Nonlinear Cross-phase Research Articles

Ultra-compact all-optical plasmonic switch for three telecommunication windows using a nonlinear Kerr material and Fano resonance.

In this study, an all-optical plasmonic switch based on a metal-insulator-metal (MIM) waveguide coupled to two rectangular cavities that are perpendicularly connected to each other through a vertical stub is proposed and analyzed both theoretically and numerically. Rectangular cavities are filled with a nonlinear Kerr material, and the switching operation is achieved by applying a high-intensity pump input into the MIM waveguide to obtain nonlinear cross-phase modulation (XPM) effect. The proposed structure is designed so that it can realize the switching operation at each of the three telecommunication windows of 850, 1310, and 1550nm. Realizing the switching operation at these three wavelength bands is accomplished by the Fano resonance. In fact, the Fano resonance is utilized to create a band-stop area that is crucial for building a suitable OFF state for the switching operation at two of the three telecommunication windows of 1310 and 1550nm. The theoretical and numerical results are obtained using the transmission-line model (TLM) and the finite difference time domain (FDTD) method, respectively, the results of which comply well. The proposed ultra-compact all-optical switch has significant applications in photonic integrated circuits (PICs).

High-speed passive optical networks performance signature in downstream direction based on the engagement of both nonlinear cross-phase modulation (XPM) and cross-gain modulation (XGM) techniques

Abstract This work clarified the engagement of both nonlinear XPM/XGM in conventional band applications with the wide band traveling semiconductor optical amplifiers (WBTWSOAs) for passive optical network applications in downstream directions. The max. Q, total output power versus up/down wavelength conversion by using cascaded XPM with XGM at 10 Gbps are simulated. Besides, the max. Q Factor, conversion efficiency, and total optical power (TOP) variations are clarified in relation to bit rate variations for cascaded CPM&XGM and CPM, XGM stages. Moreover, the enhancement percentage ratio (EPR) in Q factor and TOP are analyzed and demonstrated versus bit rate variations for cascaded CPM&XGM stage over both CPM stage and XGM stage. The study emphasized the network reach can be extended to 80 km with available maximum data rates up to 250 Gb/s with power budget of 28.65 dB based on the cascaded CPM&XGM technique.

Modulated wave and modulation instability gain brought by the cross-phase modulation in birefringent fibers having anti-cubic nonlinearity

In this paper, we investigate the modulated wave and W-shaped profile in birefringent fibers having the anti-cubic nonlinearity terms. We use the traveling wave hypothesis to show out the velocity of the soliton and the constraint relation on the anti-cubic nonlinear terms. We use the Jacobi elliptic function solutions to point out two types of combined solutions. After some assumption on the modulus of the Jacobi elliptic function, we have shown out the combined bright-bright soliton and dark-dark soliton-like solutions. We use the linearizing algorithm to analyze the modulation instability (MI) growth rate. We have shown that the anti-cubic nonlinear terms and cross-phase modulation (XPM) can increase MI bands and the amplitude of the MI growth rate. To corroborate the prediction made on analytical results, we use the numerical investigation to show the propagation of the modulated wave and W-shaped profile in terms of cell index. We exhibited through the numerical results that the modulated wave can conserve high energy during its propagation in birefringent fibers. The obtained results will certainly open new perspectives in optical fibers during the transmission of huge data.

Design and analysis of an all-optical NAND logic gate using a photonic crystal semiconductor optical amplifier based on the Mach–Zehnder interferometer structure

In this study, a high-speed all-optical NAND logic gate (AO-NAND-LG) was designed and numerically simulated. The simulation was performed using the photonic crystal-semiconductor optical amplifier (PC-SOA) structure based on the Mach–Zehnder interferometer and nonlinear cross-phase modulation mechanism. The input optical pulse sequence used in the design was the return-to-zero type. Moreover, two PC-SOAs were utilized in the design of the NAND-LG. The rate and propagation equations were solved using the finite difference method. The optimal mode was achieved for NAND-LG with an energy value of 2.2 fJ for input pulse trains A and B, and an injection current of 1 mA at a bit rate of 80 Gbps. Furthermore, the impacts of the pattern effect, conversion efficiency, extinction ratio, and gain recovery on the design of the AO-NAND-LG were analyzed for the first time in simulations to enhance the performance and efficiency of the PC-SOA. Furthermore, the results demonstrated that the PC-SOA exhibited better logical performance than the ordinary SOA, and it is a suitable candidate for integrated optical circuits because it is much shorter than the SOA.

