Discrete Diffraction And Topological Manipulation In Synthetic Photonic Lattices

The development of novel artificial structures and materials is one of the major research topics in optics.In most studies so far,such structures have been applied to modulate photon flow by designing the refraction index in real space.Analogies of the artificial structures,the concept of photonic lattices has been extended to synthetic dimensions of time,frequency,phase and angular momentum and constructed the synthetic lattices.Based on band theory in solids,the synthetic lattices provide a flexible and controllable method to manipulate photons in different dimensions.Additionally,it is possible to emulate the quantum effects of electrons and investigate the topological properties of photons by introducing the effective scalar potential and vector potential.At present,the synthetic time and frequency lattices have been studied in various optical structures and systems,such as optical micro-resonators,modulated waveguides and optical fiber network.The above studies not only provide a new exploration direction for the design and development of novel optical communication and optical information processing devices,but offer an effective platform for studying the physical phenomena and topological properties of photons in a high dimensional space.In the work,the synthetic time and frequency lattices are constructed by using optical fiber-loop circuits with phase modulation and fiber dispersion,which can be used to manipulate the evolution of pulse waveform and spectrum envelope.The main contents are listed as follows:Firstly,we experimentally observe the frequency Bloch oscillations in a modulated fibre-loop circuit with detuned time.The spectrum evolution occurs in a frequency lattice which is formed by the phase modulation.The detuned time between the circulating time of the fibre loop and modulation period plays the role of an effective vector potential and gives rise to the Bloch oscillations in frequency dimension.Additionally,the transient evolution of the spectrum can be precisely measured by the dispersive Fourier transformation(DFT)technique which maps the pulse spectrum into the temporal waveform.The study not only introduces a novel platform to emulate the electron dynamics in solid state physics,but provides a new application scenario for Bloch oscillations such as the spectral imaging and multiplexing.Secondly,by using a fiber loop with phase modulation,the refraction and reflection of optical pulse have been studied at several kinds of heterointerface in time domain.The phase modulation provides the periodic potential and the fiber dispersion enables the tunneling of photons in the potential.Thus the one-dimension lattices can be constructed in time dimension.By periodically changing the modulation depth or frequency,the heterointerface is vertical and may induces total internal reflection.The temporal refraction can be adjusted by setting the initial Bloch wave vector at incidence.As the variation of modulation occurs at a specific moment,a horizontal interface could be introduced.The combination between straight and tilted lattice could provide another way to control the temporal refraction.The pulse negative refraction in time dimension could also be observed.The study may finds applications in optical communication and signals processing.Thirdly,we construct a dimerized lattices in time dimension by composing a fundamental frequency and frequency-doubled modulation signals.Based on the dimerized lattices,the topological boundary states can be achieved at a vertical interaface to suppress the fiber dispersion.Relative to frequency-doubled signal,the phase of fundamental frequency modulation is linearly adjusted continuously and slowly,so that the coupling strength and on-site potential of the lattices are changed and form a closed path around a degeneracy point in parameter space.Then the charge adiabatic pumping can be extended to the time lattices and induces a quantized transport of optical pulse.The study demonstrates the feasibility for exploring the topological properties of photons in one-dimensional time lattices and provides a novel platform for topological photonics.Finally,we design a fiber network to construct the two-dimensional synthetic time lattices to realize discrete diffraction and Bloch oscillations of optical pulses.Here the length difference among the fibers in network is used to introduce time delay,which generate a series of pulse trains.Each pulse corresponds to the site in the two-dimensional lattices.The coupling between the adjacent sites is supported by the optical couplers in the network.Using a variable optical coupler,two different boundaries and the related topological properties are studied in a honeycomb lattice.Then a contracted and expanded honeycomb lattices can also be constructed.By combining the lattices and forming a vertical interface,we construct pseudospin topological edge states which induce a directional transport of optical pulse in time domain.The works provide a feasible method for the studies of high-dimensional physical problems and have applications in two-dimensional imaging and time division multiplexing.