WOLFRAM|DEMONSTRATIONS PROJECT

Polarized Polariton Fields on the Poincaré Sphere

​
system settings
Rabi frequency g
4
phase delay ϕa
0
polariton lifetime γ
2
right polarized pulse settings

α
R
i
θ
α
R
e
〉 and 
β
R
i
θ
β
R
e
〉
α
R
0.41
θ
α
R
0
β
R
1
θβR
0
left polarized pulse settings

α
L
i
θ
α
L
e
〉 and 
β
L
i
θ
β
L
e
〉
α
L
1.
θ
α
L
0
β
L
0.415
θ
β
L
0
time
0
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
ψ=
α
R
i
θ
α
R
e
⊗
β
R
i
θ
β
R
e
⊗
α
L
i
θ
α
L
+ϕa
e
⊗
β
L
i
θ
β
L
+ϕa
e

at
t=0
[4].
This Demonstration lets you tune these parameters as well as the system parameters (Rabi frequency
g
, polariton lifetime
γ
) and track the state of polarization in time. Without decay (
γ=0
), the polarization describes a green circle, whereas with decay (
γ≠0
), 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.