An unsettled discussion on the bounds of the geometric phase motivates us to explore its differences with the propagation phase. We prepare an experiment that allows us to modify both phases in the same setup and record the effect this has on white light interference fringes. Our results show clear differences between the phases where the propagation phase moves the white light interference pattern as a whole but the geometric phase does not. We present the addition of the geometric phase as we stack two retarders and compare it to the addition of the propagation phase obtained when stacking two glass windows.
We present a summarized and simplified introduction to our wave description of geometric phase. We start by discussing the addition of cosine waves of different amplitudes and a phase between them, from which immediately arises the geometric phase in 1D. We then expand on the analysis to the 2D case using the orthogonal components of a polarized light wave. We then show a graphic visualization that facilitates the analysis of geometric phase and use it to quantify the geometric phase obtained by passing different states of polarization through a quarter wave plate.
In a typical interferometric experiment, the overlap between the reference and probe beams produces an intensity pattern composed of fringes. This fringe pattern contains information regarding the interaction of the probe beam with the sample. If the probe beam passes through a polarizing system, it acquires both a dynamic and geometric phase. The former related to the optical pathlength, whereas the latter related to changes in the state of polarization. As a consequence, the fringe pattern suffers a lateral spatial shift and, mainly due to the geometric phase, change its visibility. In this work, we derive simple expressions relating the fringe visibility with the geometric phase and retardance introduced by the polarizing optical system, in terms of the input polarization state. By doing so, we extract the eigenvectors and eigenvalues of the Jones matrix that characterizes the sample. Therefore, our results enable the implementation of a fringe polarimetry technique, i.e., we can infer the polarization properties of the test sample through visibility measurements.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.