Spot size circular fiber

The profile function of Eq. (17-8) becomes the profile function f R ) for the circular fiber, and the spot-size equations of Table 17-1 are transformed to... 

We substitute Eqs. (17-14) to (17-17) into Eq. (17-12a) and equate powers of e. To lowest order we recover the spot-size equation of Table 15-1, page 339, for the circular fiber, and to second order deduce that... 

Thus, if the spot size for the circular fiber is known, the spot sizes for the... 

The step profile has uniform core and cladding indices and n, respectively, separated by the elliptical interface (x/p,) + y/Pyf = 1, relative to the axes in Fig. 16-1. The spot-size equations of Eq. (17-12) are expressed in terms of the profile function for the step-profile, circular fiber. Hence df/dR = 5 R — 1), where 6 is the Dirac delta function, and, on adding and subtracting Eqs. (17-12a) and (17-12b), we find that... 

Once a suitable crystal has been obtained, the structure of a molecule of moderate size can often be determined in a day or so. The crystal is mounted on a glass fiber (or in a glass capillary containing an inert gas, if the substance reacts with air) and placed on a pin or spindle within the circular assembly of the x-ray diffractometer (Figure 11.50). The crystal and x-ray detector (placed on the opposite side of the crystal from the x-ray tube) rotate under computer control, while the computer records the intensities and angles of thousands of x-ray reflection spots. After computer analysis of the data, the molecular structure is printed out. 

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