Direct Observation of Subluminal and Superluminal Velocity Swinging in Coupled Mode Optical Propagation

A direct measure of the periodical power exchange between optical coupled modes with different polarization states is presented. The effects of the coupling on the relative velocity of the two modes are experimentally observed and analytically explained. Coupled modes are discovered to periodically attract and repel under the effect of swinging subluminal and superluminal regimes. The measurement technique is based on a novel polarization-sensitive scheme for optical low-coherence interferometry, providing in time domain the complex amplitudes of the interacting fields.

Figure 1

Polarization-sensitive OLCI: schematic of the relative time delay introduced by the two PM fibers at the input and output of the DUT (a) and OLCI experimental setup for measurements of polarization coupling in optical devices (b).

Figure 2

OLCI interference pattern of the phase shifter ($\mathrm{FSR}=100\mathrm{GHz}$) shown in the inset. Each set $S_n$, corresponding to the field outgoing the resonator after $n$ round-trips, contains the four time-resolved contributions $h_{uv,n}$ disclosed in Fig. 1a.

Figure 3

Coupled mode propagation along the bend of the ring-resonator phase shifter of Fig. 2. (a) Measured conversion efficiency $K_{me}$ (circles) and $K_{mm}$ (squares). In solid lines, the CMT numerical fitting is reported. The dashed-dotted line shows the predicted conversion in the synchronous coupling case. (b) Measured relative group delay ${\tau }_r$ between the TM and TE coupled modes (circles) and CMT prediction (solid line). Dashed line and dashed-dotted line show the relative delay in the case ${\kappa }_p=0$ and $\Delta \beta ({\lambda }_0)=0$, respectively. (c) Normalized instantaneous group velocity of the coupled (solid lines) and uncoupled (dashed lines) modes in the bend.

Figure 4

CMT simulation of the temporal envelopes of the coupled modes $h_{mm,n}(\tau )$ and $h_{me,n}(\tau )$ after $n=0$, 5 and 7 round trips in the ring resonator of Fig. 2.