Second-harmonic generation of single-mode Laguerre-Gaussian beams with an improved quasi-phase-matching method.

In the second-harmonic generation processes involving Laguerre-Gaussian (LG) beams, the generated second-harmonic wave is generally composed of multiple modes with different radial quantum numbers. To generate single-mode second-harmonic LG beams, a type of improved quasi-phase-matching method is proposed. The Gouy phase shift has been considered in the optical superlattice designing and an adjustment phase item is introduced. By changing the structure parameters, each target mode can be phase-matched selectively, whose purity can reach up to 95%. The single LG mode generated from the optical superlattice can be modulated separately and used as the input signals in the mode division multiplexing system.

Nearly Diffraction-Free Nonlinear Imaging of Irregularly Distributed Ferroelectric Domains.

Second-harmonic generation is used experimentally for the nonlinear imaging of two-dimensional irregular domain structures. Analytical solutions and simulation results for the Fresnel distribution of domain walls are obtained. The results show that the domain wall plays an important role in the imaging process and the corresponding diffraction effect is greatly suppressed (we call it a nearly diffraction-free effect), thus providing a simple way to realize high-resolution imaging for ferroelectric domains.

Time-reversed and reciprocal second-harmonic generation with pump depletion.

The time-reversed second-harmonic generation in one-dimensional nonlinear photonic crystals has been theoretically studied without the undepleted pump approximation. A simple criterion has been deduced which determines the energy flow. Based on it, two kinds of structures with different symmetries are presented to realize the nonlinear time reversal effect. A completely reciprocal nonlinear response is also found in the same process. Furthermore, a multi-section-cascaded structure is proposed to realize the nonlinear time reversal at any given position.

Analytical investigation of nonreciprocal response in 1D nonlinear photonic crystals.

The nonreciprocal response of the SHG process in 1D periodical nonlinear photonic crystals with a defect embedded has been theoretically studied by solving the nonlinear coupled equations. The nonreciprocal response has been deduced analytically with the solution of non-reciprocity parameters obtained. The result shows that as the non-reciprocity approaches 100%, the crystal length and the input power needed increase at a logarithmic rate. Any target nonreciprocal response can be reached in this structure by adjusting the structure parameters.

Theoretical study on the Cerenkov-type second-harmonic generation in optical superlattices without paraxial approximation.

In this paper, the Cerenkov-type second-harmonic generation in bulk optical superlattices has been studied theoretically with the non-paraxial wave equations, where the paraxial approximation is avoided. The corresponding phase-matching condition is determined strictly by solving the non-paraxial wave equations under proper boundary conditions, and the result coincides well with the traditional Cerenkov phase-matching condition. In addition, a backward Cerenkov phase-matching condition is deduced from the wave equations as well, and the physical requirement of this condition is clarified.

2D wave-front shaping in optical superlattices using nonlinear volume holography.

Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO3 crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology.

Rigorous intensity and phase-shift manipulation in optical frequency conversion.

A simple method is employed to investigate the nonlinear frequency conversion in optical superlattices (OSL) with pump depletion. Four rigorous phase-matching conditions for different purposes are obtained directly from the nonlinear coupled equations, and the resulting OSL domain structures are generally aperiodic rather than periodic. With this method, not only the intensity but also the phase-shift of the harmonic waves can be manipulated at will. The second-harmonic generation of Gaussian beam is further investigated. This work may provide a guidance for the practical applications of designing nonlinear optical devices with high conversion efficiency.

Nonlinear optical Fourier transform in an optical superlattice with "x+2" structure.

We proposed a simple method to realize optical Fourier transform during the nonlinear wave shaping processes. In this method, an integrated optical superlattice is designed to realize multiple optical functions, which plays important roles in both the nonlinear harmonic generation process and the optical Fourier Transform process. We demonstrated our method by the nonlinear generation of Airy beams as an example. It is a universal method for beam shaping and is of practical importance for designing compact nonlinear optical devices.