The geometric phase in nonlinear frequency conversion

The geometric phase of light has been demonstrated in various platforms of the linear optical regime, raising interest both for fundamental science as well as applications, such as flat optical elements. Recently, the concept of geometric phases has been extended to nonlinear optics, following advances in engineering both bulk nonlinear photonic crystals and nonlinear metasurfaces. These new technologies offer a great promise of applications for nonlinear manipulation of light. In this review, we cover the recent theoretical and experimental advances in the field of geometric phases accompanying nonlinear frequency conversion. We first consider the case of bulk nonlinear photonic crystals, in which the interaction between propagating waves is quasi-phase-matched, with an engineerable geometric phase accumulated by the light. Nonlinear photonic crystals can offer efficient and robust frequency conversion in both the linearized and fully-nonlinear regimes of interaction, and allow for several applications including adiabatic mode conversion, electromagnetic nonreciprocity and novel topological effects for light. We then cover the rapidly-growing field of nonlinear Pancharatnam-Berry metasurfaces, which allow the simultaneous nonlinear generation and shaping of light by using ultrathin optical elements with subwavelength phase and amplitude resolution. We discuss the macroscopic selection rules that depend on the rotational symmetry of the constituent meta-atoms, the order of the harmonic generations, and the change in circular polarization. Continuous geometric phase gradients allow the steering of light beams and shaping of their spatial modes. More complex designs perform nonlinear imaging and multiplex nonlinear holograms, where the functionality is varied according to the generated harmonic order and polarization. Recent advancements in the fabrication of three dimensional nonlinear photonic crystals, as well as the pursuit of quantum light sources based on nonlinear metasurfaces, offer exciting new possibilities for novel nonlinear optical applications based on geometric phases.     

Periodically poled potassium niobate for second-harmonic generation at 463 nm

We report on the fabrication and characterization of quasi-phase-matched potassium niobate crystals for second-harmonic generation. Periodic 30-mum -pitch antiparallel ferroelectric domains are fabricated by means of poling in an electrical field. Both birefrigence and periodic phase shift of the generated second harmonic contribute to phase matching when the d(31) nonlinear optical tensor element is used. 3.8 mW of second-harmonic radiation at 463 nm is generated by frequency doubling of the output of master-oscillator power-amplifier diode laser in a 5-mm-long crystal. The measured effective nonlinear coefficient is 3.7pm/V. The measured spectral acceptance bandwidth of 0.25 nm corresponds to the theoretical value.     

Design of an Ultrafast Frequency Doubling Photonic Device

Ultrashort pulses complicate the frequency conversion in a nonlinear crystal,where group velocity mismatch becomes the main obstacle due to dispersion.We present a design for group velocity compensated second harmonic generation in a modulated nonlinear structure,embedded in a liquid crystal box.In this structure,nonlinear crystals act as sources of signal and liquid crystals compensate for group velocity mismatch originating from nonlinear crystals.There are the advantages of the flexible,controllable birefringence of liquid crystals.Meanwhile,a method calculating the parameters of this type of structure is presented.To make it clear,an example is provided.Furthermore,the structure can also be shaped as a waveguide to support integration into other optical devices,applicable to all-optical processing systems.     

New approaches for the fabrication of photonic structures of nonlinear optical materials

We revisited two different strategies to fabricate 1D photonic crystals of nonlinear optical dielectric materials based on ultrafast laser ablation of the surface of an RbTiOPO₄ crystal, and selective etching of ferroelectric domains of the surface of a periodically poled LiNbO₄ crystal. We evaluated their behaviour as Bragg diffraction gratings. We also presented the recent advances we developed in a new procedure of fabrication of 2D and 3D photonic crystals of KTiOPO₄ (KTP) grown on the surface of a KTP substrate by liquid phase epitaxial means within the pores of a silicon macroporous template. Optical, structural, morphological, and compositional characterization for the photonic crystals produced through this technique are presented.     

Broad angle phase matching in subdiffractive photonic crystals

We show that photonic crystals made of materials with normal dispersion allow broad angular range phase matching in nonlinear wave mixing processes if tuned to the subdiffractive (or equivalently self-collimated) beam propagation regimes for the frequencies of both interacting waves. This allows efficient parametric mixing of narrow beams. We demonstrate this idea by numerical simulation of the second harmonic generation in two-dimensional photonic crystal in particular nonlinear material (AlGaAs) in planar waveguide geometry.     

