Modulated traveling wave

For 7 > 6.1 we are unable to compute stable TWl modes. Rather, we find modulated traveling waves consisting of a single hot spot which alternately speeds up and slows down and its intensity alternately increases and decreases as it rotates around the cylinder, thus describing a modulated traveling wave for a 1-headed spin (MTWl). A space time plot of such a mode is shown in Figure 6 for i = 6.1. 

The infinite flower in Figure 5 that separates the MRW states with inward and outward petals is an example from a class of states known as modulated traveling waves (MTW). These are states which are periodic in a uniformly translating reference frame. Strictly speaking, they occur only in spatially infinite or spatially periodic systems [39]. However, these states behave indis-tinguishably from those which would be found in infinite medium, so long a the spiral center is far from any boundary. The MTW solutions can travel in any direction the direction being determined by initial conditions. 

Fig. 8. Bifurcation diagram for the one-parameter cut shown in Figure 5. The radius ratio, r2/ri, for MRW states is plotted as a function of the parameter a. Also shown as a horizontal line is the branch of RW states (for which r2 = 0) solid indicates stable RW states and dashed indicates unstable RW states. The hollow squares denote Hopf-bifurcation points. Both Hopf bifurcations are supercritical and near the bifurcations the radius ratio scales as the square-root of the distance from the bifurcation points. The radius ratio diverges as a approaches the value where exists a modulated-traveling-wave state.

Away from the Hopf bifurcations, the radius ratio ceases to obeys the square-root scaling and the secondary radius diverges as the value of a approaches the value where the MTW (modulated-traveling-wave) state is found. It is computationally too expensive to simulate states with very large radius ratios, and so there is a gap in the bifurcation diagram over the range of a where r2/r > 10. 

Hopf locus. At the codimension-two point u>i = (jJ2, and there is a resonance between the primary and secondary frequencies of the spiral wave. This is consistent with the fact that the locus of modulated traveling waves (for which... 

Figure 6.11. Traveling wave single-mode LiNbOj electro-optic modulator.

V at 100 MC/sec compared with 10 kV in Kerr cells) and they transmit over a wide spectral range (2500-12000 A). When designed as travelling wave modulators, they can be used even up to micro-wave modulation frequencies... 

The simple analysis presented above confirms that new formulations are required to produce stable, reliable products for field use. Practical system requirements, as defined by Mil Spec conformity and the use of standard fabrication and assembly processes, definitely require that a electro-optic polymer system with better thermal properties than thermoplastic acrylates be developed. That this is true for optical interconnection boards and modules is not surprising because of their complexity. It is perhaps remarkable that it remains true for even simple devices, such as a packaged, pigtailed traveling-wave modulator. The ultimate success of electro-optic polymers will be their use in cost-effective products that are used by systems designers. 

Figure 4.9 Schematic of bulk electro-optic phase modulator in transverse geometry (a) standard electrode arrangement for static measurements, (b) travelling wave configuration...

The rise time of a traveling wave modulator is given by t, thus a lower dielec-... 

DPPH = 2,2-diphenyl-1-picrylhydrazyl ENDOR= electron-nuclear double resonance EPR = electron paramagnetic resonance ESE = electron spin echoes ESEEM = electron spin echo envelope modulation EFT = fast fourier transformations FWHM = fidl width at half maximum HYSCORE = hyperfine sublevel correlation nqi = nuclear quadrupole interaction TauD = taurme/aKG dioxygenase TWTA = traveling wave tube amphfier ZFS = zero field sphtting. 

In last years one observes a fast progress in synthesis and elaboration of non-centrosymmetric functionalized polymers for applications primarily in electrooptic modulation and frequency conversion. These materials possess large second order nonlinear optical susceptibility x and can be easily processed into good optical quality thin films for travelling wave applications. Essentially four types of polymeric structures have been developed, as shown in Fig. 1 ... 

Zhao, Y.G., A. Wu, H.L. Lu, S. Chang, W.K. Lu, S.T. Ho, M. Van der Boom, and T.J. Marks. 2001. Traveling wave electro-optic phase modulators based on intrinsically polar self-assembled chro-mophoric superlattices. Appl Phys Lett 79 587-589. 

The results presented above can be expanded to modulated, noncoherent, and nonparallel beam mixing. As an example, we consider two ideal amplitude-stabilized nonparallel [9>X/d) plane traveling waves impinging on a two-quantum detector, so that washboarding can occur. In contrast to the one-quantum case, the detector responds to the square of this spatiotemporal... 

Teng, C. C Traveling-wave polymeric optical intensity modulator with more than 40 Ghz of 3-dB electrical bandwidth, App. Phys. Lett., 60,1538-1540 (1992). 

In this equation, a one-dimensional coordinate system z is laid alongthe direction of traveling waves and the electron beam. It is assumed that the interaction of electrons and traveling electromagnetic waves started at z = 0 and the time t = 0. In Eq. (6.2), Urn is the magnitude of velocity modulation at the initial location, the attenuation constant of the velocity modulation, Pe the phase constant of the electronic velocity modulation waves in the beam, and co the operating microwave frequency. 

When the TWT is amplifying, the traveling wave electric field grows as it travels. Therefore, the magnitude of the velocity modulation also grows as the electronic waves travel in the beam. 

The catcher of a two-cavity klystron amplifier can be replaced by the slow-wave structure of a traveling wave tube, as shown in Fig. 6.24(b). This type of tube is termed the twystron (Ishii, 1989). The slow-wave structure provides a broader frequency bandwidth than a regular two-cavity klystron. A microwave input fed into the buncher cavity produces velocity modulation to the electron beam. The electron beam is bunched while drifting, and the bunched electrons induce a microwave voltage in the microwave slow-wave structure. The electron beam is focused by the use of longitudinally applied magnetic flux density B. 

FIGURE 9.54 (a) General layout of an intensity modulator based on a Mach Zehnder interferometer, (b) detail of output waveguides, (c) electrode configuration for lumped element modulators, (d) electrode configuration for traveling wave modulators. 

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