Effective Nonlinear Coefficient Research Articles

Theoretical Analysis of a 750-nm Bandwidth Hollow-Core Ring Photonic Crystal Fiber With a Graded Structure for Transporting 38 Orbital Angular Momentum Modes

In this paper, a novel hollow-core ring photonic crystal fiber (HR-PCF) is proposed based on As2S3. It supports the transmission of up to 38 orbital angular momentum (OAM) modes. It is composed of a concentric ring cladding of air holes gradually increasing in diameter. In addition, the center also has a large circular air hole. A numerical simulation is accomplished using the finite-element method. Different geometrical parameters of the proposed HR-PCF include the number of air hole rings in the cladding and the background material. These parameters are varied to determine the optimal structure. The properties of the synthesized OAM vector modes are simulated and analyzed systematically and theoretically. Through the simulation of different parameters, we show that the optical fiber structure based on a three-ring cladding and As2S3 material can support 38 OAM modes. This configuration also has better eigenmode characteristics, such as the effective refractive index difference between vector modes with the same topological charge number. This difference can exceed 10−4, preventing these modes from coupling to linear polarization modes. In addition, the vector mode dispersion curve becomes smoother with increasing wavelength, and the confinement loss remains low, ranging from 10−10–10−9dB/m. Moreover, we also discuss effective mode area and nonlinear coefficients and their applications. We also investigated that various effects on the dispersions by details of the proposed HR-PCF, such as air hole spacing between adjacent rings and the diameter of the center circular air hole. This system offers some promising applications for short-distance, high-volume communications due to the increased number of OAM transfer modes.

Investigation of hybrid mode in cylindrical nonlinear waveguide

HE hybrid mode in cylindrical nonlinear waveguide has been investigated by means of cylindrical Maxwell's equations. These equations along with boundary and continuity conditions have been solved numerically and propagation constant has been obtained. Amplitudes of electric field components and power flow in nonlinear core have been plotted. The effect of effective nonlinear coefficient on these quantities has been verified and TE and HE power flow compared to each other.

Broadband Nonlinear Photonics in Few‐Layer MXene Ti3C2Tx (T = F, O, or OH)

AbstractStudies of the nonlinear optical phenomena that describe the light‐matter interactions in 2D crystalline materials have promoted a diverse range of photonic applications. MXene, as a recently developed new 2D material, has attracted considerable attention because of its graphene‐like but highly tunable and tailorable electronic/optical properties. In this study, we systematically characterize the nonlinear optical response of MXene Ti3C2Tx nanosheets over the spectral range of 800 nm to 1800 nm. A large effective nonlinear absorption coefficient (βeff∼‐10−21 m2/V2) due to saturable absorption is observed for all of the testing wavelengths. The contribution of saturable absorption is two orders of magnitude higher than other lossy nonlinear absorption processes, and the amplitude of βeff strongly depends on the light bleaching level. A negative nonlinear refractive index (n2∼‐10−20 m2/W) with value comparable to that of the intensively studied graphene was demonstrated for the first time. These results demonstrate the efficient broadband light signal manipulating capabilities of Ti3C2Tx, which is only one member of the large MXene family. The capability of an efficient broadband optical switch is strongly confirmed using Ti3C2Tx as saturable absorbers for mode‐locking operation at 1066 nm and 1555 nm, respectively. A highly stable femtosecond laser with pulse duration as short as 159 fs in the telecommunication window is readily obtained. Considering the diversity of the MXene family, this study may open a new avenue to advanced photonic devices.

