Group-velocity-matched multistep cascading in nonlinear photonic crystals

We demonstrate that simultaneous phase- and group-velocity-matched cascaded parametric processes can be achieved in two-dimensional quadratic nonlinear photonic crystals by proper matching of noncollinear processes with front tilting of the fundamental pulse. We present examples of cascaded third- and fourth-harmonic generation in a poled LiNbO3 planar structure.     

Frequency conversion in nonlinear photonic crystal of strontium tetraborate

Using a nonlinear photonic crystal (NPC) of strontium tetraborate, we obtained the second-harmonic generation of femtosecond pulses in the nonlinear diffraction regime with an efficiency of 1.9% that is tunable in the near-UV spectral range, as well as fourth-harmonic generation under the conditions of random quasi-phase-matching with maximum efficiency of 10⁻⁵ that is tunable in the far-UV spectral range. The efficiency of second-harmonic generation in strontium tetraborate NPC under the conditions of random quasi-phase-matching was significantly lower. The fourth-harmonic was tunable between 187.5 and 232.5 nm. The previously predicted red shift of spectral components in the generated radiation spectrum upon NPC rotation is demonstrated experimentally.     

Conical second harmonic generation in a two-dimensional chi(2) photonic crystal: a hexagonally poled LiTaO3 crystal

A new type of conical second-harmonic generation was discovered in a 2D chi((2)) photonic crystal-a hexagonally poled LiTaO3 crystal. It reveals the presence of another type of nonlinear interaction-a scattering involved optical parametric generation in a nonlinear medium. Such a nonlinear interaction can be significantly enlarged in a modulated chi((2)) structure by a quasi-phase-matching process. The conical beam records the spatial distribution of the scattering signal and discloses the structure information and symmetry of the 2D chi((2)) photonic crystal.     

Hexagonally poled lithium niobate: A two-dimensional nonlinear photonic crystal

We report on the fabrication of what we believe is the first example of a two-dimensional (2D) nonlinear photonic crystal [Berger, Phys. Rev. Lett. 81, 4136 (1998)], where the refractive index is constant but where the 2nd order nonlinear susceptibility is spatially periodic. Such crystals allow for efficient quasi-phase-matched 2nd harmonic generation using multiple reciprocal lattice vectors. External 2nd harmonic conversion efficiencies >60% were measured with picosecond pulses. The fabrication technique is extremely versatile and should allow for the fabrication of a broad range of 2D crystals including quasicrystals.     

Two-dimensional materials-decorated microfiber devices for pulse generation and shaping in fiber lasers

Two-dimensional(2D) materials have been regarded as a promising nonlinear optical medium for fabricating versatile optical and optoelectronic devices. Among the various photonic applications, the employment of 2D materials as nonlinear optical devices such as saturable absorbers for ultrashort pulse generation and shaping in ultrafast lasers is one of the most striking aspects in recent years. In this paper, we review the recent progress of 2D materials based pulse generation and soliton shaping in ultrafast fiber lasers, and particularly in the context of 2D materials-decorated microfiber photonic devices. The fabrication of 2D materials-decorated microfiber photonic devices, high performance mode-locked pulse generation, and the nonlinear soliton dynamics based on pulse shaping method are discussed. Finally, the challenges and the perspective of the 2D materials-based photonic devices as well as their applications are also discussed.     

Reflected fourth-harmonic radiation from a centrosymmetric crystal

We present measurements of fourth-harmonic generation in reflection from the interface between two centrosymmetric media [Si(001)- SiO(2)] , using femtosecond pulses well below damage threshold. Analyses of signal amplitudes, rotational anisotropy, and sensitivity to surface roughening reveal that the surface dipole fourth-harmonic contribution dominates the bulk quadrupole contribution much more strongly than for second-harmonic generation.     

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.     

Phase matching in nonlinear chi((2)) photonic crystals

We analyze harmonic generation in a two-dimensional (2D) chi((2)) photonic crystal and demonstrate the possibility of multiple phase matching and multicolor parametric frequency conversion. We suggest a new type of photonic structure to achieve simultaneous generation of several harmonics; we also present both general analytical results and design parameters for 2D periodically poled LiNbO(3) structures.     

