Slow light in coupled periodic photonic structures

Slow light has established itself over the past decade as one of the most active research fields in multiple disciplines. Intrigued by its fundamental science and practical application of delay for all-optical signal processing and many others, various approaches for reducing the group velocity - including periodic photonic structures - have developed the key principles of achieving individual slow-light states. To contribute to the cause, we propose new approaches for light manipulation based on the interaction between multiple slow-light states in coupled periodic waveguides. We first study Bragg grating couplers and reveal that if the gratings are shifted longitudinally - ideally by half a period - two different slow modes exist near the photonic band-edge. In the linear regime, the interaction manifests in the form of slow-light tunnelling between the waveguides, and we experimentally measure the transmission from directly laser-written structures to demonstrate the precise control of the shift needed for observing such phenomenon. In the nonlinear regime, we can control the optical power to compensate for dispersion-induced broadening of pulses through the formation of gap solitons, switch the output between the waveguides, and tune the delay simultaneously. We find that the conditions for slow-light tunelling are in fact generic and can be satisfied similarly in other anti-symmetrically coupled periodic structures. Such a slow-light regime, as our studies reveal, is unique in that it features non-vanishing vortex energy flows inside the structure even at zero group velocity. In antisymmetric photonic crystal couplers, the frequency-independent, short coupling length allows dispersionless tunnelling of slow-light pulses. Experimental study of slow light in periodic waveguides requires accurate data analysis, and the spatial Fourier analysis is conventionally used for extracting the dispersion relations from measurements with near-field scanning optical microscopy. However, its resolution in k-space is inversely proportional to the length of the structure. By using the properties of Bloch-wave symmetry, we develop a general approach that has no inherent resolution limit. Furthermore, it can extract both the real and the imaginary parts of the wavenumber and the spatial profiles of the individual modes, none of which is possible with the spatial Fourier analysis. We demonstrate these abilities by analysing numerical and experimental data for short slow-light waveguides that support multiple propagating and evanescent modes. Finally, we present the first experimental proof of principle for slow-light tunnelling, in antisymmetrically coupled array of pillars scaled to operate at the microwave frequencies. We apply our Bloch-mode extraction method to retrieve the dispersion relations and the two-dimensional profiles of the individual modes. Such structures also act as side-coupled cavities and we show that breaking the structure symmetry through the longitudinal shift adds another degree of flexibility in controlling the frequency detuning between cavity modes. Shifted cavities allow nontrivial coupling between two pairs of counter-propagating waves due to split band-edges, and we experimentally confirm that this leads to the reduction of the detuning, even down to zero. Our results suggest new possibilities for light manipulation based on the interaction between multiple slow-light states, including resonators, nonlinear wave mixing and switching in tunable structures