Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency

We introduce a new all-optical mechanism that can compress the bandwidth of light pulses to absolute zero, and bring them to a complete stop. The mechanism can be realized in a system consisting of a waveguide side coupled to tunable resonators, which generates a photonic band structure that represents a classical analogue of the electromagnetically induced transparency. The same system can also achieve a time-reversal operation. We demonstrate the operation of such a system by finite-difference time-domain simulations of an implementation in photonic crystals.

Figure 1

Schematic of a tunable waveguide system used to stop light. The disks and block represent the cavities and the waveguide. The arrows indicate available evanescent coupling pathways between the cavities and the waveguide. The system consists of a periodic array of two side cavities coupled to the waveguide, with a coupling rate of $1/\tau$. The distance between the nearest neighbor side cavities is $l_1$, and the length of the unit cell is $l=l_1+l_2$.

Figure 2

The photonic bands of the system of Fig. 1 for three different choices of $\Delta \equiv |{\omega }_A-{\omega }_B|\tau$. (a) $\Delta =3.277$. The bandwidth of the middle band is large. (b) $\Delta \approx 0.341$. The bandwidth goes to zero. (c) $\Delta =0$. The slope of the band flips its sign. The cavity resonance frequencies are given by ${\omega }_{A,B}={\omega }_c\mp \Delta /2\tau$ where ${\omega }_c=0.357(2\pi \mathrm{c}/a)$ and $1/\tau ={\omega }_c/235.8$. Here, $a$ is a length unit. The distances between the cavities are ${\ell }_1=2a$ and $\ell =8a$. The waveguide has a dispersion of $\beta =[0.278+0.327(\omega a/2\pi c-2.382)]/a$, which is actually a fit for the photonic crystal waveguide in Fig. 3.

Figure 3

Propagation of an optical pulse through a waveguide-resonator complex in a photonic crystal system as the resonant frequencies of the cavities are varied. The photonic crystal consists of 100 cavity pairs. Fragments of the photonic crystal are shown in (b). The three fragments correspond to unit cells 12–13, 55–56, and 97–98. The dots indicate the positions of the dielectric rods. The black dots represent the cavities. (a) The dashed green and black lines represent the variation of ${\omega }_A$ and ${\omega }_B$ as a function of time, respectively. The blue solid line is the intensity of the incident pulse as recorded at the beginning of the waveguide. The red dashed and solid lines represent the intensity at the end of the waveguide, in the absence and the presence of modulation, respectively. (b) Snapshots of the electric field distributions in the photonic crystal at the indicated times. Red and blue represent large positive and negative electric fields, respectively. The same color scale is used for all the panels.