High-precision passive stabilization of repetition rate for a mode-locked fiber laser based on optical pulse injection

We have proposed and implemented a novel scheme to obtain high-precision repetition rate stabilization for a polarization-maintaining mode-locked fiber laser. The essential technique lies in the periodic injection of electronically modulated optical pulses into a nonlinear amplifying loop mirror within the laser resonator. Thanks to the nonlinear cross-phase modulation effect, the injected pulses referenced to an external clock serves as a stable and precise timing trigger for an effective intensity modulator. Consequently, synchronous mode-locking can be initiated to output ultrafast pulses with a passively stabilized repetition rate. The capture range of the locking system reaches to a record of 1 mm, which enables a long-term stable operation over 15 hours without the need of temperature stabilization and vibration isolation. Meanwhile, the achieved standard deviation is as low as 100 μHz with a 1-s sample time, corresponding to a fluctuation instability of 5.0×10-12. Additionally, the repetition rate stabilization performance based on the passive synchronization has been systematically investigated by varying the average power, central wavelength and pulse duration of the optical injection.

Polarization dynamics of a vector cavity soliton in a birefringent fiber resonator

We investigate theoretically the polarization dynamics of vector cavity solitons in a birefringent fiber resonator exhibiting net anomalous dispersion. The well-known Lugiato-Lefever equation is adopted to capture the intracavity field dynamics when two orthogonal modes are coupled via nonlinear cross-phase modulation. Numerical simulations reveal the coexistence of different nonlinear states, such as cavity solitons (CSs) with a modulation instability pattern, two identical CSs, or a nonidentical pair of CSs depending on the external parameters. We distinguish three different types of coexisting CSs based on their polarization properties. Stokes parameters and Jones vector analysis are employed to extract the spatial energy flux distribution and the complex electric field associated with each polarization mode, respectively. We observe that the group-velocity mismatch affects the individual CS dynamics which has direct consequences of their polarization states. Our detailed findings with the polarization properties of CSs will enrich the understanding of dissipative vector CS dynamics in a passive birefringent fiber resonator.

Observation of extremely efficient terahertz generation from mid-infrared two-color laser filaments

Extreme nonlinear interactions of THz electromagnetic fields with matter are the next frontier in nonlinear optics. However, reaching this frontier in free space is limited by the existing lack of appropriate powerful THz sources. Here, we experimentally demonstrate that two-color filamentation of femtosecond mid-infrared laser pulses at 3.9 μm allows one to generate ultrashort sub-cycle THz pulses with sub-milijoule energy and THz conversion efficiency of 2.36%, resulting in THz field amplitudes above 100 MV cm−1. Our numerical simulations predict that the observed THz yield can be significantly upscaled by further optimizing the experimental setup. Finally, in order to demonstrate the strength of our THz source, we show that the generated THz pulses are powerful enough to induce nonlinear cross-phase modulation in electro-optic crystals. Our work paves the way toward free space extreme nonlinear THz optics using affordable table-top laser systems.

Vectorial dispersive shock waves in optical fibers

Dispersive shock waves are a universal phenomenon encountered in many fields of science, ranging from fluid dynamics, Bose-Einstein condensates and geophysics. It has been established that light behaves as a perfect fluid when propagating in an optical medium exhibiting a weakly self-defocusing nonlinearity. Consequently, this analogy has become attractive for the exploration of dispersive shock wave phenomena. Here, we observe of a novel class of vectorial dispersive shock waves in nonlinear fiber optics. Analogous to blast-waves, identified in inviscid perfect fluids, vectorial dispersive shock waves are triggered by a non-uniform double piston imprinted on a continuous-wave probe via nonlinear cross-phase modulation, produced by an orthogonally-polarized pump pulse. The nonlinear phase potential imparted on the probe results in the formation of an expanding zone of zero intensity surrounded by two repulsive oscillating fronts, which move away from each other with opposite velocities.

Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials

We consider coupled nonlinear Schrodinger equation (CNLSE) of the Gross-Pitaevskii-type, with linear mixing and nonlinear cross-phase modulation. Motivated by the study of matter waves in Bose-Einstein condensates and multicomponent (vectorial) nonlinear optical systems, we investigate the eigenvalue problem of the CNLSE with double external potentials in a self-defocusig Kerr medium. For this system, we obtain different kinds of wave structures induced by two injected beams, of physical relevance in nonlinear optics and Bose-Einstein condensation. Exact solutions are found by the extended unified method. The linear stability of these solutions is analyzed through the formulation of an eigenvalue problem. The spectral problem is constructed by perturbing the frequency of stationary solutions and by linearizing the resulting equations near the stationary (or steady) states. Our study may simulate experimental work on multiple injected laser beams in a medium with Kerr-type nonlinearity.

