Time-dependent physical Stokes parameters and degree of polarization of light

We extend the concept of the Eberly-Wódkiewicz time-dependent physical spectrum of light to electromagnetic fields by considering the observable time dependence of four appropriately defined Stokes parameters. We also define the concept of time-dependent physical degree of polarization of light by means of these parameters, and discuss the measurement of these quantities using a tunable spectral filter and a detector with a finite response time. The concepts are illustrated by examples with spectrally phase-modulated fully and partially coherent model pulse trains.

Figure 1

Schematic diagram for the measurement of time-dependent physical Stokes parameters of a pulse train using a spectral filter F with spectral response $\mathbf{T}(\omega ,{\omega }_{\mathrm{F}})$, a retarder R with retardation $\delta$, a polarizer P oriented at an angle $\theta$, and a square-law detector D with temporal response $R\left(t\right)$.

Figure 2

(a) Distributions of the $x$ (thick solid) and $y$ (colored) components of the temporal intensity profile, normalized by $I_0={\mathrm{\Gamma }}_0/2$, and (b) the time-dependent degree of polarization $P\left(t\right)$ for the model pulse train. Here $\beta =1$, $A=1$, $\kappa =0$, and $\tau =0.25T$ (solid red), $\tau =0.5T$ (dashed green), $\tau =T$ (dotted blue).

Figure 3

Same as Fig. 2 but $\tau =0$ and $\kappa =2$. Solid red: $\beta =1$. Dashed green: $\beta =0.5$. Dotted blue: $\beta =0.25$.

Figure 4

Distributions of (normalized) time-dependent physical Stokes parameters (a, d) $S_0(t,{\omega }_{\mathrm{F}},R)$ and (b, e) $S_1(t,{\omega }_{\mathrm{F}},R)$, and (c, f) the degree of polarization $P(t,{\omega }_{\mathrm{F}},R)$ plotted as a function of $t/T$ (time axis) and $\left({\omega }_{\mathrm{F}}-{\omega }_0\right)/\mathrm{\Omega }$ (frequency axis). Left column: parameters $A=1$, $\beta =1$, $\tau =0$, $\kappa =5$, ${\mathrm{\Omega }}_{\mathrm{F}}=0.1\mathrm{\Omega }$, and $T_{\mathrm{R}}=10T$. Right column: parameters $A=1$, $\beta =0.5$, $\tau =T$, $\kappa =5$, ${\mathrm{\Omega }}_{\mathrm{F}}=0.1\mathrm{\Omega }$, and $T_{\mathrm{R}}=10T$. The plot range is [0,1] in (a, c, d, f), $\left[-0.025,0.04\right]$ in (b), and $\left[-0.055,0.055\right]$ in (e).