Experimental observation of the spectral self-imaging effect with a four-wave mixing time lens.

Here we use a four-wave mixing time lens to demonstrate the spectral self-imaging effect for a frequency comb. The time lens is built by imposing a temporal quadratic phase modulation onto the input signal pulses, which corresponds to a frequency comb in the Fourier spectrum. The modulation is implemented by a Gaussian pump pulse propagating in an external single-mode fiber. Both the signal and pump pulses are injected into a highly nonlinear fiber and four-wave mixing Bragg scattering occurs. We observe periodic revivals of the input frequency comb as the pump pulse propagates periodic distances. The comb-spacing is squeezed at fractional ratios to its original value. Meanwhile, the central-frequency undergoes redshifts and blueshifts subject to the scattered frequencies. We also find that the envelope width of input pulses has an effect on the output spectrum width. The study may find great applications in spectral reshaping and frequency metrology used for optical communication and signal processing.

Real-time observation of frequency Bloch oscillations with fibre loop modulation.

Bloch oscillations (BOs) were initially predicted for electrons in a solid lattice to which a static electric field is applied. The observation of BOs in solids remains challenging due to the collision scattering and barrier tunnelling of electrons. Nevertheless, analogies of electron BOs for photons, acoustic phonons and cold atoms have been experimentally demonstrated in various lattice systems. Recently, BOs in the frequency dimension have been proposed and studied by using an optical micro-resonator, which provides a unique approach to controlling the light frequency. However, the finite resonator lifetime and intrinsic loss hinder the effect from being observed practically. Here, we experimentally demonstrate BOs in a synthetic frequency lattice by employing a fibre-loop circuit with detuned phase modulation. We show that a detuning between the modulation period and the fibre-loop roundtrip time acts as an effective vector potential and hence a constant effective force that can yield BOs in the modulation-induced frequency lattices. With a dispersive Fourier transformation, the pulse spectrum can be mapped into the time dimension, and its transient evolution can be precisely measured. This study offers a promising approach to realising BOs in synthetic dimensions and may find applications in frequency manipulations in optical fibre communication systems.

Bloch oscillations in photonic spectral lattices through phase-mismatched four-wave mixing.

Here we investigate the Bloch oscillations (BOs) in a photonic spectral lattice created with four-wave mixing Bragg scattering (FWM-BS). By injecting a signal and two pumps with different frequencies into a silicon nitride waveguide, a spectral lattice can be created for the generated idlers through successive FWM-BS. The phase-mismatch during FWM-BS acts as an effective force that induces BOs in the spectral lattice. Both the oscillation period and amplitude are determined by the magnitude of the effective force. With cascaded FWM-BS processes, the spectrum of idlers experiences a directional shift as the phase differences of pumps are modulated. Additionally, introducing long-range couplings in the spectral lattice will change the trajectory of BOs within each period. The pattern of BOs for a single frequency input can also be tailored. This Letter provides a new platform to realize BOs in the frequency dimension and paves a promising way for broadband frequency control with all-optical schemes.