Two-dimensional Nonlinear Photonic Crystal Research Articles

Engineering multipartite coupling in doubly pumped parametric down-conversion processes

We investigate the quantum state generated by optical parametric down-conversion in a $\chi^{(2) } $ medium driven by two noncollinear light modes. The analysis shows the emergence of multipartite, namely 3- or 4-partite, entangled states in a subset of the spatio-temporal modes generated by the process. These appear as bright spots against the background fluorescence, providing an interesting analogy with the phenomenology recently observed in two-dimensional nonlinear photonic crystals. We study two realistic setups: i) Non-critical phase-matching in a periodically poled Lithium Tantalate slab, characterized by a 3-mode entangled state among hot spots. ii) A type I setup in a Beta-Barium Borate crystal, where the spatial walk-off between the two pumps can be exploited to make a transition to a quadripartite entangled state. In both cases we show that the properties of the state can be controlled by modulating the relative intensity of two pump waves, making the device a versatile tool for quantum state engineering.

Flexible tuning of nonlinear non-diffracting array beams using wavelengths and angles

We present a simple method to enable flexible tuning of non-diffracting beams in a two-dimensional nonlinear photonic crystal, based on the interference of two or more non-collinear second-harmonic beams. By manipulating the wavelengths of the beams and the angle of incidence of the fundamental wave, the arbitrary period and propagation length, as well as the wavelength of the generated nonlinear non-diffracting array beams, can be tuned flexibly. These light beams can trap and manipulate multiple particles, create new forms of optical imaging systems, and act within nonlinear devices to bring novel functionalities to integrated optics.

Multichannel nonlinear holography in a two-dimensional nonlinear photonic crystal

To manipulate the wave front of the harmonic wave, nonlinear photonic crystals (NPCs) have been employed in constructing nonlinear holography. Through designing a multi-channel ${\ensuremath{\chi}}^{2}$ structure, nonlinear multiplexing holography is reported here in NPCs. We propose a multi-channel nonlinear holography in an orbital-angular-momentum- (OAM-)multiplexing NPC. In experiment, three images encoded in a single NPC are reconstructed in second-harmonic waves distinctively, when the necessary Fourier-domain OAM-matching conditions are met, respectively. Our method not only conceptually extends nonlinear holography, but also provides a multifunctional platform for high-capacity security storage.

Engineering multipartite entanglement in nonlinear photonic crystals

We study the quantum state of twin photons generated by parametric down-conversion in a two-dimensional nonlinear photonic crystal, driven by a dual pump beam. The interplay between the grating of the ${\ensuremath{\chi}}^{(2)}$ nonlinear response and the transverse spatial modulation of the pump opens a rich scenario of possibilities for controlling the quantum state. We focus on a spatial resonance condition between the pump and the nonlinear grating, where a quadripartite entangled state is generated in proper light modes. The device is shown to implement the mixing of a pair of independent two-mode squeezed states onto four separate spatial modes, without the need of any external beam-splitter. Remarkably, both the squeezing parameters and the mixing coefficients can be reconfigured by modulating the relative phase and intensity of the two pumps, enabling thus the generation of a variety of quantum states in a single device.

Complete photonic band gap characteristics of two-dimensional Kerr nonlinear plasma photonic crystals

In this paper, the characteristics of the complete photonic band gaps for two-dimensional nonlinear plasma photonic crystals are studied theoretically by using the finite-difference time-domain method. The two-dimensional structure comprises nonlinear rods with different geometrical shapes and orientations in a plasma background with square and honeycomb lattices. The embedded dielectric rods containing Kerr nonlinearity have a relative permittivity that is a function of the external light intensity. Our simulation results show that almost all designed nonlinear structures represent noticeable complete band gaps whose position and width can be tuned by altering the light intensity. Furthermore, the influence of geometrical parameters on properties of the band spectra is discussed.

Application of the pseudospectral method to the finite difference frequency domain method

Application of the pseudospectral method in numerical calculations is well established. The method is used in several disciplines, from geology to applied mathematics. The pseudospectral method also appears in computational electromagnetism. Its implementation already has been carried out for the finite element method and finite difference time domain method. In this study, we implement the pseudospectral method for the finite difference frequency domain (FDFD) method, and hence the resulting method is called the pseudospectral frequency domain (PSFD) method. The PSFD method is compared to the FDFD method in terms of the numerical phase velocity and anisotropy. The method is extended for the nonlinear process PSFD (NL-PSFD) of second-harmonic generation. It is shown how a plane wave source at oblique incidence can be implemented, and its performance for tilted quasi-phase-matched grating is discussed. Finally, a specific method is deduced from NL-PSFD for large-volume simulation, where only second-order nonlinearity is spatially structured, and a two-dimensional nonlinear photonic crystal is simulated.

Compact generation of a two-photon multipath Dicke state from a single χ(2) nonlinear photonic crystal.

