One-dimensional Photonic Lattices Research Articles

Multiple exceptional points and phase transitions of a one-dimensional PT-symmetric Lieb photonic lattice

Exceptional points (EPs) in non-Hermitian systems have attracted enormous attention and spawned intriguing prospects for the manipulation of waves. Despite many efforts focusing on the exotic behaviors about EPs, there are only a few studies of phase transitions involving multiple EPs. Here, by employing staggered couplings as well as two pairs of on-site gain/loss, we propose a one-dimensional parity-time (PT)-symmetric Lieb photonic lattice and demonstrate diverse phase transitions of such a multiband structure. Owing to the non-Hermitian chiral symmetry, symmetry-protected higher-order EPs are constructed, and the system exhibits PT symmetry breaking beyond a certain threshold. More importantly, both the relative couplings and the on-site gain/loss can be flexibly reconfigured on demand, which yields the degeneracy of different bands, i.e., the emergence of multiple EPs. We also unveil that the EPs will no longer exist in the presence of a non-Hermitian diagonal disorder. In contrast, the spectrum remains symmetric and the EPs, along with the flatband, are robust against the off diagonal disorder due to the preserved non-Hermitian particle-hole symmetry. Our work not only provides a controllable platform for studying EPs but also sheds light on the exciting non-Hermitian physics based on exceptional degeneracies.

Edge-to-edge topological spectral transfer in diamond photonic lattices

The transfer of information between topological edge states is a robust way of spatially manipulating spatial states in lattice environments. This method is particularly efficient when the edge modes are kept within the topological gap of the lattice during the transfer. In this work, we show experimentally the transfer of photonic modes between topological edge states located at opposite ends of a dimerized one-dimensional photonic lattice. We use a diamond lattice of coupled waveguides and show that the topological transfer is insensitive to the presence of a high density of states in the form of a flat band at an energy close to that of the edge states and prevails in the presence of a hopping impurity. We explore the dynamics in the waveguide lattice using a wavelength-scan method, where different input wavelengths translate into different effective lattice lengths. Our results offer an alternative way to the implementation of efficient transfer protocols based on active driving mechanisms.

Topological edge states in photonic decorated trimer lattices.

In recent years, topological insulators have been extensively studied in one-dimensional periodic systems, such as Su-Schrieffer-Heeger and trimer lattices. The remarkable feature of these one-dimensional models is that they support topological edge states, which are protected by lattice symmetry. To further study the role of lattice symmetry in one-dimensional topological insulators, here we design a modified version of the conventional trimer lattices, i.e., decorated trimer lattices. Using the femtosecond laser writing technique, we experimentally establish a series of one-dimensional photonic decorated trimer lattices with and without inversion symmetry, thereby directly observing three kinds of topological edge state. Interestingly, we demonstrate that the additional vertical intracell coupling strength in our model can change the energy band spectrum, thereby generating unconventional topological edge states with a longer localization length in another boundary. This work offers novel insight into topological insulators in one-dimensional photonic lattices.

Asymmetric localized states at a nonlinear interface of fractional systems with optical lattices

We investigate the existence and stability of localized gap states at a non-linear interface of non-linear fractional systems in a one-dimensional photonic lattice. By using the direct numerical simulations and linear stability analysis, we obtain the stability of the asymmetric localized gap states in the first and second finite gaps. Our theoretical results show that the power of the localized gap states decrease gradually as the increase of propagation constant and the non-linear landscape (non-linear coefficient ratio between the left and right interface), providing insights into soliton physics in non-linear periodic systems with fractional-order diffraction.

Winding number and bulk-boundary correspondence in a one-dimensional non-Hermitian photonic lattice

A topological phase transition and the related bulk-boundary correspondence in a class of one-dimensional non-Hermitian photonic lattice with chiral symmetry are studied. We find that the corresponding topological number should be defined by adding up winding numbers calculated under the chiral symmetry. The Wilson loop method is used to calculate this topological number. We reveal the topological phase transition in one-dimensional non-Hermitian systems with chiral symmetry and provide a convenient and general pathway to characterize the related topology.

