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Nonlinear Optics of Fibre Waveguides
Published in Yu. N. Kulchin, Modern Optics and Photonics of Nano and Microsystems, 2018
It is relatively easy to ensure that the phase‐matching condition is fulfilled in the case of partially degenerate four‐wave mixing, when ω1 = ω2. In this case, a powerful pump wave with a frequency ω1 generates two symmetrically located sidebands with frequencies ω3 and ω4, shifted from the pumping frequency by an amount Ωs: Ωs=ω1-ω3=ω4-ω1, $$ \Omega _{{\text{s}}} = \omega _{1} - \omega _{3} = \omega _{4} - \omega _{1} , $$
Semiconductor Optical Amplifiers
Published in Jerry D. Gibson, The Communications Handbook, 2018
The four-wave mixing causes the generation of new optical frequencies in closely spaced WDM systems. This phenomenon is similar to interharmonic distortion in electronic systems. The presence of multiple wavelengths in the amplifier results in nonlinear amplification. Two wavelengths can generate additional optical frequencies, as shown in Figure 51.16. If these frequencies coincide with existing channels, crosstalk results. This crosstalk can be incoherent [Darcie and Jopson, 1988] or coherent [Blumenthal and Kothari, 1996] in direct detection systems and limitations on the input power can be computed for each case [Darcie and Jopson, 1988; Blumenthal and Kothari, 1996] for a given number of channels,
Coherent Optical Measurements in 1D
Published in Thomas C. Weinacht, Brett J. Pearson, Time-Resolved Spectroscopy, 2018
Thomas C. Weinacht, Brett J. Pearson
We can draw a number of conclusions from our results. Since changes in the probe fluence are small, one needs to make sensitive measurements, and fluctuations in the probe fluence should be avoided as much as possible since they can easily overwhelm any pump-induced changes. Furthermore, the polarization is proportional to the second power of the pump field amplitude (the intensity), but only the first power of the probe field amplitude (square root of the intensity). Thus the signal, which is proportional to the product of the polarization and probe field, is linear in both the pump and probe fluences. Therefore, the fractional change in the probe fluence, SESA/(∫dt|E0probe(z,t)|2), is independent of probe fluence. In other words, increasing the pump-pulse energy can improve the signal, but increasing the probe energy will not. Finally, since the change in fluence is proportional to the product of the probe field times the polarization (which itself is proportional to three field amplitudes), the measured signal involves four fields and a third-order nonlinearity. Nonlinear optical processes of this type are known as “four-wave mixing.” There are many possible variations of the general technique, one of which is CARS (see Section 8.3).
Generation of four-wave mixing in molybdenum ditelluride (MoTe2)-deposited side-polished fibre
Published in Journal of Modern Optics, 2021
H. Ahmad, M. K. A. Zaini, A. A. Kamely, M. Z. Samion, M. F. Ismail, K. S. Lim, A. K. Zamzuri, K. Thambiratnam
Four-wave mixing (FWM) is a nonlinear effect that arises from the third-order nonlinear susceptibility, χ(3) of a nonlinear medium and it occurs when two or more wavelength components propagate and interact in the nonlinear medium to generate new wavelength components [1]. Over the last decade, the generation of FWM has been the focus of substantial research efforts due to their various potential applications in optical switching [2], signal de-multiplexing [3], phase conjugated signal generation [4], wavelength conversion [5], and laser spectroscopy [6]. The FWM effect has been demonstrated in various types of specialty optical fibres exhibiting high nonlinearity coefficients. For example, Wu et al. [7] demonstrated the FWM effect in a 54-metre long photonic crystal fibre (PCF) at the 900 nm wavelength region. Ma et. al [8] reported an FWM-based optical wavelength conversion using a 1-km long highly nonlinear dispersion-shifted fibres (HNL-DSF) as the nonlinear medium. Friis et al. [9] recently demonstrated the generation of FWM among different spatial modes in a 1-km long two-mode fibre. In spite of these demonstrations, the need for a more compact and cost-effective nonlinear device has spurred researchers in finding alternatives to the afore-mentioned specialty optical fibres.
A Comparative Study of Nature-Inspired Metaheuristic Algorithms in Search of Near-to-optimal Golomb Rulers for the FWM Crosstalk Elimination in WDM Systems
Published in Applied Artificial Intelligence, 2019
There exists a rich collection of nonlinear optical effects (Aggarwal, 2001; Babcock 1953; Chraplyvy 1990; Forghieri et al. 1994; Kwong and Yang 1997; Saaid 2010; Singh and Bansal 2013; Sugumaran et al. 2013; Thing, Shum, and Rao 2004) in optical WDM systems, each of which manifests itself in a unique way. Out of these nonlinearities the FWM crosstalk signal is the major dominant noise effects in optical WDM systems employing equal channel spacing (ECS). Four-wave mixing is a third-order nonlinear optical effect in which two or more wavelengths (or frequencies) combine and produce several mixing products. For uniformly spaced WDM channels, the generated FWM product terms fall onto other active channels in the band, causing inter-channel crosstalk. The performance can be substantially improved if FWM crosstalk generation at the channel frequencies is prevented. The efficiency of FWM signals depends on the channel spacing and fiber dispersion. If the frequency separation of any two channels of an optical WDM system is different from that of any other pair of channels, no FWM crosstalk signals will be generated at any of the channel frequencies (Aggarwal, 2001; Babcock 1953; Chraplyvy 1990; Forghieri et al. 1994; Kwong and Yang 1997; Saaid 2010; Singh and Bansal 2013; Sugumaran et al. 2013; Thing, Shum, and Rao 2004).
CMOS compatible on-chip telecom-band to mid-infrared supercontinuum generation in dispersion-engineered reverse strip/slot hybrid Si3N4 waveguide
Published in Journal of Modern Optics, 2018
Zhanqiang Hui, Lingxuan Zhang, Wenfu Zhang
Because of relatively large non-linear coefficient and engineered dispersion of the designed waveguide, it is very potential to use it for SC generation (SCG). Nevertheless, SCG is a complex process and it involves various non-linear effects including SPM, XPM, stimulated Raman scatter, FWM and soliton fission. Most of them can be influenced by the dispersion property of the waveguide. As far as FWM are concerned, four waves with different frequencies interact via third-order nonlinearity under the rules of energy/momentum conservation. Generally speaking, FWM can be divided into two categories: in-band FWM and discrete FWM. In the former, phase-matching is achieved in a continuous band of wavelength beginning from pump wavelength, while in the latter, phase-matching is achieved between discrete wavelength far away from the pump wavelength (29). When two pump waves have the same frequency, the process is called degenerate four wave mixing (DFWM). Traditionally, merely the second-order dispersion is considered and higher order dispersion is neglected. Under this assumption, only when the central wavelength of input pulse is in anomalous dispersion region and near the zero dispersion point (the total phase-mismatch term Δβ is zero), the degenerate in-band FWM processes can efficiently occur (i.e. achieve high gain), and further enhance the spectrum broadening greatly. The conversion efficiency for degenerate in-band FWM is determined by the total phase-mismatch term Δβ, which can be calculated by (28),