844 research outputs found
Perturbative Analysis of Spectral Singularities and Their Optical Realizations
We develop a perturbative method of computing spectral singularities of a
Schreodinger operator defined by a general complex potential that vanishes
outside a closed interval. These can be realized as zero-width resonances in
optical gain media and correspond to a lasing effect that occurs at the
threshold gain. Their time-reversed copies yield coherent perfect absorption of
light that is also known as an antilaser. We use our general results to
establish the exactness of the n-th order perturbation theory for an arbitrary
complex potential consisting of n delta-functions, obtain an exact expression
for the transfer matrix of these potentials, and examine spectral singularities
of complex barrier potentials of arbitrary shape. In the context of optical
spectral singularities, these correspond to inhomogeneous gain media.Comment: 13 pages, 2 figures, one table, a reference added, typos correcte
Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
Spectral singularities are spectral points that spoil the completeness of the
eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify
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. We show that a wave guide
modeled using such a potential operates like a resonator at the frequencies of
spectral singularities. As a concrete example, we explore the spectral
singularities of an imaginary PT-symmetric barrier potential and demonstrate
the above resonance phenomenon for a certain electromagnetic wave guide.Comment: Published versio
Is the CPT-norm always positive?
We give an explicit example of an exactly solvable PT-symmetric Hamiltonian
with the unbroken PT symmetry which has one eigenfunction with the zero
PT-norm. The set of its eigenfunctions is not complete in corresponding Hilbert
space and it is non-diagonalizable. In the case of a regular Sturm-Liouville
problem any diagonalizable PT-symmetric Hamiltonian with the unbroken PT
symmetry has a complete set of positive CPT-normalazable eigenfunctions. For
non-diagonalizable
Hamiltonians a complete set of CPT-normalazable functions is possible but the
functions belonging to the root subspace corresponding to multiple zeros of the
characteristic determinant are not eigenfunctions of the Hamiltonian anymore
Optical realization of relativistic non-Hermitian quantum mechanics
Light propagation in distributed feedback optical structures with gain/loss
regions is shown to provide an accessible laboratory tool to visualize in
optics the spectral properties of the one-dimensional Dirac equation with
non-Hermitian interactions. Spectral singularities and PT symmetry breaking of
the Dirac Hamiltonian are shown to correspond to simple observable physical
quantities and related to well-known physical phenomena like resonance
narrowing and laser oscillation.Comment: 4 page
Unidirectional Invisibility and PT-Symmetry with Graphene
We investigate the reflectionlessness and invisibility properties in the
transverse electric (TE) mode solution of a linear homogeneous optical system
which comprises the -symmetric structures covered by graphene
sheets. We derive analytic expressions, indicate roles of each parameter
governing optical system with graphene and justify that optimal conditions of
these parameters give rise to broadband and wide angle invisibility. Presence
of graphene turns out to shift the invisible wavelength range and to reduce the
required gain amount considerably, based on its chemical potential and
temperature. We substantiate that our results yield broadband reflectionless
and invisible configurations for realistic materials of small refractive
indices, usually around , and of small thickness sizes with graphene
sheets of rather small temperatures and chemical potentials. Finally, we
demonstrate that pure -symmetric graphene yields invisibility at
small temperatures and chemical potentials.Comment: 20 pages, 1 table 17 figure
Resonance Phenomenon Related to Spectral Singularities, Complex Barrier Potential, and Resonating Waveguides
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 resonator. We show that for the
easily accessible sizes of the waveguide and its gain region, we can realize
the spectral singularity-related resonance phenomenon at almost every
wavelength within the visible spectrum or outside it.Comment: Published version, 20 pages, 2 tables, 7 figure
Relativistic Harmonic Oscillator Revisited
The familiar Fock space commonly used to describe the relativistic harmonic
oscillator, for example as part of string theory, is insufficient to describe
all the states of the relativistic oscillator. We find that there are three
different vacua leading to three disconnected Fock sectors, all constructed
with the same creation-annihilation operators. These have different spacetime
geometric properties as well as different algebraic symmetry properties or
different quantum numbers. Two of these Fock spaces include negative norm
ghosts (as in string theory) while the third one is completely free of ghosts.
We discuss a gauge symmetry in a worldline theory approach that supplies
appropriate constraints to remove all the ghosts from all Fock sectors of the
single oscillator. The resulting ghost free quantum spectrum in d+1 dimensions
is then classified in unitary representations of the Lorentz group SO(d,1).
Moreover all states of the single oscillator put together make up a single
infinite dimensional unitary representation of a hidden global symmetry
SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these
new results in string theory and other areas of physics and mathematics are
briefly mentioned.Comment: 41 pages, 2 figures, LaTe
Self-dual Spectral Singularities and Coherent Perfect Absorbing Lasers without PT-symmetry
A PT-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 PT-symmetric complex potentials are always
accompanied by their time-reversal dual. We investigate the significance of
PT-symmetry for the appearance of these self-dual spectral singularities. In
particular, using a realistic optical system we show that self-dual spectral
singularities can emerge also for non-PT-symmetric configurations. This
signifies the existence of non-PT-symmetric CPA-lasers.Comment: 11 pages, 3 figures, 1 table, accepted for publication in J. Phys.
Spectral Theory of Time Dispersive and Dissipative Systems
We study linear time dispersive and dissipative systems. Very often such
systems are not conservative and the standard spectral theory can not be
applied. We develop a mathematically consistent framework allowing (i) to
constructively determine if a given time dispersive system can be extended to a
conservative one; (ii) to construct that very conservative system -- which we
show is essentially unique. We illustrate the method by applying it to the
spectral analysis of time dispersive dielectrics and the damped oscillator with
retarded friction. In particular, we obtain a conservative extension of the
Maxwell equations which is equivalent to the original Maxwell equations for a
dispersive and lossy dielectric medium.Comment: LaTeX, 57 Pages, incorporated revisions corresponding with published
versio
Spectral singularities and Bragg scattering in complex crystals
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 spectral singularities in complex
crystals and secularities that arise in Bragg diffraction patterns. Signatures
of spectral singularities in a scattering process with wave packets are
elucidated for a PT-symmetric complex crystal.Comment: 6 pages, 5 figures, to be published in Phys. Rev.
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