All-optical Construction Of Synthetic Frequency Lattices And Resultant Manipulation Of Discrete Frequency Diffraction

Spectrum manipulation of photon is one of the important research directions in the fields of optics and photonics,which has great significance for basic science and practical engineering applications.In recent years,relying on the synthetic frequency lattices,the method of controlling electron motion in traditional lattice has been skillfully extended to photonic system,which achieved more flexible and convenient manipulation of frequency.For example,many novel manipulation methods,such as spectrum directional shifting,perfect focusing and non-reciprocal transmission,have been realized by using the photonic gauge potential in frequency lattice,and these results may find practical applications in wavelength division multiplexing,secure communication and signal processing.At present,the construction of synthetic frequency lattices is always based on electro-optical effect.However,due to the limited bandwidth of electrical devices,the modulation frequency of electro-optical modulation is usually in the order of GHz,which greatly astrict the applied prospect of synthetic frequency lattices.Except the electro-optical modulation,synthetic frequency lattices can also be created by the third-order nonlinear effects.Compared with the electro-optical effect,the nonlinear approach,which has advantages of fast optical response and large manipulation range,provides an all-optical scheme and further improves the ability of frequency manipulation.In this paper,the four-wave mixing effect is utilized to construct the synthetic frequency lattice.Through introducing the gauge potential,effective electric force and second temporal phase modulation into frequency dimension,the flexible manipulation of frequency can be realized.The main contents are as follows:Firstly,we theoretically create a discrete frequency lattice and photonic gauge potential by four-wave mixing effect and experimentally achieve the precisely manipulation of spectrum under the effect of gauge potential.Two pump lights are used to generate a Bragg grating through interference,which scatters the signal lights to idlers around the center frequency,so as to create a synthetic frequency lattice.The phase difference between two pump lights can be regarded as the gauge potential in frequency lattice.Through cascading two processes of FWM with different gauge potentials,we can observe the phenomena of bandwidth expansion and spectrum directional shift.Additionally,for the specific gauge potential,we can also realize the arbitrary refraction and perfect imaging of spectrum.The study paves a promising way to achieve broadband frequency manipulation and may has important application value in the fields of time-frequency imaging and frequency shifting.Secondly,we utilize the phase-mismatch during four-wave mixing process to induce an effective gauge field and theoretically investigate the optical Bloch oscillation effect in frequency dimension.The dispersion relation of a silicon nitride waveguide is approximately linear over a sufficiently small frequency range.Thus,a tiny phase-mismatch will exist in the nonlinear process,which introduce an effective force into the frequency lattice.Under the action of effective force,we can realize the spectral Bloch oscillations.In addition,with the third pump light,the anharmonic Bloch oscillations can also be achieved by introducing longrange coupling into frequency lattice.Furthermore,through cascading multiple waveguides with the same length and modulating the phase of pumps,we can break the inherent periodicity of Bloch oscillations and realize the broadband spectrum shift and spectrum expansion.This work finds a novel physical mechanism to realize Bloch oscillations in frequency dimension and may find great potential applications in information encryption,time-frequency reconstruction and other fields.Then,we design the nonlinear optical fiber system and experimentally observe the spectral self-imaging process based on four-wave mixing time lens.The linear frequency chirp of pump light,which accumulated in single mode fiber,provides the quadratic phase modulation for incident signal in time domain.Under this modulation,the self-imaging process of spectrum can be realized.We further theoretically analyze the influence of the repetition frequency of incidence and the bandwidth of individual frequency comb on the spectral self-imaging.Through increasing the bandwidth of individual frequency comb,the distortion of self-imaging can be inhibited.These results not only provide a novel and powerful approach to achieve the spectral self-imaging of frequency comb,but also can be applied to optical communication and optical signal processing,such as frequency division multiplexing and spectral domain stealth technology.Finally,the fractional Talbot effect in frequency dimension is experimentally realized by four-wave mixing time lens,which can flexibly manipulate the free spectral range of frequency comb,thus the construction of invisibility cloak can be achieved in frequency dimension.On the basis of spectral self-imaging,through applying the specific quadratic phase modulation on the input frequency comb and adjusting the group delay dispersion of pumps accumulated during the propagation,the free spectral range of idler lights can be changed into any integer and fractional multiples of that of the incidence.Additionally,since the energy of spectrum will be redistributed during the propagation,we can achieve the process of cloaking in frequency dimension by cascading two four-wave mixing time lens.This study provides a new platform for changing the free spectral range of frequency comb and constructs a stealth cloak with flexible stealth range in frequency dimension.These results may find practical applications in information transmission and processing,such as optical frequency comb generation and secure communication.