- Cross-phase modulation (XPM, or sometimes, CPM) is similar to SPM, but the origin of the spectral broadening of the pulses are the other pulses propagating at the same time in the waveguide; they will mutually influence each other, via the alteration of the intensity-dependent refractive index.
For dip‐coating, ~10 mg SWNTs were first functionalized by bath sonication (2 hr) in 70% nitric acid. These SWNTs were recovered by filtration, rinsed with nanopure water (> 18 MΩ cm) and by sonication (2 hr) in nanopure water, and then re‐dispersed by sonication in 10 mL DMF. After the acid‐treatment the SWNTs disperse readily in DMF producing a black suspension. The opticalfibers were then coated by dipping the section containing the TFBG,
However, despite the existing analogies between optics and acoustics, acoustical resonators in the nonlinear regime have been much less explored than their optical counterparts. Furthermore, pattern formation studies in acoustics are almost lacking. The main reason lies in the weak dispersion of sound in common homogeneous media, which is responsible for the growth of higher harmonics, leading to wave distortion and shock formation. These effects are absent in optics, which is dispersive in nature. However, in some special cases it is possible to avoid the nonlinear distortion and recover the analogies . It is, for example, the case of sound beams propagating in viscous media characterized by a strong absorption (e.g. glycerine), where sound velocity depends on fluid temperature, resulting in an additional nonlinearity mechanism of thermal origin. For the majority of fluids, temperature variations induced by an intense acoustic field result in a decrease of sound velocity, leading to a self-focusing of the beam. In the case of viscous fluids the characteristic length of self-focusing effects is much shorter than the corresponding to the development of shock waves . Also, high frequency components are strongly absorbed in such media, so in practice the use of a quasimonochromatic description for wave propagation is justified.
A study of the nonlinearopticaleffects observed in the propagation of chirped picosecond optical pulses in photonic crystal fibers (PCF) is presented in this work. Also known as microstructured opticalfibers, the PCFs are a kind of opticalfibers with a microstructured cladding formed by a periodic array of air holes in silica. The dis- persion properties of the fiber can be controlled by manipulating its geometry. Special attention is taken to the Four Wave Mixing process (FWM) because of its application in the generation of correlated photon pairs, which is a subject of interest for our work group. The picosecond optical pulses were obtained by stretching the femtosecond op- tical pulses generated by a mode-locked Ti:Saphire laser with a stretcher fabricated in the laboratory, and by means of a conventional telecommunication fiber (SMF-28). The dispersion of the microstructured fibers employed was characterized applying the step-index method which consists in considering a PCF like a step-index fiber. The phase-matching diagrams for the Partially Degenerated Four Wave Mixing process (PDFWM) were estimated for each fiber from its calculated dispersion. The experimen- tally captured optical spectrums were compared with theoretical models. Particularly, the pulse propagation along the fibers was simulated by using an algorithm to solve the Schr¨ odinger nonlinear equation with the fourth-order Runge-Kutta in the interaction picture method. A good agreement between experiments and simulations was found. In some cases, a reduction of the transmitted pulses spectral width was observed. An unexpected result was the the observation of second harmonic generation in the fibers because it is a second order nonlinearoptical effect that should not happen inopticalfibers under normal conditions.
In this chapter we have shown that intracavity second harmonic generation can be used for all-optical image processing. Operating in a linear regime it is possi- ble to transfer an image from the fundamental to the second harmonic frequency. More important, by taking advantage of the system bistability it is possible to magnify the contrast in the fundamental field of any part of the image whose intensity is above a given reference level while simultaneously the second har- monic field displays the contour of the same part of the image. Furthermore, the reference level can be tuned allowing for a complete scan of the image. This sys- tem also displays interesting noise filtering properties. Another advantage of this scheme is that, for being founded in an all-optical process the image processing could be implemented in an optical cavity without need of a computer or having to digitalize the image. This reduces errors due to an imperfect calibration of the individual photodetectors as well as noise introduced by the measurement and discretization process, and subsequent electronic transmission. These effects, which deteriorate the image quality of the image before processing, are, in the all-optical case, absent or postponed to the very end of the information process- ing chain. Moreover, the resolution of this scheme is only limited by diffraction, and not by the number of pixels in the detection plane. And finally, the all- optical processing is intrinsically parallel, while image processing in computers is usually done in a serial way.
The remaining of the paper is organized as follows: In Section 2, we briefly review an expression for the MI gain that contemplates all relevant nonlineareffects. Section 3 is devoted to the description of the modulation instability gain in the pump-power-versus-frequency plane and introduces the geometrical model. Analytical expressions for finding gain maxima and the influence of high-order dispersion are presented in Section 4. Concluding remarks are presented in Section 5.
The directly modulated laser (DML) is usually used in access/metro networks with a bit rate of up to 10 Gb/s. This configuration has several advantages over external modulation, such as low cost, simplicity of design, small size and high output power. However, the frequency shift of the laser (chirp), associated with the DML, is a serious drawback to be approached in systems using this transmitter model. This work proposes a method for optimizing directly modulated systems. This method determines under what conditions the accumulated chromatic dispersion in the link can be counteracted through proper choice of laser chirp and nonlinear phenomena inoptical fiber.
