Conical quasi-phase-matching second harmonic generation in a 2D photonic crystal with hybrid Ewald geometric method.

The direction variation of the fundamental wave in the same nonlinear photonic crystal would cause different pattern of harmonics generation. In a 2D/3D crystal with dense reciprocal lattice vectors, there will be large numbers of conical harmonic beams evolving with direction change of the fundamental wave. By rearranging the Ewald sphere and superposing it into the Ewald shell, we have a hybrid Ewald construction. It becomes a simple but useful geometric method to comprehensively depict the distribution of these quasi-phase-matching second harmonics and their conical form evolution. It presents conical second harmonic beams by their related reciprocal lattice vectors and simplifies the beams' distribution according to spatial arrangement of those reciprocal lattice vectors. It finds that the conical beams will create, annihilate, or get enhanced in specific order when fundamental waves change incident directions. We applied the method on a periodically poled 2D LiTaO3 crystal and all observed phenomena, meet the method's predictions. In our experiment, we observed that the conical beams distorted along the optic axis of the sample due to anisotropy, which was generally overlooked by earlier researches. The eccentricities of their ring projections suggest a potential auxiliary approach for crystal dispersion measurement.

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.

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.

From Ewald sphere to Ewald shell in nonlinear optics.

Ewald sphere is a simple vector scheme to depict the X-ray Bragg diffraction in a crystal. A similar method, known as the nonlinear Ewald sphere, was employed to illustrate optical frequency conversion processes. We extend the nonlinear Ewald sphere to the Ewald shell construction. With the Ewald shell, a variety of quasi-phase-matching (QPM) effects, such as the collective envelope effect associated with multiple QPM resonances, the enhanced second- harmonic generation due to multiple reciprocal vectors etc., are suggested theoretically and verified experimentally. By rotating the nonlinear photonic crystal sample, the dynamic evolution of these QPM effects has also been observed, which agreed well with the Ewald shell model.

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.

Miniature spectrometer based on diffraction in a dispersive hole array.

We present an ultra-compact spectrometer that uses a 10×10 hole array as the dispersive component. Our analysis shows that the two-dimensional intensity distribution can be modeled by a system of simultaneous linear equations when the size of each hole in the dispersive component has been pre-designed appropriately. One can readily recover the spectral contents of the input radiation by solving the linear equation system with regularized procedure. Experimental results show that the reconstruction range is at least within the entire visible band, which can be further extended if a near-infrared CCD is used. One therefore envisions strong potential for many wavelength analysis applications.

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.

Nonlinear volume holography for wave-front engineering.

The concept of volume holography is applied to the design of an optical superlattice for the nonlinear harmonic generation. The generated harmonic wave can be considered as a holographic image caused by the incident fundamental wave. Compared with the conventional quasi-phase-matching method, this new method has significant advantages when applied to complicated nonlinear processes such as the nonlinear generation of special beams. As an example, we experimentally realized a second-harmonic Airy beam, and the results are found to agree well with numerical simulations.

Controllable polarization coupled dual-focused second-harmonic generations in a two-dimensional optical superlattice.

The nonlinear Huygens-Fresnel principle has been used to design multifunctional nonlinear optical devices. Focused second-harmonic generations have been observed with strong polarization sensitivity. Numerical simulations have been performed, and the results fit well with the experiments.