Donna D. Castellone, MS, MT(ASCP)SH

• Clinical Projects Manager, Hemostasis/Hematology
• Medical, Clinical, and Statistical Affairs
• Siemens Healthcare Diagnostics
• Tarrytown, New York

Here 340b medications purchase isoniazid 300 mg amex, the pulse formation process is triggered by an external event treatment carpal tunnel isoniazid 300 mg with mastercard, which is not influenced by the current energy content of the gain medium symptoms 4 days before period generic 300 mg isoniazid fast delivery. Still treatment table buy 300mg isoniazid mastercard, the temporal position of the generated pulse depends on the energy stored in the gain medium: the more energy there is medicine 003 300 mg isoniazid, the higher the laser gain in the pulse-build-up phase treatment 1st degree burns buy 300 mg isoniazid free shipping, and the earlier the pulse maximum will be reached. Therefore, in a situation with a fixed repetition rate of the active Q switch, pump noise can cause bounded fluctuations of the pulse energy, the pulse duration, and the temporal pulse position. In contrast, pulse formation in a passively Q-switched laser (with a saturable absorber in the cavity) is triggered not by an external signal but rather at the time where the energy stored in the gain medium becomes sufficient to generate a positive net gain per cavity round trip. Assuming constant cavity losses and an always fully recovered saturable absorber, this occurs always for the same level of stored energy, independent of the pump power. In principle, the pump power can still have an influence during the pulse buildup time, but this time is often so short that the pump influence is negligible. Therefore, the pulse energy and the pulse duration are then nearly independent of the pump power, and changes of the pump power only affect the pulse repetition rate, as observed, for example, in passively Q-switched microchip lasers [31]. This can cause reduced noise in the pulse energy at the expense of higher timing jitter. Note, however, that this does not fully hold for cases with incomplete absorber recovery between the pulses. In contrast to noise in continuous-wave lasers, pulse parameters - similar to energy, temporal position, duration, etc. A consequence of this is that noise spectra can be specified only up to half the pulse repetition rate, corresponding to the Nyquist frequency. A mathematically more subtle point is that the optical phase (or amplitude) of a mode is actually well defined only over time scales well above the pulse period, as required to spectrally resolve the line. However, this is normally not a problem, as one usually considers the phase noise at lower frequencies. In principle, all kinds of noise of the output of a mode-locked laser are determined by the specification of the amplitude and phase noise of all the lines in the optical spectrum, plus the correlations between these fluctuations. Therefore, one may see quantities like timing jitter or intensity noise as projections of the overall noise on some smaller (typically one-dimensional) spaces. In practice, one is mostly dealing with such projections, which often embrace everything relevant for a particular experiment. For example, the phase noise in a single line largely determines the beat frequency noise with a (noiseless) single-frequency reference signal. We do not claim to present a complete picture - which is hardly possible, given that a great variety of coupling effects can occur in different situations - but rather try to discuss the most important mechanisms and to create a reasonable understanding of what consequences such coupling mechanisms can have. The basic idea is to consider the noise in different dynamical variables describing the pulse properties and to discuss in which ways different kinds of noise can affect each other. However, the picture used in the following is natural because it involves experimentally very relevant variables. We supplement these variables by the gain g of the laser medium, which is directly related to the energy stored in the gain medium (at least if homogeneously broadened media are considered and spatial mode profiles are disregarded). Note that some analytical models have been described (see, for example, Reference 33) which work with differential equations for some limited set of such dynamical variables. As is well known, the evolution of pulse energy and gain is closely coupled by the effects of laser amplification and gain saturation: any deviation of the gain from the net loss in the cavity leads to changes of the pulse energy, whereas larger pulse energies tend to reduce the gain. Both effects are typically of integrating nature; for example, gain saturation in a mode-locked solid-state laser (where the pulse energy is typically far below the saturation energy) affects the temporal derivative of the gain, rather than its current value. Note, however, that these dynamics can be coupled to other variables; for example, the gain can also depend on the spectral width of the pulses. For example, a shorter pulse has a higher peak power, leading to a lower loss on a fast saturable absorber (but not on a slow absorber) [34]. In lasers with a soliton circulating in the cavity, pulse duration and pulse energy are coupled to each other by the interplay of dispersion and nonlinearity. The center frequency can affect the pulse energy via the frequency-dependent laser gain and/or cavity losses, and can itself be influenced by pulse energy fluctuations if the Raman self-frequency shift [37] of pulses is relevant (for example, in some fiber lasers). It is apparent that the situation can be rather complex, even though not all possible coupling effects will usually be simultaneously relevant in any concrete situation. The simplest consequence of such coupling effects is that noise of one quantity is transferred into noise of some other quantity. However, strong bidirectional coupling can also introduce complicated nonlinear dynamics, and even in a numerical model as presented, for example, in Reference 38 the interpretation of the overall dynamics may not always be simple. However, at least for passively mode-locked lasers this is not true because the saturable absorber can significantly alter the gain dynamics, and in fact usually does so in practical situations. The key point is that the cavity losses become dependent on the pulse energy (for a slow absorber) or the peak power (for a fast absorber) [34]; usually, they are reduced for higher pulse energies. In effect, the damping of the relaxation oscillations is reduced, or the relaxation oscillations can even become undamped - typically, for pump powers below a certain well defined threshold value. In the latter case, the continuous-wave mode-locked regime becomes unstable [39,40]. The resulting regime with strong oscillations of the pulse energy is called Q-switched mode locking. This regime can be rather noisy with large fluctuations of maximum pulse energy, pulse duration, optical phase, etc. Even if this regime is avoided, the reduced damping of the relaxation oscillations increases the intensity noise around the relaxation oscillation frequency, whereas the width of the relaxation oscillation peak is reduced [41]. Transfer function measurements with a sinusoidally modulated pump power have demonstrated the increased peak height and decreased peak width [42], and the mentioned effect on the noise is clearly to be expected. On the other hand, the impact on noise at frequencies far below or far above the relaxation oscillation frequency should not too strongly deviate from that of a continuous-wave laser. The intensity noise of any laser can, of course, be strongly increased by excess noise of its pump source. For a discussion in the context of a passively mode-locked dye laser, see Reference 43. Therefore, we also focus