Polarization perturbed fibers

The description of the modal fields on the perturbed fiber will be complete once the polarization of the transverse components is specified. 

If the unperturbed fiber is noncircular, the transverse electric field of each mode is polarized parallel to one of the optical axes, Xq or as discussed in Sections 13-5 and 13-8. The directions of the optical axes on the perturbed fiber, which determine the polarization of the perturbed mode fields, are found either by inspection or by the formal methods of Section 32-5. 

In many of the examples below, the unperturbed fiber has a circularly symmetric cross-section and profile. For perturbations which maintain this symmetry, the polarization of each mode is unchanged, and obeys the rules laid down in Sections 13-4 and 13-7. However, for perturbations which break circular symmetry, the modes are polarized along the optical axes and y of the perturbed fiber. Only the fundamental and HE, modes remain plane polarized on the circular and noncircular fibers. If the perturbation is sufficiently small, the polarization of all other modes lies in the transition region between the circular and noncircular situations, as discussed in Section 13-9. 

The unperturbed fiber has refractive-index profile h(x, y) and the perturbed fiber has z-dependent nonuniformities described by n(x, y, z). Both fibers are weakly guiding and we assume h = n s n j everywhere. For reasons given in the previous section, we ignore all polarization effects and work solely with solutions of the scalar wave equation. For convenience we assume the electric field is x-polarized and set... 

The standard measurement of different properties of quantum electromagnetic radiation is based on the photodetection, which is field destructive. Following our consideration of the possibility of the Aharonov-Bohm effect at optical frequencies [100], we propose here a new nondemolition method of polarization measurement in which the linearly polarized longitudinal mode of the field is detected without any perturbation of its quantum state (Section VI.D). The estimation of physical conditions shows that such a measurement can be done either for the photons propagating through the fiber, or for the superradiant photons in radioband frequencies. 

Due to of the mass-production of single-mode fibers, they are cheaper than other t3rpes and therefore often preferred for sensor purposes. For special purposes, such as pressure or current measurements, and sometimes for impact detection, high-birefringent (Hi-Bi) polarization-maintaining (PM) fibers are used because the polarization state of the output signal is definitely affected by external perturbations. 

Fig. 1. Schematic diagram of the electric field/temperature-jump apparatus. The equilibrium solution in the sample cell is perturbed by a square pulse produced by the high voltage pulse generator (HV PG). It consists of an energy storage (ES) unit, spark gaps (G I and G II) and a probe (PR). The analyzing light source [power supply (PS), lamp (L), monochromator (M), polarizer (P)] and the detector [analyzer (A), fiber optic (FO), photo multiplier (PM), power supply (PS), oscilloscope (OSC)] represent the detection system. The timing control provides for synchronization.

Perturbation solution for isolated fibers 18-2 Polarization of the perturbed fields 18-3 Uniform changes in profile... 

For slight perturbations, it is normally sufficient to assume that the transverse, or X, y dependence of the modal fields on the perturbed and unperturbed fibers is similar, i.e. e S e, h = h, and consequently T =. An exception is the calculation of the polarization corrections to the scalar propagation constant, discussed in the following section, for which higher-order corrections to are required. These can be obtained using either eigenfunction expansions, as outlined in Sections 33-9 and 33-10, or Green s functions, as discussed in Chapter 34. 

The polarization corrections, and SPy, to the scalar propagation constant P for the Xq- and yo-polarized modes on the perturbed, noncircular fiber are in general unequal, and their difference describes the anisotropic, or birefringent, nature of propagation. This is of basic interest for the two fundamental modes on single-mode fibers. The calculation of the corrections from the formula in Table 13-1, page 288, requires first-order corrections to the approximation We derive these corrections for the slightly elliptical fiber in Section 18-10. 

Consider an unperturbed fiber with the step profile of Fig. 18-7. The perturbed profile includes the narrow hatched region. Relative to the cylindrical polar directions in Fig. 14-1, the tangential, i.e. azimuthal and longitudinal components and e of the perturbed electric field are continuous across the interfaces at r = r, and r = rj. Hence e = e and e, S e everywhere including the perturbation region. However, since n changes abruptly from n to Hq at the interfaces, the normal, or radial, component e must be discontinuous to ensure continuity of n e. Consequently e differs from e within the perturbation region, the difference... 

Radiation from the sinusoidally perturbed interface of a weakly guiding, step-profile fiber was discussed in Section 22-5 in terms of the induced current of Eq. (22-15). When the fiber is single moded, power is scattered into both forward- and backward-propagating x-polarized fundamental modes from the incident mode. Following the discussion of Section 22-5, we set... 

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