Negative Nonlinear Coefficient Research Articles

Piezoelectric metamaterial with digitally controlled nonlinear shunt circuit for broadband wave attenuation

This Letter reports a nonlinear piezoelectric metamaterial with pure digital inductance shunt circuits for adjustable broadband wave attenuation. The proposed nonlinear piezoelectric metamaterial is comprised of arrayed piezoelectric unit-cells with individually connected digital nonlinear inductive shunt circuits. Taking advantage of the programmed nonlinear behavior of the shunt circuits, we can expand the frequency region of wave attenuation at an arbitrary frequency. This broadband wave attenuation mechanism is facilitated by modifying the poles, zeros, and nonlinearity in the control algorithm, whereas the mechanical and electrical configurations are not altered. Our experimental analysis confirmed the adjustability and broadband features of the proposed system. The results demonstrated 3.84 times enlargement of the bandwidth under negative nonlinear coefficient K of −3 × 10−12. This piezoelectric metamaterial shows promising potential for active control in broadband wave attenuation.

Urbanization and water consumption at national- and subnational-scale: The roles of structural changes in economy, population, and resources

This work is aimed to explore the impact of structural changes in economy (primary industry/total GDP), population (population aged 15-64/total population), and resource (groundwater resource/total water) on the correlation between urbanization and water consumption at national and subnational level. To this end, a fixed effect panel regression approach and three panel threshold regression approaches are developed using updated data of China's 31 provinces. The results show that there is a threshold between urbanization changes and water consumption, which means that there is a nonlinear relationship between changes in social structure and water consumption. There is a significant negative non-linear correlation between urbanization changes and water consumption. From a national scale, when the economic structure and resource structure change, the value of the negative non-linear coefficient between urbanization change and water consumption becomes larger. When the population structure changes, the negative non-linear correlation between urbanization changes and water consumption shows a "U"-shaped change. The threshold effect and structural mutation points in different regions are heterogeneous. There are differences in coefficient change trends for the three threshold variables. Some policy implications are put forward related to our empirical results.

Photon-conserving generalized nonlinear Schrödinger equation for frequency-dependent nonlinearities

Pulse propagation in nonlinear waveguides is most frequently modeled by resorting to the generalized nonlinear Schrödinger equation (GNLSE). In recent times, exciting new materials with peculiar nonlinear properties, such as negative nonlinear coefficients and a zero-nonlinearity wavelength, have been demonstrated. Unfortunately, the GNLSE may lead to unphysical results in these cases since, in general, it does not preserve the number of photons and, in the presence of a negative nonlinearity, predicts a blue shift due to Raman scattering. In this paper, we put forth a modified GNLSE that can be used to model the propagation in media with an arbitrary, even negative, nonlinear coefficient. This novel photon-conserving GNLSE (pcGNLSE) ensures preservation of the photon number and can be solved by the same tried and trusted numerical algorithms used for the standard GNLSE. Finally, we compare results for soliton dynamics in fibers with different nonlinear coefficients obtained with the pcGNLSE and the GNLSE.

Jackiw-Rebbi states in interfaced binary waveguide arrays with Kerr nonlinearity

We systematically investigate the optical analogs of quantum relativistic Jackiw-Rebbi states in binary waveguide arrays in the presence of Kerr nonlinearity with both self-focusing and self-defocusing cases. The localized profiles of these nonlinear Jackiw-Rebbi states can be calculated exactly by using the shooting method. We show that these nonlinear Jackiw-Rebbi states have a very interesting feature which is totally different from all other well-known nonlinear localized structures, including optical solitons. Namely, the profiles of nonlinear JR states with higher peak amplitudes can totally envelope the ones with lower peak amplitudes. We demonstrate that media with the positive nonlinear coefficient can support stable Jackiw-Rebbi states for a wide range of peak amplitudes, whereas media with the negative nonlinear coefficient are only able to support Jackiw-Rebbi states with low peak amplitudes. A general rule for the detuning of nonlinear Jackiw-Rebbi states in binary waveguide arrays is found.

Modulation Instabilities in Asymmetric Fiber Coupler

We study modulation instability (MI) in an asymmetric two-core fiber coupler. The analysis is performed for the MI gain and MI bandwidth. Effects of the parameters, input power and nonlinear coefficients on the MI are investigated. The results show that input power and nonlinear coefficients of two cores influence the MI gain and MI bandwidth. When nonlinear coefficients of two cores are both negative, better modulation stability can be obtained than other situations. In particular, if the negative nonlinear coefficients are equal, the modulation instabilities will not appear.

