Polarized Polariton Fields on the Poincaré Sphere

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The state of polarization of light can be represented on the so-called Poincaré sphere, which provides a graphic representation of the Stokes parameters [1]. The circular-right polarization R corresponds to the north pole of the sphere and the circular-left polarization L to the south pole. The other cardinal points define the diagonal D, antidiagonal A, horizontal H, and vertical V polarizations. The Poincaré sphere can be used to track the state of polarization in a variety of contexts, such as spatial variations [2].


This Demonstration addresses the case of temporal variation. It shows the evolution in time of the polarization of light emitted by superimposing polariton fields, that is, from the light-matter interaction (Rabi coupling) in a semiconductor microcavity. It was recently proposed theoretically, and demonstrated experimentally [3], that such systems can afford a largely tunable spanning of the Poincaré sphere, depending on the parameters of two pulses exciting the system to create the state

at [4].

This Demonstration lets you tune these parameters as well as the system parameters (Rabi frequency , polariton lifetime ) and track the state of polarization in time. Without decay (), the polarization describes a green circle, whereas with decay (), the polarization drifts around the sphere to converge to an asymptotic value, pointed to by the red arrow; the blue line shows the polarization trajectory between these two points, which can be tracked in time with the purple arrow.


Contributed by: David Colas, Elena del Valle, and Fabrice P. Laussy (February 2015)
Open content licensed under CC BY-NC-SA



Various trajectories of the polarization on the Poincaré sphere:

Snapshot 1: spanning of the hemisphere from linear to right-circular polarization

Snapshot 2: close to full span of the Poincaré sphere, approaching so-called full Poincaré beams

Snapshot 3: nontrivial fast-varying polarization trajectory in strongly dissipative systems


[1] D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, "Spanning the Full Poincaré Sphere with Polariton Rabi Oscillations." arxiv.org/abs/1412.4758.

[2] L. Dominici, D. Colas, S. Donati, J.  P. Restrepo Cuartas, M. De Giorgi, D. Ballarini, G. Guirales, J. C. López Carreño, A. Bramati, G. Gigli, E. del Valle, F.  P. Laussy, and D. Sanvitto, "Ultrafast Control and Rabi Oscillations of Polaritons," Physical Review Letters, 113, 2014 p. 226401. journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.226401.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.