Low-power, ultrafast, and dynamic all-optical tunable plasmon induced transparency in two stub resonators side-coupled with a plasmonic waveguide system

We theoretically and numerically investigate a low-power, ultrafast, and dynamic all-optical tunable plasmon induced transparency (PIT) in two stub resonators side-coupled with a metal-dielectric-metal (MDM) plasmonic waveguide system. The optical Kerr effect is enhanced by the local electromagnetic field of surface plasmon polaritons (SPPs) and the plasmonic waveguide based on graphene-Ag composite material structures with large effective Kerr nonlinear coefficient. An ultrafast response time of the order of 1 ps is reached because of ultrafast carrier relaxation dynamics of graphene. With dynamically tuning the propagation phase of the plasmonic waveguide, π-phase shift of the transmission spectrum in the PIT system is achieved under excitation of a pump light with an intensity as low as 5.8 MW cm−2. The group delay is controlled between 0.14 and 0.67 ps. Moreover, the tunable bandwidth of about 42 nm is obtained. For the indirect coupling between two stub cavities or the phase coupling scheme, the phase shift multiplication effect of the PIT effect is found. All observed schemes are analyzed rigorously through finite-difference time-domain simulations and coupled-mode formalism. This work not only paves the way towards the realization of on-chip integrated nanophotonic devices but also opens the possibility of the construction of ultrahigh-speed information processing chips based on plasmonic circuits.

CMOS compatible on-chip telecom-band to mid-infrared supercontinuum generation in dispersion-engineered reverse strip/slot hybrid Si3N4 waveguide

A silicon nitride (Si3N4)-based reverse strip/slot hybrid waveguide with single vertical silica slot is proposed to acquire extremely low and flat chromatic dispersion profile. This is achieved by design and optimization of the geometrical structural parameters of the reverse hybrid waveguide. The flat dispersion varying between ±10 ps/(nm·km) is obtained over 610 nm bandwidth. Both the effective area and nonlinear coefficient of the waveguide across the entire spectral range of interest are investigated. This led to design of an on-chip supercontinuum (SC) source with −30 dB bandwidth of 2996 nm covering from 1.209 to 4.205 μm. Furthermore, we discuss the output signal spectral and temporal characteristic as a function of the pump power. Our waveguide design offers a CMOS compatible, low-cost/high yield (no photolithography or lift-off processes are necessary) on-chip SC source for near- and mid-infrared nonlinear applications.

Impact of carbon-ion implantation on the nonlinear optical susceptibility of LiNbO3.

In this work we study the impact of ion implantation on the nonlinear optical properties in MgO:LiNbO3 via confocal second-harmonic microscopy. In detail, we spatially characterize the nonlinear susceptibility in carbon-ion implanted lithium niobate planar waveguides for different implantation energies and fluences, as well as the effect of annealing. In a further step, a computational simulation is used to calculate the implantation range of carbon-ions and the corresponding defect density distribution. A comparison between the simulation and the experimental data indicates that the depth profile of the second-order effective nonlinear coefficient is directly connected to the defect density that is induced by the ion irradiation. Furthermore it can be demonstrated that the annealing treatment partially recovers the second-order optical susceptibility.

Bi-directional top-hat D-Scan: single beam accurate characterization of nonlinear waveguides

The characterization of a third-order nonlinear integrated waveguide is reported for the first time by means of a top-hat dispersive-scan (D-Scan) technique, a temporal analog of the top-hat Z-Scan. With a single laser beam, and by carrying two counterdirectional nonlinear transmissions to assess the input and output coupling efficiencies, a novel procedure is described leading to accurate measurement of the TPA figure of merit, the effective two-photon absorption (TPA), and optical Kerr (including the sign) coefficients. The technique is validated in a silicon strip waveguide for which the effective nonlinear coefficients are measured with an accuracy of ±10%.

Cascaded third-harmonic-generation converter based on a single ADP crystal**Project supported by the National Natural Science Foundation of China (Grant Nos. 61178060, 51202129, and 91022034), the Independent Innovation Foundation of Shandong University, China (Grant No. 2011GN056), and the Natural Science Foundation for Distinguished Young Scholar of Shandong Province, China (Grant No. 2012JQ18).

