Real-Space Observation of Ultraslow Light in Photonic Crystal Waveguides

We show the real-space observation of fast and slow pulses propagating inside a photonic crystal waveguide by time-resolved near-field scanning optical microscopy. Local phase and group velocities of modes are measured. For a specific optical frequency we observe a localized pattern associated with a flat band in the dispersion diagram. During at least $3\mathrm{p}\mathrm{s}$, movement of this field is hardly discernible: its group velocity would be at most $c/1000$. The huge trapping times without the use of a cavity reveal new perspectives for dispersion and time control within photonic crystals.

Figure 1

(a) Schematic representation of a pulse tracking experiment on a W3 PhCW. The evanescent field of a propagating pulse is picked up by a metal coated fiber probe with a subwavelength-sized aperture and interferometrically mixed with light from a reference branch. The inset shows the probe used in the experiment. The aperture size ($\varphi =240\mathrm{n}\mathrm{m}$) in the first approximation determines the optical resolution. Measurements are done by raster scanning the optical probe across the structure at a constant height ($<10\mathrm{n}\mathrm{m}$). (b) Top view of the PhCW under study, although with a shorter device length.

Figure 2

A time-resolved NSOM measurement on a W3 PhCW ($a=460\mathrm{n}\mathrm{m}$). (a) Topographic image of the structure rotated $90°$ with respect to Fig. 1b. (b)–(g) The optical amplitude in the W3 PhCW for different reference times ($400\pm 1\mathrm{f}\mathrm{s}$ between frames; all frames have the same color scale). A movie displaying the pulse propagation is available [20]. It is apparent that pulses with different modal distributions and group velocities are excited in the W3 waveguide. (h) The measured position of the center of mass for pulses with different modal distributions (and different wave vectors) as a function of the delay time. The dotted line represents the start of the PhC.

Figure 3

(a) Experimental dispersion diagram of the modes excited in the W3 PhCW. Displayed is the spatial Fourier transform of data for multiple excitation frequencies. The location of the slowest mode ($k=0.607$) observed in Fig. 2 is indicated by 1. Its measured group velocity gives an independent measure for the slope of its dispersion curve (green dotted line). (b) Simulated dispersion diagram. The local slope of the calculated band structure for $k=0.607$ (indicated by $1$) gives an expected group velocity of $0.115\times c$ in good agreement with the measured value of $(0.121\pm 0.001)\times c$. Comparing Fig. 3b with the measured band structure in Fig. 3a reveals a flat band around $\omega =0.305$ (indicated by $3$).

Figure 4

Pulse tracking experiment at a flat band at $\omega =0.305$ ($\lambda =1310\mathrm{n}\mathrm{m}$, $a=400\mathrm{n}\mathrm{m}$). (a) Topography of the PhCW. (b)–(k) The optical amplitude as a function of reference time (all frames have the same color scale). A movie displaying the pulse propagation is available [20]. We observe a complex and stationary localized modal pattern in the first $25\mu \mathrm{m}$ of the PhCW which exists for more than $3.6\mathrm{p}\mathrm{s}$ after the excitation pulse has moved away. The field pattern moves by less than $0.9\mu \mathrm{m}$ in $3\mathrm{p}\mathrm{s}$, suggesting a group velocity of less than $c/1000$. Note that all light observed in (f) through (k) belongs to the same mode located between $k=0.4–0.6$, unlike in Fig. 2 where various discrete wave vectors are present simultaneously.