Focal fields

Finally, FDTD may be used to model the coupling of the focal field into the PhC-waveguide, potentially with the presence of an air or glue gap. Even such a simulation procedure with adapted numerical methods for each part of the propagation requires a considerable computation time. To speed up the simulation process for system optimisation remarkably, the FDTD-simulation can be replaced by a formula for the coupling efficiency to a conventional high-index or a PhC-waveguide, ... 

FIGURE 9.1 Amplitude and phase profiles of focal fields. Amplitude (a) and (b) phase in the focal xy-plane. Amplitude (c) and phase (d) in the yz-plane. The phase difference below and above the focal plane is a signature of the Gouy phase shift. The propagation phase was subtracted for clarity. Calculations are for a 1.1 NA water immersion lens and the wavelength is 800 nm. In the panels the lateral axis runs from -1.0 xm to 1.0 xm and the axial axis from -3 4m to 3 xm. 

A cross-sectional view (yz) of the amplitude and phase of the focal field along the optical axis is depicted in Figure 9.1c and d, respectively. The phase distribution is plotted in its unwrapped representation and the linear phase due to propagation has been subtracted for clarity. It is evident that the phase before the focal plane and the phase after the focal plane (z = 0) are not the same. Along the optical axis, the phase... 

We will assume that all the incident fields are polarized in the x-direction. The pump and Stokes focal fields, which each look like the complex fields depicted in Figure 9.1, set up an effective CARS excitation field E = (r) (r). The anti-Stokes polarization in the excitation volume induced by the effective excitation field can be considered as a collection of radiating dipoles. The resulting CARS amplitude at any far-field point Q with coordinates R = (R, 6, (j)) is a sum of the amplitude contributions form all these dipoles and is given by... 

The ability to control the phase of focal fields at different locations in the interaction volume has interesting applications when combined with interferometric mixing techniques. When a local oscillator field is focus engineered and overlapped with... 

The factors g (6), used in the calculation of the focal fields, are given as... 

Linear dispersion defines the extent to which a spectral interval is spread out across the focal field and is expressed in nanometre per millimetre (nm/mm) -(or its inverse, the reciprocal dispersion in mm/nm). Linear dispersion is associated with an instrument s ability to resolve fine spectral detail. It depends of several parameters such as the focal distances and the widths of entrance and exit slits of the instrument. In general the better the dispersion the greater is the physical separation distance between two given wavelengths (Figure 14.11). 

This phenomenon can be understood by considering the depolarization effect predicted by electromagnetic focusing theory [163, 164], It is already known that when the beam incident angle a is small, the focal field ( Ey> Ez) is sufficiently described by a cylindrically symmetric function [E(r), 0,0]... 

To decrease the contact surface (to assimilate it to a point) by the focalization of the magnetic field. 

We first supposed that the field radiated into the piece by the transducer is known, thanks to the Champ-Sons model. Then, the main approximation used consists in making far field assumptions in the beam defect interaction area. In the case of a focused transducer we assume that the incident wavefronts on the defect are plane. This is equivalent to say that the defect is located in or near the transducer focal area and that a defect located outside this zone does not cause a significant echo. In the case of planar contact transducer, the incident wavefronts on the defect are assumed to be spherical The incident field on the defect is therefore approximated by the product of a spatial function gfp,0,z)describing the amplitude distribution in the beam and a time-delayed waveform < ) ft) representing the plane or spherical propagation in the beam. The incident field on the defect can therefore be approximated for ... 

Similarly, the focusing capability of an array is the strongest focused beam which can be steered. The simplest way to evaluate it is to test a theoretical focusing time delay law, in the near-field and in the natural direction of propagation of the array. The beam pattern characteristics depth, lateral size and length of the focal spot must be found consistent with modelling and no lobe must appear above a predetermined level. 

Figure Bl.6.1 Equipotential surfaces have the shape of lenses in tlie field between two cylinders biased at different voltages. The focusing properties of the electron optical lens are specified by focal points located at focal lengthsandy2, measured relative to the principal planes, The two principal rays emanating...

From the early 1980s to present, infrared sensitive two dimensional arrays were mated to integrated circuits for signal processing and sensitivity to better than 0.03 K (see Photodetectors). These focal plane arrays of some 500 by 500 elements eliminate the need for scanning and provide good spatial resolution. Some versions have no special cooling requirements. The development trend is to increase the number of pixels to improve resolution, increase the field of view and keep the size and cost of the optics within acceptable bounds. 

In the x-ray portion of the spectmm, scientific CCDs have been utilized as imaging spectrometers for astronomical mapping of the sun (45), galactic diffuse x-ray background (46), and other x-ray sources. Additionally, scientific CCDs designed for x-ray detection are also used in the fields of x-ray diffraction, materials analysis, medicine, and dentistry. CCD focal planes designed for infrared photon detection have also been demonstrated in InSb (47) and HgCdTe (48) but are not available commercially. 

There are three primary image modes that are used in conventional TEM work, bright-field microscopy, dark-field microscopy, and high-resolution electron microscopy. In practice, the three image modes differ in the way in which an objective diaphragm is used as a filter in the back focal plane. 

Figure 5. Simplified schematic of the 2-D array of pixels in a focal plane array. The thin wafer of light sensitive material is partitioned into a two-dimensional array of pixels that collect the electric charge produced by the light. Each pixel is a three-dimensional volume that is defined by electric fields within the light sensitive material.

Although astronomy is accustomed to the detection of a few photons per pixel, the electric charge of a few electrons is extremely small. A critical part of the design of a focal plane array is the amplifier which converts the small amount of charge in each pixel into a signal that can be transmitted off the detector. The amplifier in an optical or infrared detectors is typically a field effect transistor (FET), a solid state structure which allows a very small amount... 

Very large diameters, beyond 100 m, now correspond exclusively to diluted apertures and amplitude interferometry. Another big challenge for the next two decades to develop kilometric arrays of telescopes, having optical coherent recombination, presumably with fiber optics, focal instmmentation with a significant field of view, etc. 

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