Modulational instability of nonlinear polarization mode coupling in microresonators

We investigate frequency comb generation in the presence of polarization effects induced by nonlinear mode coupling in microresonator devices. A set of coupled temporal Lugiato-Lefever equations are derived to model the propagation dynamics, and an in-depth study is made of the modulational instability of their multistable homogeneous steady-state solutions. It is shown that new kinds of instabilities can occur for co-propagating fields that interact through nonlinear cross-phase modulation. These instabilities display properties that differ from their scalar counterpart, and are shown to result in the generation of new types of incoherently coupled frequency comb states.

Observation of gain spiking of optical frequency comb in a microcavity.

Optical frequency combs are crucial for both fundamental science and applications that demand a wide frequency range and ultra-high resolution. Recent advances in optical frequency combs based on the nonlinear Kerr effect in microcavities have opened up new opportunities with such compact platforms. Although optical frequency combs have previously been well studied in the steady state, some fundamental perspectives such as nonlinear phase modulation during comb generations are yet explored. Here we demonstrate transient nonlinear dynamics during the formation of optical frequency combs inside a Kerr microcavity. We show that gain spiking forms due to nonlinear phase modulation causing comb lines' self-detuning from nearby cavity resonances, which provides one key mechanism to stabilize optical frequency combs. Moreover, we have observed nonlinear beating by injecting an external probe to examine nonlinear cross-phase modulation between comb lines. These nonlinear dynamics reveal the hidden features of self-stabilization and cross modulation during transient comb generations, which may enable new applications in mode-locking comb and tunable comb generation in microcavities.

All-optical controlling based on nonlinear graphene plasmonic waveguides.

We give the effective refractive index of graphene plasmonic waveguides with both linear and nonlinear effects based on the nonlinear cross-phase modulation, and address the effects of photo-induced refractive index change and absorption change. A non-resonant all-optical nonlinear graphene plasmonic switch with an ultra-compact size of 0.25 μm2 is proposed and numerically analyzed based on the dynamics of the photo-induced absorption change. The results show that the all-optical graphene plasmonic switch can realize a broad bandwidth over 5 THz, a potentially very high switching speed and an extinction ratio of 18.14 dB with the electric amplitude of the pump light of 1.5 × 107 V/m at the signal frequency of 28 THz. Our study could provide a possibility for future all-optical highly integrated optical components.

Observation of spectral self-imaging by nonlinear parabolic cross-phase modulation.

We report an experimental demonstration of spectral self-imaging on a periodic frequency comb induced by a nonlinear all-optical process, i.e., parabolic cross-phase modulation in a highly nonlinear fiber. The comb free spectral range is reconfigured by simply tuning the temporal period of the pump parabolic pulse train. In particular, undistorted FSR divisions by factors of 2 and 3 are successfully performed on a 10 GHz frequency comb, realizing new frequency combs with an FSR of 5 and 3.3 GHz, respectively. The pump power requirement associated to the SSI phenomena is also shown to be significantly relaxed by the use of dark parabolic pulses.

A Nonlinear Microresonator Refractive Index Sensor

We propose an ultrasensitive refractive index (RI) sensor based on the nonlinear index of refraction in a microring resonator coupled to waveguides in an add-drop configuration. The nonreciprocity caused by the difference between the nonlinear self-phase and cross-phase modulation leads to a bifurcation of the optical intensities for two counterpropagating modes. The magnitude of the splitting depends sensitively on the resonance frequency of the resonator, and hence, the effective index of refraction. This nonlinear system is up to two orders of magnitude more sensitive to RI changes than the theoretical sensitivity of a linear microresonator RI sensor. We discuss potential material implementations of the microresonator and the detection limit for these materials.

All-optical nonlinear plasmonic ring resonator switches

In this paper, all-optical nonlinear plasmonic ring resonator (PRR) switches containing 90o sharp and smooth bends have been proposed and numerically analyzed by the finite-difference time-domain method. Kerr nonlinear self-phase modulation (SPM) and cross-phase modulation (XPM) effects on the switching performance of the device have been studied. By applying a high-power lightwave, the signal can switch from one port to the other port due to the ON/OFF resonant states of the ring. We have shown that by utilizing the XPM effect, the output power ratio is improved by a factor of 2.5 and the required switching power is 31% of that of the case with only the SPM effect. Moreover, by utilizing sharp bend square-shaped ring resonators, the switching power is 10.4% lower than that of the smooth ones. The nonlinear PRR switches are suitable for application in photonic-integrated circuits as all-optical switches because of their nanoscale size and low required switching power.