on timing jitter in this book chapter but also present some results on optical phase noise in Subsection 12. The current section is devoted to the mathematics and physics of timing jitter, whereas the section following it addresses jitter measurements. Before going into details of pulse generation, we briefly discuss how timing jitter is usually specified. Conceptually, one can consider the timing errors of the pulses emitted by a mode-locked laser, as obtained by comparing their temporal positions with the ideal temporal positions for a noiseless pulse source (absolute jitter), or with some real source which will itself have some noise (relative jitter). One can specify the statistical properties of timing noise by the power spectral density St(f) of the timing errors. It is actually quite common to replace the timing error t with a timing phase error t = 2frept, where frep is the pulse repetition rate, and the corresponding power density is St (f) = 2 frep 2 St (f). The optical field oscillation (sometimes called the carrier oscillation) is disregarded in this picture, which basically describes the output of a photodiode illuminated with the pulse train. Note that using the term phase noise in this case can provoke confusion with optical phase noise, so we suggest using the term timing phase noise, instead. A rather different method of specifying timing noise of oscillators, which is often used in metrology, is the Allan variance [44,45]. It is a generally agreed [46] means to characterize frequency fluctuations in time domain. The so-called two-sample variance without dead time is commonly referred to as 2 (2,) or 2 and is defined as y y 2 y with yk = 1 tk + 1 < (y k + 1 - y k)2 > 2 (12. The Allan variance and its square root, sometimes called the Allan (standard) deviation, are based on differences of adjacent (time-averaged) frequency values rather than on frequency differences from the mean value, as is the "conventional" standard deviation. Plots usually show the Allan variance as a function of the averaging time, and the shape of such curves can be used to retrieve information on the noise processes. Alternatively, the Allan variance can be determined from the normalized phase or timing deviation x(t). For a given measurement interval it follows that yk = which after insertion gives 2 = y 1 (x k + 2 - 2 x k + 1 + x k)2. White frequency noise S(f) = S0, for example, results in 2 = S0 / 2, whereas so-called y flicker frequency noise S(f) = a/f leads to an Allan variance which is independent of the measuring time: 2 = 2 a ln(2). A linear frequency drift y y(t) = bt, which is typical for frequency standards, results in an Allan variance that increases with the squared measuring time: 2 = (b)2 / 2. The fundamental difference between those laser types is that an actively mode-locked laser has a timing reference connected to its modulator, which introduces a kind of restoring force for the relative timing error between both signals. Passively mode-locked lasers, on the other hand, have no timing reference (unless they are equipped with some active timing stabilization), so that the timing errors can undergo an unbounded drift. In the noise spectrum, this kind of random walk leads to a divergence for zero noise frequency, similar to the one for the optical phase noise. There have been a number of publications presenting theoretical results for the timing jitter of actively and/or passively mode-locked lasers. In this chapter, we focus on three kinds of models, which are based on somewhat different approaches. Mecozzi [33], which has been developed on the basis of soliton perturbation theory and the assumption of a fast saturable absorber. Here, it is assumed that the pulse dynamics are basically determined by soliton effects, with additional influences from quantum noise which are treated as weak perturbations. The circulating pulse is described with four dynamical variables, namely pulse energy, optical phase, temporal position, and spectral position. Of course, this is already a simplification, as additional degrees of freedom such as chirps or pulse shape distortions are not included. Also, the pulse duration is not rigidly coupled to the pulse energy even for the case of soliton pulses; only in the stationary case, the soliton dynamics lead to a constant product of pulse energy and pulse duration. In addition, the description of the gain dynamics is rather crude: there is no additional dynamical variable for the laser gain, so that relaxation oscillation dynamics can not be described. However, an extension in this direction is possible and has indeed been reported [49]. The quantum noise can then be projected onto the dynamical variables of the model, leading to Langevin-type equations, and analytical results for the noise spectra corresponding to these variables have been obtained. As a brief review of the results, we focus on the central result concerning timing jitter, which has two contributions. The second contribution comes from fluctuations of the optical center frequency, which are bounded due to the limited laser gain bandwidth (which always tends to pull the spectrum back to its equilibrium position) and couple to the pulse timing via dispersion - that is, the dependence of the group velocity on the center frequency. Technically, this involves including an additional term in the dynamical equation of the temporal position, representing a "restoring force" as generated by the active modelocker. The result is that the power spectral density of the timing noise levels off at f = 0, eliminating the mentioned divergence. As such lasers are also very important, a numerical model has recently been developed [38] that requires only a significantly less restricting set of assumptions. Here, the pulse is represented by an array of complex amplitudes, which resemble the pulse shape in the time or frequency domain. A wide range of effects acting on the pulse can be described in the time or frequency domain, and fast Fourier transforms allow to switch between domains as required. Thus, the model allows us to treat basically all kinds of mode-locked lasers, regardless of their mode-locking mechanism (active or passive, fast or slow absorber), gain dynamics, and additional coupling effects. After applying some trivial corrections to the latter (see the erratum [51] and Reference 38), perfect agreement was obtained, as had been expected. An initially quite surprising result was that the agreement persisted in cases without any dispersion and Kerr nonlinearity, i. This lead to the insight that the noise properties (including the timing jitter) are not directly affected by the detailed pulse-shaping processes. This new insight triggered the development of a new analytical model [52] which does not reduce the dynamics to the interplay of a few dynamical parameters and emphasizes less the role of the pulse-shaping mechanism. In this model, the above mentioned direct effect of quantum noise on the pulse timing can be explained as follows. The quantum noise added to the pulse during one cavity round trip can be described by adding uncorrelated noise amplitudes with equal noise variance to all samples (complex amplitudes) in the time domain. The total power in each sample can be increased or reduced, depending on the relative phase of original amplitude and noise contribution. In effect, the pulse position (defined as the "center of gravity") experiences some random change while the pulse shape distortions are subsequently dampened by the pulse shaping mechanism. As a consequence, we can now apply such analytical results to a much wider range of lasers. However, we have to keep in mind that a great variety of coupling effects (as discussed in Section 12. In any particular case, one has to check which coupling effects can occur and analyze their importance.

