## Publications

117 results found

Jones HF, 2019, Exact Results for a Special PT-Symmetric Optical Potential, Parity-time Symmetry and its Applications, Editors: Christodoulides, Yang, Publisher: Springer, Pages: 185-214, ISBN: 9789811312465

We present exact analytical results for the sinusoidal optical potentialsυ(x) ∝ cosKx + iλ sinKx, particularly for the special case λ = 1. This is at the borderline between broken and unbroken PT symmetry, and propagation through such an optical lattice exhibits many remarkable properties.

Jones HF, 2018, PT Symmetry in Optics, PT Symmetry In Quantum and Classical Physics, Editors: Bender, Publisher: World Scientific Publishing, Pages: 351-392, ISBN: 9781786345974

The ideas of PT symmetry were originally introduced in the context of quantum mechanics, but in recent years they have led to rapid developments in the apparently unconnected field of classical optics ...

Bender CM, Gianfreda M, Hassanpour N,
et al., 2016, Comment on "On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator" [J. Math. Phys. 48, 032701 (2007)], *Journal of Mathematical Physics*, Vol: 57, ISSN: 1089-7658

In a remarkable paper Chandrasekar et al. showed that the (second-order constant-coefficient) classical equation of motion for a damped harmonic oscillator can be derived from a Hamiltonian having one degree of freedom. This paper gives a simple derivation of their result and generalizes it to the case of an nth-order constant-coefficient differential equation.

Jones HF, Kulishov M, Kress B, 2016, Parity time-symmetric vertical cavities: intrinsically single-mode regime in longitudinal direction, *Optics Express*, Vol: 24, Pages: 17125-17137, ISSN: 1094-4087

We explore a new class of distributed feedback (DFB) structures that employ therecently-developed concept of parity-time (PT) symmetry in optics. We show that, based onPT-symmetric pure reflective volume gratings, a vertical surface-emitting cavity can beconstructed. We provide a detailed analysis of the threshold conditions as well as thewavelength and angular spectral characteristics using the Kogelnik coupled-waveapproximation, backed up by an exact solution of the Helmholtz equation. We show that sucha PT-symmetric cavity can be configured to support one and only one longitudinal mode,leading to inherently single-mode lasing.

Jones HF, Kulishov M, 2016, Extension of analytic results for a PT-symmetric structure, *Journal of Optics*, Vol: 18, ISSN: 2040-8986

The PT-symmetric optical grating with index profile e2ibz has been shown to have the interestingproperty of being essentially invisible for light incident from one side, while possessing greatlyenhanced reflection at a particular wavelength for light incident from the other side. We extend aprevious analysis of this grating to obtain an analytic solution for the case when the grating isembedded on a substrate, with different refractive indices on either side. We also generalize theprevious case of normal incidence to incidence at an arbitrary angle. In that case the enhancedreflection occurs at a particular angle of incidence for a given wavelength. Finally we discusshow the grating may be used to give lasing.

Kulishov M, Jones HF, Kress B, 2015, Analysis of unidirectional non-paraxial invisibility of purely reflective PT-symmetric volume gratings, *Optics Express*, Vol: 23, Pages: 18694-18711, ISSN: 1094-4087

We study the diffraction produced by a slab of purely reflectivePT-symmetric volume Bragg grating that combines modulations ofrefractive index and gain/loss of the same periodicity with a quarter-periodshift between them. Such a complex grating has a directional couplingbetween the different diffraction orders, which allows us to find an analyticsolution for the first three orders of the full Maxwell equations withoutresorting to the paraxial approximation. This is important, because onlywith the full equations can the boundary conditions, allowing for thereflections, be properly implemented. Using our solution we analyzeunidirectional invisibility of such a grating in a wide variety ofconfigurations.

Kulishov M, Jones HF, Kress B, 2015, Analysis of PT-symmetric volume gratings beyond the paraxial approximation, *OPTICS EXPRESS*, Vol: 23, Pages: 9347-9362, ISSN: 1094-4087

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- Citations: 14

Jones HF, 2014, Singular mapping for a PT-Symmetric sinusoidal optical lattice at the symmetry-breaking threshold, *International Journal of Theoretical Physics*, Vol: 54, Pages: 3986-3990, ISSN: 1572-9575

A popular PT-symmetric optical potential (variation of the refractive index) thatsupports a variety of interesting and unusual phenomena is the imaginary exponential, thelimiting case of the potential V0[cos(2πx/a) + iλ sin(2πx/a)] as λ → 1, the symmetrybreakingpoint. For λ < 1, when the spectrum is entirely real, there is a well-known mappingby a similarity transformation to an equivalent Hermitian potential. However, as λ → 1,the spectrum, while remaining real, contains Jordan blocks in which eigenvalues and thecorresponding eigenfunctions coincide. In this limit the similarity transformation becomessingular. Nonetheless, we show that the mapping from the original potential to its Hermitiancounterpart can still be implemented; however, the inverse mapping breaks down. We alsoilluminate the role of Jordan associated functions in the original problem, showing that theymap onto eigenfunctions in the associated Hermitian problem.