Periodic,quasi‐periodic,and random quadratic nonlinear photonic crystals

Quadratic nonlinear photonic crystals are materials in which the second order susceptibility χ⁽²⁾ is spatially modulated while the linear susceptibility remains constant. These structures are significantly different than the more common photonic crystals, in which the linear susceptibility is modulated. Nonlinear processes in nonlinear photonic crystals are governed by the phase matching requirements, which are determined by the reciprocal lattice of these crystals. Therefore, the modulation of the nonlinear susceptibility enables to engineer the spatial and spectral response in various three‐wave mixing processes. It enables to support the efficient generation of new optical frequencies at multiple directions. We analyze three wave mixing processes in nonlinear photonic crystals in which the modulation is either periodic, quasi‐periodic, radially symmetric or even random. We discuss both one‐dimensional and two‐dimensional modulations. In addition to harmonic generations, we outline several new possibilities for all‐optical control of the spatial and polarization properties of optical beams in specially designed nonlinear photonic crystals.     

Spatial solitons in chi(2) planar photonic crystals

We analyze light self-confinement induced by multiple nonlinear resonances in a two-dimensional chi(2) photonic crystal. With reference to second-harmonic generation in a hexagonal lattice, we show that the system can not only support two-color (1+1)D solitary waves with enhanced confinement and steering capabilities but also enable novel features such as wavelength-dependent soliton routing.     

Guided-wave second-harmonic generation in a LiNbO3 nonlinear photonic crystal

We demonstrate twin-beam second-harmonic generation from telecommunications wavelengths in an optimized buried reverse proton exchanged planar waveguide made in 2D hexagonally poled LiNbO3. Experiments carried out with a nanosecond narrow-bandwidth, high-power fiber source thoroughly explored the response of the nonlinear photonic crystal device in terms of its power, wavelength, and angle tunability.     

Computer simulation and observation of anomalous light emission from nonlinear photonic crystal with various geometry of its elements

Recently, in papers [1, 2] were described the effect of long-time emission of photonic crystal (synthetic opals) under the action of nanosecond laser pulse. The duration of the luminescence is of the order of seconds. Despite on the other phenomena, which were considered in these papers, below we focus our attention on possible explanation of long time emission from nonlinear photonic crystal. The basis of our consideration is papers [3, 4], those deal with soliton formation in several layers of 1D nonlinear photonic crystal. Because of this, the light wave can exist in photonic crystal a long time (in ideal case—infinite time interval). Taking into account a relation between soliton duration and its maximum intensity, the leaving of laser energy from the layer of photonic crystal takes place due not full reflection from boundaries of layer. The time of light emission for this case depends on nonlinear susceptibility of photonic crystal and the intensity of laser pulse. Hence, soliton formation inside the nonlinear elements of photonic crystal can be one of the reasons of long time emission. We got in computer simulation a long time emission of 1D (layered) and 2D (circular or rectangular elements) nonlinear photonic crystal under the action of laser pulse with femtosecond duration under the conditions of soliton formation in some elements of photonic crystal. Input intensity of laser pulse, at which a soliton appears in nonlinear photonic crystal, can be ten times less due to effects of enhancement of optical intensity in periodic structure [4, 5].     

Quadripartite entangled state from cascaded second-harmonic generation

A generation system of continuous-variable （CV） quadripartite entangled state based on two cascaded second- harmonic generation （SHG） cavities below the threshold is investigated. Two reflected fundamental bearias of the first cavity, the reflected second-harmonic beam and the output fourth-harmonic beam of the second cavity are proved to be entangled, and the dependence of the entanglement degree on the normalized frequency, pump parameter, fourth-harmonic loss parameter, and second-harmonic loss parameter is also analyzed. Due to the fact that the cavity parameters and the nonlinear crystals of the two SHG cavities can be freely chosen, the practicality of the proposed protocol is relatively perfect and the system can also be extended to the preparation of multicolor entangled states for a quantum network.     

A new fabrication technique for photonic crystals: Nanolithography combined with alternating-layer deposition

We propose two photonic crystal structures that can be created by combining nanolithography with alternating-layer deposition. Photonic band calculations suggest that a drilled alternating-layer photonic crystal combining two-dimensional (2D) alternating multilayers and an array of vertically drilled holes may achieve a full photonic bandgap. In addition, a 3D/2D/3D cross-dimensional photonic crystal, which sandwiches a 2D photonic crystal slab between three-dimensional (3D) alternating-layer photonic crystals, should provide better vertical confinement of light than a conventional index guiding slab. Fabrication techniques based on existing technologies (electron beam lithography, bias sputtering, and low-pressure ECR etching) require very few process steps. Our preliminary fabrication suggests that, by refining these technologies, we will be able to realize photonic crystals.     