The same process is then repeated from site 2 to site 3 and so on treatment restless leg syndrome cheap 300 mg isoniazid amex, with the net result that a pressure wave is propagated down the artery medications like adderall purchase isoniazid 300mg otc. Fluid just to the right of site 1 moves slightly to the right in the above scenario medications jaundice generic isoniazid 300 mg fast delivery, but only enough to cause fluid displacement at site 2 symptoms 6 dpo generic 300 mg isoniazid overnight delivery. When the next bulge travels down the tube to cause distension at point 1 medications given before surgery buy isoniazid 300mg lowest price, the displaced fluid packet moves back towards site 1 treatment 6th feb generic 300 mg isoniazid amex. Thus, fluid particles execute back-and-forth oscillatory motions but never go anywhere in the sense that their mean (cycle-averaged) velocity is zero. A fluid packet just to the left of site 1 moves to the left in the above discussion and so contributes to the next "bulge" traveling down the tube. The entire process depends critically on a balance between fluid inertia and wall distension. The same process will occur if an oscillatory flow (with zero mean) is imposed at one end of the tube, rather than an oscillatory pressure. Based on the above discussion, we expect that this will depend on the elastic properties of the tube, as well as on the inertia of the fluid. In addition to , we expect that the wave speed will depend on the fluid inertia, which is characterized by the fluid density. Since there is only one dimensionless group, must be a constant, and thus c2 = constant. We consider a section of artery of internal diameter D and wall thickness t and assume that the thickness is small, i. The artery is pressurized, with a transmural (internal minus external) pressure p, as shown in. This transmural pressure is supported by stresses in the artery wall, which, by virtue of the assumption t D, are hoop stresses. Denoting the hoop stresses by, we may express the tension within the wall per unit depth into the page, T, as T = t. A static force balance in the vertical direction yields p D = 2T, so the hoop stress may be written as =p D. The increase in strain resulting from an increment in transmural pressure p is, therefore, approximated by = p D. In practice this is not the case, since arterial wall thicknesses are usually 4 to 10% of arterial diameter [5]. This is definitely not true, since artery walls exhibit both elastic non-linearity and viscoelastic behavior. We seek to derive an equation describing the propagation of a transverse elastic wave along the artery, that is, an equation describing the dependence of R on axial position x and time t. To accomplish this, we will apply conservation of fluid mass, a fluid momentum balance (unsteady Bernoulli equation), and a constitutive relationship for the tube wall. Average fluid velocity entering the segment is u, exit velocity is u + du, and length of segment is dx. We then consider a small pillbox-shaped control volume of radius R and length dx. Next, observe that the pressure pulse travels as a wave whose wavelength is much longer than the arterial radius. This implies that on the length scale of the control volume, the dependence of R on axial position can be neglected. Denoting the cross-sectionally averaged axial velocity by u, we see that fluid accumulation in the control volume is balanced by net fluid influx. Applying this equation between two points 1 and 2, located a distance dx apart, 193 4. We now use the fact that points 1 and 2 are very close, and thus in view of the long wavelength of the pressure pulse, we can assume that u/t is constant over dx, so that the above integral equals u/t dx. Similarly, for small wall deformations and a long pressure pulse, u 2 - u 2 can be neglected. Finally, in the limit as dx becomes 1 2 small, (p2 - p1)/dx equals the axial pressure gradient, dp/dx. Thus, the momentum equation simply reduces to a balance between fluid inertia and the axial pressure gradient, u p =-. This proves that, under the stated assumptions, transverse elastic waves travel at speed 1/. This occurs naturally in aging: the arteries of elderly people are stiffer and have thicker walls than those of young people. Hence, we expect wave speed (c0) to increase with age, which is confirmed by data from Caro et al. In order to quantify these effects, it is necessary to develop relationships between pressure and flow in oscillatory systems, to which we now turn. To recap, the combination of distensible artery walls and a time-varying (periodic) pressure input from the heart causes elastic waves (pressure pulses) to travel along the arteries. Mathematically, the pressure, therefore, depends on time t as well as on axial location in the arterial tree, x. If we assume the simplest possible case, in which the pressure varies harmonically in time with zero mean at a given location, we can express the pressure as10 p(x, t) = p0 cos 2 (ct - x) 2 x. It is assumed that the blood is inviscid (no shear stresses are present) and that fluid motion is purely axial, i. If we then consider a thin fluid element with cross-sectional area A and volume V. This, therefore, represents a wave propagating in the positive x-direction at velocity c. The former case corresponds to fluid with a great deal of inertia, which resists motion driven by the oscillatory pressure gradient p/ x. The latter case corresponds to frequencies so high that fluid elements only just get started moving in one direction before the pressure gradient changes sign; as a result, the net motion and velocity are never allowed to become large. Consequently, the instantaneous flow rate Q(x, t) is simply the tube cross-sectional area A multiplied by u(x, t), i. By similar analogy, we define the characteristic impedance, Z 0, as the ratio of pressure to flow in an oscillatory system p Z0 =. Physical effect Viscous flow resistance Elastic vessel walls Fluid inertia Name Resistance Compliance Inertance Electrical analogue Resistance Capacitance Inductance the analogy between electrical capacitance and fluid compliance is a little bit tricky; an electrical capacitor has an inlet and an outlet, and the current in must equal the current out. A fluid compliance chamber often has only one inlet, and flow rate in does not have to equal flow rate out. This can be handled by suitable placement of the elements