Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal

We investigate efficient fourth-harmonic generation in a single two-dimensional (2D) quadratically nonlinear photonic crystal. We propose a novel parametric process that starts with phase-matched generation of a pair of symmetric second-harmonic waves, which then interact to produce a fourth-harmonic wave that is collinear to the fundamental. We show that this process is more efficient than conventional fourth-harmonic-generation schemes by a factor that reaches 4 at low intensities and discuss how to design and optimize the nonlinear 2D photonic crystals that are implemented in LiNbO(3) and LiTaO(3) .     

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.     

Supercontinuum generation in a two-dimensional photonic kagome crystal

We demonstrate the generation of ultrabroad spectra in a photonic crystal fiber with a kagome-lattice transverse structure. This two-dimensional periodic photonic lattice allows for strong confinement of light without employing defect states nor using photonic bandgap guiding. Light guiding is mediated by total internal reflection in the intersections of the lattice structure, similar to tapered or micro-structured fibers. The kagome lattice structure is manufactured from a soft glass with a high nonlinearity. Using a Ti:sapphire oscillator as a pump source, we observe for the first time impressive supercontinuum generation in the guided modes of a 2D photonic lattice. Supercontinuum generation is caused by fission and radiation of higher-order solitons in the anomalous dispersion range. Our spectrum encompasses the spectral range from 200 to 1750 nm. The dependence of the continuum on coupling spot location, fiber length, and pump wavelength and power as well as on pulse duration and polarization state is investigated. Using a numerical simulation for the lattice structure, pulse propagation through this structure is theoretically studied. Our model reveals the mechanism of supercontinuuum generation in the 2D photonic structure and explains the essential experimental findings.Electronic supplementary material to this article is avaiable at and accessible for authorized users.     

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.     

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.     

Evanescent Bessel beam generation through filtering highly focused cylindrical vector beams with a defect mode one-dimensional photonic crystal

We propose a simple setup for generating evanescent Bessel beams using the defect mode of one-dimensional (1D) photonic crystal. The angular selectivity provided by the defect mode mimics the role of an axicon for Bessel beam generation. When an azimuthally polarized beam is strongly focused onto a 1D defect mode photonic crystal interface, an evanescent Bessel beam of the first-order is produced, while an evanescent Bessel beam of the zeroth-order will be created under a radially polarized beam illumination. Switching between a donut shape and a solid focal distribution can be easily realized by controlling the polarization of the illumination. Such a versatile evanescent Bessel beam generation may find potential applications in optical trapping.     

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.     

Photonic band gaps based on tetragonal lattices of slanted pores

We describe broad new classes of three-dimensional (3D) structures which, when made of silicon, exhibit robust 3D photonic band gaps of up to 25% of the gap center frequency. The proposed photonic crystals are readily amenable to very high precision microfabrication using established techniques such as x-ray lithography and template inversion. Each architecture consists of a set of oriented cylindrical pores emanating from a two-dimensional (2D) square lattice mask with a two-point basis. Large bandwidth, microcircuits for light may be incorporated within the resulting photonic band gaps using an intercalated 2D photonic crystal layer.     

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.     

Diffractionless optical networking in an inverse opal photonic band gap micro-chip

We present a design for a photonic crystal (PC) all-optical micro-chip based on a three-dimensional (3D) inverse opal heterostructure intercalated with a two-dimensional (2D) triangular lattice photonic crystal slab. Within the 2D micro-chip layer, we demonstrate single-mode (diffractionless) waveguiding of light in air, throughout a bandwidth of more than 70 nm near 1.55 μm. This suggests that inverse opal photonic band gap (PBG) materials can facilitate on-chip optical networking functions over the telecommunication frequency band used in current-day optical fibers.     

Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals

We have observed a dramatic enhancement of third-harmonic generation in 3D polystyrene-air photonic crystals pumped by a near infrared laser beam. As the pump wavelength is tuned, the peak of the enhancement occurs when the third-harmonic wavelength approaches the short-wavelength edge of the band gap. We show that the origin of the enhancement is phase matching provided by the periodic structure of the photonic crystals.     

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.     

