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Trajectories Describing the Evolution of Polarized Light in Homogeneous Anisotropic Media and Liquid Crystals
Full text linkTrajectories are given that describe the evolution of the ellipse of polarization in the complex plane for light propagating in a homogeneous anisotropic medium and along the helical axis of a cholesteric liquid crystal. For the general homogeneous anisotropic medium that exhibits combined birefringence and dichroism the trajectory is a spiral that converges to the low-absorption eigenpolarization. For pure birefringence the trajectory becomes a complete circle that encloses one eigenpolarization, whereas for pure dichroism the trajectory becomes an arc of a circle that ends at the low-absorption eigenstate. The case of a cholesteric (or twisted nematic) liquid crystal leads to an interesting family of trajectories that can be considered as distorted hypo- or epicycloids. These trajectories are nonrepetitive (open) and may show multilobes or branches depending upon the initial polarization and the properties of the liquid crystal. Graphs are also presented where the ellipticity and azimuth are plotted separately as functions of distance along the helical axis
Loci of Invariant-Azimuth and Invariant-Ellipticity Polarization States of an Optical System
Full text linkThe loci of polarization states for which either the ellipticity alone or the azimuth alone remains invariant upon passing through an optical system are introduced. The cartesian equations of these two loci are derived in the complex plane in which the polarization states are represented. The equations are quartic and are conveniently expressed in terms of the elements of the Jones. matrix of the optical system. As an exple the loci are determined for a system composed of a π/4 rotator followed by a quarter-wave retarder
Analogy Between Linear Optical Systems and Linear Two-Port Electrical Networks
Full text linkAttention is called to the analogy between linear optical systems and linear two-port electrical networks. For both, the transformation of a pair of oscillating quantities between input and output is of interest. The mapping of polarization by an optical system and of impedance (admittance) by a two-port network is described by a bilinear transformation. Therefore for each transfer property of a system of one type, there is a similar property for the system of the other type. Two-port electrical networks are synthesized whose impedance-(or admittance-) mapping properties are the same as the polarization-mapping properties of a given optical system. The opposite problem of finding the optical analogs of two-port networks is also considered. Besides unifying the methods of handling these two different kinds of systems, the analogy appears fruitful if used reciprocally to simulate electrical networks by optical systems, and vice versa. Linear mechanoacoustic systems have optical analogs besides their well-known electrical analogs
The Creole Case
Full text linkOn November 7, 1841, the slaves on board the American brig Creole bound from Richmond, Virginia, to New Orleans, rose in revolt and forced the crew to sail the vessel to the British port of Nassau in the Bahamas. There the authorities imprisoned 19 of those involved in the mutiny but freed the remaining blacks. Later, after receiving instructions from London, the 19 mutineers were also liberated despite the angry protests of southerners in the United States.
The Creole incident became the subject of acrimonious debate in both houses of Congress and resulted in the breaking of the gag rule: the self imposed regulation by which the House of Representatives attempted to avoid the time-consuming and disruptive debates which inevitably accompanied the introduction of the topic of slavery. Additionally the Creole case threatened to jeopardize the attempt of Lord Ashburton, the British special envoy, to solve many of the problems which were sources of tension between Great Britain and the United States.
As a result of the Creole mutiny, several insurance suits were filed. During the trials, held in New Orleans, Judah P. Benjamin wrote a rather remarkable brief in which he argued on behalf of the municipal theory of slavery before the bar of a southern court. Most of the owners of the Creole slaves were blocked at the local level in their attempts to recover damages for the loss of their property. They were forced to turn to the federal government for aid and were eventually reimbursed when their claims. were accepted according to the terms of the Anglo-American Claims Convention of 1853.
The Creole mutiny was the largest and perhaps the only successful revolt among United States blacks, yet, despite the recent burgeoning of black history and literature, the Creole case has received little attention. Most volumes concerned with slavery and slave revolts scarcely mention the Creole case and its dramatic qualities and historical importance remain virtually ignored