Enhancement of resolution and quality of nano-hole structure on GaN substrates using the second-harmonic beam of near-infrared femtosecond laser

By using a second harmonic of near infrared femtosecond (fs) laser (λ=387 nm, 150 fs) with high NA objective lens, fabrication resolution has been greatly improved in nano-fabrication of wide band-gap semiconductor gallium nitride (GaN). We have carried out a wet-chemical-assisted fs laser ablation method, in which the laser beam is focused onto a single-crystal GaN substrate immersed in a concentrated hydrochloric (HCl) acid solution. A two-step processing involving irradiation with a fs laser beam in air followed by wet chemical treatment is also performed for comparison. In the wet-chemical-assisted ablation, theoretical diameters of ablation craters are calculated as a function of pulse energy by assuming that the reaction is based on two-photon absorption. In lower energy, the calculated curve is close to the experimental value, while the actual measured diameters in the region of higher energy are larger than calculated values. In the condition of the highest fabrication resolution, we obtained ablation craters smaller than 200 nm at full width at half maximum. We have also demonstrated the fabrication of two-dimensional (2D) periodic nanostructures on surface of a GaN substrate using the second harmonic single fs-laser pulse. Uniform ablation craters with the size as small as 410 nm in diameter are arranged with a periodicity of 1 μm. Such structures are applicable to 2D photonic crystals which improve the light extraction efficiency for blue LEDs in the near future.     

Two-dimensional nonlinear beam shaping

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.     

The development of new borate-based UV nonlinear optical crystals

The developments of nonlinear optical (NLO) crystals in the last decade are reviewed from two aspects. In the theoretical part, on the ab initio plane-wave pseudopotential energy method, calculation of the optical responses, including the second harmonic generation coefficients, a computer-program package, and a real-space atom-cutting method are described and employed to evaluate the degree of approximation of the anionic group theory for nonlinear optical crystals. The ab initio method combined with the anionic group theory gives much more insight into the understanding of the relationship between the optical responses and microscopic structures of NLO crystals, borate-based NLO crystals in particular. In the experimental part, we describe how to use the anionic group theory method and an experimental evaluation system to develop a series of borate-based UV-NLO crystals such as KBe₂BO₃F₂ (KBBF) and K₂Al₂B₂O₇ (KABO). The capability of these new UV-NLO crystals in producing deep-UV harmonic output is evaluated and determined. Finally, recent advances in the generation of deep- and vacuum-UV harmonic output with these new NLO crystals are reported. PACS 42.65.Ky; 42.70.Mp     

Growth and physicochemical properties of second-order nonlinear optical 2-amino-5-chloropyridinium trichloroacetate single crystals

The growth of organic nonlinear optical (NLO) crystal 2-amino-5-chloropyridinium trichloroacetate (2A5CPTCA) has been synthesized and single crystals have been grown from methanol solvent by slow evaporation technique. The grown crystals were subjected to various characterization analyses in order to find out the suitability for device fabrication. Single crystal X-ray diffraction analysis reveals that 2A5CPTCA crystallizes in monoclinic system with the space group Cc. The grown crystal was further characterized by Fourier transform infrared spectral analysis to find out the functional groups. The nuclear magnetic resonance spectroscopy is a research technique that exploits the magnetic properties of certain atomic nuclei. The optical transparency window in the visible and near-IR (200--1100 nm) regions was found to be good for NLO applications. Thermogravimetric analysis and differential thermal analysis were used to study its thermal properties. The powder second harmonic generation efficiency measurement with Nd:YAG laser (1064 nm) radiation shows that the highest value when compared with the standard potassium dihydrogen phosphate crystal.     

行波管中二次谐波注入对三阶互调的抑制

 利用Christine 1维多信号非线性互作用物理模型,对螺旋线行波管中注入二次谐波后三阶互调的输出进行了模拟。模拟结果表明：在螺旋线大功率行波管中,通过二次谐波注入能有效地抑制三阶互调输出,从而降低了行波管的非线性输出,并存在最佳的注入功率和相位条件,使三阶互调可被抑制到最低。介绍了二次谐波注入抑制三阶互调的实验研究,并与模拟结果进行了比较,两者基本一致。     

A GaAs planar Schottky varactor diode for left-handed nonlinear transmission line applications

The left-handed nonlinear transmission line(LH-NLTL) based on monolithic microwave integrated circuit(MMIC) technology possesses significant advantages such as wide frequency band,high operating frequency,high conversion efficiency,and applications in millimeter and submillimeter wave frequency multiplier.The planar Schottky varactor diode(PSVD) is a major limitation to the performance of the LH-NLTL frequency multiplier as a nonlinear component.The design and the fabrication of the diode for such an application are presented.An accurate large-signal model of the diode is proposed.A 16 GHz-39.6 GHz LH-NLTL frequency doubler using our large-signal model is reported for the first time.The measured maximum output powers of the 2nd harmonic are up to 8 dBm at 26.4 GHz,and above 0 dBm from 16 GHz to 39.6 GHz when the input power is 20 dBm.The application of the LH-NLTL frequency doubler furthermore validates the accuracy of the large-signal model of the PSVD.     

