Coherence Constraints and the Last Hidden Optical Coherence

We have discovered a new domain of optical coherence, and show that it is the third and last member of a previously unreported fundamental triad of coherences. These are unified by our derivation of a parallel triad of coherence constraints that take the form of complementarity relations. We have been able to enter this new coherence domain experimentally and we describe the novel tomographic approach devised for that purpose.

Figure 1

Schematic experimental setup. Light field (14) is prepared with a spatial light modulator (SLM) and a modified Mach-Zehnder interferometer (MZI), where filter (F) controls $\theta$ and the translation stage (TS) manages $\delta$ and $\varphi$. The Stokes parameters are measured with different combinations of a mode converter (MC), a Dove prism (DP2), and a Mach-Zehnder interferometer with an additional mirror (MZIM).

Figure 2

Experimental data of various time-space polarization states. Plot (a) is a Poincaré sphere representation of all measured states where the blue dots, black triangles, and red squares denote linear, elliptical (including circular), and partial (including completely unpolarized) polarization states, respectively. Plot (b) shows points on the equatorial plane $S_3=0$, and it contains all the linear $tr$ states. Plot (c) shows points in the $S_1=0$ plane where the black upward triangles, black downward triangles, and red squares denote elliptical, circular and partially coherent $tr$ states, respectively. The red dotted curve is the logarithmic polar spiral function $\delta =e^{-0.23\varphi }$ tracking states with smaller and smaller degrees of $tr$ coherence. Note: the error bars of the measured Stokes parameters are relatively small and not shown, but the magnitude of the maximum error is given in Table 1.