Multipartite quantum entanglement is a powerful resource for enriching the functionality of quantum computation and quantum communication. In this Letter, we propose a new method to generate a two-photon multipath Dicke state with concurrent spontaneous parametric downconversion processes from a single periodically poled nonlinear photonic crystal. We design the poling structure to produce a three-path Dicke state where three quasi-phase-matching conditions are fulfilled simultaneously by a hybrid one- and two-dimensionally poled nonlinear photonic crystal. We use genuine multipartite entanglement concurrence to quantify the entanglement of the Dicke state. Using a more complicated poling configuration like multiple-periodically poled two-dimensional nonlinear photonic crystal, we can also produce four-path, five-path, or multipath Dicke states by a single crystal. The multiple-periodically poled two-dimensional nonlinear photonic crystal provides a new method, to the best of our knowledge, for the integrated generation of multipartite quantum light sources.

All-optical simultaneous AND & XOR logic gates based on nonlinear micro-ring resonator

ABSTRACTIn this paper, we have proposed AND and XOR logic gates simultaneously in one structure. The presented structure is based on two-dimensional (2D) nonlinear photonic crystal with T–shaped waveguide and micro-ring resonator. In the proposed structure, the power consumption is that is lower than similar logic gates and the extinction ratio is about 6.5 dB. Also, the switching time is attained to be 0.2 and 0.26 ps for AND and XOR logic gates, respectively. Simplicity and small size (18.4 µm×18.4 µm) of the structure make it suitable for photonic integrated circuits (PICs). All simulations are based on finite-difference time-domain (FDTD) and plane wave expansion (PWE) numerical methods.

Effect of field modulation on the quasi-phase-matching for second harmonic generation in a two-dimensional nonlinear photonic crystal

Second harmonic generation (SHG) in a two-dimensional (2D) nonlinear photonic crystal (NPC) with finite width along [Formula: see text]-direction that is embedded in air is investigated, without adopting the traditional approximations such as a plane-wave approximation (PWA) and slowly varying amplitude approximation (SVAA). The so-called quasi-phase-matching (QPM) and the corresponding SHG conversion efficiency can be modulated significantly by the field of fundamental wave (FW). It is assumed that the incident light, along [Formula: see text]-direction, is normally launched upon the surface of the sample, and QPM for different directions is investigated. It is found that the QPM shows significant differences, compared with the traditional QPM along the two different directions: in the direction of finite width of the sample, the peak value of SHG conversion efficiency is deviated from the traditional case and it gets to its peak values when the transmittance resonance occurs. However, in the other direction, the deviation from the traditional QPM arises from the field modulation of the second harmonic wave (SHW) and in this direction, it is investigated that the full width at half maximum of QPM is much wider than that in the direction of finite width of the sample. These results can be used to provide a theoretical guidance for achieving QPM SHG.

Theoretical study on second-harmonic generation in two-dimensional nonlinear photonic crystals.

We theoretically study second-harmonic generation in two-dimensional nonlinear photonic crystals and obtain a unified expression that combines nonlinear Raman-Nath diffraction, Čerenkov-type second-harmonic generation, and nonlinear Bragg diffraction. The analytical solution is deduced, and the theoretical result coincides well with the nonlinear Raman-Nath, nonlinear Čerenkov, and nonlinear Bragg diffraction phase-matching conditions. This method has potential applications in second-harmonic generation of more complicated two-dimensional and even three-dimensional nonlinear photonic crystals.

Simultaneous negative refraction and focusing of fundamental frequency and second-harmonic fields by two-dimensional photonic crystals

Simultaneous negative refraction for both the fundamental frequency (FF) and second-harmonic (SH) fields in two-dimensional nonlinear photonic crystals have been found through both the physical analysis and exact numerical simulation. By combining such a property with the phase-matching condition and strong second-order susceptibility, we have designed a SH lens to realize focusing for both the FF and SH fields at the same time. Good-quality non-near field images for both FF and SH fields have been observed. The physical mechanism for such SH focusing phenomena has been disclosed, which is different from the backward SH generation as has been pointed out in the previous investigations. In addition, the effect of absorption losses on the phenomena has also been discussed. Thus, potential applications of these phenomena to biphotonic microscopy technique are anticipated.

Nonlinear Raman-Nath diffraction of femtosecond laser pulses in a 2D nonlinear photonic crystal.

We study second-harmonic generation (SHG) of femtosecond laser pulses in a rectangular two-dimensional nonlinear photonic crystal (NLPC). Multiple SH beams were observed in the vicinity of the propagation direction of the fundamental beam. It has been verified that the angular positions of these beams obey the conditions of nonlinear Raman-Nath diffraction (NRND). The measured SH spectra of specific NRND orders consist of narrow peaks that experience a high-frequency spectral shift as the order grows. We derive an analytical expression for the process studied and find the theoretical results to be in good agreement with the experimental data. We estimate the enhancement factor of nonlinear Raman-Nath diffraction in 2D NLPC to be 70.

