SUSY transformation of guided modes in semiconductor waveguides

Kočinac, S.; Milanović, V.; Ikonić, Z.; Indjin, D.; Radovanović, J.; Harrison, P.

doi:10.1002/pssc.200461823

Cited by 4 publications

(6 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Liouville transformation in [29], [30], [32] involved no independent-variable transformation contrary to what was done in the present paper (see eq. ( 6)).…”

Section:  contrasting

confidence: 69%

“…). For solving this difficulty, a (partial) Liouville transformation was implemented in [29], [30] involving a dependent-variable transformation but no independent-variable transformation. The Darboux transformation (or the equivalent supersymmetry process) was then performed on the resulting stationary Schrödinger equation for building sequences of solvable profiles related to an effective permittivity.…”

Section:  mentioning

confidence: 99%

“…It was also recently applied to the synthesis of Bragg filters with a given number of resonances at desired frequencies [24]. SUSY optics was applied for tailoring the refractive index structure in the active (waveguide) layer of quantum cascade lasers [29] and for designing a partner permittivity-profile leading to the same scattering characteristics (reflection/transmission) as the original one but presenting lower contrast dielectric arrangements thus allowing to meet the technical (fabrication) specifications more easily [30]. In the latter works, the SUSY methodology was applied to the Helmholtz equation satisfied by the electric field in the TE mode when expressed in the physical-depth space.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sequences of exact analytical solutions for plane waves in graded media

Krapez

2017

Journal of Modern Optics

View full text Add to dashboard Cite

We present a new method for building sequences of solvable profiles of the electromagnetic (EM) admittance in lossless isotropic materials with 1D graded permittivity and permeability (in particular profiles of the optical refractive-index). These solvable profiles lead to analytical closed-form expressions of the EM fields, for both TE and TM modes. The Property-and-Field Darboux Transformations method, initially developed for heat diffusion modelling, is here transposed to the Maxwell equations in the optical-depth space. Several examples are provided, all stemming from a constant seed-potential, which makes them based on elementary functions only. Solvable profiles of increasingly complex shape can be obtained by iterating the process or by assembling highly flexible canonical profiles. Their implementation for modelling optical devices like matching layers, rugate filters, Bragg gratings, chirped mirrors or 1D photonic crystals, offers an exact and cost-effective alternative to the classical approaches.

show abstract

“…The Liouville transformation in [29], [30], [32] involved no independent-variable transformation contrary to what was done in the present paper (see eq. ( 6)).…”

Section:  contrasting

confidence: 69%

Section:  mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sequences of exact analytical solutions for plane waves in graded media

Krapez

2017

Journal of Modern Optics

View full text Add to dashboard Cite

show abstract

“…As previously shown [13], the SUSY formalism can be generally used in arbitrary one-dimensional refractive index landscapes. In fact, this is the case even under high-contrast conditions where the degeneracy between TE and TM waves is broken and necessitates the use of the Helmholtz equation [13,45]. Here, for brevity, we limit our scope to one-dimensional weakly guiding settings.…”

Section: Susy In Pt -Symmetric Optical Potentialsmentioning

confidence: 99%

Supersymmetry-generated complex optical potentials with real spectra

2013

View full text Add to dashboard Cite

We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT) symmetric optical potentials, can give rise to novel refractive index landscapes with altogether non-trivial properties. In particular, we find that the presence of gain and loss allows for arbitrarily removing bound states from the spectrum of a structure. This is in stark contrast to the Hermitian case, where the SUSY formalism can only address the fundamental mode of a potential. Subsequently we investigate isospectral families of complex potentials that exhibit entirely real spectra, despite the fact that their shapes violate PT-symmetry. Finally, the role of SUSY transformations in the regime of spontaneously broken PT symmetry is investigated.Comment: 6 pages, 4 figure

show abstract

“…In optics, SUSY can be introduced by exploiting the mathematical isomorphism between the Schrödinger and the optical wave equation [18]. In this setting, the optical refractive index profile plays the role of the potential ( ), which in the context of supersymmetry can be used for mode conversion [19,20], transformation optics [21], design of Bragg gratings [22], and Bloch-like waves in random-walk potentials [23], to mention a few [24][25][26]. However, the implications of SUSY isospectrality in active platforms, as well as its interplay with nonlinearity and non-Hermiticity has so far remained unexplored.…”

mentioning

confidence: 99%

Supersymmetric laser arrays

Hokmabadi

Nye

El‐Ganainy

et al. 2019

Science

View full text Add to dashboard Cite

The theoretical framework of supersymmetry (SUSY) aims to relate bosons and fermions-two profoundly different species of particles-and their interactions. While this space-time symmetry is seen to provide an elegant solution to many unanswered questions in high-energy physics, its experimental verification has so far remained elusive. Here, we demonstrate that, notions from supersymmetry can be strategically utilized in optics in order to address one of the longstanding challenges in laser science. In this regard, a supersymmetric laser array is realized, capable of emitting exclusively in its fundamental transverse mode. Our results not only pave the way towards devising new schemes for scaling up radiance in integrated lasers, but also on a more fundamental level, they could shed light on the intriguing synergy between non-Hermiticity and supersymmetry.Symmetries play a fundamental role in physical sciences. Symmetry principles ensure energy and momentum conservation and dictate the allowable dynamical laws governing our world. The Lorentz invariance embodied in Maxwell's equations was crucial in developing the theory of relativity, while the exchange symmetry allows one to classify fundamental particles as either bosons or fermions. In high-energy physics, other overarching symmetries like that of chargeparity-time (CPT) and supersymmetry (SUSY) have also emerged as a means to unveil the laws of nature [1,2]. SUSY, first proposed within the context of particle physics as an extension of the Poincare space-time symmetry, makes an ambitious attempt to provide a unified description of all fundamental interactions. In general, SUSY relates bosonic and fermionic degrees of freedom in a cohesive fashion. This directly implies that each type of boson has a supersymmetric counterpart, a superpartner fermion, and vice versa [3]. Even though the full ramification of SUSY in high energy physics is still a matter of debate that awaits experimental validation, supersymmetric techniques have already found their way into low energy physics, condensed matter, statistical mechanic, nonlinear dynamics and soliton theory as well as in stochastic processes and BCS-type theories, to mention a few [4][5][6][7][8][9].

show abstract

SUSY transformation of guided modes in semiconductor waveguides

Cited by 4 publications

References 5 publications

Sequences of exact analytical solutions for plane waves in graded media

Sequences of exact analytical solutions for plane waves in graded media

Supersymmetry-generated complex optical potentials with real spectra

Supersymmetric laser arrays

Contact Info

Product

Resources

About