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Synthetic Dimension in Photonics
Luqi Yuan, Qian Lin, Meng Xiao, Shanhui Fan
TL;DR
The paper addresses how photonic structures can access physics in dimensions higher than their apparent geometry. It reviews synthetic-dimension approaches based on photonic states, parameter spaces, and their use in gauge and topological photonics, reporting theoretically proposed and experimentally demonstrated effects with potential applications.
Problem
Photonic structures are commonly described by apparent geometric dimensionality, limiting direct access to physics in higher-dimensional spaces.
Method
The paper reviews synthetic dimensions formed by combining photonic-state couplings or parameter degrees of freedom with geometric dimensions.
Results
The review finds that synthetic-dimension approaches have produced a rich set of theoretically proposed and experimentally demonstrated photonic physics effects.
Takeaways & Limitations
Synthetic dimensions provide photonics with approaches for exploring higher-dimensional phenomena and manipulating or controlling photonic degrees of freedom.
Abstract
from arXiv · showhide
The physics of a photonic structure is commonly described in terms of its apparent geometric dimensionality. On the other hand, with the concept of synthetic dimension, it is in fact possible to explore physics in a space with a dimensionality that is higher as compared to the apparent geometrical dimensionality of the structures. In this review, we discuss the basic concepts of synthetic dimension in photonics, and highlighting the various approaches towards demonstrating such synthetic dimension for fundamental physics and potential applications.
I. INTRODUCTION
Synthetic dimension lets photonic structures explore spaces whose dimensionality exceeds their apparent geometry by configuring couplings or using parameter degrees of freedom. This review surveys these approaches, their physics, and potential applications.
- Synthetic dimensions combine with geometric dimensions to form higher-dimensional synthetic spaces in photonics.
- 1. Forming a lattice: Coupling physical states determines lattice dimensionality: nearest-neighbor coupling produces a one-dimensional lattice, while longer-range coupling can generate a two-dimensional lattice.
- 2. Exploiting parameter dependency: Hamiltonian parameters can be treated as extra synthetic dimensions alongside the system’s spatial coordinates.
- Synthetic dimensions offer an experimental route to rich physics, including topological physics beyond three dimensions, while retaining easier-to-construct one- or two-dimensional structures.
- Photonics uniquely supports synthetic lattices built from internal photonic degrees of freedom such as frequency and orbital angular momentum.
- The review covers coupling-designed synthetic lattices, photonic gauge potentials, topological effects, and parameter-space approaches, with applications in communications and information processing.
II. FORMING A SYNTHETIC LATTICE OF PHOTONIC STATES
The review describes forming synthetic photonic lattices by selecting photonic states and engineering their couplings. Frequencies, spatial modes, temporal pulses, and modulation-based interactions provide the main construction routes.
- II. FORMING A SYNTHETIC LATTICE OF PHOTONIC STATES: Synthetic lattices require a set of physical photonic states and mechanisms that specifically configure coupling among those states.
- II. FORMING A SYNTHETIC LATTICE OF PHOTONIC STATES: Candidate lattice sites include modes with different frequencies, orbital angular momenta, spatial distributions, or temporal pulses.
- A. Using photonic modes with different frequencies: Dynamic modulation couples photonic modes and lets the electromagnetic field be described through modal amplitudes.
- A. Using photonic modes with different frequencies: A phase-matched permittivity modulation in a waveguide couples modes at frequencies ωm = ω0 + mΩ and produces the same one-dimensional synthetic-frequency tight-binding model.
- A. Using photonic modes with different frequencies: A modulated ring resonator uses an equally spaced frequency comb, with modulation at the free-spectral range resonantly coupling neighboring modes.
- A. Using photonic modes with different frequencies: The ring-resonator Hamiltonian describes a photon in a one-dimensional tight-binding lattice along the synthetic frequency dimension.
- A. Using photonic modes with different frequencies: Frequency-domain synthetic lattices can be implemented with electro-optic or acousto-optic modulation, and related effects can use nonlinear optics, four-wave mixing, or Raman processes.
B. Using photonic modes with different orbital angular momentum
Orbital angular momentum can serve as a synthetic coordinate when a degenerate cavity makes different angular-momentum modes resonant at the same frequency and spatial modulation couples neighboring values.
- B. Using photonic modes with different orbital angular momentum: A specially designed degenerate cavity gives resonant modes with different orbital angular momenta the same frequency.
- B. Using photonic modes with different orbital angular momentum: Spatial light modulators can transfer amplitude between angular-momentum states l, l −1, and l +1.
- B. Using photonic modes with different orbital angular momentum: The resulting cavity is described as a tight-binding model and provides a synthetic dimension based on orbital angular momentum.