Two-dimensional aperiodic nonlinear photonic crystal in a dual-wavelength Nd:YVO_4 laser for pulsed orange generation

We report the design and construction of a highly integrated two-dimensional (2D) aperiodic nonlinear photonic crystal (NPC) for working in a diode-pumped, dual-wavelength (1064 and 1342 nm) Nd:YVO₄ laser to demonstrate a compact, high-peak-power intracavity sum-frequency generator (ISFG) radiating at orange 593.5 nm. The 2D aperiodic NPC was built in quasi-phase-matched LiNbO₃whose crystal domain was structured based on the aperiodic optical superlattice technique to best achieve its simultaneous performance of a dual-wavelength electro-optic Bragg Q-switch and a SFG in the Nd:YVO₄ laser. When the NPC device was driven with a 350-V Q-switching voltage and a 1-kHz switching rate, we measured pulse energy of ~4.3 μJ (or peak power of ~531 W) at orange 593.5 nm from the constructed ISFG with 5.28-W diode power.

BaMgF4: An Ultra‐Transparent Two‐Dimensional Nonlinear Photonic Crystal with Strong χ(3) Response in the UV Spectral Region

Ferroelectric patterning is often used in advanced photonics and optoelectronic devices to increase their operational bandwidth and functionality, providing novel and unique performances. However, the extension of the ferroelectric structures to two‐dimensional geometries is currently limited to very few oxides and phosphates systems, which constrains its current and future applications. Here, careful processing based on e‐beam lithography and poling is employed to fabricate the first example of a two‐dimensional nonlinear photonic crystal in Barium Magnesium Fluoride, BaMgF4, a ferroelectric fluoride crystal with an extraordinary transparency ranging from the deep ultraviolet (≈126 nm) to the mid infrared (≈13 μm). The optical characterization shows the possibility of obtaining simultaneously up to three different Cerenkov‐type second harmonic generation processes distributed in a conical geometry via χ(2)‐quasi‐phase‐matching technique. Additionally, the remarkably high χ(3) nonlinear response of BaMgF4 crystal in the UV spectral region is exploited to demonstrate what is believed to be the highest direct UV‐third harmonic generation conversion efficiency in a solid state system via pure χ(3) nonlinear process. Together, the results highlight the outstanding opportunities offered by nonlinear photonic structures as innovative avenues to manipulate the light generation and control with reliable multifunctional optical character.

Experimental study of multiwavelength parametric generation in a two-dimensional periodically poled lithium tantalate crystal

In this Letter, we experimentally investigate multiwavelength parametric generation in two-dimensional second-order nonlinear photonic crystals. For this purpose, a 2D periodically poled lithium tantalate crystal with rectangular lattice was fabricated and characterized. We demonstrate multiple and simultaneous wavelength generation due to the contribution of different lattice vectors. Numerical simulations emphasize the agreement of our phase matching scheme with the experimental results and made it possible to assign the observed wavelengths to the reciprocal lattice vectors involved in the parametric generation process. Moreover, our results indicate that some signals are the result of the joint contribution of more than one lattice vector.

Heralded generation of multipartite entanglement for one photon by using a single two-dimensional nonlinear photonic crystal

We propose a compact scheme for the heralded generation of single-photon multipartite entanglement by using a single two-dimensional nonlinear photonic crystal. Studies have shown that by appropriate structure design, the single-photon entanglement shared among three spatially distinct optical modes can be generated through three concurrent spontaneous parametric down-conversion processes by using the other photon in an identical spatial mode as a trigger. Furthermore, we analyze the entanglement of such heralded single-photon tripartite W-type state theoretically. This method can be expanded for the heralded single-photon N-partite entanglement generation. This compact and stable quantum light source may act as a key ingredient in quantum information science.

Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal

We report on the experimental realization of Cerenkov second harmonic generation and sum-frequency generation in a two-dimensional (2D) LiTaO3 nonlinear photonic crystal. The ferroelectric domain wall enhanced Cerenkov radiations were created by the modulations induced corresponding to the reciprocal vectors along the direction of propagation of the fundamental beams. The (electric field) polarizations of the fundamental beams were found to affect the Cerenkov angles and the intensities of the radiations. In addition, the variations in the characteristics of the radiations varying with the wavelength of the incident fundamental waves were investigated.

Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal

We present experimental realization of Čerenkov difference frequency generation (CDFG) in a 2-dimentional rectangular periodically poled LiTaO3. The backward reciprocal vector of the nonlinear photonic crystal accelerates the phase velocity of the nonlinear polarization wave so as to exceed the phase speed limit of achieving Čerenkov down-conversions in this normal dispersion medium. Some characteristics of CDFG, such as radiation angles, pumping power, and pulse temporal overlapping dependences were discussed. The experimental results matched well with theoretical predictions.

Multi-directional Čerenkov second harmonic generation in two-dimensional nonlinear photonic crystal

We study Čerenkov-type second-harmonic generation in a two-dimensional quasi-periodically poled LiNbO3 crystal. We employ a new geometry of interaction to observe simultaneous emission of multi-directional nonlinear Čerenkov radiation with comparable intensities. This opens a way to control the angle of Čerenkov emission by tailoring the nonlinearity of the material, which is otherwise intrinsically defined by dielectric constants of the medium and their dispersion.

基于二维非线性光子晶体的全光开关特性

基于二维非线性光子晶体的全光开关特性