Optical Physics

Prof. Enrique J. Galvez is directing a new project to study the manifestations of Geometric Phase in optics. When a system is transported through a path in the space of parameters or states it acquires a phase that depends on the topology of the phase. This is a consequence of parallel transport (an interesting website on this). We have been involved in studying three manifestations:

Coiled Light in Polarization Rotation

One manifestation is in Polarization Rotators. If we send an optical beam in a three-dimensional path, geometric phase will manifest itself by a rotation of the polarization of a linearly polarized optical beam. This phenomenon has important and new applications. An article describing a geometric phase rotator that rotates the polarization of an infra-red beam by 90 degrees using four mirrors is:

Unfortunately one cannot make a simple Geometric-Phase rotator based on reflections in the visible because ordinary reflections change the state of polarization. Matt Cheyne worked on designing a reflector that preserved the state of polarization for his Phys310 project (Spring 98). It involved coating glass surfaces with dielectric thin films. These reflections were used to construct the prism-version of the Variable-Angle Porro (VAP), a variable geometric phase rotator for the visible. Below is a photo of Matt testing the polarization properties of the VAP made of uncoated prisms.

An article that describes the theory and test results of the VAP and the new Variable Compensating Phase-Shift  Rotator (VCPS), which is achromatic, appeared recently:
    Variable Geometric Phase Polarization Rotators for the Visible, E.J. Galvez, M.R. Cheyne, J.B. Stewart, C.D. Holmes and H.I. Sztul. Optics Communications 171, 7-13 (1999). Reprints available

This work was presented at the 1999 OSA Meeting in Santa Clara:

New Geometric-Phase Polarization Rotators for the Visible
E.J. Galvez and H.I. Sztul
Abstract

We present new pure polarization rotators based on coiled-light geometric phase. They preserve the state of polarization and rotate linear or elliptical polarization by a variable amount. Operation in the visible is either broadband with polarization-preserving reflectors or achromatic with a polarization-preserving system of reflections.

 

In the summer of 1998 Jason Stewart later found a set of commercial mirrors that preserved the state of polarization at the HeNe laser wavelength (633 nm). Below he is shown testing a mirror-based VAP.

An offspring of the VCPS rotator is a CPS Beam displacer, a device that displaces an optical beam preserving the state of polarization. An article on this topic has been submitted for publication (2001): "Achromatic Polarization-Preserving Beam Displacer." 

Coiled Light in Image Rotation

Geometric Phase also manifests in the rotation of images. An article describing the theory and experiments of the geometric phase of image-bearing optical beams via reflections is:

Chris Holmes (Norwich Highschool-- now at Williams College) was instrumental in the development and testing of this theory (summer 1998).

Initial stages of the work described above were presented at the 1998 OSA Meeting in Baltimore:

 

Pancharatnam Phase

More recently we have been studying the connections between Coiled-light phase and Pancharatnam phase. A recent presentation on the topic was:

"Toward a Unified Optical Geometric Phase: Equivalences between Coiled Light and Pancharatnam Phases," E.J. Galvez and H.I. Sztul, 1999 Atomic Physics Gordon Conference, Plymouth NH.

Below is Henry Sztul working on the experiments on the summer  of 1999:

henry1.tif (1156508 bytes)

[Background image is an interference pattern using a corner-cube Michelson Interferometer taken by Chris Eger '99: when the two corner cubes are not axially oriented 60 degrees from each other the non-polarization-conserving properties of the reflections in the corner cubes manifest--the interference pattern is not smooth and continuous as with a plane mirror interferometer.]

Geometric Phase of Gaussian Beam Mode Transformations

A new and recent project we are working on involves the geometric phase that results from cyclic changes in the modes of a higher-order Gaussian beam. A set of the beam modes carry orbital angular momentum. Henry Sztul (Spring 2000 and 2001) and PJ Haglin (Summer 2000) have been working on this project. We have done the first measurements of this phase for optical beams. This work was be presented at the 2001 Meeting of the Division of the Atomic Molecular and Optical Physics of the American Physical Society: "Experiments on a New Optical Geometric Phase in Gaussian Beam Mode Transformations" by E.J. Galvez, H.I. Sztul and P.J. Haglin. An article describing this measurements will appear in Coherence and Quantum Optics VIII (preprint). In progress: direct measurements of this phase.

One way to produce orbital-angular-momentum-bearing optical beams involves forcing an open-frame HeNe laser to lase in a high-order mode, such as a  Hermite- Gauss (HG) TEM01 beam (). This beam does not carry orbital angular momentum. However, it is transformed into one by taking advantage of the Gouy phase shift, the phase shift that a beam experiences when it goes through a focal point (see it for yourself -mpg video by Henry Sztul). This method is well known [see for example M. Padgett et al. Am. . Phys 64, 77-82 (1996)]. The resulting orbital angular momentum bearing beam is described by Laguerre-Gauss functions. The first-order Laguerre-Gauss (LG) TEM01 mode looks like: . The orbital angular momentum property comes from the phase structure of the beam. For the beam shown above the phase depends on the axial angle. This angular dependence of the phase is manifested by unique interference patterns, like the one shown below:

This pattern was generated  with a Mach-Zender interferometer, with one arm carrying a LG beam and the other one an HG beam (part of the one that generated the LG beam). One lobe of the HG beam is expanded and interfered with the LG beam. If we change the optical path length of one of the arms we get the ...Mesmerizer! (Short mpg video made by Henry Sztul.) More recently we have been producing LG beams with computer- generated holograms.

This work has received support by an award from Research Corporation: "Geometric Phase of Optical Beams Possessing Angular Momentum" (2000-2002) and from NSF grant RUI-9988004.

 

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