in the electrical and fluid circuits. It is important to understand the meanings of p and Q in the above derivation: p is the oscillatory pressure (measured about some mean value), while Q is the corresponding oscillatory flow. For flow with zero mean, as considered above, that means that Q can be thought of as a "sloshing" flow, in which fluid oscillates back and forth but (on average) never goes anywhere. Evidently this is not the situation in vivo, since the cycle-averaged flow rate in the cardiovascular system is nonzero. This can be accounted for by adding a steady mean flow (and corresponding pressure gradient) to the above description. In this case, the motion of a fluid 198 the circulatory system particle consists of a steady translation with a sinusoidal oscillation superimposed on it. This situation does not occur physiologically, and we must, therefore, examine what effect relaxing each of the above assumptions has on pulse wave propagation and flow dynamics. Viscous losses In the analysis above, no account has been taken of viscous losses, which will arise from the action of fluid viscosity and arterial wall viscoelasticity. Generally speaking, viscosity dissipates energy and, therefore, diminishes the amplitude of the pressure pulse. More specifically, inclusion of fluid viscosity affects the above analysis in two ways. First, the amplitude of Q(x, t) is reduced compared with that predicted by Equation (4. The coefficients M10 and 10 have been computed as a function of flow parameters [8]; M10 is <1. This causes the amplitude of the pressure pulse to increase distally, and the amplitude of the flow waveform to decrease distally, as the following qualitative argument shows. If the artery is smaller and stiffer at point 2, a given fluid displacement will cause a proportionally larger pressure increase at point 2 than would occur if arterial properties were uniform. In other words, if the amplitude of the flow waveform is kept constant, the amplitude of the pressure waveform will increase distally. Note the increase in the pressure wave amplitude and the decrease in the flow wave amplitude with distance from the heart. Instead, the amplitude of the flow waveform decreases somewhat, while the amplitude of the pressure pulse increases somewhat, moving distally in the arterial tree. This represents a compromise between the two scenarios outlined in the previous paragraph. Effects of branching and taper the arteries are not infinitely long and straight, but rather are tapered, curved, and typically delimited by branches (bifurcations) both upstream and downstream. These effects, particularly branching, have a major effect on pulse wave 200 the circulatory system Figure 4. The incident pressure pulse travels from left to right; the reflected and transmitted pressure waves are also shown. Here we analyze in some detail the behavior of the pressure wave at a single bifurcation. The characteristic impedance of the daughter arteries will in general be different from that of the parent artery, since c and A will differ from daughter to parent. This means that the ratio of the pressure pulse amplitude to the flow pulse amplitude must change as the pulse wave passes through the junction. In other words, the impedance mismatch across the junction will force the amplitude of the pressure pulse passing through the junction to be different from the amplitude of the incident pressure pulse. Since the pressure pulse carries energy with it, and there are no losses in the system, some energy must be reflected back into the parent artery in the form of a reflected pressure wave. Hence, the junction gives rise to both a transmitted and a reflected pressure pulse. We seek to characterize the amplitude of these pulses in terms of arterial properties. To develop such a characterization, the arteries and junction are treated as a onedimensional system in which pressure is uniform across the artery at each axial station, while pressure and flow rate vary axially. Consider a very thin control volume (thickness dx) positioned at the junction. Since the control volume is very thin, the mass within it can be considered negligible. Consequently, the forces acting on fluid within this control volume must sum to zero at every instant; if not, a finite force would act on an infinitesimal mass, thereby producing an infinite acceleration. Note that the dependence of pressure on x is harmonic, and that the sum of pressures upstream of the junction equals the pressure downstream of the junction. The pressure on the upstream face has two contributions, namely the incident and reflected pulse waves. Therefore, we may state: the sum of the incident and reflected pressure pulses must equal the transmitted pressure pulse. The force balance can then be written as [p0,i + p0,r] cos(t +) = p0,t cos(t +) which implies that the pressure pulse amplitudes must satisfy p0,i + p0,r = p0,t. Although we did not explicitly say so previously, our convention is that positive oscillatory flow corresponds to the direction of propagation of the pressure wave. As dx approaches zero, no fluid can be stored in the control volume, and thus the volume flow rate entering the control volume must balance the volume flow rate leaving at every instant. Adopting notation similar to that describing the pressure waves, we write Q i (xjunction, t) = Q 0,i cos(t +) Q r (xjunction, t) = -Q 0,r cos(t +) Q t (xjunction, t) = Q 0,t cos(t +) (4. But this is the same as them being in phase but with one wave having a negative amplitude, so we need not consider this case any further. It shows that for a right-propagating wave, the oscillatory flow was taken as positive in the x-direction, i. To maintain a positive impedance in this case, oscillatory flow must be taken as positive when it is propagating leftward. If R is zero, or nearly zero, the junction is said to be matched, since all, or nearly all, of the pulse energy passes through the junction. This corresponds to the daughter tubes having a very high impedance, which can occur, for example, if Ad Ap. This situation is therefore called a closed end reflection, analogous to what would occur if the end of the artery was completely blocked. The net pressure at the junction is therefore pnet (xjunction, t) = 2 p0,i cos(t +) (4. At such sites, the incident and reflected pressure waves are in phase, while the incident and reflected flow waves are 180 out of phase.

