Limits...
Robust light transport in non-Hermitian photonic lattices.

Longhi S, Gatti D, Della Valle G - Sci Rep (2015)

Bottom Line: Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes.While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport insensitive to disorder or imperfections in the structure.The possibility to observe non-Hermitian delocalization is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica- Politecnico di Milano and Istituto di Fotonica e Nanotecnologie-Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy.

ABSTRACT
Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a two-dimensional structure, which break time reversal symmetry and enable one-way guiding at the edge of the medium. Here we suggest a different route toward robust transport of light in lower-dimensional (1D) photonic lattices, in which time reversal symmetry is broken because of the non-Hermitian nature of transport. While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport insensitive to disorder or imperfections in the structure. Non-Hermitian asymmetric transport can occur in tight-binding lattices with an imaginary gauge field via a non-Hermitian delocalization transition, and in periodically-driven superlattices. The possibility to observe non-Hermitian delocalization is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.

No MeSH data available.


Related in: MedlinePlus

Wave packet evolution in a tight-binding lattice with two potential defects V0 at sites n0 and n1 (upper inset) for (a) the Hermitian lattice (h = 0), and (b) in the presence of an imaginary gauge field (h = 0.2). Parameter values are  and n1 − n0 = 20. Initial condition corresponds to the Gaussian wave packet . The figures show the evolution of the normalized amplitude probabilities an(t) (modulus of an(t)) in a pseudo color map; the two vertical dashed lines in the maps show the position in the lattice of the two defects. While in the Hermitian case the two potential defects cause multiple wave packet reflection back and forth and echoes of the transmitted wave packet, multiple reflections and echoes are suppressed when the imaginary magnetic field is applied.
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f3: Wave packet evolution in a tight-binding lattice with two potential defects V0 at sites n0 and n1 (upper inset) for (a) the Hermitian lattice (h = 0), and (b) in the presence of an imaginary gauge field (h = 0.2). Parameter values are and n1 − n0 = 20. Initial condition corresponds to the Gaussian wave packet . The figures show the evolution of the normalized amplitude probabilities an(t) (modulus of an(t)) in a pseudo color map; the two vertical dashed lines in the maps show the position in the lattice of the two defects. While in the Hermitian case the two potential defects cause multiple wave packet reflection back and forth and echoes of the transmitted wave packet, multiple reflections and echoes are suppressed when the imaginary magnetic field is applied.

Mentions: for the Hermitian Fig. 2(a) and non-Hermitian Fig. 2(b) lattices. As in the former case clearly ceases to increase as t increases (this is a clear signature of Anderson localization), in the latter case a secular growth of is observed, indicating the existence of delocalized (mobility) states. The robustness of the transport against disorder in the non-Hermitian lattice is also observed when the lattice is initially excited in a single site in the bulk, i.e. far from the lattice boundary, or by a localized wave packet. As an example, Fig. 2(c) shows the numerically-computed dynamics in the disordered lattice with initial excitation of site n = 100. Since the non-Hermitian dynamics does not conserve the norm, for the sake of clearness in the figure the evolution of the site occupation probabilities for the normalized amplitude probabilities is depicted. The figure clearly shows that, in spite of disorder, transport is observed in the forward direction. The same scenario is found for initial wave packet excitations, as discussed in the Methods. In this case, even in the absence of disorder, owing to the dependence of the complex energy dispersion curve E(q) on the Bloch wave number qEq. (3), during the propagation an initial wave packet of the form , with carrier Bloch wave number q0 and slowly-varying amplitude F(n), suffers for reshaping (distortion) effects because of both group velocity (phase) and amplification (amplitude) dispersion, i.e. because and . For the Hatano-Nelson model, both group velocity and amplitude dispersion effects are minimized at q0 = π/2, where . Examples of wave packet propagation are discussed in the Methods. Finally, it should be pointed out that non-Hermitian transport is robust also against structural imperfections or defects in the lattice. Let us consider, as an example, a lattice with two potential defects at sites n0 and n1, i.e. let us assume in Eq. (4), where V0 is the strength of the potential defect. In the Hermitian lattice (h = 0), a propagating wave packet undergoes multiple reflections back and forth between the two defects, like in a Fabry-Perot cavity. This yields multiple transmitted wave packets, i.e. echoes of the original wave packet, as illustrated in Fig. 3(a). Application of the imaginary gauge field to the lattice (h ≠ 0) suppresses multiple reflections (echo effects), as shown in Fig. 3(b).