Symmetrically glass-clad photonic crystal nanocavities with ultrahigh quality factors

We design and fabricate ultra-high-quality (Q) photonic nanocavities in a symmetrically glass-clad silicon (Si) two-dimensional (2D) photonic crystal (PhC) structure. We theoretically investigate the dependence of the refractive index of the glass on the Q factors for asymmetric and symmetric structures. We show that the index-symmetric distribution of the glass is a critical factor to realize ultrahigh Q factors for glass-clad 2D PhC structures. We fabricate symmetrically glass-clad Si PhC nanocavities and achieve a record Q factor of 1×10(6), comparable with the highest Q factors of nanocavities in air-bridge structures.     

Thermal emission properties of 2D and 3D silicon photonic crystals

We present measurements of the thermal emission properties of 2D and 3D silicon photonic crystals with and without substrate heated resistively as well as passively with an aluminium hotplate. The out-of-plane and in-plane emission properties were recorded and compared to numerical simulation. It turned out that for the in-plane 2D photonic crystal and out-of-plane 3D photonic crystal emission a photonic stop gap effect is visible. For the out-of-plane 2D photonic crystal emission, no photonic bandgap effect is observable but instead strong silicon oxide emission from native oxide inside the pores of silicon are observable. A model for the modified thermal emission is presented.     

Dispersion management in soft glass all-solid photonic crystal fibres

The development of all-solid photonic crystal fibres for nonlinear optics is an alternative approach to air-glass solid core photonic crystal fibres. The use of soft glasses ensures a high refractive index contrast (> 0.1) and a high nonlinear coefficient of the fibres. We report on the dispersion management capabilities in all-solid photonic crystal fibres taking into account four thermally matched glasses which can be jointly processed using the stack-and-draw fibre technique. We present structures with over 450 nm broadband flat normal dispersion and ultra-flat near zero anomalous dispersion below 5 ps/nm/km over 300 nm dedicated to supercontinuum generation with 1540 nm laser sources. The development of an all-solid photonic crystal fibre made of F2 and NC21 glasses is presented. The fibre is used to demonstrate supercontinuum generation in the range of 730?C870 nm (150 nm) with flatness below 5 dB.     

Silicon-based two-dimensional photonic crystal waveguides

A review of the properties of silicon-based two-dimensional (2D) photonic crystals is given, essentially infinite 2D photonic crystals made from macroporous silicon and photonic crystal slabs based on silicon-on-insulator basis. We discuss the bulk photonic crystal properties with particular attention to the light cone and its impact on the band structure. The application for wave guiding is discussed for both material systems, and compared to classical waveguides based on index-guiding. Losses of resonant waveguide modes above the light line are discussed in detail.     

Multiple slow light bands in photonic crystal coupled resonator optical waveguides constructed with a portion of photonic quasicrystals

Coupled resonator optical waveguides (CROWs) in complex two-dimensional (2D) photonic crystals (PCs) constructed with a portion of 12-fold photonic quasicrystals (PQs) are proposed. We show that enhanced transmission and slow light can be simultaneously achieved in such waveguides as well as general CROWs. Moreover, due to higher degree of flexibility and tunability of PQs for defect mode properties compared to conventional periodic PCs, multiple slow light bands can be flexibly obtained in CROWs constructed with complex 2D PCs. Our results may lead to the development of a variety of novel ultracompact devices for photonic integrated circuits.     

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.     

Out-of-plane scattering in 1-D photonic crystal slabs

We present a detailed study of out-of-plane scattering losses in a 1D approximation of 2D photonic crystal slabs. In 2D photonic crystals with a waveguide structure in the third dimension, the periodic structure (in a lot of applications a 2D arrangement of holes etched through the core and cladding) will cause light to scatter out of the waveguide plane. We studied the out-of-plane scattering losses of these holes using a 2D approximation of this 3D structure, with etched slots instead of holes. Our simulation techniques included mode expansion with PML and FDTD. We will present the influence of the refractive index contrast between core and cladding of the layered structure. We show that the losses increase with higher index contrast between core and cladding, but that with very high index contrasts and under the right circumstances light can be coupled into lossless Bloch modes.