Resonantly absorbing one-dimensional photonic crystals

Light propagation in optical lattices of driven cold atoms exhibits non-Hermitian degeneracies when the first-order modulation amplitudes of real and imaginary parts of the probe susceptibility are manipulated to be balanced. At these degeneracies, one may observe complete unidirectional reflectionless light propagation. This strictly occurs with no gain and can be easily tuned and fully reversed as supported by the transfer-matrix calculations and explained via a coupled-mode analysis. DOI: 10.1103/PhysRevLett.113.123004 PACS numbers: 37.10.Jk, 11.30.Er, 42.25.Bs, 42.50.Gy Much attention has been devoted to the development of artificial metamaterials for achieving optical functionalities not available in nature. Photonic crystals [1] and lefthanded materials [2] are prominent instances tailored to stretch the rules of light propagation and interaction. Such metamaterials have seeded new paradigms in optical, optoelectronic, and optomechanical devices [3][4][5][6]. Nevertheless, some tasks are more difficult than others with unidirectional light transport being a most pronounced example. Significant progress has been made in recent years by developing optical materials with parity-time (PT) symmetry to attain unidirectional light invisibility [7][8][9][10][11][12][13][14][15][16]. PT-symmetric metamaterials require a delicate balance of gain and loss whereby the complex refraction index satisfies nðzÞ ¼ n Ã ð−zÞ and are typically made of periodic solid microstructures. Homogeneous atomic vapors driven into three-level [17,18] or four-level [19] configurations have also been proposed to realize PT-symmetric optical potentials via rather complicated spatial modulations of two driving fields. Such proposals have obvious advantages of real-time all-optical reconfigurable capabilities and implicit disadvantages of intractable field modulations and considerable symmetry errors. Large optical nonreciprocities may also be achieved by exploiting the asymmetric Doppler shift in moving atomic Bragg mirrors [20], and proofof-principle experiments have been carried out [21].The great interest in PT-symmetric complex media stemmed, however, from the non-Hermitian extensions of quantum mechanics and quantum field theories [22,23], and it is perhaps worth going back to the essential nonHermitian behavior of light transport to get a broader picture on reciprocity violations and unidirectional reflectionlessness. Take, e.g., a typical one-dimensional (1D) light scattering process as shown in Fig. 1(a) where the outgoing field amplitudes fE − L ; E þ R g are related to the incoming field amplitudes fE − R ; E þ L g by a scattering matrix S [24], the eigenvectors of which are defined byThe complex amplitudes t, r L , and r R of the (S) matrix in Eq.(1) denote, as usual, the reciprocal transmission and the reflection for incidence from the left and from the right. In general, the matrix S is non-Hermitian, its eigenvalues λ AE s ¼ t AE ffiffiffiffiffiffiffiffiffi ffi r L r R p are complex, and its eigenvectors ðAE ffiffiffiffiff...

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“…(3) into a transfer-matrix calculation [39] or by incorporating Eq. (4) into a coupled-mode analysis as shown below.…”

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Non-Hermitian Degeneracies and Unidirectional Reflectionless Atomic Lattices

2014

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“…This can be attained by small tunings of the probe misalignment angle (θ p ) with respect to the crystal z axis. Within different parameter regimes than used here, even fully developed photonic stop bands may be obtained [47]. Two entirely different regimes of symmetric Figs.…”

Section: A the Photonic Crystalmentioning

confidence: 99%

“…with the corresponding reflection and transmission complex amplitudes r j (z l ) and t j (z l ) determined by the complex refractive index n pj (z l ) 1 + χ p j (z l )/2 [47]. The j th-period matrix is then…”

Section: A the Photonic Crystalmentioning

confidence: 99%

“…One important application of P T -antisymmetric susceptibilities is to realize high-contrast asymmetric reflectivities including fully unidirectional reflection, which one can examine by directly adopting transfer matrix methods to Eq. (2) [47]. To this end, we first derive the 2 × 2 unimodular transfer matrix M j of the j th lattice site by dividing the period into, e.g., 100 thin layers of identical thickness δz but distinct atomic density N j (z l ) for l ∈ {1,100}.…”

Section: A the Photonic Crystalmentioning

confidence: 99%

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Perfect absorption and no reflection in disordered photonic crystals

Artoni

Rocca

2017

Phys. Rev. A

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Understanding the effects of disorder on the light propagation in photonic devices is of major importance from both fundamental and applied points of view. Unidirectional reflectionless and coherent perfect absorption of optical signals are unusual yet fascinating phenomena that have recently sparked an extensive research effort in photonics. These two phenomena, which arise from topological deformations of the scattering matrix S parameters space, behave differently in the presence of different types of disorder, as we show here for a lossy photonic crystal prototype with a parity-time antisymmetric susceptibility or a more general non-Hermitian one.