After exiting the second mirror medicine articles isoniazid 300 mg lowest price, the beam is first redirected by a curved mirror of radius R 2 and then retroreflected by a second curved mirror of radius R1/2 situated at a distance of L0 from the mirror M2 treatment dvt quality 300mg isoniazid. In such a case symptoms kidney pain cheap 300 mg isoniazid with visa, it is of interest to know how much deviation occurs from the ideal qpreserving configuration medicine 5e buy isoniazid 300 mg mastercard. It is well known that in a standard four-mirror laser resonator treatment plans for substance abuse buy cheap isoniazid 300mg, the long arm determines the maximum spotsize of the beam at the center of the stability region symptoms hiv purchase 300 mg isoniazid amex. The exiting beam is retroreflected by a flat mirror M3 placed at a distance of L1 from the second mirror M2. In this case, the main effect of the deviation from ideal q-preserving operation is simply a shift in the stability region of the cavity. When the non-q-preserving cavity is added to the short cavity, the position of the focusing mirrors around the gain medium can then be readjusted in order to obtain lasing again. It is important to note that the mirror separations cannot be arbitrary chosen due to two limitations. First, the multipass cavity arrangement must be stable as summarized by Equation 8. In general, only a discrete set of mirror separations satisfies both of these constraints. However, the q-preserving condition = m/n is satisfied only at certain discrete values of L0, as we discuss below for specific cases. Note that for a fixed m, different q-preserving mirror separations are found by changing the value of n. For a fixed value of m, this gives infinitely many possible q-preserving mirror separations. For a given value of m, there exists an optimum value nopt of n, independent of R, which maximizes the effective optical length and minimizes the pulse repetition rate. This gives the following transcendental equation for nopt: m m m 1 = cos + n sin n. Each solid square, corresponding to an integer value of n, represents a q-preserving configuration. In particular, the repetition rate attains a minimum value for both cases as n is varied. This choice of n gives the minimum possible repetition rate that can be obtained for these two configurations. A practical constraint on the maximum allowed value of n comes from the loss per bounce introduced by the highly reflecting mirror. Hence, use of very high quality reflectors with ultralow reflective loss is critical in minimizing passive losses while achieving very long effective optical path lengths. Once lasing is obtained, the power performance and mode matching of this cavity can be optimized further. At this stage, once the partial reflector of the short cavity is removed, the lasing of the extended cavity is readily obtained because the stability region should remain nearly the same as that of the short cavity. The most important reason is that a large prism separation may be necessary to provide sufficient dispersion for high pulse energies, and this can make the setup rather bulky. In addition, if highly dispersive prisms are instead used to obtain the same amount of second-order dispersion with shorter prism separation, it may become difficult to control the higher order contributions to phase distortions. The technique was applied to a Ti3+:Al2O3 oscillator and both q-preserving and non-q-preserving configurations were investigated. The short cavity that extended up to the reference plane zR, was a folded, astimatically compensated x cavity containing a short (2 mm) Brewster-cut Ti3+:Al2O3 crystal with a pump absorption of about 75% at 532 nm. The estimated pump and laser beam radii inside the gain medium were 7 m and 9 m (1/e2 radius), respectively. The beam leaving the second flat mirror was reflected by a flat high reflector (M8) through the notch and then sent back by a curved retroreflector (M9) whose radius was 1 m. For this case, the threshold pump power and the slope efficiency were 510 mW and 20%, respectively. Femtosecond pulse generation experiments were carried out with the 11% transmitting output coupler. Once the focusing of the cavity beam was optimized inside the gain medium, mode-locked operation could be readily obtained by moving one of the resonator end mirrors. Once initiated, stable, uninterrupted mode-locked operation could be sustained for many hours. By assuming a hyperbolic secant pulse profile, the pulse duration was further determined to be 23 fs, with a corresponding time-bandwidth product of 0. Because L1 < L0 and L0 << R (R = 200 cm), for both the short and the extended cavities, the beam waist at the center of the stability region remains nearly the same but the stability regions are shifted. This made the alignment of the extended cavity more difficult in comparison with the qpreserving cavity. The pulsewidth is shorter than that for the q-preserving case discussed above due to slightly higher available pulse energy as is predicted by the soliton mode-locking theory (see Equation 8. One important advantage of this gain medium is that the absorption band around 670 nm allows direct diode pumping. Although broad-stripe diodes are available as pump sources, they are typically expensive and suffer from low mode quality, making it difficult to obtain good mode matching between the pump and the laser resonators. A cost-effective alternative is to use inexpensive, single-spatial-mode diodes to improve mode matching. The radius of the curved mirror was 4 m, giving an angular advance of /2 for the spot pattern after each round trip. An alternative method is to use small pick-off mirrors to direct the incident and exit beams. In this particular case, small pick-off mirrors were used for beam injection and extraction. The short cavity was a standard x-folded configuration containing a 3-mm-long Ti:Al2O3 crystal between two curved high reflectors each with a radius of 10 cm. Also, a 25% output coupler was used to decrease the intracavity intensity and to minimize instabilities due to excess Kerr nonlinearity. In order to use the pump more efficiently, a curved retroreflector was used