Silicon and porous silicon mid-infrared photonic crystals

A 3D silicon micromachining method based on proton beam writing combined with electrochemical anodization of p-type silicon enables fabrication of mid-infrared photonic crystals made of silicon and porous silicon. Here, example structures of silicon 1D and 2D photonic crystals are demonstrated. Progress and problems of fabricating 3D photonic crystals made of silicon are discussed. The strategy of fabricating photonic crystals purely made of porous silicon, and the characterization method of all these mid-infrared structures, are discussed. Due to the flexibility of this fabrication method, photonic devices and integrated photonic circuits may be built on a single chip, for which two 2D silicon photonic crystals with one on top of the other are demonstrated.     

Effects of harmonic phase on nonlinear surface acoustic waves in the (111) plane of cubic crystals

Spectral evolution equations are used to perform numerical studies of nonlinear surface acoustic waves in the (111) plane of several nonpiezoelectric cubic crystals. Nonlinearity matrix elements which describe the coupling of harmonic interactions are used to characterize velocity waveform distortion. In contrast to isotropic solids and the (001) plane of cubic crystals, the nonlinearity matrix elements usually cannot be written in a real-valued form. As a result, the harmonic components are not necessarily in phase, and dramatic variations in waveforms and propagation curves can be observed. Simulations are performed for initially monofrequency surface waves. In some directions the waveforms distort in a manner similar to nonlinear Rayleigh waves, while in other directions the velocity waveforms distort asymmetrically and the formation of shocks and cusped peaks is less distinct. In some cases, oscillations occur near the shocks and peaks because of phase differences between harmonics. A mathematical transformation based on the phase of the matrix elements is shown to provide a reasonable approximation of asymmetric waveform distortion in cases where the matrix elements have similar phase.     

Potassium Titanyl Phosphate and Its Isomorphs: Growth,Properties, and Applications

Potassium titanyl phosphate (KTP) and its isomorphs have received enormous attention in the last 2 decades. In particular, KTP assumes importance due to its large nonlinear optic and electrooptic coefficients together with the broad thermal and angular acceptance for second harmonic generation. This article provides an overview of the material aspects, structural, physical, and chemical properties and device feasibility of the KTP family of crystals. Some of the current areas of research and development along with their significance in understanding the physical properties as well as device applications are addressed. Optical waveguide fabrication processes and characteristics with their relevance to the present-day technology are highlighted. Studies performed so far have enabled us to understand the fundamental aspects of these materials and what needs to be pursued vigorously is the exploitation of their device applications to the maximum extent.     

夹持方式和加工误差对大口径薄型KDP晶体附加面形的影响

惯性约束聚变频率转换系统中,大口径薄型KDP晶体的面形质量是影响频率转换效率能否达到设计要求的关键因素之一。针对45放置状态下口径为400 mm400 mm的三倍频KDP晶体,采用ANSYS有限元分析软件,建立了不同夹持方式和具有不同加工误差的KDP晶体模型和夹具模型,分析了加工误差对不同夹持方式下KDP晶体附加面形的影响,给出了不同加工误差和不同夹持情况下,KDP晶体附加面形的P-V值和RMS值。研究结果表明,夹持方式和加工误差是引起KDP晶体附加面形变化的重要因素,正面压条夹持方式即使在晶体和夹具存在加工误差时也可以较好地控制晶体的附加面形。     

Ultrasonic waves in crystals with charged dislocations

A system of equations for charged dislocations, where the quadratic nonlinear terms are taken into account, is derived using the variational principle. This system describes the propagation of ultrasonic (US) waves in crystals with charged dislocations. From the linearized system of equations a linear dispersion equation is derived. Formulas for the phase linear velocity of the wave and the absorption coefficient are obtained, which show essential influence of charged dislocations and electrical properties of media on the mentioned quantities. For a nonlinear US wave an equation for the amplitude of the first harmonic is derived and, as a consequence, expressions are obtained for the nonlinear velocity of the US wave, for the attenuation of the first harmonic's amplitude, and for phase variation.     

Modified solution-processible fabrication of metallic photonic crystals with template removal

High-temperature annealing and pre-annealing lift-off procedures are employed to improve the solutionproeessible technique for the fabrication of one- （1D） and two-dimensional （2D） metallic photonic crystals （MPCs） based on colloidal gold nanoparticles. This enables the successful fabrication of gold nanowires or nanocylinder array structures with the photoresist template removed completely, which is crucial for the application of MPCs in biosensors and optoelectronic devices. Microscopic measurements show homogeneous 1D and 2D photonic structures with an area as large as 100 mm2. Plasmonic resonance of the gold nanostructures and its coupling with the resonance mode of the planar waveguide underneath the photonic structures are observed, implying the excellent optical properties of this kind of MPCs based on the improved fabrication technique.     

Second optical harmonic generation in nonlinear crystals with a disordered domain structure

A theory describing the second harmonic generation in nonlinear-optical crystals with random domains is developed. The theory takes into account the fluctuations of both the phase mismatch and the nonlinear coupling coefficient of the interacting waves. It is shown that, in such crystals, the maximal efficiency of fundamental-to-second harmonic conversion is low, and the dependence of the average intensity of the second harmonic on the fundamental intensity differs considerably from a square law.