Modulation instabilities in asymmetric nonlinear fiber coupler

We have investigated the modulation instability (MI) in a nonlinear optical coupler using a generalized model describing the pulse propagation of two-core fiber. In particular, we discuss some influence of the MI of asymmetric nonlinear fiber coupler. The results show that input power and nonlinear coefficients of two cores influence the maximum value of the MI gain and MI bandwidth. When nonlinear coefficients of two cores are both negative, better modulation stability can be obtained than other situations. In particular, if the negative nonlinear coefficients are equal, the modulation instabilities will not appear.

Simulations of an all-optical flip-flop with a reset pulse frequency exceeding operating frequency

An all-optical flip-flop based on a nonlinear multi-section DFB semiconductor laser structure is proposed. Holding beam is not required for device's operation. A section of the DFB structure is detuned to prevent lasing in the “OFF” state, and it is accompanied with a negative nonlinear coefficient that is due to partial absorption of photons at Urbach tail. At a high light intensity in the structure the nonlinear coefficient reduces the detuning, and the device is in lasing state; “ON” state. The device is reset by an optical pulse at a shorter wavelength through cross gain modulation. The reset pulse is absorbed in a middle section in the device before reaching the detuned nonlinear section. The switching times between the states are in nanoseconds time scale.

Numerical Simulation of an All Optical Flip-Flop Based on a Nonlinear Distributed Bragg Reflector Laser Structure

A new design for an all optical flip flop is introduced. It is based on a nonlinear Distributed Bragg Reflector (DBR) semiconductor laser structure. The device does not require a holding beam. An optical gain medium confined between 2 Bragg reflectors forms the device. One of the Bragg reflectors is detuned from the other by making its average refractive index slightly higher, and it has a negative nonlinear coefficient that is due to direct absorption at Urbach tail. At low light intensity in the structure, the detuned Bragg reflector does not provide optical feedback to start a laser mode. An optical pulse injected to the structure reduces the detuning of the nonlinear Bragg reflector and a laser mode builds up. The device is reset by detuning the second Bragg reflector optically by an optical pulse that generates electron-hole pairs by direct absorption. A mathematical model of the device is introduced. The model is solved numerically in time domain using a general purpose graphics processing unit (GPGPU) to increase accuracy and to reduce the computation time. The switching dynamics of the device are in nanosecond time scale. The device could be used for all optical data packet switching/routing.

Simulations of a Novel All-Optical Flip-Flop Based on a Nonlinear DFB Laser Cavity Using GPGPU Computing

A new all-optical flip-flop based on a nonlinear Distributed feedback (DFB) structure is proposed. The device does not require a holding beam. A nonlinear part of the grating is detuned from the remaining part of the grating and has negative nonlinear coefficient. Optical gain is provided by an injected electrical current into an active layer. In the OFF state, due to the detuned section, no laser light is generated in the device. An injected optical pulse reduces the detuning of the nonlinear section, and the optical feedback provided by the DFB structure generates a laser light in the structure that sustains the change in the detuned section. The device is switched “OFF” by detuning another section of the grating by a Reset pulse. The Reset pulse reduces the refractive index of that section by the generation of electron-hole pairs. The Reset pulse wavelength is adjusted such that the optical gain provided by the active layer at that wavelength is zero. The Reset pulse is prevented from reaching the nonlinear detuned section by introducing an optical absorber in the laser cavity to attenuate the pulse. The device is simulated in time domain using General Purpose Graphics Processing Unit (GPGPU) computing. Set-Reset operations are in nanosecond time scale.

Modulation instabilities in two-core fiber coupler

We have investigated the modulation instability (MI) in a nonlinear optical coupler using a generalized model describing the pulse propagation of two-core fiber. In particular, we discuss some influence of the maximum MI gain and MI bandwidth of two-core fiber coupler. The results show that the anomalous dispersion influences the MI bandwidth, but not the maximum value of the MI gain, and the maximum value of the MI gain, as well as its bandwidth, has been also affected by input power, the ratio of power of two cores and positive nonlinear coefficient. In particular, the MI cannot be produced with negative nonlinear coefficient. In addition, when powers of two cores are not equal, coupling coefficient influences the MI, and when they are equal, the MI will not be affected.

