Propagation distance

The optical power A oscillates between tlie guides depending upon tlie propagation distance. Clearly, by controlling z, (3 and k, a wide variety of passive devices (beam splitters, combiners, attenuators, and interferometers) can be readily constmcted. 

Throughout this book, a shock pulse (a steady compression wave followed by an expansion wave) will be represented as a profile, such as in Fig. 2.6. In Fig. 2.8 we show a series of P-x snapshots of pressure versus propagation distance x for an initially square pulse, at a series of times t. For a fluid with... 

Asay and Gupta [25] measure elastic precursor amplitudes as functions of propagation distance for two different divalent impurity concentrations in <100)-loaded LiF. It is shown that not only does the presence of divalent ions affect the precursor amplitude, but also that the state of the dispersion plays an important part. It is concluded that, for a given concentration of defects, the rate of precursor attenuation is reduced if the defects are clustered. 

The thorough and persistent work on precursor decay (the dependence of Hugoniot elastic limit on propagation distance) of Duvall s Washington State University group was successful in demonstrating that precursor attenuation was due to both stress relaxation and hydrodynamic attenuation. Typical data on crystalline LiF is shown in Fig. 2.7. Observed plastic strain... 

Fig. 2.7. Elastic precursor decay in which elastic waves are observed to decrease in amplitude with propagation distance is a typical behavior. The data of this figure describe the behavior of crystalline LiF samples of different yield strengths (after Asay et al. [72A02]).

Self-focusing occurs when power, Pq, exceeds the critical self-focusing power Per- A Gaussian beam experiences self-focusing after propagating distance, isf [46] ... 

The nonlinear directional coupler is potentially a useful device because it has four ports, two input and two output, and because the outputs can be manipulated with either one or two inputs. Optimally the two channels are identical, and the coupling occurs through field overlap between the two channels. As a result, when only one of the channels is excited with low powers at the input, the power oscillates between the two channels with a beat length Lb, just like what occurs in a pair of weakly coupled identical pendulii. As the input power is increased, a mismatch is induced in the wavevectors of the two channels, which decreases the rate of the power transfer with propagation distance. This leads to an increase in the effective beat length. There is a critical power associated with this device, for which an infinitely long, lossless NLDC acts as a 50 50 splitter, that is, Lb oo. 

Figure 4. Propagation distance, Lx, for surface electromagnetic waves on a Cu-...

Semiconductors with free carriers can support SEW. This has been demonstrated for a number of materials, but little use has been made of them as substrates for adsorbed molecules. To illustrate that interesting possibilities exist, Fig. 20 shows the propagation distance for SEW on GaAs as a function of free carrier concentration for a frequency of about 80 cm. These data were taken with a molecular laser.The observed distances are of order 1 cm, sufficient for use with the two prism technique... 

Ionic crystals also support SEW, but again no data exists where they have been used as substrates for attached molecule studies. That such studies may be feasible is illustrated in Fig. 21, which shows measured and calculated propagation distances for SrTi03 in the far infrared.— Again, these measurements were made with a molecular laser as a source. Unfortunately, for many crystals the frequency region over which SEW exist is very narrow (between the transverse and longitudinal optic phonon frequencies), and propagation distances are very short. However, ferroelectrics (and near-ferroelectrics like SrTiC ) may prove useful substrates for SEW spectroscopy. 

Figure 18. (A) Propagation distance for a Cu-vacuum interface as a function of...

Figure 20. Propagation distance of surface electromagnetic waves on GaAs as a function of carrier concentration for a frequency of 84 cm 1 (23)...

Figure 21. Propagation distance of surface electromagnetic waves on SrTiO,. The solid curve is calculated from the two points measured with a molecular laser (24).

However, subsequent detailed studies [33,55,56] have shown that the curvature of 100 faces in polyethylene can be explained quantitatively by applying Frank s model of initiation and movement of steps [57]. Curvature occurs when the average step- propagation distance is no more than about two orders of magnitude larger than the stem width. 

Fig. 7. The evolution of the harmonic power with propagation distance (arbitrary units) for ADM,WBM and MD phase-matching (solid line). The Cerenkov power changes from quadratic (solid line) to linear long (dashed line) growth. For QPM for alternate sections with no X1-2 1 (short dashed line). The phase-mismatched case is also shown (dotted line)...

For applications an integration of the elements on a wafer or some other substrate is important to allow a large scale production. Propagation distances of at... 

To implement an all-optical switch based on the nonlinear refractive index n(I)= n0+n2-I a nonlinear phase (f>MI shift of 2 n or a multiple of 27ris required, depending on the geometry of the switch [1]. As the absorption of the material attenuates the intensity and consequently diminishes the nonlinear phase shift, low absorption is advantageous. To determine the net nonlinear phase shift over the propagation distance the signal depletion by absorption has to be included. 

Fig. 1a-c. Absorption and nonlinear phase shift as a function of the propagation distance for a dominating a one-, b two-, and c three-photon absorption process. The dashed line indicates the nonlinear phase shift without any absorption... 

The intensity is, on the one hand, bound to the laser systems in telecommunication technology or the laboratory, and, on the other hand, the intensity may reach the damage threshold of the material and create irreversible degradation. In Table 1 the necessary nonlinearities n2 to reach a 2 n-phase shift over one centimeter propagation distance in a waveguide are roughly estimated for some common laser sources. 

Table 1. Necessary nonlinearities for a nonlinear phase shift of 27rover a propagation distance of one centimeter for different laser sources. A refractive index of n = 1.5 is assumed for the nonlinear material. Note that the tabulated values are only estimates and correct only on the scale of one order of magnitude. But the consequences we conclude from these estimations are nevertheless correct and important...

Fig. 8.5. Evolution of the laser beam profile in an ionizing medium calculated by 3D simulation. L is the propagation distance measured from the entrance plane of a 9-mm gas jet. The gas jet positions are az = 0 and b z = —18 mm...

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