Defective photonic crystals with greatly enhanced second-harmonic generation

A one-dimensional defective photonic crystal structure is proposed with the aim of studying its nonlinear optical properties. In such a structure, extremely enhanced second-harmonic generation with an efficiency ~5 orders of magnitude higher than that of ordinary films is demonstrated in a numerical simulation. Extraordinary phase conditions of the process in such a structure were explored, and efficient forward and backward second-harmonic generation could be achieved simultaneously. The mechanism of the enhancement is the high field intensity and efficient wave coupling introduced by light localization in defect states, from which many other nonlinear processes can also benefit.     

Continuous-wave frequency tripling and quadrupling by simultaneous three-wave mixings in periodically poled crystals: application to a two-step 1.19-10.71-microm frequency bridge

We observed cw third-harmonic generation in a periodically poled LiNbO(3) crystal by cascading optimally phase-matched second-harmonic and sum-frequency generation. Other processes, such as fourth-harmonic generation, are allowed by the flexibility of quasi-phase matching. We demonstrate a divide-by-nine (1.19- 10.71-microm) frequency chain that uses only two lasers.     

High-power ultraviolet 278 nm laser from fourth-harmonic generation of a Nd:YAG laser in CsB3O5

We demonstrate a high-power UV 278 nm laser by fourth-harmonic generation (FHG) of a 1112 nm Nd:YAG laser in a nonlinear optical (NLO) crystal CsB3O5 (CBO) for the first time, to our best knowledge. A 30 W level diode-pumped Q-switched Nd:YAG laser at 1112 nm with beam quality factor M2=1.2 was used as the fundamental light source at a pulse width of 500 ns. With an LiB3O5 crystal, the 1112 nm laser was first frequency-doubled to 556 nm with an average output power of 13.5 W. It was then frequency doubled again in a CBO crystal to obtain the FHG output at 278 nm. The maximum average output power of the 278 nm laser is up to 1.5 W. The results demonstrated that CBO crystal is a promising NLO material for UV high-power lasers below 300 nm.     

Third-Order Optical Nonlinearity in Two-Dimensional Transition Metal Dichalcogenides

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer twodimensional (2D) transition-metal dichalcogenides (TMDCs), having the formula MX₂ with M=Mo, W and X=S, Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semi-classical perturbation analysis of response functions. We numerically calculate the linear χ_μν⁽¹⁾ (-ω;ω) and nonlinear surface susceptibility tensors χ_μνζη⁽³⁾(-ω_Σ; ω_r; ω_s; ω_t) with ω_Σ=ω_r+ω_s+ω_t. Both non-degenerate and degenerate cases are studied for thirdharmonic generation and nonlinear refractive index, respectively. Computational results obtained with no external fitting parameters are discussed regarding two recent reported experiments on MoS₂, and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a π/4-rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and highharmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.     

Photonic band structure of one-dimensional metal/dielectric structures calculated by the plane-wave expansion method

The plane-wave expansion(PWE) method is employed to calculate the photonic band structures of metal/dielectric(M/D) periodic systems. We consider a one-dimensional(1D) M/D superlattice with a metal layer characterized by a frequency-dependent dielectric function. To calculate the photonic band of such a system, we propose a new method and thus avoid solving the nonlinear eigenvalue equations. We obtained the frequency dispersions and the energy distributions of eigen-modes of 1D superlattices. This general method is applicable to calculate the photonic band of a broad class of physical systems, e.g. 2D and 3D M/D photonic crystals. For comparison, we present a simple introduction of the finite-difference(FD) method to calculate the same system, and the agreement turns out to be good. But the FD method cannot be applied to the TM modes of the M/D superlattice.     

Femtosecond two-photon LIF imaging of atomic species using a frequency-quadrupled Ti:sapphire laser

Femtosecond (fs)-duration laser pulses are well suited for two-photon laser-induced-fluorescence (TPLIF) imaging of key atomic species such as H, N, and O in gas-phase reacting flows. Ultrashort pulses enable efficient nonlinear excitation, while reducing interfering photochemical processes. Furthermore, amplified fs lasers enable high-repetition-rate imaging (typically 1–10 kHz) for capturing the dynamics of turbulent flow fields. However, two-dimensional (2D), single-laser-shot fs-TPLIF imaging of the above species is challenging in most practical flow fields because of the limited ultraviolet pulse energy available in commercial optical parametric amplifier (OPA)-based tunable laser sources. In this work, we report the development of an efficient, fs frequency-quadrupling unit [i.e., fourth-harmonic generator (FHG)] with overall conversion efficiency more than six times greater than that of commercial OPA-based systems. The development, characterization, and application of the fs-FHG system for 2D imaging of H atoms in flames are described in detail. The potential application of the same laser system for 2D imaging of N and O atoms is also discussed.