Based on a specially designed optical structure, an efficient cascaded third-harmonic-generation (THG) output of a 1064-nm, pico-seconds pulse laser is successively realized by using an NH4H2PO4 (ADP) crystal that acts as the second-harmonic-generation component and sum-frequency-generation component. The maximum THG output is 1.61 mJ, and the highest conversion efficiency from 1064 nm to 355 nm reaches 35%, which are obviously superior to the results obtained using a KDP crystal under the same circumstance. The further phase-matching analysis indicates that this THG configuration of ADP crystal can be applied to various fundamental wavelengths in a range of 1 μm–1.1 μm. Compared with the previously reported KDP THG converter, which is based on a similar principle, the present ADP THG converter is favorable for large-energy, high-efficiency operation because of the larger effective nonlinear optical coefficient deff and higher laser damage threshold.

Coherent field transients below 15 THz from phase-matched difference frequency generation in 4H-SiC

We experimentally demonstrate tunable, phase-matched difference frequency generation covering the spectral region below 15THz using 4H-SiC as a nonlinear crystal. This material combines a non-centrosymmetric lattice and strong birefringence with broadband transparency at low optical frequencies. Thorough refractive index measurements in the terahertz spectral range allow us to calculate phase-matching conditions for any near-infrared pump laser source. 4H-SiC is also exploited as a detector crystal for electro-optic sampling. The results allow us to estimate the effective second-order nonlinear coefficient.

Angular non-critical phase-matching second-harmonic-generation characteristics of RECOB (RE = Tm, Y, Gd, Sm, Nd and La) crystals.

For the first time, the angular non-critical phase-matching (A-NCPM) second-harmonic-generation (SHG) characteristics of a family of monoclinic oxoborate crystals, RECa4O(BO3)3 (RECOB, RE = Tm, Y, Gd, Sm, Nd and La), were comprehensively investigated. For all of the realizable A-NCPM SHG styles, the feature parameters including PM wavelength, angular, wavelength and temperature acceptance bandwidths, have been derived from the theory and verified by the experiments. We discovered that the closer the ion radius between RE3+ and Ca2+, the smaller the birefringence, and the better the A-NCPM SHG properties. As a result, for the Type-I SHG on Y-axis which has the largest effective nonlinear optical coefficient (deff) among the three realizable A-NCPM styles, NdCOB crystal presents the longest PM wavelength (927 nm), the largest angular acceptance bandwidth (Δθ⋅l1/2 = 84.3 mrad·cm1/2, Δϕ⋅l1/2 = 58.8 mrad·cm1/2), and the broadest wavelength acceptance bandwidth (8.7 nm). This discovery will contribute to the design of new NCPM materials, at the same time the parameter formula will be helpful for the theoretical prediction of NCPM performance.

Nonlinear lateral vibrations and two-to-one resonant responses of a single pile with soil-structure interaction

Nonlinear responses of a single pile with soil-structure interaction under primary resonance and two-to-one internal resonance are investigated. Considering the effect of soil-structure interaction and geometric nonlinearity, the Hamilton principle is applied to derive the equation of motion of the pile subjected to a lateral excitation and axial load. Then, the effective nonlinear coefficient and the frequency-response equation are presented by employing the multimode discretization and the method of multiple scales. Moreover, the nonlinear frequencies are obtained for the analysis of the nonlinear dynamic characteristics of the pile. The equilibrium and dynamic solutions of modulation equations are examined by using the Newton-Raphson, shooting, and continuation methods. The nonlinear responses of the pile are explored by means of the backbone curves and the frequency (force)-response curves. Meanwhile, the effect of the axial load on the nonlinear dynamic characteristics of the pile is discussed. The numerical results show that the nonlinear responses of the pile exhibit some rich and complex nonlinear phenomena.

Bandwidth analysis of non-collinear fourth and fifth harmonic generation in nonlinear uniaxial crystals

The optimal angle bandwidth and wavelength bandwidth of fourth-harmonic generation (FHG) and fifth-harmonic generation (FIFHG) of the 1064[Formula: see text]nm laser are analyzed based on the numerical calculation results of non-collinear type-I and type-II phase matching processes for general nonlinear uniaxial crystals with 1[Formula: see text]cm length. The non-collinear phase matching angles and effective nonlinear coefficients of FHG and FIFHG are calculated. The optimal angle bandwidth and wavelength bandwidth are obtained. The results are beneficial to broadband and efficient non-collinear phase matching FHG and FIFHG experiments and studies.