- B. Using photonic modes with different orbital angular momentum: The basic construction assumes nearest-neighbor coupling along the l-axis, while alternative spatial-light-modulator designs can realize long-range coupling.
C. Using multiple pulses
Multiple pulses and unequal fibre-loop delays map temporal evolution onto a synthetic lattice. The same framework supports pulse-position sites, angular-momentum lattices, higher dimensions, boundaries, and large numbers of sites.
- C. Using multiple pulses: Two fibre loops with different round-trip times, connected by a 50/50 coupler, form an equivalent lattice network for pulse dynamics.
- C. Using multiple pulses: Phase modulation in the long loop and repeated loop circulation determine how pulses move between lattice sites.
- C. Using multiple pulses: Spatial light modulators can couple a beam with angular momentum l to beams with l ± 1, producing a lattice along angular momentum.
- C. Using multiple pulses: The pulse sequence maps onto lattice dynamics, with temporal motion along the m-axis and a one-dimensional lattice labelled by n.
- C. Using multiple pulses: More complex couplings can produce synthetic lattices with dimensions higher than one, including long-range coupling among ring-resonator modes.
- C. Using multiple pulses: Ring-resonator implementations can potentially couple hundreds of distinct modes, while boundaries arise from dispersion or can be designed through memory effects.
III. THE PHYSICS OF SYNTHETIC LATTICE
Synthetic photonic lattices provide platforms for studying fundamental physics and controlling light. The review highlights effective gauge potentials and topological photonics as emerging directions.
- III. THE PHYSICS OF SYNTHETIC LATTICE: Synthetic lattices are used to explore fundamental physics effects, including analogues of bulk physics in synthetic space.
- III. THE PHYSICS OF SYNTHETIC LATTICE: Because synthetic lattices use different degrees of freedom of light, controlling propagation in them can control light properties relevant to practical applications.
- III. THE PHYSICS OF SYNTHETIC LATTICE: Related work has applied dynamically modulated-ring descriptions to mode-locked lasers and investigated parity-time symmetry, Anderson localization, and time-reversal effects.
- III. THE PHYSICS OF SYNTHETIC LATTICE: The review focuses on creating effective gauge potentials for light and investigating topological photonics.
A. Effective gauge potential
Photonic synthetic lattices can emulate gauge potentials and effective electric or magnetic fields by controlling hopping phases and modulation phases. In the frequency dimension, these effects produce Bloch oscillations and directed, topologically protected frequency translation.
- Gauge potentials: Dynamic modulation phases act as effective gauge potentials for photons, including effective electric and magnetic fields.The approach relies on designing hopping phases in photonic synthetic lattices.
- Effective electric field: A modulation frequency slightly detuned from the ring mode spacing creates a time-independent effective electric field along the synthetic frequency axis.The phase varies as φ(t) = (Ω−ΩR)t, producing the effective field.
- Effective electric field: Excited spectral components oscillate over time, realizing Bloch oscillation in the spectral domain.The effect is illustrated for a few spectral components initially excited at t = 0.
- Effective electric field: Periodic switching of the modulation frequency around the mode spacing can produce a unidirectional photon shift along the frequency axis.This provides a capability for controlling the frequency of light.
- Effective magnetic field: A ring-resonator array with modulation phases increasing as nφ realizes a uniform effective magnetic field φ/ΩRd in the synthetic space.The construction uses evanescent coupling between nearest-neighbor rings and is described in the Landau gauge.
B. Topological Photonics
Synthetic dimensions provide a route to higher-dimensional topological physics using photonic structures with lower apparent geometric dimensionality. The review discusses realizations including Weyl-point physics, topological models, flat bands, and nonlinear-interaction challenges.
- Topological models: Orbital-angular-momentum modes can form a one-dimensional synthetic lattice realizing the SSH model with a sharp boundary and bulk-edge correspondence.This provides a synthetic-space implementation of a topological model using coupled angular-momentum modes.
- Higher-dimensional topology: Synthetic dimensions provide a pathway to higher-dimensional topological effects that lack lower-dimensional counterparts.The approach allows higher-dimensional physics to be explored in photonic systems.
- Weyl-point physics: Weyl-point physics can be explored with two-dimensional geometries that are easier to construct than typical three-dimensional photonic structures.A two-dimensional honeycomb ring-resonator array becomes a three-dimensional lattice model through its frequency-axis synthetic dimension.
- Weyl-point physics: Appropriate modulation phases on the honeycomb lattice produce Weyl-point physics in the resulting three-dimensional synthetic lattice model.The relevant phases are φA and φB on the A and B sublattice sites.