to double-pass the pump beam. During mode-locked operation, the resonator produced 877 mW of output power with 9. This laser system has been used in the microfabrication of photonic components on transparent glass [22]. Direct scaling to even higher pulse energies becomes quite challenging due to the possibility of pulse instabilities caused by excessive nonlinearities in the gain medium. The pulses extracted from the cavity were then compressed with an extracavity dispersive delay line consisting of a pair of LaK16 prisms. Tight focusing was employed to create peak intensities exceeding 1014 W/cm2, and ionization of helium, which requires simultaneous absorption of at least 17 photons, was experimentally demonstrated [23]. The duration of the output pulses was independent of the repetition rate and was measured to be 13 ps by assuming a sech2 intensity profile. By changing the alignment of the plane or concave mirrors, the number of passes and hence the repetition rate of the laser could be adjusted. Q-preserving multipass cavities were introduced, and their analytical design rules derived. 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Minoshima, Threedimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator, Opt. Morgner, Ionization of noble gases with pulses directly from a laser oscillator, Opt. Shestakov, Lasing due to impurity color centers in yttrium aluminum garnet crystals at wavelengths in the range 1. Keller, Powerful redgreen-blue laser source pumped with a mode-locked thin disk laser, Opt. Kuizenga, Active mode-coupling phenomena in pulsed and continuous lasers, Optoelectronics, Vol. Krausz, Chirped multilayer coatings for broadband dispersion control in femtosecond lasers, Opt. Fujimoto, Design criteria for Herriott-type multi-pass cavities for ultrashort pulse lasers, Opt. Angelow, Generation of 150-nJ pulses from a multiple-pass cavity Kerr-lens modelocked Ti:Al2O3 oscillator, Opt. Apolonski, Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification, Opt. The application of these lasers outside research laboratory environments has been, up to now, very limited because of their complexity and difficulty of operation, and because of the high prices of commercially available laser systems. In terms of both pulse energy and repetition rate, cavity-dumped laser systems are in between oscillators and amplifier systems, and thus are ideal laser sources for many applications such as microstructuring, laser surgery, tissue manipulation, multiphoton microscopy, and laser spectroscopy. However, because these lasers are pumped in the green spectral region, where no laser diodes are available, their application is limited to a small community of users due to the high cost of the green pump lasers. Recently, we became aware of the potential of diodepumped laser oscillators with cavity-dumping in terms of performance and reliability. However, this material is limited in terms of power scaling because of its low absorption and emission cross sections, which makes it necessary to use relatively long laser rods with tight focusing [8]. Therefore, self-phase modulation is the limiting parameter and cannot be further reduced easily [7,9]. Additionally, due to the poor thermal conductivity of Yb:glass and the need of tight pump focusing, the maximum pump power is limited to a few watts. One possible way to overcome these disadvantages is to use a laser material with larger cross sections having a shorter pump absorption length at a given doping concentration. This would allow one to increase the spot size of the laser mode and also to shorten the crystal. Second, the improved thermal conductivity leads to reduced thermal effects in comparison with Yb:glass. Therefore, it is possible to use low-brightness, highpower multi-emitter diode bars for pumping, which reduces costs and increases the reliability compared with high-brightness diode-pumping options [11]. Even though the nonlinear refractive index is higher than in Yb:glass, all the properties mentioned above make this crystal an almost ideal candidate for high-peak-power laser systems. The pulse-to-pulse stability, the transient spectra, and autocorrelations are discussed with respect to the theoretical model. A numerical evaluation of the laser dynamics is carried out and compared to the experimental results. The major pulse shaping mechanism is shown to be caused by solitary pulse propagation, but the spectral properties of the laser pulses are strongly influenced by the generation of Kelly sidebands. On the other hand, the lasing transition of Yb3+ from 2F7/2 to 2F5/2 is rather simple and broad-band due to Stark degeneration without significant upconversion or cross relaxation channels; furthermore, the absence of concentration quenching allows for high doping levels [13]. The small quantum defect leads to self-absorption in the lower wavelength edge of the emission band, and Ybdoped laser materials can be described by a quasi-three-level model with the resulting requirements for the pump intensity. High-power cw demonstrations with innovative Yb-doped materials are given in [22,23]. The field amplitude is normalized in a way that A(t,T) 2 describes the power envelope. The gain equals the loss, and the pulse broadening due to gain dispersion equals the shortening from the saturable absorber. Assuming that, in this case, their contribution to the pulse shaping can be neglected, Equation 9. Later, we will show that besides the sidebands, according to the laser roundtrip time, an additional set of Kelly sidebands will appear in the case of cavity dumping, where due to the periodic dumping an additional disturbance of the soliton on a second time scale is imposed. This is a very stable mode of operation that we call the relaxed regime, where the dumping frequency is much smaller than the energy relaxation frequency, fdump fenergy. Things become more complicated in the so-called resonant regime with fdump 2 fenergy. We observe a subperiodic behavior, where a pulse with high pulse energy is followed by a small one and vice versa. At even higher dumping frequencies, a third mode of operation can be identified, the transient regime with fdump fenergy, shown in Figure 9.

