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Z-scan. In this problem we develop a mathematical description of the zscan procedure for measuring the nonlinear refractive index. The basis of this procedure is that a sample is translated longitudinally through the beam-waist region of a focused gaussian laser beam, and the variation of the on-axis intensity in the far field is measured as a function of sample position. The on-axis intensity in the far field is usually determined by measuring the power transmitted through a small aperture placed on the system axis. The variation of measured power with sample position is found to be proportional to the nonlinear phase shift experienced in passing through the sample, and from this measured phase shift the value of n2 of the sample can be determined from the known sample thickness L and laser intensity at the sample In detail, you are to derive an expression for the dependence of the fractional change in on-axis intensity ?I/I on the sample position z relative to the position z0 of the beam waist of the incident laser beam. This expression will also depend on the values of n2, of L, and on the parameters of the incident laser beam. For simplicity, assume that the sample is thin both in the sense that L is much smaller than the confocal parameter b of the incident laser beam and in that the maximum nonlinear phase shift acquired in passing through the sample is much smaller than unity. Here are some suggestions on how to proceed. Begin with the expression for a gaussian laser beam. Determine first how the beam will be modified in passing through the nonlinear material. Note that under the assumed conditions the beam diameter at the sample will be unchanged, but that the wave front curvature will be modified by nonlinear refraction. Note that the modified beam itself approximates a gaussian beam, but with a different value of the wavefront radius of curvature. By assuming that this beam propagates according to the same laws that govern the propagation of a gaussian beam, determine its on-axis intensity in the far field as a function of z - z0. Note that a more detailed analysis of the z-scan procedure (SheikBahae et al., 1990) leads to the somewhat different result
Where max is the nonlinear phase shift on-axis when the sample is at the beam waist of the incident laser beam. Plot the functional dependence of both your result and the literature result
At a given instant, the position of a plane at A and a train at B are measured relative to a radar antenna at O. Determine the distance d between A and B at this instant.
Consider a wide flange steel beam of size W10x60 subjected to a negative bending moment of 24 kip ft. Calculate the maximum compressive and maximum tensile stresses and indicate where the stress will be tensile and where compressive.
two links AB and DE are connected by a bell crank as shown. Determine the maximum force that can be safely exerted by link AB on the bell crank if the maximum allowable value for the reaction at C is 1600N.
Calculate the time average F of the total force tangent to the toad exerted on the tires during the 8 s. Treat the car as a particle and neglect air resistance.
A natural-draft cooling tower is to remove 50 MW of waste heat from the cooling water that enters the tower at 42°C and leaves at 27°C.
Drawdown at a 0.20-m-diameter, fully penetrating well, which has been pumping at the rate of 1000 m^3/day for a long enough time that steady-state conditions have been reached, is determined to be 0.70 m.
A 6-lane freeway horiz. alignment has a 1200' C.L. radius going into a tangent and then a reversing 1800' radius. How much tangent distance between the two curves is needed to meet the superelevation runoff requirements
Calculate the minimum set-back distance required for a national highway of 4 lane divided carriageway having circular curve of radius of 350 m & design speed 100 km/hr.
Box I contains 3 red and 5 white balls, while Box II contains 4 red and 2 white balls. A ball is chosen at random from the first box and placed in the second box without observing it's color. Then a ball is drawn from the second box.
An important dimensionless parameter in certain types of fluid flow problems is the Froude number defined as V/(gl)^1/2 where V is a velocity, g the acceleration of gravity, and l a length
The natural air flow rate to this industrial shade structure is 90 m3/hour. Determine the risk to the workers who work 8 hours/day, 50 weeks/year for 30 years. Assume workers are 75 kg and live for 70 years.
Block A, 5lb, strikes block B, 10lb. Block A is moving with the intial velocity, Va, and block B is at rest. After striking block B, block A travels 2 in. to the right and block B travels 3 in. to the right.
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