- Long-range coupling: Long-range coupling in synthetic space can create topological flat bands and novel band structures such as a single Dirac cone without breaking time-reversal symmetry.Topological flat bands are discussed in connection with simulating many-body physics, including the fractional quantum Hall effect.
- Nonlinear effects: Frequency-axis synthetic dimensions typically yield nonlinear interactions that are nonlocal across lattice sites, limiting direct simulation of local-interacting Hamiltonians.Achieving local interaction for other synthetic-space approaches remains an open question.
A. Physics concept
Synthetic dimensions represent parameter directions as additional coordinates, allowing lower-dimensional photonic systems to exhibit higher-dimensional physics. This framework extends band-structure and topological concepts to parameter spaces and enables Weyl-point physics in one-dimensional photonic crystals.
- A. Physics concept: A parameter-dependent Hamiltonian H(p) can be represented in a synthetic space where p acts as an extra dimension alongside physical space.This makes higher-dimensional physics manifest through parameter dependence in a lower-dimensional system.
- A. Physics concept: Gauge potentials and topological effects arise naturally when parameter axes are incorporated into the synthetic space.Berry phase, Berry connection, and Berry curvature provide the corresponding topological description.
- A. Physics concept: Adiabatically varying parameters in time gives dynamics with signatures of higher-dimensional topological physics.The same topological reasoning used for band structures can be applied to parameter dependencies.
- A. Physics concept: For p = q = 0, bands are two-fold degenerate with linear k-axis dispersion; small deviations open a gap scaling linearly with both p and q.The four-layer unit cell becomes primitive when p and q deviate from zero, producing the Brillouin-zone-edge gap.
- A. Physics concept: A one-dimensional photonic crystal with parameters p and q realizes a three-dimensional k, p, q space containing a Weyl point.At k = π/2(da + db), p = 0, and q = 0, the Weyl-point signature appears through winding of the reflection phase as p and q vary.
C. Adiabatic evolution in the parameter space
The Aubry-André model uses its modulation phase as a synthetic dimension, mapping a one-dimensional system onto a two-dimensional Quantum Hall setting. Adiabatic phase variation produces edge-state transport that can be directly simulated in photonic waveguide arrays.
- C. Adiabatic evolution in the parameter space: Treating φ as a synthetic dimension makes the one-dimensional Aubry-André model describe a synthetic two-dimensional space.The model is closely related to a square-lattice Quantum Hall system, with b mapping to magnetic field and φ to k_y.
- C. Adiabatic evolution in the parameter space: Finite Aubry-André structures exhibit spectral gaps, and particular φ values produce edge states inside those gaps.The eigenfrequency variation with φ corresponds directly to one-way edge-state dispersion in the Quantum Hall system.
- C. Adiabatic evolution in the parameter space: Adiabatically varying φ evolves an edge state from one end into a bulk state and then reemerges at the opposite end.This evolution directly probes properties of the corresponding two-dimensional system.
- C. Adiabatic evolution in the parameter space: In the experiment, injected light evolves from an edge state into a bulk state and eventually appears as an edge state on the other side.The observed evolution matches the expected adiabatic dynamics of the Aubry-André model.
- C. Adiabatic evolution in the parameter space: Waveguide arrays simulate the temporal dynamics by replacing time evolution with field-amplitude variation along propagation direction z.The experimental implementation uses coupling modulation and a spatially varying φ.
- C. Adiabatic evolution in the parameter space: Adiabatic evolution in waveguide arrays has also been used to explore topological phase transitions and four-dimensional quantum Hall effects.These applications extend the parameter-space approach beyond the illustrated Aubry-André example.
V. SUMMARY AND OUTLOOK
This review surveys synthetic dimensions in photonics, connecting them with gauge fields and topology. It reports a broad range of proposed and experimentally demonstrated effects and points to applications in manipulating and controlling light.
- V. SUMMARY AND OUTLOOK: The review provides a brief account of synthetic dimensions in photonics and their connection with gauge-field and topological concepts.The topic is described as rapidly developing.
- V. SUMMARY AND OUTLOOK: The initial motivation was to create a versatile photonic approach for demonstrating fundamental effects, particularly topological physics.The review frames synthetic dimensions as a route for exploring fundamental physics.
- V. SUMMARY AND OUTLOOK: A rich set of effects has been theoretically proposed and experimentally demonstrated using synthetic dimensions.The statement summarizes the range of results covered by the review.
- V. SUMMARY AND OUTLOOK: Synthetic dimensions may prove significant for practical applications and for manipulating and controlling fundamental properties of light.The outlook links the concept to both applications and fundamental optical control.