With regard to the category of "image of negativity" treatment yeast infection discount isoniazid 300mg overnight delivery, Respective metaphors and their frequency distributions are displayed on Table 10 severe withdrawal symptoms buy cheap isoniazid 300 mg on line. Metaphors under the category of image of negativity medicine search generic isoniazid 300 mg without prescription, and their frequency distributions medicine 60 discount isoniazid 300mg without a prescription. Despite being lesser in number among the total of the participants of this study medicine 1975 lyrics purchase isoniazid 300mg free shipping, it is noteworthy that 4 medications walgreens purchase isoniazid 300mg amex, participant teachers apply to metaphors in tune with the image of negativity. Opinions, representing this category, are as follows: "Like a chatterbox, because no one does its work on time" (Student). While 14 students suggest 10 metaphors with regard to the category of "image of love", one teacher suggests one metaphor respectively. Upon reviewing the respective opinions, it is noteworthy that, one teacher and 14 students suggest opinions in tune with this category. Definitions from students with regard to the metaphors, representing the category of school health as "the image of love" are as follows: "Like world; because it encompasses all the beauties" (Student). While 24 students suggest 10 metaphors with regard to the category of "well of life", 4 teachers suggests 4 metaphors respectively. Metaphors, suggested by students and teachers, and their frequency distributions are displayed 200 Afr. Metaphors under the category of directive and instructive, and their frequency distributions. Upon reviewing the statements from the participants under this category, a consideration as being the basic need of life, such as water, oxygen, etc. Opinions related with this category are as follows: "Like a tree; because it produces the oxygen for our living" (Student) "Like a seed sowed in soil; because it grows healthily, while being fed with water and sun" (Teacher) While 21 students suggest 14 metaphors with regard to the category of "directive and instructive", four teachers suggest three metaphors respectively. Upon reviewing the respective opinions from the participants, they describe the school health as a guide, paving the path to success. Related opinions are as follows: "Like a ship; because its route decided" (Student). While vocational schools in industrial regions provide opportunities for easier employment, in industrially undeveloped regions, children, or their parents see vocational schools as the last chance to obtain a degree. We may discern such a tendency among the metaphors on school health, being suggested by the participant teachers of this study. Metaphors from students and teachers are classified under 10 different conceptual categories. Conceptual categories of "image of love, means of knowledge and illumination, hope of the future, directive and instructive, well of friendship, image of negativity, image of assiduousness, well of life, and well of joy", composed in terms of this study. Difference between the numbers of metaphors being suggested in tune with this category by the students and teachers is thought-provoking. Metaphors under the conceptual category of image of assiduousness are suggested only by students. Upon reviewing these opinions, working is seen to be taken into consideration as the basic condition for success. Under the conceptual category of "well of friendship", suggested only by students, opinions, pointing to the creation of an environment suitable for developing new ties of friendship, come to the fore. Under the conceptual category of "well of joy", metaphors of which again suggested only by students, it is agreed upon the opinion that, educational activities are maintained at a joyful environment. In tune with the conceptual category of hope of the future, the common opinion, derived from 11 metaphors from students, and five from the teachers, is that, school health is an important asset for the individuals in their developments towards their future lives. Students, suggesting the two metaphors under the title of well of peace, describe school health as a concept, in which they may feel content. Majority of the teachers describe school health by suggesting metaphors in tune with image of negativity. Metaphors, in tune with the conceptual category of image of love, are suggested mostly by the students. Thus, it may be suggested that, students approach to school health more endearingly than the teachers. While 24 of the metaphors in tune with the conceptual category of well of life come from students, teachers suggest four metaphors in kind. Upon reviewing these metaphors, the opinion, that school health is under a constant development hand in hand by students and teachers, comes to the fore. While 21 of the metaphors in tune with the conceptual category of directive and instructive come from students, teachers suggest four metaphors in kind. Common point among the opinions of the participants is that, school health is a "guide" on the road to success. In accordance with the outcomes, attained from this study, metaphors being suggested by students with regard to school health as per their schools, are more optimistic than those being suggested by teachers. While 47% of the metaphors being suggested by teachers are concentrated under the title of the image of negativity, such a fact may arise from the heavy workload burdened on them, or from their economical discomforts, or from the level of their professional exhaustion. Such a development has eased the enrolment of students with lower levels of knowledge capacity to these schools, and negatively affected the effective instructing environment of teachers. It is also thought that, this has caused most of the metaphors being suggested by teachers with regard to school health tending to concentrate under the image of negativity. At this point, decision-takers are to conduct studies on assessing the professional exhaustion levels of teachers, and to take precautions to eliminate such a problem accordingly. Teachers and students may be asked to bring out metaphors with regard to different concepts and facts (school, school health, student and teacher, etc. Having the outcomes of such studies dealt with and discussed in routine assemblies of teachers, or in seminars on assessment of educational processes, will provide great benefit in developing, and examining the perspectives of teachers and students with regard to the concept of school health, as well as in the professional behaviors of teachers. Metaphorical Images of School: School Perceptions of Students, Teachers and Parents from Four Selected Schools (In Ankara). Organizational Communication and Culture: A Study of 10 Italian High-Technology Companies. Accepted 16 November, 2009 this exploratory study serves to investigate the perceptions of fast moving private label brands in the South African grocery food sector. Successful positioning of these brands has been achieved globally, most notably in developed markets. To this end, research has been undertaken in order to better understand the current position these brands occupy in the minds of South African consumers. Included in the study is the