Nonlinear Kerr Coefficient Research Articles

Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system

We study the enhanced Kerr-nonlinear coefficient in a three-level A-type atomic system for various coupling-beam powers. The Kerr-nonlinear coefficient behaves very differently in the strong and the weak coupling power regions and changes sign when the coupling or probe frequency detuning changes sign. Comparisons of Kerr-nonlinear coefficients as functions of probe frequency detuning, coupling power, and coupling frequency detuning are presented.

Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system.

We measure the Kerr-nonlinear index of refraction of a three-level Lambda-type atomic system inside an optical ring cavity. The Kerr nonlinearity is modified and greatly enhanced near atomic resonant conditions for both probe and coupling beams. The Kerr nonlinear coefficient n(2) changes sign when the coupling beam frequency detuning switches sign, which can lead to interesting applications in optical devices such as all-optical switches.

The multispan effects of Kerr nonlinearity and amplifier noises on Shannon channel capacity of a dispersion-free nonlinear optical fiber

We present a general treatment of multispan effects on Shannon channel capacity for dispersion-free nonlinear optical fiber transmission. We have derived a closed-form formula that is exact and applicable for arbitrary input signal power and noise power. The nonlinear interference among the accumulated Kerr nonlinear noises and the amplifier noises along each span will be investigated. The dependence of the channel capacity on various operating renditions and system parameters will be studied. We have derived a simple scaling law for the Shannon capacity as given by log, [1+CN/sub s//sup -4/3/N/sub c//sup -2/3//spl gamma//sup -2/3/P/sub W//sup -2/3/] for Nb spans and N/sub c/ channels, where /spl gamma/ is the Kerr nonlinearity coefficient and P/sub W/ is the average noise power density for each amplifier.

Self-induced transparency solitary waves in a doped nonlinear photonic band gap material

We derive the properties of self-induced transparency (SIT) solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort (picosecond) laser pulses which propagate near the band edge of the nonlinear photonic band gap (PBG) material doped with rare-earth atoms such as erbium. Solitary wave formation involves the combined effects of group velocity dispersion (GVD), nonresonant Kerr nonlinearity, and resonant interaction with dopant atoms. We derive the general Maxwell-Bloch equations for a nonlinear PBG system and then demonstrate the existence of elementary solitary wave solutions for frequencies far outside the gap where GVD effects are negligible and for frequencies near the photonic band edge where GVD effects are crucial. We find two distinct new types of propagating SIT solitary wave pulses. Far from Bragg resonance, we recapture the usual McCall-Hahn soliton with hyperbolic secant profile when the nonlinear Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ However, when the host nonresonant Kerr coefficient is nonzero, we obtain the first new type of soliton. In this case, the optical soliton envelope function deviates from the hyperbolic secant profile and pulse propagation requires nontrivial phase modulation (chirping). We derive the dependence of the solitary wave structure on the Kerr coefficient ${\ensuremath{\chi}}^{(3)},$ the resonance impurity atom density, and the detuning of the average laser frequency from the atomic transition. When the laser frequency and the atomic transition frequencies are near the photonic band edge we obtain the second type of soliton. To illustrate the second type of soliton we consider two special cases. In the first case, GVD facilitates the propagation of an unchirped SIT-gap soliton moving at a velocity fixed by the material's parameters. The soliton structure changes dramatically as the laser frequency is tuned through the atomic resonance. In the second illustrative case we set the Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ In this case, the solution is a chirped pulse which arises from the balance between GVD and the resonance interaction with the dopant atoms. Finally, we show that under certain circumstances, these solitary wave solutions may persist even in the presence of (subpicosecond) dipolar dephasing of the dopant atoms and absorption losses of the host PBG material, provided that the system is incoherently pumped. These results may be relevant to the application of PBG materials as optical devices in fiber-optic networks.

Nonlinear optical Kerr coefficients of disordered media

The degenerate and nondegenerate nonlinear Kerr coefficients ${n}_{2}$ of disordered media composed of submicrometer dioxide titania particles embedded in a dye solution were measured using an interferometric technique. The influence of the scattering particles on the value of ${n}_{2}$ are discussed in the light of stimulated emission in these systems. The results obtained can be useful for applications in nonlinear ultrashort pulse propagation in disordered media.

Optical Kerr-like response of dye-doped nematics

When small amounts of suitable dyes are added to a pure nematic liquid crystal, its nonlinear optical response may be enhanced by over two orders of magnitude and even be reversed in sign. This feature may be interesting for applications. We measured the enhancement of the nonlinear optical Kerr coefficient of several dye-nematic mixtures, in order to gain some insight on the molecular mechanism that is supposed to be the basis of the phenomenon.

Near Field and Propagation Constant of Nonlinear Single-mode Optical Fibers: A Simple Numerical Technique

Near field distribrution and propagation constant of nonlinear single-mode optical fibers have been investigated. The shooting method technique is used and implemented into a computer code for the case of step index and graded index fibers. Some reasonable and accurate approximations were made to match the cylindrical geometry. An error function is defined to estimate the discrepancy between the expected boundary values and the computed ones obtained by numerical integration through the use of Runge-Kutta method. More accurate values are then depicted using the secant method. The accuracy and convergence of the results have been considered by performing these methods in a two-path iterative manner. The effects of various guiding parameters and the nonlinear Kerr coefficient on the modal field distribution and on the effective index are studied. Typical b-V curves for both linear and nonlinear fibers are presented. The cutoff value of the normalized frequency is investigated and approximate relations with the Kerr coefficient are deduced for both fiber types.