Direct Observation of a Localized Flat-Band State in a Mapped Moiré Hubbard Photonic Lattice

When two identical periodic structures are stacked at a series of discrete rotation angles, the resulting moir\'e pattern brings an extreme flat band with transport enhancement. It provides insights into the fascinating physics of insulating states and unconventional superconductivity with delocalization-localization transitions and commensurable-incommensurable phases. However, the exploration of symmetry- and geometry-independent flat-band physics with moir\'e patterns is still rare, limited by the stringent requirement in high dimension. Here, we experimentally observe the localized flat-band state by mapping a moir\'e model into a one-dimensional photonic lattice using a femtosecond laser direct writing technique. By accurately controlling the external periodic field, we construct moir\'e photonic lattices with different moir\'e band structures. We successfully observe the photon-walker evolution from splitting with dispersion to nondispersive propagation with larger localization in the input ports as the result of a flat band induced by moir\'e patterns with larger period. Our approach to engineering moir\'e model, together with the integrated photonic implementation, establishes a powerful tool for exploring the effects accompanying the transition from commensurate to incommensurate phases.

Comprehensive study of singular points in a PT-symmetric Thue-Morse multilayer

Parity-time symmetric optical systems have a non-Hermitian Hamiltonian with a purely real spectrum. These systems have been extensively explored owing to their ability to generate exotic photon transport phenomena. In this work, we report the spectral singularity of the one-dimensional aperiodic odd-generation Thue-Morse photonic lattice with parity time symmetry. We showed that this multilayer in addition to obvious unidirectional and bidirectional transparencies, displays interesting and singular properties including absorption, lasing and coherent perfect absorption-lasing singularities. Based on the transfer matrix and scattering matrix (S matrix) methods, the behavior of these singular points and reflectionless and invisibility properties of the structure is analyzed with respect to the thickness of the passive film sandwiched between active layers due to phase shift changes, frequency and incident angle of light. The available values of the structural parameters are investigated to obtain extraordinary transmission and reflection phenomena. These optical systems may possess the potential in the design of novel lasing and coherent perfect absorption optical devices with adjustable applications.

Experimental band flip and band closure in guided-mode resonant optical lattices

We demonstrate band flip in one-dimensional dielectric photonic lattices presenting numerical and experimental results. In periodic optical lattices supporting leaky Bloch modes, there exists a second stop band where one band edge experiences radiation loss resulting in guided-mode resonance (GMR), while the other band edge becomes a nonleaky bound state in the continuum (BIC). To illustrate the band flip, band structures for two different lattices are provided by calculating zero-order reflectance with respect to wavelength and incident angle. We then provide three photonic lattices, each with a different fill factor, consisting of photoresist gratings on Si3N4 sublayers with glass substrates. The designs are fabricated using laser interferometric lithography. The lattice parameters are characterized and verified with an atomic force microscope. The band transition under fill-factor variation is accomplished experimentally. The measured data are compared to simulation results and show good agreement.

Experimental Realization of Reconfigurable Photonic Lattices in Coherent Rydberg Atomic Vapors

We experimentally demonstrated the formation of a one-dimensional electromagnetically induced optical lattice in coherently prepared three-level 85Rb Rydberg atomic vapors with electromagnetically induced transparency (EIT). The one-dimensional photonic lattice was optically induced by a coupling field with a spatially periodical intensity distribution deriving from the interference of two strong Gaussian beams from the same laser source (~480 nm). Under the Rydberg-EIT condition, the incident weak probe beam can feel a tunable spatially modulated susceptibility, which is verified by the controllable discrete diffraction pattern observed at the output plane of the vapor cell. This investigation not only opens the door for experimentally introducing the strong interaction between Rydberg atoms to govern the beam dynamics in photonic lattices based on atomic coherence but also provides an easily accessible periodic environment for exploring Rydberg-atom physics and related applications.

Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices.

Symmetries play a major role in identifying topological phases of matter and in establishing a direct connection between protected edge states and topological bulk invariants via the bulk-boundary correspondence. One-dimensional lattices are deemed to be protected by chiral symmetry, exhibiting quantized Zak phases and protected edge states, but not for all cases. Here, we experimentally realize an extended Su-Schrieffer-Heeger model with broken chiral symmetry by engineering one-dimensional zigzag photonic lattices, where the long-range hopping breaks chiral symmetry but ensures the existence of inversion symmetry. By the averaged mean displacement method, we detect topological invariants directly in the bulk through the continuous-time quantum walk of photons. Our results demonstrate that inversion symmetry protects the quantized Zak phase but edge states can disappear in the topological nontrivial phase, thus breaking the conventional bulk-boundary correspondence. Our photonic lattice provides a useful platform to study the interplay among topological phases, symmetries, and the bulk-boundary correspondence.