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“…1) whose thickness d is essentially given by the rms position spread around the minima of the optical potential and is much smaller than the lattice periodicity a [35]. The corresponding periodically modulated refractive index has been predicted to give rise to pronounced photonic stop-bands [36][37][38][39]. In spite of the fact that efficient photonic structures with cold atoms are difficult to make because dilute atomic clouds have a low refractive index contrast and intrinsically short lengths, efficient Bragg reflection has recently been demonstrated in atomic multilayers which yield a well developed one-dimensional photonic gap with nearly 80% reflectivity [22].…”

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Optical Nonreciprocity of Cold Atom Bragg Mirrors in Motion

et al. 2013

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Reciprocity is fundamental to light transport and is a concept that holds also in rather complex systems. Yet, reciprocity can be switched off even in linear, isotropic and passive media by setting the material structure into motion. In highly dispersive multilayers this leads to a fairly large forwardbackward asymmetry in the pulse transmission. Moreover, in multilevel systems, this transport phenomenon can be all-optically enhanced. For atomic multilayer structures made of three-level cold 87 Rb atoms, for instance, forward-backward transmission contrast around 95% can be obtained already at atomic speeds in the meter per second range. The scheme we illustrate may open up avenues for optical isolation that were not previously accessible.PACS numbers: 42.50. Wk, 42.70.Qs, 42.50.Gy, 37.10.Vz Much attention has been devoted to the development of advanced materials and composite systems to achieve optical functionalities not readily available in natural media. Such optical metamaterials can be engineered to stretch the rules that govern light propagation and lightmatter interaction, potentially seeding a new paradigm in all-optical, optoelectronic and optomechanical devices. Photonic crystals and negatively refracting media are prominent instances of man-made systems the optical properties of which can be tailored to a great extent. Nevertheless, some tasks are more difficult than others. Already in the familiar process of linear reflection and transmission of light [1] it is in general hard to achieve non-reciprocity. In particular, multilayer photonic structures made with linear isotropic media with dissipation and/or gain may exhibit reflection non-reciprocity, i.e., an unbalance between the forward and backward reflectivities. There are even cases in which one of them can be made negligible and the other one can increase without limit with the sample thickness [2]; this occurs in the so called P T -symmetric media which exhibit a variety of peculiar optical properties [3,4]. Yet, it is not possible to achieve a non-reciprocal transmissivity in such linear and passive systems. Transmission reciprocity is almost ubiquitous in optics [1,5].Non-reciprocal transmission is however rather desirable for information processing and crucial to the development of optical-based functional components in photonics. In much the same way in which electrical nonreciprocity has been realized through diodes, devising an optical diode is challenging, even in theory. Ideally, an optical diode would allow total light transmission over a bundle of wavelengths in one direction, providing total isolation in the reverse direction. Previous * s.horsley@exeter.ac.uk work on non-reciprocal transmission has been based on either magneto-optical effects [6][7][8] or non linear processes [9,10]. Other mechanisms have also been explored [11][12][13] and realized experimentally [14], including more involved diode designs based on two-dimensional square-lattice photonic crystals [15] or non-symmetric photonic crystal gratings exhibiting anomal...

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Resonantly absorbing one-dimensional photonic crystals

Cited by 112 publications

References 64 publications

Non-Hermitian Degeneracies and Unidirectional Reflectionless Atomic Lattices

Non-Hermitian Degeneracies and Unidirectional Reflectionless Atomic Lattices

Perfect absorption and no reflection in disordered photonic crystals

Optical Nonreciprocity of Cold Atom Bragg Mirrors in Motion

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