Polarization mode dispersion

As the design of optical communication systems becomes more and more complex, an optical circulator with many input and output ports has become highly desirable. However, the port numbers for presently most commercial optical circulators are limited. In 2004, based on holographic spatial- and polarization-modules (HSPMs), two kinds design of holographic-type multi-port optical circulator were also proposed [Chen et al., 2004 Chen et al., 2004]. The HSPM is consisted of two HSWPs, an half-wave plate (H), and a Faraday rotator (FR). The merits of these designs include polarization-independence, compactness, high isolation, low polarization mode dispersion, and easy fabrication. Furthermore, the number of port can be scaled up easily. 

If the PBSs are located accurately in the configurations of Fig. 13(b) and 13(d), there will be no optical path difference between s- and p-polarizations for any route. Hence, this optical circulator can function as a polarization-independent 4-port optical circulator without polarization mode dispersion (PMD). 

Fig. 16. Structure and operation principles of the proposed multi-port optical quasicirculator without polarization mode dispersion.

Polarization-Selective Substrate-Mode Volume Holograms and Its Application to Optical Circulators introduces polarization-selective substrate-mode volume holograms which are applied in several novel designs of optical circulator. The described optical circulators have a number of advantages such as polarization-independence, compactness, high isolation, low polarization mode dispersion, easy fabrication, and low cost. In addition, the port number of the proposed multi-port device can be expanded easily. 

Polarization mode dispersion (PMD) Relative time (or phase) delay introduced by an optical device between two orthogonal polarization vectors of a light beam after passing through the device. 

Key performance parameters for all types of optical isolators are insertion loss and isolation, and in addition, for the polarization-independent optical isolators, polarization-dependent loss (PDL) and polarization mode dispersion (PMD) are important parameters as well. Performances (insertion loss and isolation) of an optical isolator can be estimated by using the Jones matrix. For example, insertion loss and isolation of a polarization-dependent isolator can be expressed as... 

There are three types optical signal of dispersion to consider and each has its own characteristics and challenges based on the specifics of the operating system. They are modal dispersion, chromatic dispersion, and polarization mode dispersion. 

Polarization mode dispersion (PMD) is comparatively more complex a concept than the other types of optical fiber dispersion discussed earlier, and until relatively recently it wasn t even considered to be a limitation that needed to be specified or addressed. As the effects of system chromatic dispersion have been mitigated by improved, complex fiber designs, and by the availability of dispersion compensating modules, the increased distances of long-haul transmission systems have moved PMD to the forefront as a major performance limiting factor. 

After ealeulating discrete values of frequency and relaxation time for the polarization mode and different wave veetors, a continuous function for the relaxation time and dispersion relations can be established for eaeh mode. The results shown in Fig. 3 are obtained with the Lennard-Jones potential for Argon. An approach similar to that described above can be applied with the Stillinger-Weber potential for silieon. 

In most materials, however, the modification of the forces at the surface is such that the surface localized modes have frequencies which lie below the frequencies of an associated bulk band with the same symmetry they have the appearance of having been peeled down from this bulk band [24]. In the usual case, the lowest energy of all these peeled -down modes derives from the bulk transverse acoustic band and is normally sagittally polarized. This dispersion branch is called the Rayleigh wave (RW) because it was predicted by Lord Rayleigh from continuum wave theory over a century ago [38]. Helium atom scattering experiments on virtually every material so far investigated have detected the RW on clean crystalline surfaces. 

Fig. 23. Phonon dispersion curves for a Xe monolayer on Cu(lOO) along the [100] substrate direction (after [97G]). Notations used R Cu(lOO) surface Rayleigh wave and SH perpendicular and shear horizontal Xe adlayer modes, respectively. The SH mode was first explained by assigning it to the longitudinal branch [97G,99S2], which required a large softening of the inplane Xe-Xe force constant. Later it was suggested [97B1,00B] that it should be assigned to the SH-polarized mode.

Fig. 30. Mixed-mode dispersions in ferromagnetic PrAlj at T = 4.4 K for the [001] direction. Full points represent experimental data from Purwins et al (1976), full curves are calculations by Aksenov et al. (1981), TA stands for transverse acoustic phonon, and and are exdton branches with different polarizations.

For the SN2 mode, however, increasing solvent polarity is found to have a much less marked effect, resulting in a slight decrease in reaction rate. This occurs because in this particular example new charge is not developed, and existing charge is dispersed, in the T.S. compared with the starting materials ... 

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