Extraordinary directional optical properties of a parity-time symmetric one-dimensional photonic lattice

Recently, photonic structures with non-Hermitian Hamiltonians have attracted few attentions for engineering materials with new directional functionalities. In this paper, we have investigated the transmittance and reflectance of the one-dimensional photonic lattice with parity-time symmetric quintuple unit cell. Exceptional points, unidirectional and bidirectional reflectionless are obtained by judicious choice of materials and period number. Directional phenomena are examined with respect to the incident angle of light and wavelength for both TE and TM polarizations. More complicated reflection/transmission is observed at the considerable incident angle at some multilayer structures. These findings may provide attractive applications in optical devices with extraordinary directional responses.

Band dynamics accompanied by bound states in the continuum at the third-order Γ point in leaky-mode photonic lattices

Bound states in the continuum (BICs) and Fano resonances in planar photonic lattices, including metasurfaces and photonic-crystal slabs, have been studied extensively in recent years. Typically, the BICs and Fano resonances are associated with the second stop bands open at the second-order Γ point. This paper addresses the fundamental properties of the fourth stop band accompanied by BICs at the third-order Γ point in one-dimensional leaky-mode photonic lattices. At the fourth stop band, one band edge mode suffers radiation loss, thereby generating a Fano resonance, while the other band edge mode becomes a nonleaky BIC. The fourth stop band is controlled primarily by the Bragg processes associated with the first, second, and fourth Fourier harmonic components of the periodic dielectric constant modulation. The interplay between these three major processes closes the fourth band gap and induces a band flip whereby the leaky and BIC edges transit across the fourth band gap. At the fourth stop band, an accidental BIC is formed owing to the destructive interplay between the first and second Fourier harmonics. When the fourth band gap closes with strongly enhanced radiative Q factors, Dirac cone dispersions can appear at the third-order Γ point.

Transmission through a one-dimensional photonic lattice modulated by the side-coupled PT-symmetric non-Hermitian Su–Schrieffer–Heeger chain

We theoretically study the quantum transmission through a one-dimensional photonic lattice that couples laterally to the one parity-time ( P T )-symmetric non-Hermitian Su–Schrieffer–Heeger (SSH) chain. It is found that the SSH chain plays important roles in modifying the transmission properties of this system. In the case of weak coupling, the effect of the SSH chain is manifested mainly as the antiresonance caused by the edge states when it is in a topologically nontrivial region. And when the P T -symmetric complex potentials are introduced at the ends of the SSH chain, the edge states undergo P T -symmetry breaking accompanied by a notable change in transmission function spectra. On the other hand, few changes can be observed in the topologically trivial region of the SSH chain. For the strong coupling case, the antiresonance effect of the non-Hermitian SSH chain is apparently modified. Our findings provide helpful content for describing the physics properties of the P T -symmetric non-Hermitian SSH chain.

Topological input-output theory for directional amplification

We present a topological approach to the input-output relations of photonic driven-dissipative lattices acting as directional amplifiers. Our theory relies on a mapping from the optical non-Hermitian coupling matrix to an effective topological insulator Hamiltonian. This mapping is based on the singular value decomposition of non-Hermitian coupling matrices, whose inverse matrix determines the linear input-output response of the system. In topologically non-trivial regimes, the input-output response of the lattice is dominated by singular vectors with zero singular values that are the equivalent of zero-energy states in topological insulators, leading to directional amplification of a coherent input signal. In such topological amplification regime, our theoretical framework allows us to fully characterize the amplification properties of the quantum device such as gain, bandwidth, added noise, and noise-to-signal ratio. We exemplify our ideas in a one-dimensional non-reciprocal photonic lattice, for which we derive fully analytical predictions. We show that the directional amplification is near quantum-limited with a gain growing exponentially with system size, $N$, while the noise-to-signal ratio is suppressed as $1/\sqrt{N}$. This points out to interesting applications of our theory for quantum signal amplification and single-photon detection.

