Kerr nonlinearity

X in most strong Kerr, nonlinear refraction, etc. media. For use in extremely high bandwidth applications, such as totally optical processing, predominantly electronic responding media are needed (M). 

Keywords Kerr nonlinearity, nonlinear optics, nonlinear periodic structures, optical... 

Many interesting phenomena can arise in nonlinear periodic structures that possess the Kerr nonlinearity. For analytic description of such effects, the slowly varying amplitude (or envelope) approximation is usually applied. Alternatively, in order to avoid any approximation, we can use various numerical methods that solve Maxwell s equations or the wave equation directly. Examples of these rigorous methods that were applied to the modelling of nonlinear periodical structures are the finite-difference time-domain method, transmission-line modelling and the finite-element frequency-domain method." ... 

Key words Kerr nonlinearity, planar waveguides, optical pulses, numerical modeling, nonlinear modes, waveguide junctions. 

A common way to treat the problem of a picosecond pulse propagation in regular dielectric waveguide with Kerr nonlinearity was to solve the nonlinear Schrodinger equation (NLSE) for the slowly varying temporal amplitude of electrical field ... 

One of the best known and most intensively studied optical models is an oscillator with Kerr nonlinearity. Mutually coupled Kerr oscillators can be successfully used for a study of couplers the systems consist of a pair of coupled Kerr fibers. The first two-mode Kerr coupler was proposed by Jensen [136] and investigated in depth [136,137]. Kerr couplers affected by quantization can... 

In this section we consider a model of interactions between the Kerr oscillators applied by J. Fiurasek et al. [139] and Perinova and Karska [140]. Each Kerr oscillator is externally pumped and damped. If the Kerr nonlinearity is turned off, the system is linear. This enables us to perform a simple comparison of the linear and nonlinear dynamics of the system, and we have found a specific nonlinear version of linear filtering. We study numerically the possibility of synchronization of chaotic signals generated by the Kerr oscillators by employing different feedback methods. 

Let us consider a system of two classical oscillators with Kerr nonlinearity. Both oscillators interact with each other by way of a linear coupling moreover, they are pumped by external time-dependent forces. The Hamiltonian for the system is given by... 

The single Kerr anharmonic oscillator has one more interesting feature. It is obvious that for Cj = 0 and y- = 0, the Kerr oscillator becomes a simple linear oscillator that in the case of a resonance 00, = (Do manifests a primitive instability in the phase space the phase point draws an expanding spiral. On adding the Kerr nonlinearity, the linear unstable system becomes highly chaotic. For example, putting A t = 200, (D (Dq 1, i = 0.1 and yj = 0, the spectrum of Lyapunov exponents for the first oscillator is 0.20,0, —0.20 1. However, the system does not remain chaotic if we add a small damping. For example, if yj = 0.05, then the spectrum of Lyapunov exponents has the form 0.00, 0.03, 0.12 1, which indicates a limit cycle. 

These Kerr oscillators, with j = 2 = 0, are linear subsystems that in the case of resonance (oa = (Oi = (02) exhibit a common instability—the solutions of Eqs. (43) and (44) for t > 00 grow linearly without bound. This resonance instability of our linear subsystems vanishes for C / 0 and 2 / 0. The subsystems become stable but only for small values of ei and 2. For example, beats generated by the first oscillator for C = 10 9, A = 200, and fi>o = i = 1 are illustrated in Fig. 29a, and the appearing beats originate from the Kerr nonlinearity. 

More precisely the slight negative GVD in the cold cavity compensates with the Kerr nonlinearity to sustain an optical soliton. 

In conclusion, we have presented a reliable method for selective production and detection of high-order atomic polarization moments based on the nonlinear magneto-optical effects with frequency modulated light. This method can be used for the selective control of higher order atomic coherences in multilevel systems exploiting large Kerr nonlinearities for the construction of all-optical quantum phase gates. 

Approximate versions of the translational EPR state, wherein the -function correlations are replaced by finite-width (Gaussian) distributions, have been shown to characterize the quadratures of the two optical-field outputs of parametric down-conversion, or of a fiber interferometer with Kerr nonlinearity. Such states allow for various schemes of continuous-variable quantum information processing such as quantum teleportation [Braunstein 1998 (b) Furu-sawa 1998] or quantum cryptography [Silberhorn 2002], A similar state has also been predicted and realized using collective spins of large atomic samples [Polzik 1999 Julsgaard 2001]. It has been shown that if suitable interaction schemes can be realized, continuous-variable quantum states of the original EPR type could even serve for quantum computation. 

The study of self-phase modulation of one wave may not neglect the statistical properties of the quantum phase. The study of statistical properties of the quantum phase in the situation of self-phase modulation of one wave has a long tradition. To the investigation of the propagation in the Kerr medium including the Kerr nonlinear devices, the nonlinear oscillator model has been applied (see Ref. 210 and references cited therein). The work has been reviewed laying the emphasis on properties of the nonlinear phase shift such as a generation of superposition states. 

Another alternative for the generation of ultrafast pulses is the passive mode locking by fast semiconductor saturable absorbers in front of chirped mirrors (Fig. 6.35) in combination with Kerr lens mode locking [694]. The recovery time of the saturable absorber must be generally faster then the laser pulse width. This is provided by KLM, which may be regarded as artificial saturable absorber that is as fast as the Kerr nonlinearity following the laser intensity. Since the recovery time in a semi-... 

Sinee the linear and Kerr nonlinear dispersions in such EIT medium change dramatically as fimctions of various parameters, such as the coupling beam Rabi frequency and its frequency detuning, the probe beam frequency detuning, and the cavity frequency detuning, the WLC condition can be easily satisfied by choosing the appropriate and different sets of parameters. To... 

Wang H, Goorskey D, and Xiao M. Enhanced Kerr nonlinearity via atomie eoherenee in a three-level atomic system. Physical Review Letters 2001Aug 13 87(7) 073601(4). 

Double-dark resonances have been demonstrated in a variety of four-level systems [39-50], where the probe absorption spectrum is characterized by two HIT windows, separated by a sharp absorption peak [51]. The appearance of the central narrow structure is due to the coherent interaction between the two dark states [39], which greatly enhances the Kerr nonlinear susceptibility [55]. In this section, we present our atom localization schemes based on double-dark resonance effects in two different four-level atomic systems. 

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