# Resonance phenomenon related to spectral singularities, complex barrier potential, and resonating waveguides

@article{Mostafazadeh2009ResonancePR, title={Resonance phenomenon related to spectral singularities, complex barrier potential, and resonating waveguides}, author={Ali Mostafazadeh}, journal={Physical Review A}, year={2009}, volume={80}, pages={032711} }

A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission coefficients. This property reveals an interesting resonance effect with possible applications in waveguide physics. We study the spectral singularities of a complex barrier potential and explore their application in designing a waveguide that functions as a…

## 51 Citations

### Spectral singularities of a complex spherical barrier potential and their optical realization

- Physics, Mathematics
- 2011

### Nonlinear spectral singularities of a complex barrier potential and the lasing threshold condition

- Physics
- 2013

A spectral singularity is a mathematical notion with an intriguing physical realization in terms of certain zero-width resonances. In optics it manifests as lasing at the threshold gain. We explore…

### Harnessing Spectral Singularities in Non- Hermitian Cylindrical Structures

- MathematicsIEEE Transactions on Antennas and Propagation
- 2020

Non-Hermitian systems characterized by suitable spatial distributions of gain and loss can exhibit “spectral singularities” in the form of zero-width resonances associated with real-frequency poles…

### Spectral singularities and Bragg scattering in complex crystals

- Mathematics, Physics
- 2010

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between…

### Self-dual spectral singularities and coherent perfect absorbing lasers without -symmetry

- Physics
- 2012

A -symmetric optically active medium that lases at the threshold gain also acts as a complete perfect absorber at the laser wavelength. This is because spectral singularities of -symmetric complex…

### Optical spectral singularities and coherent perfect absorption in a two-layer spherical medium

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2012

An optical spectral singularity is a zero-width resonance that corresponds to lasing at threshold gain. Its time-reversal causes coherent perfect absorption of light and forms the theoretical basis…

### Transmission singularities in resonant electron tunneling through double complex potential barrier

- Physics
- 2017

### Scattering cross-section resonance originating from a spectral singularity

- Physics, Mathematics
- 2011

Using techniques of supersymmetric quantum mechanics, scattering properties of Hermitian Hamiltonians, which are related to non-Hermitian ones by similarity transformations, are studied. We have…

### Spectral singularities in a non-Hermitian Friedrichs-Fano-Anderson model

- Physics
- 2009

Spectral singularities are predicted to occur in a non-Hermitian extension of the Friedrichs-Fano-Anderson model describing the decay of a discrete state $|a >$ coupled to a continuum of modes. A…

### Perfectly absorbed and emitted currents by complex potentials in nonlinear media

- MathematicsPhysical Review A
- 2021

Recently it was demonstrated that the concept of a spectral singularity (SS) can be generalized to waves propagating in nonlinear media, like matter waves or electromagnetic waves in Kerr media. The…

## References

SHOWING 1-10 OF 41 REFERENCES

### Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies.

- Mathematics, PhysicsPhysical review letters
- 2009

This work identifies spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width and shows that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularity.

### Delta-function potential with a complex coupling

- Mathematics, Physics
- 2006

We explore the Hamiltonian operator , where is the Dirac delta function and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a spectral singularity at . For Re(z) 0, H has…

### Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions

- Mathematics
- 2009

A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an…

### LETTER TO THE EDITOR: Spectral singularities of non-Hermitian Hamiltonians and SUSY transformations

- Mathematics, Physics
- 2005

Simple examples of non-Hermitian Hamiltonians with purely real spectra defined in L2(R+) having spectral singularities inside the continuous spectrum are given. It is shown that such Hamiltonians may…

### Experimental observation of the topological structure of exceptional points.

- PhysicsPhysical review letters
- 2001

A microwave cavity experiment where exceptional points (EPs), which are square root singularities of the eigenvalues as function of a complex interaction parameter, are encircled in the laboratory and one of the Eigenvectors undergoes a sign change which can be discerned in the field patterns.

### Mode degeneracies and the petermann excess-noise factor for unstable lasers

- Physics
- 2003

Abstract The linewidth of an unstable laser exceeds the quantum minimum by the Petermann factor K, which depends on the overlap between left and right eigenvectors of the (non-unitary) round-trip…

### Physical realization of -symmetric potential scattering in a planar slab waveguide

- Physics
- 2005

A physical realization of scattering by -symmetric potentials is provided: we show that the Maxwell equations, for an electromagnetic wave travelling along a planar slab waveguide filled with gain…

### Trapping of an electron due to molecular vibrations

- PhysicsPhysical review letters
- 2000

It is shown that the nuclear motion of H-2 generates a continuum of autoionization resonance states that increases the lifetime of the trapped electron in the e(-)/H(2) scattering experiments and leads to asymmetric oscillations in the phase of the excitation probability amplitude.