Wave propagation in the presence of a dielectric slab: The paraxial approximation

Cruz, Sara Cruz y; Razo, Rubén

doi:10.1088/1742-6596/624/1/012018

Cited by 10 publications

(8 citation statements)

References 25 publications

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“…This is the reason for which we started from initial refractive indices admitting no leaky modes. In previous works we have studied such possibility by analyzing the resonances of the initial structure [16,47,57]. It is viable to construct the supersymmetric partners using resonances of the initial system [31], a technique implemented also in the cosh-like case [52,53] and for soliton-like models [58].…”

Section: Discussion Of Results and Conclusionmentioning

confidence: 99%

Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM

2021

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The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux–Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive indices admitting all-real eigenvalues in their point spectrum. The new refractive indices are such that their imaginary part gives zero if it is integrated over the entire domain of definition. This property, called condition of zero total area, ensures the conservation of optical power so the refractive index shows balanced gain and loss. Consequently, the complex-valued refractive indices reported in this work include but are not limited to the parity-time invariant case.

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Section: Discussion Of Results and Conclusionmentioning

confidence: 99%

Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM

2021

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“…Additional applications may include the propagation of electromagnetic signals in waveguides, where the Helmholtz equation is formally paired with the Schrodinger one [86][87][88], and the self-focusing is relevant [82][83][84][85]. Finally, the approach can be extended to study supersymmetric structures in quantum mechanics [89] with time-dependent potentials [16,17] Using (9) and (A-1), the Schrödinger equation of the stationary oscillator (3) becomes a partial differential equation of the desired form S def .…”

Section: Discussionmentioning

confidence: 99%

Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations

Zelaya

Rosas-Ortiz

2020

Phys. Scr.

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We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with timedependent frequencies that are subjected to the action of a time-dependent driving force, and have a time-dependent zero point energy. Our approach uses the method of point transformations to construct the physical solutions of the parametric oscillator as mere deformations of the well known solutions of the stationary oscillator. In this form, the determination of the quantum integrals of motion is automatically achieved as a natural consequence of the transformation, without necessity of any ansätz. It yields the mechanism to construct an orthonormal basis for the nonstationary oscillators, so arbitrary superpositions of orthogonal states are available to obtain the corresponding coherent states. We also show that the dynamical algebra of the parametric oscillator is immediately obtained as a deformation of the algebra generated by the conventional boson ladder operators. A number of explicit examples is provided to show the applicability of our approach.

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“…Other applications may include the study of electromagnetic signals propagating in waveguides, where the Helmholtz equation is formally paired with the Schrödinger one. 61,62 In such a picture, the complex-valued potential V (x) can be identified with a refractive index of balanced gain/loss profile. 48 The study of non-Hermitian coherent states associated with finite-dimensional systems 63 is also available.…”

Section: Discussionmentioning

confidence: 99%

Interplay between Riccati, Ermakov, and Schrödinger equations to produce complex‐valued potentials with real energy spectrum

Blanco-Garcia

Rosas-Ortiz

Zelaya

2018

Math Methods in App Sciences

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Nonlinear Riccati and Ermakov equations are combined to pair the energy spectrum of 2 different quantum systems via the Darboux method. One of the systems is assumed Hermitian, exactly solvable, with discrete energies in its spectrum. The other system is characterized by a complex‐valued potential that inherits all the energies of the former one and includes an additional real eigenvalue in its discrete spectrum. If such eigenvalue coincides with any discrete energy (or it is located between 2 discrete energies) of the initial system, its presence produces no singularities in the complex‐valued potential. Non‐Hermitian systems with spectrum that includes all the energies of either Morse or trigonometric Pöschl‐Teller potentials are introduced as concrete examples.

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Wave propagation in the presence of a dielectric slab: The paraxial approximation

Cited by 10 publications

References 25 publications

Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM

Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM

Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations

Interplay between Riccati, Ermakov, and Schrödinger equations to produce complex‐valued potentials with real energy spectrum

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