Light capturing within the defect located in linear one-dimensional photonic lattice

Numerically investigated the light beam propagation through one-dimensional photonic lattice possessing one linear defect. It is shown how capturing of light depends on lattice characteristics as well as the width and wavelength of input light beam. Results may be useful for all-optical control of transmission of waves in interferometry.

Bifurcation-tunable Diffractionless Light Propagation in One-dimensional Non-Hermitian Photonic Lattice

Bifurcation-tunable Diffractionless Light Propagation in One-dimensional Non-Hermitian Photonic Lattice

Polarization-differentiated band dynamics of resonant leaky modes at the lattice Γ point.

In the physical description of photonic lattices, leaky-mode resonance and bound states in the continuum are central concepts. Understanding of their existence conditions and dependence on lattice parameters is of fundamental interest. Primary leaky-wave effects are associated with the second stop band at the photonic lattice Γ point. The pertinent band gap is defined by the frequency difference between the leaky-mode band edge and the bound-state edge. This paper address the polarization properties of the band gaps resident in laterally periodic one-dimensional photonic lattices. We show that the band gaps pertinent to TM and TE leaky modes exhibit significantly differentiated evolution as the lattice parameters vary. This is because the TM band gap is governed by a surface effect due to the discontinuity of the dielectric constant at the interfaces of the photonic lattice as well as by a Bragg effect due to the periodic in-plane dielectric constant modulation. We find that when the lattice is thin (thick), the surface (Bragg) effect dominates the Bragg (surface) effect in the formation of the TM band. This leads to complex TM band dynamics with multiple band closures possible under parametric variation. In complete contrast, the TE band gap is governed only by the Bragg effect thus exhibiting simpler band dynamics. This research elucidates the important effect of polarization on resonant leaky-mode band dynamics whose explanation has heretofore not been available.

Dimensional Transformations of Guided-Mode Resonant Photonic Lattices

Reflection spectra based on guided-mode resonance (GMR) are simulated and discussed with transformation between one-dimensional (1-D) and two-dimensional (2-D) photonic lattices by introducing intermediate structures consisting of vertically-stacked 1-D and 2-D gratings. Dependences of reflection spectra on a 2-D fractional ratio are investigated for two examples of narrowband and broadband resonance elements. Observed complicated spectrum transformations for the narrowband example are successfully explained by combining simple models with guided-mode indices and multilayer reflection. The understanding of the fundamental transformation dynamics will aid in the reflection band engineering for development of new optical components.

Discrete optical propagation in one-dimensional synthetic mesh lattice

Synthetic mesh lattice (SML) with temporally controlled potential is a versatile platform for realizing wave dynamics associated with physical areas of optics and quantum physics. Here, discrete optics in one-dimensional synthetic photonic lattice is investigated systematically, in which the light behavior is highly analogous to that in evanescently coupled one-dimensional discrete waveguides. Such a synthetic dimension is constructed with position-dependent periodic effective gauge fields based on the Aharonov–Bohm effect arising from the phase accumulation of the fiber loops. By tuning the phase accumulation and coupling coefficient of the coupler, the band translation and gap property can be modulated, which further results in the impulse and tailored Gaussian wave packet responses as well as Talbot recurrences. In addition, Bloch oscillations and Anderson localization can also be obtained when the phase accumulations are linearly changed and weakly modulated in a random manner, respectively. The periodic effective gauge fields configuration in our protocol enables SML to be a research platform for one-dimensional dynamically modulated elements or even non-Hermitian waveguides.

Topological and flat-band states induced by hybridized linear interactions in one-dimensional photonic lattices

We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the interaction between the different orbital modes, this minimal model exhibits rich transport and topological properties. By varying the detuning coefficient we find a regime where bands become flatter (with reduced transport) and, a second regime, where both bands connect on at a gap-closing transition (with enhanced transport). We detect an asymmetric transport due to the asymmetric inter-mode coupling and a linear energy exchange mechanism between modes. Further analysis show that the bands have a topological transition with a non-trivial Zak phase which leads to the appeareance of edge states in a finite system. Finally, for zero detuning, we found a symmetric condition for coupling constants, where the linear spectrum becomes completely flat, with states fully localized in space occupying only two lattice sites.