Source-linked AI summary
Robust light transport in non-Hermitian photonic lattices
Stefano Longhi, Davide Gatti, Giuseppe Della Valle
TL;DR
Disorder causes back-reflections that limit light transport in integrated photonic devices. The paper proposes non-Hermitian one-dimensional lattices with direction-dependent amplification and attenuation, finding robust asymmetric transport and disorder-induced delocalized states that prevent Anderson localization.
Problem
Disorder and imperfections cause back-reflections in ordinary waveguides, motivating robust light transport in lower-dimensional photonic lattices.
Method
The paper studies one-dimensional non-Hermitian lattices whose complex dispersion amplifies forward modes and attenuates backward modes, including Hatano–Nelson and driven binary models.
Results
Non-Hermitian transport remains robust against disorder, with an imaginary gauge field producing a mobility region containing delocalized states that prevent Anderson localization.
Takeaways & Limitations
Non-Hermitian photonic lattices provide a distinct route to one-way robust light transport, based on non-Hermitian delocalization rather than topologically protected edge modes.
Takeaways & Limitations
Wave packets generally undergo propagation distortion because the complex energy dispersion causes both phase and amplitude dispersion.
Abstract
from arXiv · showhide
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 {\it 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 that is rather insensitive to disorder or imperfections in the structure. Non-Hermitian transport in two lattice models is considered: a tight-binding lattice with an imaginary gauge field (Hatano-Nelson model), and a non-Hermitian driven binary lattice. In the former case transport in spite of disorder is ensured by a mobility edge that arises because of a non-Hermitian delocalization transition. The possibility to observe non-Hermitian delocalization induced by a synthetic 'imaginary' gauge field is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.
RESULTS
The results show that non-Hermitian one-dimensional lattices support asymmetric, disorder-insensitive transport because forward waves are amplified while backward waves are damped. In the Hatano–Nelson model, an imaginary gauge field enables delocalized states despite disorder, with implementation proposed in coupled-resonator optical waveguides.
- One-way transport in non-Hermitian photonic lattices: Forward modes are amplified and backward modes damped, creating preferred-direction propagation that suppresses disorder-induced backscattering.This asymmetric amplification/attenuation causes backward-propagating waves to vanish after sufficient propagation distance.
- Imaginary gauge field and non-Hermitian delocalization: The Hatano–Nelson lattice realizes the mechanism through an imaginary gauge field, with dispersion E(q) = 2κ cos(q + ih).The model is the simplest non-Hermitian one-dimensional tight-binding example satisfying the required asymmetric transport condition.
- Imaginary gauge field and non-Hermitian delocalization: For h = 0, all eigenstates localize through Anderson localization, whereas h ≠ 0 allows some delocalized states to survive.Delocalized and localized states generally correspond to complex and real energies, respectively.
- Imaginary gauge field and non-Hermitian delocalization: Despite disorder, normalized wave-packet dynamics shows forward transport, while the Hermitian case exhibits saturation of the mean position associated with localization.The non-Hermitian case instead displays secular growth of the mean position, indicating delocalized transport.
- Realization of an imaginary gauge field in coupled resonator optical waveguides and non-Hermitian delocalization: Engineered gain and loss in auxiliary rings can implement an imaginary gauge field in a one-dimensional coupled-resonator optical waveguide.Reversing light circulation changes h → −h and reverses the direction of robust transport.
DISCUSSION
Non-Hermitian photonic lattices can enable robust light transport through asymmetric amplification and attenuation of counter-propagating modes, preventing Anderson localization in disordered systems. The mechanism is rooted in the non-Hermitian delocalization transition proposed by Hatano and Nelson for lattices with an imaginary gauge potential.
- Robust transport: Asymmetric amplification and attenuation of counter-propagating modes provide a route toward robust light transport in disordered non-Hermitian photonic lattices.This mechanism can prevent Anderson localization in the presence of disorder.
- Physical origin: The one-way transport mechanism is rooted in the non-Hermitian delocalization transition originally discussed by Hatano and Nelson.The transition was proposed in quantum mechanics for a lattice with an imaginary gauge potential.
- Physical origin: The discussion identifies non-Hermitian delocalization as the physical origin of robust transport in the non-Hermitian lattices considered.The relevant lattice framework includes an imaginary gauge potential.
METHODS
The methods derive the driven lattice’s quasi-energy spectrum and characterize wave-packet propagation, then develop a coupled-microring realization of the Hatano–Nelson imaginary gauge field, including fabrication-induced anti-resonance deviations.
- Quasi-energy spectrum: Floquet theory applies under the resonance condition F = (M/N)ω, with quasi energies defined as eigenvalues of the 2 × 2 matrix R(q).The quasi energies are defined modulo integer multiples of ω/N, with real parts chosen in (−ω/2N, ω/2N).
- Wave packet distortion effects: Wave packets generally distort because the complex energy or quasi-energy depends on Bloch wave number q.For time-periodic Hamiltonians, the corresponding expression applies at integer multiples of the modulation period 2π/ω.
- Wave packet distortion effects: Nearly undistorted propagation occurs when Im(dE/dq)q0 = 0 and Re(d2E/dq2)q0 = 0, yielding group velocity vg with uniform amplification or attenuation.The leading-order intensity follows |c(n, t)|2 ≃ exp(2gt)|c(n − vgt, 0)|2, where g = ImE(q0) and vg = Re(dE/dq)q0.
- Imaginary gauge field in a chain of microrings: The auxiliary microring indirectly couples main-chain rings with unbalanced hopping rates κ exp(−h) and κ exp(h).The auxiliary ring contains two gain/loss sections, and κ is defined by Eq.(26).
FIGURE CAPTIONS
The figures illustrate robust light transport through asymmetric non-Hermitian propagation, disorder-resistant wave-packet evolution, and a proposed coupled-microresonator realization. They compare Hermitian and non-Hermitian lattices, including the Hatano–Nelson and driven models and a disordered CROW laser.
- Robust transport principle: Fig. 1 contrasts topologically protected edge states with asymmetric non-Hermitian transport as routes to robust light transport.The comparison frames the paper’s alternative lower-dimensional transport mechanism.
- Wave-packet evolution: Fig. 2 computes wave-packet center-of-mass evolution for edge excitation in Hermitian and non-Hermitian semi-infinite lattices and bulk excitation in the non-Hermitian lattice.The cases use h = 0 for the Hermitian lattice and h = 0.2 for the non-Hermitian lattice.
- Disorder and defects: Fig. 3 compares wave-packet evolution across two potential defects in Hermitian transport and transport with an imaginary gauge field.The defects satisfy V0/κ = 1 and n1 − n0 = 20, with a Gaussian initial wave packet.
- Driven non-Hermitian lattice: Fig. 4 plots the real and imaginary quasi-energy spectrum of the non-Hermitian driven lattice, distinguishing amplified forward modes from backward propagating waves.The plotted parameters are ω/κ = 1, F/ω = 2, GR/κ = 4.7, and GI/κ = 4.26; forward modes have vg = Re(dE/dq) > 0 and positive imaginary quasi-energy.
- Optical realization: Fig. 5 schematically realizes an imaginary gauge field in coupled microresonators using auxiliary rings that amplify and attenuate different perimeter segments.The figure includes both the full CROW structure and indirect coupling between two main microrings.
- Disordered optical systems: Figs. 6–7 show disorder in a 60-microring CROW laser and compare wave-packet evolution in Hatano–Nelson and driven lattices with and without disorder.Fig. 6 uses h = 0 and h = 0.05 for lasing-mode intensity distributions; Fig. 7 uses two-humped initial wave packets.