In this work the experimental investigation of photosensitivity in two types of opticalfibers was performed, for special fiber of high photosensitivity and one standard telecommunications fiber. An interferometric method for measurements of optically induced refractive index change in the core of the fiber by intense UV light has been developed. The method allows to carry out measurements of photosensitivity in the initial stage of Bragg grating formation at different regimes of its recording. The results obtained by this technique and also by a common method for measurement of photosensitivity inopticalfibers allow us to conclude, that at least three mechanisms of photosensitivity are involved in the formation of fiber Bragg gratings. At the initial stage of the fiber Bragg recording at low pulse fluence, the dominant mechanism was found to be the so called “Color Center formation”. When a higher pulse fluence is applied and also a higher accumulated fluence “compaction of the glass structure” plays a more important role. We also found, that when exceeding a threshold level of the intensity, a third mechanism takes part significantly in the photosensitivity, such a mechanism which is a formation of micro pores in the glass structure. This third mechanism can explain an observed non-monotonic dependency with pulse fluence in the development of reflectivity of Bragg gratings type IIA, and the additional attenuation of the probe light, and the changes in the mechanical resistance of the optical fiber. In this work we observed for the first time the formation of type IIA fiber Bragg gratings in a standard telecommunication fiber. We also showed, that at the initial stage of the Bragg gratings there are transitory effects of heating of the fiber by light UV that can influence the Bragg grating formation significantly under a high UV fluence per pulse.
Optical waveguides and periodic optical structures have remained in the focus of many researchers for obvious reasons. Waveguide configurations offer effective solutions to implementing many desired processing functions via efficient changes of refractive index due to diffraction-less propagation of high power densities. Also the use of otherwise weak optical nonlinearities is a possible way to establish opticalnonlinear operations such as bistability. When Gibbs  showed bistable switching in a semiconductor and Chemla  successfully studied nonlinearopticaleffectsin semiconductor quantum-well structures, many new exciting developments took place, for example bistability in waveguides proposed, studied and successfully developed by Stegeman . Optical periodic configurations, (first investigated by Rayleigh , then by Bragg brothers  and Brillouin , and examined by Winful  in the nonlinear regime), were used for the first time for optical mixing in integrated optics by Normandin . These then led to various new photonic devices proposed by many other researchers including Cada .
261]. Instead of adding QDs, one can consider to include additional terminals to the system. This was previously discussed as an energy harvester in which the temperature of the third reservoir is able to con- trol the transport between the two additional reservoirs . Further- more, thermoelectrics was deeply studied in DQDs attached to three terminals . Another additional consideration is the case of a QD attached to different type of reservoirs. In Sec. 8.2 we have considered tight-binding leads, but we can still consider graphene leads , which are interesting due to the linear dispersion relation, or superconducting leads, which have been demonstrated theoretically to exhibit intriguing features [208, 264, 265]. The field of spintronics is also interesting to dis- cuss because additional concepts like the spin Seebeck [207, 266, 267] or spin drag effect  can be introduced. For large temperatures, we can not avoid the effect of phonons in the system. The thermoelectric ef- fects of a QD including elecron-phonon contributions was investigated recently . A decrease of the lattice thermal conductivity has been also studied due to the phonon contribution in QD superlattices . In general, experiments in QD are performed at temperatures where the effect of phonons is negligible. Nevertheless, one can also find ex- periments at higher temperatures as shown in Sec. 7.2. The connection between quantum noise and thermoelectric effects would also be a fas- cinating topic that has been less studied. Several works can be found combining QDs and Kondo correlations with noise [241, 270, 271, 272, 273], but the thermoelectric response is still an unexplored area. Finally, the nonlinear transport of QDs with time-dependent fields such as ac currents is now a very attractive topic because of the recent experiments [274, 275, 276] and theoretical calculations [261, 277, 278, 279].
Besides synchronization, in this section we study the influence of coupling on the complexity of neural dynamics  in the sense of its sensitivity to initial conditions. This research was also motivated by recently discovered deter- ministic coherence resonance in unidirectionally coupled R¨ ossler oscillators . It was found that chaotic slave oscillator exhibits more regular (almost periodic) behavior under the influence of another chaotic oscillator in the presence of a small mismatch between their parameters. To check whether or not a similar effect occurs in a neural model, we explore two coupled HR oscillators in a master-slave configuration. Choosing the parameters so that the uncoupled neurons are in a periodic spiking regime, we study how the dynamics of the slave neuron depends on the coupling strength by analyzing bifurcation diagrams of the peak membrane potential and interspike inter- vals (ISI), calculating the normalized standard deviation (NSD) of ISI and the largest Lyapunov exponent.