consideration of critical branding elements such as trust, availability, pricing, packaging, etc. The knowledge gained through this research should ideally facilitate the process of advancing private label brand research in an academic context and improving brand positioning, increasing market share and optimizing profit extracted from private label brands in a managerial context. Key words: Private label, store brand, own label, supermarket, grocery, perceptions, South Africa. These products are typically manufactured by a third party (contract manufacturer) under licence. Private label brands then appeared in South Africa in 1956 when Raymond Ackerman introduced a no-frills brand to the market through his fledgling chain of Pick n Pay stores (Prichard, 2005). This range offered commodities to the market at lower prices than was possible through manufacturer brands. This served the purpose of defeating the regime of a small number of powerful retailers and suppliers who had been engaging in price fixing as the order of business. Originally, manufacturer brands dwarfed retailer brands in size and, through extensive marketing, led sales by suggesting their brands were synonymous with "trust, quality and affluence" (Nirmalya, 2007). However, in the early 1970s the balance of power began to shift in favour of retailers. Due to rapid expansion, retailers seized this power advantage and the inevitable negotiating prowess. With this size advantage, private label brands began to gain a stronger foothold in the market. Walker (2006) concedes that private label brands are often viewed as lower priced and hence inferior quality alternatives to manufacturer brands. Certain retailers are attempting to reposition their private label brands as premium offerings which aim to compete directly with manufacturer brands. They offered a premium product that no other retailer could imitate and thus consumers would come from all over the country to purchase these particular cookies. Internationally, private label brands constitute an average of 19% of total retail market share, with some European countries. Switzerland and the United Kingdom) fast approaching a 50/50 split in market share between manufacturer and private label brands. Share and volume of private label brand sales, as indicated by leading global retailers. Beneke 205 by a host of countries and the share of volume enjoyed by leading global retailers. It is clearly evident that European and North American retailers excel in this respect. Two anomalies present themselves in terms of penetration of private label brands in South Africa (Nielson, 2006). Firstly, it has been concluded that retail concentration (essentially an oligopoly scenario in the retail sector) is highly correlated with success of private label brands. Yet, in South Africa, despite high retail concentration enjoyed by the major supermarket chains, private label brands have not achieved the successes of their global counterparts. Secondly, lower income groups tend to be the most common purchasers of private label brands due to higher levels of affordability. Research suggests that as consumers become increasingly affluent, they are more willing to try various alternatives to trusted brands (Mawers, 2006). In general, consumers with limited financial resources are likely to purchase trusted (that is manufacturer) brands in which quality is well established and thus confidence is high (Rusch, 2002). Another factor contributing to this phenomenon has been identified as accessibility. In South Africa, lower income groups frequently do not have direct access to the large retail stores where private label brands are available. These stores tend to charge higher prices due to their location, as well as not being able to benefit from larger economies of scale (Klemz et al. It is estimated that between ten and twenty percent of fast moving consumer goods, sales are estimated to occur through the informal sector (Blottnitz, 2007), therefore representing a lost opportunity for private label brands. Direct attributes include ingredients, taste and texture, whilst indirect factors are represented by price and brand name. Direct factors are usually difficult for consumers to test without consuming the product, or completing various tests. Hence, reliance on indirect quality indicators such as brand name and price are more heavily relied upon. The authors thus suggest that a thorough understanding of how these indirect cues impact different consumer groups in their purchasing decisions may help retailers to improve success of private label brands. Through further investigation, they identified brand, package and advertising as indirect factors which impact consumer perceptions and hence influence purchasing decisions. The success of a brand in the long term is not based on the number of consumers that buy it once-off, but on the number of consumers who become regular buyers of the brand. Thus, repeat purchases and customer loyalty are prioritised by retailers (Odin et al. Chaudhuri and Holbrook (2001) suggest that consumers become brand loyal when they perceive some unique value in the brand that no alterative can satisfy. This uniqueness may be derived from a greater trust in the reliability of a brand or from a more favourable experience when a customer uses the brand. Bayus (1992) proposes that maintaining brand loyalty is becoming a critical component in the development of competitive strategy, thus highlighting the importance of developing methods to measure and evaluate brand loyalty. Davis (2002) identified further positive repercussions resulting from a strong brand other than simply increased sales. Effective brands have been correlated with increasing market share; lending credibility to new product developments; giving a clear, valued and sustainable point of difference as well as commanding a premium. Most importantly, consumers appear less pricesensitive and more trusting towards these brands. Private label branding Private label brands are available in a multitude of formats. The first being a representative brand, which is a private label brand that through its name and packaging announces that it is produced and solely owned by the retailer. In doing so, the research will ascertain the impact of various demographic factors (with particular reference to ethnicity, gender and income) on consumption of private label brands. Furthermore, it aims to shed lights on the effect that pricing, accessibility, packaging, retail communications, shelf positioning and in-store promotions have on shopping behaviour with reference to purchasing food-based private label brands. These are brands that are not owned by the retailer but are found exclusively in their stores. This type of private label brand has not been incorporated in this research study. Manufacturer brands on the other hand are controlled and produced by manufacturers and sold through a plethora of retailers. These include low quality generics; medium quality private labels; somewhat less expensive but comparable quality products; and premium quality private labels that are priced in excess of competitor manufacturer brands. According to Kumar and Steenkamp (2007), half of private label brands are copycat brands.

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