductor amplifiers

Two-dimensional complex parity-time-symmetric photonic structures

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