Robust light transport in non-Hermitian photonic lattices.

Longhi S, Gatti D, Della Valle G - Sci Rep (2015)

Wave packet evolution in a tight-binding lattice with two potential defects V0 at sites n0 and n1 (upper inset) for (a) the Hermitian lattice (h = 0), and (b) in the presence of an imaginary gauge field (h = 0.2). Parameter values are  and n1 − n0 = 20. Initial condition corresponds to the Gaussian wave packet . The figures show the evolution of the normalized amplitude probabilities an(t) (modulus of an(t)) in a pseudo color map; the two vertical dashed lines in the maps show the position in the lattice of the two defects. While in the Hermitian case the two potential defects cause multiple wave packet reflection back and forth and echoes of the transmitted wave packet, multiple reflections and echoes are suppressed when the imaginary magnetic field is applied.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4551998&req=5

f3: Wave packet evolution in a tight-binding lattice with two potential defects V0 at sites n0 and n1 (upper inset) for (a) the Hermitian lattice (h = 0), and (b) in the presence of an imaginary gauge field (h = 0.2). Parameter values are and n1 − n0 = 20. Initial condition corresponds to the Gaussian wave packet . The figures show the evolution of the normalized amplitude probabilities an(t) (modulus of an(t)) in a pseudo color map; the two vertical dashed lines in the maps show the position in the lattice of the two defects. While in the Hermitian case the two potential defects cause multiple wave packet reflection back and forth and echoes of the transmitted wave packet, multiple reflections and echoes are suppressed when the imaginary magnetic field is applied.
Mentions: for the Hermitian Fig. 2(a) and non-Hermitian Fig. 2(b) lattices. As in the former case clearly ceases to increase as t increases (this is a clear signature of Anderson localization), in the latter case a secular growth of is observed, indicating the existence of delocalized (mobility) states. The robustness of the transport against disorder in the non-Hermitian lattice is also observed when the lattice is initially excited in a single site in the bulk, i.e. far from the lattice boundary, or by a localized wave packet. As an example, Fig. 2(c) shows the numerically-computed dynamics in the disordered lattice with initial excitation of site n = 100. Since the non-Hermitian dynamics does not conserve the norm, for the sake of clearness in the figure the evolution of the site occupation probabilities for the normalized amplitude probabilities is depicted. The figure clearly shows that, in spite of disorder, transport is observed in the forward direction. The same scenario is found for initial wave packet excitations, as discussed in the Methods. In this case, even in the absence of disorder, owing to the dependence of the complex energy dispersion curve E(q) on the Bloch wave number qEq. (3), during the propagation an initial wave packet of the form , with carrier Bloch wave number q0 and slowly-varying amplitude F(n), suffers for reshaping (distortion) effects because of both group velocity (phase) and amplification (amplitude) dispersion, i.e. because and . For the Hatano-Nelson model, both group velocity and amplitude dispersion effects are minimized at q0 = π/2, where . Examples of wave packet propagation are discussed in the Methods. Finally, it should be pointed out that non-Hermitian transport is robust also against structural imperfections or defects in the lattice. Let us consider, as an example, a lattice with two potential defects at sites n0 and n1, i.e. let us assume in Eq. (4), where V0 is the strength of the potential defect. In the Hermitian lattice (h = 0), a propagating wave packet undergoes multiple reflections back and forth between the two defects, like in a Fabry-Perot cavity. This yields multiple transmitted wave packets, i.e. echoes of the original wave packet, as illustrated in Fig. 3(a). Application of the imaginary gauge field to the lattice (h ≠ 0) suppresses multiple reflections (echo effects), as shown in Fig. 3(b).

Bottom Line: Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes.While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport insensitive to disorder or imperfections in the structure.The possibility to observe non-Hermitian delocalization is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica- Politecnico di Milano and Istituto di Fotonica e Nanotecnologie-Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy.

ABSTRACT
Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a two-dimensional structure, which break time reversal symmetry and enable one-way guiding at the edge of the medium. Here we suggest a different route toward robust transport of light in lower-dimensional (1D) photonic lattices, in which time reversal symmetry is broken because of the non-Hermitian nature of transport. While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport insensitive to disorder or imperfections in the structure. Non-Hermitian asymmetric transport can occur in tight-binding lattices with an imaginary gauge field via a non-Hermitian delocalization transition, and in periodically-driven superlattices. The possibility to observe non-Hermitian delocalization is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.

No MeSH data available.


Related in: MedlinePlus