Engineering the electromagnetic vacuum for controlling light with light in a photonic-band-gap microchip

We demonstrate a trimodal waveguide architecture in a three-dimensional (3D) photonic-band-gap (PBG) material, in which the local electromagnetic density of states (LDOS) within and adjacent to the waveguide exhibits a forklike wavelength filter characteristic. This facilitates the control and switching of one laser beam with other laser beams ( similar to1 muW steady-state holding power and similar to5 nW switching power) through mutual coherent resonant interaction with quantum dots. Two waveguide modes provide narrow spectral windows where the electromagnetic LDOS is enhanced by a factor of 100 or more relative to the background LDOS of a third air-waveguide mode with nearly linear dispersion. This engineered vacuum can be used for frequency-selective, atomic population inversion and switching (by coherent resonant optical pumping) of an inhomogeneously broadened collection of atoms situated adjacent to the waveguide channel. The inverted atomic system can then be used to coherently amplify fast optical pulses propagating through the third waveguide mode. This coherent control of light with light occurs without recourse to microcavity resonances (involving long cavity buildup and decay times for the optical field). Our architecture facilitates steady-state coherent pumping of the atomic system (on the lower-frequency LDOS peak) to just below the gain threshold. The higher-frequency LDOS peak is chosen to coincide with the upper Mollow sideband of the same atomic resonance fluorescence spectrum. The probing laser is adjusted to the lower Mollow sideband, which couples to the linear dispersion (high group velocity part) of the third waveguide mode. This architecture enables rapid modulation (switching) of light at the lower Mollow sideband frequency through light pulses conveyed by the linear dispersion mode at frequencies corresponding to the central Mollow component (lower LDOS peak). We demonstrate that LDOS jumps of order 100 can occur on frequency scales of Deltaomega approximate to 10(-4) omega(c) (where omega(c) is the frequency of the jump) in a finite-size 3D photonic crystal (PC) consisting of only 10 X 10 X 20 unit cells. When the semiconductor backbone of the PC has a refractive index of 3.5 and omega(c) corresponds to a wavelength of 1.5 mum, this vacuum engineering may be achieved in a sample whose largest dimension is about 12 mum.