Use of four mirrors to rotate linear polarization but preserve input-output collinearity. II.

A geometric phase analysis is used to show that a minimum of four reflections is required to rotate the linear polarization of a laser beam by an angle 0 < ϕ < π, subject to the constraint that the final beam path be collinear with the incident one. Elementary spherical geometry is used to compute a series of beam propagation vectors that give an arbitrary ϕ rotation and to determine the necessary mirror orientations. The method is applied to the case of ϕ = π/2, which is useful for the design of a device needed in our laboratory. The properties of this device and the need for it are discussed in the light of operating experience with half-wave retardation plates used for polarization rotation of CO2 laser beams.

[1]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[2]  P. Koch,et al.  The importance of resonances in microwave “ionization” of excited hydrogen atoms , 1995 .

[3]  I. V. Goltser,et al.  Adjustable half-wave plate. , 1995, Applied optics.

[4]  Michael V Berry,et al.  Anticipations of the Geometric Phase , 1990 .

[5]  M. Berry.  Interpreting the anholonomy of coiled light , 1987, Nature.

[6]  Koch,et al.  Microwave-driven He Rydberg atoms: Floquet-state degeneracy lifted by a second frequency, Stueckelberg oscillations, and their destruction by added noise. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[7]  Kitano,et al.  Comment on "Observation of Berry's topological phase by use of an optical fiber" , 1987, Physical review letters.

[8]  Koch,et al.  Stueckelberg oscillations in the multiphoton excitation of helium Rydberg atoms: Observation with a pulse of coherent field and suppression by additive noise. , 1992, Physical review letters.

[9]  Wilkinson,et al.  Two topological phases in optics by means of a nonplanar Mach-Zehnder interferometer. , 1989, Physical review. A, General physics.

[10]  Koch,et al.  Electric-field dependence of E1 transitions between highly excited hydrogen Stark sublevels. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[11]  Mariani,et al.  Microwave multiphoton ionization and excitation of helium Rydberg atoms. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[12]  M. Berry.  Quantum chaology, not quantum chaos , 1989 .

[13]  Francis Arthur Jenkins,et al.  Fundamentals of Optics , 1976 .

[14]  Wu,et al.  Manifestations of Berry's topological phase for the photon. , 1986, Physical review letters.

[15]  Wilkinson,et al.  Observation of a topological phase by means of a nonplanar Mach-Zehnder interferometer. , 1988, Physical review letters.

[16]  F. Wilczek,et al.  Geometric Phases in Physics , 1989 .

[17]  P. Koch,et al.  Microwave “ionization” of excited hydrogen atoms: how nonclassical local stability brought about by scarred separatrix states is affected by broadband noise and by varying the pulse envelope , 1995 .

[18]  Tomita,et al.  Observation of Berry's topological phase by use of an optical fiber. , 1986, Physical review letters.

[19]  L. H. Johnston.  Broadband polarization rotator for the infrared. , 1977, Applied optics.

[20]  M. Berry.  Quantal phase factors accompanying adiabatic changes , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[21]  C E Greninger.  Reflective device for polarization rotation. , 1988, Applied optics.

[22]  Anatolii Viacheslavovich Sokolov,et al.  Optical Properties of Metals , 1967 .