High stable, high efficient ultraviolet laser with angle-phase-mismatching compensation by adjusting temperature of the nonlinear crystals

We demonstrated an ultraviolet laser at 355 nm using a type-I and a type-II phase-matching nonlinear optical crystal of LiB3O5 (LBO). A method of adjusting temperature for compensation is presented. The crystal temperature is controlled by proportional integral derivative (PID) thermal controllers with a ±0.01 °C resolution. The value of wave vector mismatch, distance of light propagation in nonlinear crystals, effective nonlinear coefficient, theoretical analysis and calculation of conversion efficiency versus temperature are discussed. The experimental results show that the average output power of the 355 nm laser is 1.24 W with the pump power of 13.33 W, when the repetition frequency is 15 kHz. The pulse duration is 9.8 ns, and the beam quality factors are of = 1.8, = 1.7. The conversion efficiency from 808 nm to 355 nm laser is 9.3%, which nearly reaches the optimum value reported so far and is limited by the wavelength mismatch between the pumping and absorbing lasers. The 355 nm output power instability of the laser device is 0.45% in 2 h. A compact no-water-cooling ultraviolet laser with high stability and high efficiency is obtained.

Mid-infrared tunable, narrow-linewidth difference-frequency laser based on orientation-patterned gallium phosphide

We report on the first characterization of orientation-patterned gallium phosphide (OP-GaP) crystals used to generate narrow-linewidth, coherent mid-infrared (MIR) radiation at 5.85 μm by difference frequency generation (DFG) of continuous-wave (cw) Nd:YAG laser at 1064nm and diode-laser at 1301nm. By comparison of the experimental absolute MIR efficiency versus focusing to Gaussian beam DFG theory, we derive an effective nonlinear coefficient for first-order quasi-phase-matched OP-GaP at the generated DFG wavelength. Using d = (2/π)d14 and taking into account Miller’s delta rule, we retrieve an absolute value of the d14 quadratic nonlinear susceptibility coefficient of GaP of d14 = 27.2(3) pm/V at 5.85 μm, in good agreement with the latest absolute measurement of this nonlinear coefficient from non-phase-matched second-harmonic generation (1.32 μm → 0.66 μm) taking into account multiple reflection effects [Shoji et al 1997 J. Opt. Soc. Am. B 14 2268]. The temperature and signal-wave tuning curves are also in qualitative agreement with a recently proposed temperature-dependent Sellmeier equation for OP-GaP when focusing effects are taken into account.

Theoretical study on the characteristics of intracavity frequency doubling of a diode-pumped cesium vapor laser

Characteristics of intracavity frequency doubling of a diode-pump cesium vapor laser (Cs-DPAL) are studied in detail utilizing the rate equations theory. For intracavity frequency doubling of Cs-DPAL, very long nonlinear crystals such as LiB3O5 (LBO) and BiB3O6 (BIBO) with a relatively small effective nonlinear coefficient are required to get the maximum second harmonic (SH) power, and periodically poled crystals such as periodically poled KTiOPO4 (ppKTP) are promising. The reason for this phenomenon is that the simulated emission section is much higher, although it is favorable to reduce the laser threshold. For intracavity frequency doubling of Cs-DPAL in the quasi-two-level limit, the optimal length of nonlinear crystal is slightly shorter than the Cs-DPAL with the assumption of a very rapid transition from the 6P23/2 to 6P21/2 levels, and a qualitative interpretation is given. The SH power by intracavity frequency doubling of Cs-DPAL is also limited by the relatively slower collisional transfer rate from the 6P23/2 to 6P21/2 levels for higher pump power intensity.

Difference frequency generation in the mid-infrared with orientation-patterned gallium phosphide crystals.