Wave propagation in nonlinear multilayer structures.

We investigate the adequacy of the Kronig-Penney \ensuremath{\delta}-function model in describing the electromagnetic wave propagation in periodic structures consisting of thin layers of materials with an intensity-dependent dielectric constant. We find that the model captures the most essential features of nonlinear response to radiation. Excellent agreement is found between the results from the \ensuremath{\delta}-function model and the exact solutions of nonlinear wave equations. However, discrepancies do exist below the bottom of transmission bands due to the rigidness of the band edge in the \ensuremath{\delta}-function model. Consequently, gap solitons cannot form in the \ensuremath{\delta}-function model when the nonlinear Kerr coefficient is positive. \textcopyright{} 1996 The American Physical Society.

Simple method for laser chirp diagnosis: application to the measurement of the YLF nonlinear Kerr coefficient

We present a simple method for diagnosis, visualizing and measuring of the frequency chirp of a laser pulse. This method relies on the use of a streak-camera to temporally resolve a spatial interference pattern produced by the pulse. Analysis of the streak-camera data gives directly the functional form of the chirp including its sign and its higher order nonlinear components which can provide information on the physical process causing it, namely the self-phase modulation that the pulse undergoes in the laser medium in the course of its amplification. By studying the temporal profile of the laser coherence we have been able to measure the gain bandwidth and the third-order nonlinear coefficient for the YLF:Nd +3 laser medium: χ (3) = (1.6±0.6) × 10 −19 m 2W −1.

Second-harmonic generation at periodic second-order susceptibility gratings with self-phase and cross-phase modulation

Quasi-phase-matched second-harmonic generation at periodic quadratic susceptibility gratings with self-phase and cross-phase modulation owing to Kerr nonlinearities is investigated. A model of interaction of monochromatic plane travelling waves is considered. The solution assumes a nondepleted pump and results for a numerical computation of second-harmonic conversion efficiency for a highly efficient process are presented. It is shown that for high spatial-frequency gratings the efficiency of second-harmonic generation depends on the reduced detuning δ and the Kerr-nonlinearity coefficient κ only. In some cases, if the signs of δ and κ are opposite, the Kerr nonlinearity can enhance the second-harmonic conversion efficiency due to the compensation of the phase mismatch attained in the below-half-conversion stage by the reversed phase mismatch in the above-half-conversion stage of the process. The computed maximum conversion efficiencies for various values of δ and κ are plotted in a contour map on the δ-κ plane.

Wave propagation in periodic nonlinear dielectric superlattices

We investigate wave propagation in a superlattice consistent of dielectric material with a nonlinear Kerr coefficient. We find gaps in the propagating properties of the medium that depend critically on the injected wave power. This property can be used for transmission of information.

Z-scan technique using top-hat beams

Top-hat instead of Gaussian beams are used in Z-scan experiments to measure nonlinear optical Kerr coefficients of materials. An empirical expression is obtained which allows direct calculation of the Kerr coefficient from measured peak–valley transmittance differences. Predictions of the model are compared with Z-scan measurement on CS2. Using top-hat beams, the sensitivity of Z-scan measurements is a factor of 2.5 greater than for Gaussian beams.

Measurement of fiber nonlinear Kerr coefficient by four-wave mixing

We demonstrate a Kerr coefficient measurement of dispersion-shifted fibers based on the nonlinear mixing process between two continuous pump waves and on the power measurements of the created frequencies. A numerical model simulates the experimental conditions and is exploited to determine the Kerr coefficient. Unavoidable polarization effects are precisely taken into account both experimentally and numerically by launching the pump waves on the principal polarization states. This allows us to obtain reproducible measured values and a better than 5% resolution. >

Effect of thermal spin-wave fluctuations on optical guided waves propagating in a magnetic film.

We examine the effect of light-scattering fluctuations arising from thermal excitation of spin waves on optical guided waves propagating in a magnetic film. These thermal spin waves induce mode conversion in optical guided waves that manifests as optical noise during Faraday rotation. The equipartition theorem links this optical noise to that encountered in phase conjugation in an optical Kerr medium. Theory asserts that one channel for third-order optical nonlinearities of optical guided waves in a magnetic film is mediated by these thermal spin waves, and an expression for their contribution to this optical nonlinear Kerr coefficient is derived.

Self-focusing in new kerr media: Large thermal nonlinearity in metallotetraphenylporphins

A large optical nonlinearity of thermal origin has been observed in acetone solutions of a series of tetraphenylporphin, TPPH2, MnTPP(CH3CO2−), FeTTPCI-, CoTPP, NiTPP, and CuTPP. The nonlinear Kerr coefficient is sensitively dependent on the nature of central metals in the compounds. The Mn compound exhibits the largest coefficient, ≅6 × 10−5 esu, for 514 nm laser wavelength. The use of prophins offers increased flexibility in the preparation of different Kerr media.

Demonstration of the optical Kerr effect in an all-fibre Mach-Zehnder interferometer at laser diode powers

The nonlinear Kerr coefficient of a germania core optical fibre has been determined by measuring the phase shift induced by a laser diode pump on a HeNe probe in an all-fibre Mach-Zehnder interferometer. It has been demonstrated that this device may be operated as an optical tap. A predicted power-length product for 100% modulation of 11 Wm has been obtained.