Coherent control of time delay and localized electromagnetic modes in active and passive one-dimensional photonic band gaps

We theoretically study coherent control of localized electromagnetic modes in one-dimensional active and passive photonic band gaps using infrared-induced quantum interference in the conduction intersubband transitions of an $n$-doped quantum well structure. For the active photonic band gap, we consider a waveguide structure containing a longitudinal corrugation of several periods of such a quantum well structure with a constant phase slip at its center. We show that interaction of the waveguide structure with an infrared laser beam can induce quantum coherence, causing localization of an optical mode as the forbidden band is coherently generated. To dynamically control localized electromagnetic modes in a passive photonic band gap we consider several periods of the same quantum well structure are inserted in a region at the middle of a waveguide structure containing corrugation of semiconductor materials with different nonresonant refractive indices. We show that when the infrared laser influences this region, which is acting as an active defect site, quantum interference in the conduction intersubband transitions resonantly enhances the effective refractive index of this region, while its absorption can become either zero, positive (loss), or negative (gain). This allows us to displace transmission peaks associated with the localized electromagnetic modes within the photonic band gap, or to annihilate them at given frequencies and recreate them at some other frequencies. We investigate how these processes can be used to coherently control time delay of the light pulses passing though these photonic band gap structures using the infrared laser intensity and frequency.

Figure 1

Schematic representations of the active 1D photonic band gap structure with a constant phase slip (a) and the passive 1D photonic band gap structure with an active defect site at its center (b). In (a) the central black part refers to the passive defect site and the gray regions with horizontal lines to the sections where the QWs are etched periodically and refilled epitaxially with a semiconductor material. The central horizontal lines in (b) refer to the QW region acting as an active defect site. The thick arrows indicate the propagation direction of the signal field. In both cases the control field, like the signal field, is polarized along the growth direction, but it propagates perpendicular to the signal field.

Figure 2

Schematic diagram of the triple $n$-doped $\mathrm{In}\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{In}\mathrm{As}$ QW structure. ∣g⟩ is the ground state of the QW, and ∣1⟩ and ∣2⟩ are its lower and upper transition subbands, respectively. ${\omega }_s$ and ${\omega }_c$ refer, respectively, to the signal and control field frequencies.

Figure 3

The absorption coefficient (a) and refractive index change (b) of the 1-2 transition. The solid, dashed, dotted, and dashed-dotted lines refer, respectively, to the simulation results obtained assuming $I_c=0.003,0.022,0.22$, and $1\mathrm{MW}∕{\mathrm{cm}}^2$.

Figure 4

Reflection of the active 1D PBG with a passive defect site at its center site for different values of the control laser intensity $I_c$ (in $\mathrm{MW}∕{\mathrm{cm}}^2$).

Figure 5

Transmission of the active 1D PBG with a passive defect site at its center for different values of the control laser intensity $I_c$ (in $\mathrm{MW}∕{\mathrm{cm}}^2$). The dashed line in (a) shows transmission when $I_c=0$.

Figure 6

Reflection of the passive 1D PBG with an active defect site at its center for different values of the control field intensity, $I_c$ (in $\mathrm{MW}∕{\mathrm{cm}}^2$).

Figure 7

Transmission time delay of the active 1D PBG with a passive defect for different values of the control laser intensity $I_c$ (in $\mathrm{MW}∕{\mathrm{cm}}^2$).

Figure 8

Transmission time delay of the passive 1D PBG with an active defect site for different values of the control laser intensity $I_c$ (in $\mathrm{MW}∕{\mathrm{cm}}^2$).