We report on the generation of coherent mid-infrared radiation around 5.85 μm by difference frequency generation (DFG) of a continuous-wave Nd:YAG laser at 1064 nm and a diode laser at 1301 nm in an orientation-patterned gallium phosphide (OP-GaP) crystal. We provide the first characterization of the linear, thermo-optic, and nonlinear properties of OP-GaP in a DFG configuration. Moreover, by comparing the experimental efficiency to Gaussian beam DFG theory, we derive an effective nonlinear coefficient d=17(3) pm/V for first-order quasi-phase-matched OP-GaP. The temperature and signal wavelength tuning curves are in qualitative agreement with theoretical modeling.

Dispersion engineering of a As2Se3-based strip/slot hybrid waveguide for mid-infrared broadband wavelength conversion

An arsenic tri-selenide-based strip/slot hybrid waveguide with a single horizontal silica slot is proposed to achieve an extremely low and flat dispersion with three zero dispersion wavelengths. By adjusting the geometrical structural parameters of the hybrid waveguide, dispersion tailoring is fully obtained. The flat group velocity dispersion varying between ±[Formula: see text]0.08 ps2/(m) is obtained over a 1253 nm bandwidth. The parameters of effective area, nonlinear coefficient, and third-order dispersion are all investigated. Moreover, a compact on-chip all-optical wavelength converter is designed based on degenerate four-wave mixing in this waveguide. The dependencies of conversion efficiency and conversion bandwidth on the pump wavelength are discussed. The impact of pump power and signal power on the conversion efficiency is also investigated. The results show that a maximal conversion efficiency of −0.46 dB, and a 3-dB conversion bandwidth of 830 nm in the mid-infrared is achieved.

Phase-matching condition of four-wave mixing in cylindrical nonlinear optical media

Propagation of cylindrical waves in homogeneous and inhomogeneous nonlinear optical media has been investigated theoretically. The coupled-wave equations for a homogeneous and inhomogeneous nonlinear media have been investigated numerically. For homogeneous media, calculations show that phase-matching condition is not fulfilled and efficiency of output wave is very low, but for inhomogeneous media, phase-matching condition is nearly fulfilled and the generated wave amplitude of the four-wave mixing (FWM) is much larger than the homogeneous media. The effect of effective nonlinear optical coefficient [Formula: see text] on the generated wave amplitude for inhomogeneous media has been investigated.

Tellurite based circular photonic crystal fiber with high nonlinearity and low confinement loss

Photonic Crystal Fibers (PCFs) generate great interest in the field of optical fiber technology because of its ability to tailor different optical characteristics such as birefringence, dispersion, mode area, nonlinearity etc. High index non silica based glass fibers have high nonlinearity and low loss in mid-infrared wavelength transmission. Out of this, tellurite glass is a highly suitable fiber material for infrared nonlinear applications because of its high nonlinear coefficient compared to other non-silica glasses. Typically in Photonic Crystal Fibers, air holes are arranged in hexagonal or octagonal structure.In the present investigation, a circular lattice PCF is designed with tellurite core and various optical properties such as confinement loss, effective mode area, dispersion and nonlinear coefficient are analyzed using COMSOL MultiPhysics. The proposed fiber gives very high nonlinearity with a maximum of 12,100W−1km−1 at 0.45μm, ultra high negative dispersion and very low confinement loss for a wide range of wavelengths. High nonlinearity is suitable for super continuum generation. This fiber can also be used as a dispersion compensation fiber.

Simulation and fabrication of micro-structured optical fibers with extruded tubes

Chalcogenide glass is fragile and devitrifiable to be fabricated into micro-structured optical fibers (MOFs). In this article, MOFs which have jacket tubes with inner hexagon are designed and fabricated. The optical properties, such as effective refractive index, electric field intensity, effective mode area, nonlinear coefficient and chromatic dispersion of the fundamental mode are simulated by using full-vectorial finite element method (FVFEM). The effects of structural parameters variation on these optical characteristics of the proposed MOFs are investigated. Furthermore, the As2S3 glass capillaries and jacket tubes are made by extrusion. The MOF with three layers of capillaries is fabricated by the “Stack & Draw” technique. The lowest attenuation of 6.34dB/m of the MOF is measured at the wavelength of 4.61μm using the cut-back method.