Bender CM, Jones HF, 2014, Calculation of low-lying energy levels in quantum mechanics, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 47, ISSN: 1751-8113

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- Citations: 3

Kulishov M, Kress B, Jones HF, 2014, Novel optical characteristics of a Fabry-Perot resonator with embedded PT-symmetrical grating, *OPTICS EXPRESS*, Vol: 22, Pages: 23164-23181, ISSN: 1094-4087

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- Citations: 6

Jones HF, 2014, The floquet method for PT-symmetric periodic potentials, *Acta Polytechnica*, Vol: 54, Pages: 122-123, ISSN: 1210-2709

By the general theory of PT -symmetric quantum systems, their energy levels are either real or occur in complex-conjugate pairs, which implies that the secular equation must be real. However, for periodic potentials it is by no means clear that the secular equation arising in the Floquet method is indeed real, since it involves two linearly independent solutions of the Schrödinger equation. In this brief note we elucidate how that reality can be established. © Czech Technical University in Prague, 2014.

Bender C, Fring A, Günther U,
et al., 2012, Quantum physics with non-Hermitian operators, *Journal of Physics A: Mathematical and Theoretical*, Vol: 45, ISSN: 1751-8113

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- Citations: 35

Bender CM, Jones HF, 2012, WKB analysis of PT-symmetric Sturm-Liouville problems, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 45, ISSN: 1751-8113

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- Citations: 7

Bender CM, Jones HF, 2012, Wentzel-Kramers-Brillouin analysis of PT-symmetric Sturm-Liouville problems, *PHYSICAL REVIEW A*, Vol: 85, ISSN: 1050-2947

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- Citations: 6

Jones HF, 2012, Analytic results for a PT-symmetric optical structure, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 45, ISSN: 1751-8113

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- Citations: 37

Jones HF, 2011, Perturbation theory for PT-symmetric sinusoidal optical lattices at the symmetry-breaking threshold, *Acta Polytechnica*, Vol: 51, Pages: 21-25, ISSN: 1210-2709

The P T symmetric potential V0 [cos(2πx/a) + iλ sin(2πx/a)] has a completely real spectrum for λ ≤ 1, and begins to develop complex eigenvalues for λ > 1. At the symmetry-breaking threshold λ = 1 some of the eigenvectors become degenerate, giving rise to a Jordan-block structure for each degenerate eigenvector. In general this is expected to give rise to a secular growth in the amplitude of the wave. However, it has been shown in a recent paper by Longhi, by numerical simulation and by the use of perturbation theory, that for an initial wave packet this growth is suppressed, giving instead a constant maximum amplitude. We revisit this problem by developing the perturbation theory further. We verify that the results found by Longhi persist to second order, and with different input wave packets we are able to see the seeds in perturbation theory of the phenomenon of birefringence first discovered by El-Ganainy et al.

Bender CM, Jones HF, 2011, Bound states of PT-symmetric separable potentials, *PHYSICAL REVIEW A*, Vol: 84, ISSN: 1050-2947

Jones HF, 2011, Use of equivalent Hermitian Hamiltonian for PT-symmetric sinusoidal optical lattices, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 44, ISSN: 1751-8113

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- Citations: 12

Graefe E-M, Jones HF, 2011, PT-symmetric sinusoidal optical lattices at the symmetry-breaking threshold, *PHYSICAL REVIEW A*, Vol: 84, ISSN: 1050-2947

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- Citations: 83

Jones HF, 2011, Green Functions for the Wrong-Sign Quartic, International Conference on Pseudo-Hermitian Hamiltonians in Quantum Physics, Publisher: SPRINGER/PLENUM PUBLISHERS, Pages: 1071-1080, ISSN: 0020-7748

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- Citations: 5

Bender CM, Jones HF, 2011, Quantum counterpart of spontaneously broken classical PT symmetry, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 44, ISSN: 1751-8113

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- Citations: 2

Jones HF, Moreira ES, 2010, Quantum and classical statistical mechanics of a class of non-Hermitian Hamiltonians, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 43, ISSN: 1751-8113

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- Citations: 15

Bender CM, Benincasa G, Jones HF, 2009, Comment on "New ansatz for metric operator calculation in pseudo-Hermitian field theory", *PHYSICAL REVIEW D*, Vol: 80, ISSN: 2470-0010

Jones HF, Rivers RJ, 2009, Which Green functions does the path integral for quasi-Hermitian Hamiltonians represent?, *PHYSICS LETTERS A*, Vol: 373, Pages: 3304-3308, ISSN: 0375-9601

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- Citations: 13

Bender CM, Besseghir K, Jones HF,
et al., 2009, Small-epsilon behavior of the non-Hermitian PT-symmetric Hamiltonian H = p(2) + x(2)(ix)(epsilon), *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 42, ISSN: 1751-8113

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- Citations: 8

Jones HF, 2009, Gauging non-Hermitian Hamiltonians, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 42, ISSN: 1751-8113

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- Citations: 12

Jones HF, 2008, Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation, *PHYSICAL REVIEW D*, Vol: 78, ISSN: 1550-7998

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- Citations: 50

Fring A, Jones H, Znojil M, 2008, 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics: Preface, *Journal of Physics A: Mathematical and Theoretical*, Vol: 41, ISSN: 1751-8113

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- Citations: 14

Bender CM, Jones HF, 2008, Interactions of Hermitian and non-Hermitian Hamiltonians, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 41, ISSN: 1751-8113

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- Citations: 27

Jones HF, 2008, Equivalent Hamiltonian for the Lee model, *PHYSICAL REVIEW D*, Vol: 77, ISSN: 1550-7998

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- Citations: 7

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