Photonic Gauge Fields Of Frequency Domain In Dynamically-modulated Optical Systems

The manipulation of photon flow has been the central goal in modern photonics and optics researches.To date,the control of photon mainly relies on its intrinsic degrees of freedom,such as the amplitude,frequency,phase and angular momentua.Owing to the rapid progress of topology in condensed-matter physics,such as the realization of the quantum Hall effect,topological insulators and topological semimetals,the topological degree of freedom has aroused more research interest in recent photonics researches.Topology is a property that characterizes the quantized global behavior of wavefunction defined in a specific space.Due to the intrinsic global nature of topology,its application in photonics could lead to rubust and unidirectional light propagation that is immune to discorders and imperfections.Current topological photonics researches focus on the realization of photonic topological insulators,topological semimetals and photonic gauge fields,among which the topological insulators and semimetals are based on the topology of photonic energy bands.Photonic gauge fields,on the other hand,concern the topological property of photon in real space due to their origins from the photonic analogue of Aharonov-Bohm phase acquired by electrons in real electromagnetic fields.Note that photons are neural particles that don't interact with real electromagnetic fields,the creation of photonic gauge fields also provides a new mechanism to control light propagation.More generally,the manipulation of light progation in other synthetic dimensions is of equal importance to the light propagation in real space.These new dimensions include the frequency,temporal,orbital angular momenta for photons.From the application perspective,such as in optical communication and signal processing,the manipulation of light spectrum is even more important than the control of light spatial evolution.The control of spectrum currently relies on nonlinear optical effects such as the sum,difference frequency and the four-wave mixing processes.However,nonlinear optical effects are usually subject to the intrinsic low conversion efficiency and required high pumped power.As a new mechanism to manipulation light spectrum,the time modulation approach can induce the discrete diffraction of photon frequency.Moreover,it is readily to introduce photonic gauge field in the frequency domain to manipulation the spectrum evolution.Apart from the potential applications,the discrete frequency lattice also provides a versatile platform to emulate the condensed-matter physical effects in an all-optical setting.Based on the above arguments,our researches works are as follows.Firstly,we theoretically and experimentally investigate photonic gauge potentials in the frequency domain and demonstrate their capabilities in the control of frequency discrete diffraction.We find that the dynamic index modulation in an optical phase modulator(PM)can induce photonic intraband transitions and create a synthetic frequency lattice for photon.The modulation phase acts as an effective gauge potential that can bring in lattice band structure shift.By cascading two PMs with different modulation phases,we demonstrate the effects of spectrum directional shift,bandwidth expansion,and arbitrary refractions for incident frequency combs as well as “spectral superlens” for the perfect focusing and imaging of arbitrarily input spectra.Secondly,we generalize the gauge potential from uniform to the time-dependent,and hence synthesize an effective electric-field force for photons.As the photonic transition carries a wave vector mismatch,the gauge potential becomes linearly varying,giving rise to a constant electric-field force applied in the frequency lattice.A harmonic oscillating force can also emerge if the modulation phase itself is subject to a periodic modulation in the propagation direction.With appropriate combinations of the constant and oscillating forces,we can emulate the frequency-domain Bloch oscillations,Anharmonic-Bloch oscillations,Super-Bloch oscillations,directional transport and dynamic localization.All above dynamics are subject to the tight-binding limitation since there is only nearest-neighbor coupling in the frequency lattice.To break this limitation,we introduce long-range couplings using multiple modulation harmonics,which enables the arbitrary engineering of lattice band structures.Particularly,we synthesize linear,bilinear and circular band structures using the sawtooth,triangular and circular modulation waveforms and realize the diffraction-free unidirectional,bidirectional and omnidirectional frequency shifts.We also revisit frequency discrete Talbot effect and generalize the allowed incident period to an arbitrary integer using linear band structures.Additionally,for different modulation waveforms,frequency Bloch oscillations can also be generalized to manifest arbitrary routing effects along any prescribed trajectories beyond the cosine type and self-focusing effects beyond conventional breathing pattern.Then we combine the frequency lattice with spatial dimensions and realize the three dimensional Weyl physics in a two-dimensional(2D)lattice struture.We choose a 2D dynamically-modulated waveguide array arranged in a brick-wall lattice and present the full phase diagram of Type-I and Type-II WPs versus the modulation phase difference and modulation amplitude ratio in the two sublattices.By truncating the brick-wall lattice,we also obtain two Fermi-arc surface states propagating in opposite and same directions at two edges for Type-I and Type-II WPs.In particular,at the phase transition point,we find one of the surface states manifests a vanishing group velocity in the frequency dimension.Finally,we investigate photonic mode transition of surface plasmon polaritons(SPPs)in dynamically-modulated graphene waveguides.We firstly investigate the supermodes of SPPs in finite-layer graphene sheets and find that the out-of-phase coupling supermode manifests the best figure of merit with shortest mode wavelength and lowest propagation loss.By introducing the dynamic modulation of graphene surface conductivity or the dielectric constant between graphene,we realize the nonrecipral interband transitions of SPP modes and demonstrate the potential applications in the nonrecirpcal mode converters and switches.Moreover,we combine the graphene with dielectric grating waveguides and find that the graphene decorated on the grating surface can induce the tunable shift of waveguide band gap,leading to the mutual conversions between propagating and evanescent Bloch modes.When the graphene sheet is incorporated into the defect cavity in the aperiodic grating,it will also bring in tunable shift of the cavity resonant frequency and mode volume.