Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

Analysis of the four wave mixing effect (FWM) in a dispersion decreasing fiber (DDF) for a WDM system

We did a numerical investigation of the propagation of short light pulses in the region of 1.55 mu m and the conversion efficiency (CE) for the four wave mixing generation (FWM) of ordinary and dispersion decreasing fibers for use in wavelength division multiplexing (WDM) systems, Our simulations studies three different profiles, linear, hyperbolic. and constant, One conclude that for all the profiles there is decrease of the conversion efficiency with the increase in the channel separation. The hyperbolic profile present a higher efficiency of around 1000 above in magnitude compared with the others profiles at 0.2 nm of channel separation. We calculate the conversion efficiency versus the fiber length for the three profiles. The conversion efficiency for the hyperbolic profile is higher when compared to the constant and linear profiles. The other interesting point of the hyperbolic profile is that the increase of the CE in the beginning of the fiber does not show my oscillation in the CE value (log eta), which was observed for the constant and linear profiles. For all the profiles there is an increase of the conversion efficiency with the increase of the pump power. The compression factor C-i for the generated FWM signal at omega(3) was measured along the DDF's and the constant profile fibers. One can conclude that with the use of decreasing dispersion profile (DDF) fibers one can have a control of the (CE) conversion efficiency and the compression factor of the four wave mixing (FWM) generation in WDM systems. (c) 2005 Elsevier B.V. All rights reserved.

Diffractive optics-based heterodyne-detected four-wave mixing signals of protein motion: From “protein quakes” to ligand escape for myoglobin

Ligand transport through myoglobin (Mb) has been observed by using optically heterodyne-detected transient grating spectroscopy. Experimental implementation using diffractive optics has provided unprecedented sensitivity for the study of protein motions by enabling the passive phase locking of the four beams that constitute the experiment, and an unambiguous separation of the Real and Imaginary parts of the signal. Ligand photodissociation of carboxymyoglobin (MbCO) induces a sequence of events involving the relaxation of the protein structure to accommodate ligand escape. These motions show up in the Real part of the signal. The ligand (CO) transport process involves an initial, small amplitude, change in volume, reflecting the transit time of the ligand through the protein, followed by a significantly larger volume change with ligand escape to the surrounding water. The latter process is well described by a single exponential process of 725 ± 15 ns at room temperature. The overall dynamics provide a distinctive signature that can be understood in the context of segmental protein fluctuations that aid ligand escape via a few specific cavities, and they suggest the existence of discrete escape pathways.

Phase discrimination and simultaneous frequency conversion of the orthogonal components of an optical signal by four-wave mixing in an SOA

Simultaneous conversion of the two orthogonal phase components of an optical input to different output frequencies has been demonstrated by simulation and experiment. A single stage of four-wave mixing between the input signal and four pumps derived from a frequency comb was employed. The nonlinear device was a semiconductor optical amplifier, which provided overall signal gain and sufficient contrast for phase sensitive signal processing. The decomposition of a quadrature phase-shift keyed signal into a pair of binary phase-shift keyed outputs at different frequencies was also demonstrated by simulation.

Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems

Limitations in the performance of coherent transmission systems employing digital back-propagation due to four-wave mixing impairments are reported for the first time. A significant performance constraint is identified, originating from four-wave mixing between signals and amplified spontaneous emission noise which induces a linear increase in the standard deviation of the received field with signal power, and linear dependence on transmission distance.

Experimental verification of four wave mixing efficiency characteristics in a few mode fibre

We introduce two techniques to measure the efficiency of inter mode FWM with respect to intra mode FWM. The first technique allows an estimation of the additional FWM penalty for any given system; the second isolates the contribution of each mode. Measurements are compared to an analytical model showing the FWM signal increases by ∼2dB with inter mode phase matching.

Inverse four-wave mixing and self-parametric amplification in optical fibre

An important group of nonlinear processes in optical fibre involve the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and those arising from self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect—self-parametric amplification—which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. Self-parametric amplification and the observed stable nonlinear spectral propagation with a random temporal waveform can find applications in optical communications and high-power fibre lasers with nonlinear intracavity dynamics.

Impact of inter-modal four-wave mixing on the performance of mode- and wavelength-division-multiplexing systems

In this paper, we investigate the impact of inter-modal four-wave mixing on mode- and wavelength-division-multiplexing systems. A set of coupled nonlinear Schrödinger equations, including linear mode coupling, is derived allowing to isolate the inter-modal four-wave mixing terms. The efficiency of inter-modal four-wave mixing between degenerate LP modes is found to be significantly higher than the intra-modal four-wave mixing efficiency. However, it is shown that the inter-modal four-wave mixing efficiency between degenerate modes is significantly reduced by the linear mode coupling.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.