Phase-Controlled Transparent Superluminal Light Propagation in a Doppler-Broadened Four-Level N-Type System

The propagation of a weak probe field in a four-level N-type quantum system in the presence of spontaneously generated coherence (SGC) is theoretically investigated. The optical properties of the system are studied and it is shown that the group velocity of light pulse can be controlled by relative phase of applied fields. By changing the relative phase of applied fields, the group velocity of light pulse changes from transparent subluminal to the transparent superluminal light propagation. Thus, the phase-controlled absorption-free superluminal light propagation is obtained without applying an incoherent laser fields to the system. The propagation of a weak probe light pulse is studied by solving the Maxwell's wave equation on numerical grid in space and time. Moreover, we study the third order self- and cross-Kerr susceptibility of probe field and calculate the nonlinear cross-phase shift for different values of intensity of applied fields. In addition, we take into account the effect of Doppler broadening on the light pulse propagation and it is found that a suitable choice of laser propagation directions allows us to preserve our results even in the presence of Doppler effect. It is demonstrated that by increasing the Doppler width of distribution to the room temperature, the dispersion changes from transparent subluminal to transparent superluminal light propagation which is our major motivation for this work.

Bright solitons in coherently coupled nonlinear Schrödinger equations with alternate signs of nonlinearities

The exact bright one- and two-soliton solutions of a particular type of coherently coupled nonlinear Schrödinger equations, with alternate signs of nonlinearities among the two components, are obtained using the non-standard Hirota's bilinearization method. We find that in contrary to the coherently coupled nonlinear Schrödinger equations with same signs of nonlinearities the present system supports only coherently coupled solitons arising due to an interplay between dispersion and the nonlinear effects, namely, self-phase modulation, cross-phase modulation, and four-wave mixing process, thereby depend on the phases of the two co-propagating fields. The other type of soliton, namely, incoherently coupled solitons which are insensitive to the phases of the co-propagating fields and arise in a similar kind of coherently coupled nonlinear Schrödinger equations but with same signs of nonlinearities are not at all possible in the present system. The present system can support regular solution for the choice of soliton parameters for which mixed coupled nonlinear Schrödinger equations admit only singular solution. Our analysis on the collision dynamics of the bright solitons reveals the important fact that in contrary to the other types of coupled nonlinear Schrödinger systems the bright solitons of the present system can undergo only elastic collision in spite of their multicomponent nature. We also show that regular two-soliton bound states can exist even for the choice for which the same system admits singular one-soliton solution. Another important effect identified regarding the bound solitons is that the breathing effects of these bound solitons can be controlled by tuning the additional soliton parameters resulting due to the multicomponent nature of the system which do not have any significant effects on bright one soliton propagation and also in soliton collision dynamics.

Interaction of short single-component vector solitons

We study interaction of different-polarization single-component vector solitons of the envelope function in anisotropic media within the framework of the system of two coupled third-order nonlinear Schrodinger equations which allow for the third-order linear dispersion, nonlinear dispersion, nonlinear cross-phase modulation, and cross-nonlinear dispersion. The regimes of mutual reflection, passage, and asymptotic approach of the solitons are obtained. It is shown that the character of interaction of such solitons is determined by the initial relationship of their amplitudes and phases. The stationary mutual locations of interacting solitons and their coupled, the so-called breather states are discussed. The roles of the cubic nonlinearity, cubic cross-nonlinearity, and cross-nonlinear dispersion during interaction of solitons are studied.

Single 10-fs deep-ultraviolet pulses generated by broadband four-wave mixing and high-order dispersion compensation

Broadband chirped-pulse four-wave mixing and a pulse compressor consisting of a prism pair and a grating pair are used to generate 10.3-fs deep-ultraviolet pulses. A large proportion of the dispersion up to 1000 fs2 is compensated without inducing third-order dispersion, which together with the smooth spectral and temporal profiles of the pulses makes them suitable for ultrafast spectroscopy. Unexpected spectral narrowing is observed when short input pulses were used for four-wave mixing. This narrowing is explained in terms of other third-order nonlinear phenomena, namely self-phase and cross-phase modulations, which occur simultaneously with four-wave mixing.

A simplified model for nonlinear cross-phase modulation in hybrid optical coherent system

Cross-phase modulation (XPM) has been considered as one of the ultimate obstacles for optical coherent dense wavelength division multiplexing (DWDM) systems. In order to facilitate the XPM analysis, a simplified model was proposed. The model reduced the distributed XPM phenomena to a lumped phase modulation. The XPM phase noise was generated by a linear system which was determined by the DWDM system parameters and whose inputs were undistorted pump channel intensity waveforms. The model limitations induced by the lumped phase modulation and undistorted pumps approximations were intensively discussed and verified. The simplified model showed a good agreement with simulations and experiments for a typical hybrid optical coherent system. Various XPM phenomena were explained by the proposed model.