Theoretical investigation of spatial optical solitons in nematic liquid crystals with negative dielectric anisotropy

In this paper, the nonlocal nonlinear medium, nematic liquid crystals (NLCs) with negative dielectric anisotropy, are studied. Theoretical research shows that NLCs with negative dielectric anisotropic have a negative nonlinear coefficient. The analytical expressions for characteristic length of the nonlocal response function and for nonlinear coefficient are given. Secondly, the solutions for spatial optical solitons in NLCs with negative dielectric anisotropic are obtained by numerical computation. Finally, the influences of beam power and bias voltage on the propagation of the beam in NLCs with negative dielectric anisotropic are investigated. The result shows that the critical power of the nonlocal spatial solitons in NLCs with negative dielectric anisotropic varies with bias voltage.

Theoretical modeling of an improved all-optical flip flop based on a nonlinear semiconductor distributed feedback laser structure

A new, improved design of an all-optical flip flop is proposed. The waveguiding layer of the device consists of a phase-shifted nonlinear grating. The grating layers of a high refractive index have a negative nonlinear coefficient. A phase-shift section exists at the middle of the waveguiding layer. The optical gain is provided by current injection into an active layer. Nonlinearity in the waveguiding layer is achieved by direct absorption at the edge of the absorption band (Urbach tail). In the "OFF" state, the waveguiding layer forms a weak grating with an optical feedback below the laser threshold. In the "ON" state, the device functions as a distributed feedback (DFB) laser due to an induced strong grating in the nonlinear waveguiding layer. The improvements of the device performance by reducing the set pulse energy and accelerating the switch-off process are discussed. Field simulations in the time domain were performed.

Zero-potential condition in thermally poled silica samples: evidence of a negative electric field outside the depletion layer

The second-harmonic signal generated within poled silica disks is monitored in real time as the sample is etched with hydrofluoric acid. An oscillating signal is observed when the cathodic side of the sample is etched. This result is in good agreement with the condition of zero potential difference between the two surfaces of the disk. As a result, a negative nonlinear coefficient is induced outside the alkali ion depleted layer.

Mirrorless optical bistability in a semiconductor-doped-glass plate as a result of oblique incidence

A procedure to obtain optical bistability in a third-order nonlinear film (or parallel plate) of low refractive index without any external mirrors is investigated both theoretically and experimentally. If an s-polarized light is incident obliquely at a large angle of incidence on the film, the generation of optical bistability can be expected because of the resulting increase in the reflectivity at the surfaces. Arigorous analysis of the stationary transmission characteristics of the nonlinear film is done for both positive and negative nonlinear coefficients with a plane-wave model. In the experimental demonstration, a CdS(x)Se(1-x)doped glass (Hoya Y-52) plate and a cw Ar(+) laser are used as the nonlinear material and the light source, respectively. It is shown that three operations of optical bistability, optical limiting, and differential gain can be easily obtained through adjustment of the angle of incidence as an initial detuning. The measured nonlinearity is thermal, and the magnitude and sign of the nonlinear refractive index are determined.

Bistable bright solitons in dispersive media with a linear and quadratic intensity-dependent refraction index change

An exact analytical bistable (or two-state) soliton solution of the generalized nonlinear Schrödinger equation has been found for a medium with a linear and quadratic intensity depending refraction index change of the form δ n = n 2| A| 2+ n 4| A| 4. It is shown that for negative nonlinear coefficients n 2 n 4<0 and k'' L n 2<0 two possible soliton states exist, which describe undistorted pulses with the same duration but different peak power. It is proven that both solution branches are stable against small fluctuations.

TE waves in a symmetric dielectric slab waveguide with a Kerr-like nonlinear permittivity

The propagation characteristics of TE waves guided by a film with a Kerr-like nonlinear permittivity are investigated theoretically. The dispersion equations for positive and negative nonlinear coefficients are derived by introducing the maximum field amplitude as a parameter for the nonlinearity. Typical numerical results for dispersion characteristics are shown. For a hollow waveguide with positive nonlinear coefficient, the threshold power flow is determined numericlly from the viewpoint of applications to optical power clipping. It is found that the threshold power flow is proportional to the square root of the unperturbed permittivity difference between the film, and cladding.