process; the lower frequency band will be amplified while the upper one attenuated, both of them suffering the same non- reciprocal BPS. For the typical case of small gain, the outputs of the SI will depend only on the shape of the phase shift and not on the gain or attenuation (see the model developed in ). Our developed experimental setup (Fig. 2) is similar to the SI-BOTDA setup used in  except for the fact that a direct current modulation of the master laser is carried out, in this case driven by a PRBS (pseudo random bit sequence) generator. This modulation scheme relies on the non-ideal behavior (chirp) of semiconductor lasers with the applied current. In this case, the applied current modulation is extremely small in comparison with the bias current, leading to an almost phase-coded system with no major amplitude noise. This method is cheaper than conventional phase coding (as no external modulator or driver is required), however it provides a deteriorated resolution over the conventional method, related to the bandwidth limitations of direct current modulation of semiconductor lasers. As in most Brillouin sensor schemes, light from a single Distributed Feedback (DFB) laser diode at 1550 nm is used as a common source for both pump and probe waves. The generator clock rate (1 T ) is in the range of 10.024 GHz, and the code length is M = 2 15 − 1 . The symbol duration is slightly swept
The remaining birefringence of the fiber in a wiring, in virtue of lack of manufacturing process accuracy or environmental changes (pressure, temperature), results in a random process of velocities difference between both polarization modes. Thus, it must be handled in statistical form.
Circular, hollow and C-shaped carbon fibers were also manufactured by melt- spun of isotropic pitch (Shim et al., 2002; Park et al., 2003, 2004). Composite materials were produced by hot-press consolidation of prepregs prepared with this set of non-circular fibers by drum winding. Interlaminar shear strength specimens (ILSS) demonstrated that C-shaped CFRPs perform better as compared with circu- lar baseline composites manufactured maintaining the same equivalent cross section. The C-shape resin contact area was 2.72 times larger that the circular cross section with the same area (Park et al., 2003). In addition, C-shaped carbon fiber com- posites exhibited excellent energy absorption under impact as well as better fiber wettability and thermal conductivity than circular fibers (Park et al., 2003, 2004). Patterned carbon fibers with customized surface contours were produced by Liu and Kumar (2012) and Hunt et al. (2012) using a combination of a bi-component fiber melt spinning and a sulphonation with polyethylene (PE) precursors. By properly designing the flow path and spinneret geometry, carbon fibers with trilobal, flower, and gear-shaped cross-sections in a diameter range from 0.5 to 20 µ m were produced. Although carbon fibers obtained by this method have not reached yet standard me- chanical properties (tensile strength 1.1 GPa and modulus 103 GPa), the customized fiber geometry may extend their application in different fields.
This problem was soon identified like severe in the early experiments on slow & fast light using atomic absorptions, the high loss rendering the output pulse unobservable for large delays. Elegant solutions were proposed to open transparency windows in narrow atomic absorption lines, such as coherent population oscillation  and electromagnetically-induced transparency , this latter demonstrating large delay with much reduced amplitude change. We demonstrate here that the high flexibility of SBS offers the possibility to synthesize a gain spectral profile, so that a signal delay or advance is achieved with an absolute null amplitude change. This can be obtained by the combination of gain and loss spectral profiles with identical depth but different width, resulting in a net zero gain and a differential delaying effect. The possibility to finely tune independently the depth of each spectral profile results in a perfect compensation of gain and loss, like an ideal electromagnetically-induced transparency spectral profile. The scheme can be applied indifferently to generate slow or fast light and this is to our knowledge the first time that continuously tunable optical delays with zero amplitude change are experimentally achieved using slow & fast light.
Until now, the usual way of performing dis- tributed chemical measurements was based upon an intermediator mechanism, such as a chemical-to-mechanical coating, acting as the transducer that allows to detect and measure the presence of certain substance, by means of the strain produced by the coating in the fiber core . This entails the use of a specific fiber coating making the sensor much more expensive and not adaptable to a wide variety of problems. The mechanism here presented as a proof-of-concept does not depend on a particular fiber for each given analyte, being fully adaptable to multiple substances as long as their absorbance spec- trum lie in a region reachable by the pump signal source. When comparing with non- optical means, the advantage in safety is clear when an inflammable or explosive sub- stance is concerned, together with the usual convenience of opticalfibers to avoid possi- ble interference issues, or their capability to operate in harsh environments . The lack of a definitive distributed chemical sensor together with the great demand of such a sensor in ﬁelds nowadays as important as biosensing, industry, oil and gas extraction, etc. settle the need to explore new and inno- vative procedures such as the one presented here.
The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25 kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi- period of modulation, giving place to a complex dynamic behavior, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by using a focused mono-element transducer excited by an amplitude modulated signal.
The subject of solitons propagating through optical lattices is a recent and novel topic research in optics. The steering and routing possibilities oﬀered by this media is a theory yet to be developed and under extensive study. As said before, nondiﬀracting beams are clever options due to their propagation invariant proﬁle, maximizing control of light. The ﬁrst part of the research corresponds to solitons propagating in the so called elliptical photonic lattice (EPL). It presents a pattern induced by a superposition of Mathieu beams, which contains non circular closed trajectories in the form of elliptic rings azimuthally modulated. This last fact was appealing for the investigation, since closed trajectories allows periodic nonstop motion and there was no precedent for such studies on elliptical trajectories. Since the EPL presents a nonuniform potential over a closed trajectory stability cannot be achieved at all times. This work presents how stable propagation is a possibility on the EPL for certain given parameters.