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Physical Review B

Functional photonic superstructures: Coherent formation of active-passive photonic band gap heterostructures and photonic subbands

Seyed M. Sadeghi, W. Li, Xinxin Li, Wei‐Ping Huang

Published Mar 10, 2008• 5 citations
Publisher

Abstract

We propose coherently generated photonic heterostructures using a functional photonic superstructure. In the absence of a laser field (control field), such a structure exhibits a conventional passive (off-resonant) photonic band gap. When a region(s) of such a structure is illuminated by the control field, coherent enhancement of refractive index increases the refractive index perturbations of that region, while electromagnetically induced transparency keeps it lossless. This forms a photonic heterostructure consisting of a passive (unilluminated region) and an active (illuminated region) photonic band gap structures. Using such a superstructure, we study a coherently generated photonic quantum well structure wherein two active photonic band gaps sandwich a passive region. We show that, since the active photonic band gaps are roughly twice wider than the passive band gap, they form two photonic barriers around the transparency band located at the longer wavelength side of the passive photonic band gap. This leads to formation of resonant transparency states or photonic subbands, similar to the conduction or valence subbands in electronic quantum well structures. We show that the energies and linewidths of such photonic subbands can be coherently controlled by just adjusting the control field beam.

DOI
10.1103/physrevb.77.125313

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We propose coherently generated photonic heterostructures using a functional photonic superstructure. In the absence of a laser field (control field), such a structure exhibits a conventional passive (off-resonant) photonic band gap. When a region(s) of such a structure is illuminated by the control field, coherent enhancement of refractive index increases the refractive index perturbations of that region, while electromagnetically induced transparency keeps it lossless. This forms a photonic heterostructure consisting of a passive (unilluminated region) and an active (illuminated region) photonic band gap structures. Using such a superstructure, we study a coherently generated photonic quantum well structure wherein two active photonic band gaps sandwich a passive region. We show that, since the active photonic band gaps are roughly twice wider than the passive band gap, they form two photonic barriers around the transparency band located at the longer wavelength side of the passive photonic band gap. This leads to formation of resonant transparency states or photonic subbands, similar to the conduction or valence subbands in electronic quantum well structures. We show that the energies and linewidths of such photonic subbands can be coherently controlled by just adjusting the control field beam.
In an active photonic band gap structure, a control laser can manipulate the probe signal coherently if the probe field satisfies the Bragg condition and is resonant or near resonant with the electronic or excitonic transitions of the constituting material structure. Using coherent effects in the conduction intersubband transitions of an n-doped quantum well, recently, we showed that one could convert a fully transparent waveguide into an active photonic band gap. Such an active photonic band gap was different from those based on superradiant excitons in two main issues: (i) the probe field was near resonant with the conduction intersubband transitions of the quantum well, and (ii) one needed a control field to generate the coherent effects and, thereafter, the band gap. Here we use such coherent processes, which include electromagnetically induced transparency and coherent enhancement of refractive index, to study a one-dimensional functional photonic band gap structure. In the absence of a control laser field such a structure acts as a conventional photonic band gap created by an off-resonant (background) refractive index perturbation. In other words, the probe field does not feel any resonance in this structure and the photonic band gap is passive. In the presence of the control field, the structure is activated and transformed into a resonant structure. Under this condition, the probe field becomes near resonant with the intersubband transitions while still satisfies the Bragg condition. We study how the coherent effects in such transitions can lead to destruction and enhancement of the photonic band gap in a waveguide structure.
We use electromagnetically induced transparency combined with coherent enhancement of refractive index in the conduction intersubband transitions of a n-doped quantum well structure to study one-dimensional functional (active) photonic band gap structures. In the absence of a control laser field, such structures act as conventional photonic band gaps created by off-resonant (background) refractive index perturbations. In the presence of the control field, they are transformed into resonant structures with transitions around the Bragg wavelength. We show that this process can be used to (i) destroy the band gap, making the structure fully transparent around the Bragg wavelength, or (ii) coherently tune the band gap while enhancing its width by nearly a factor of 2. Using these phenomena we then study coherent localization of electromagnetic modes in photonic band gap structures without having any structural defects. Such a localization process here happens via partial illumination of such structures by the control field, generating electromagnetically induced optical defects. We show that the phase associated with such defects can be adjusted by the control field, allowing us to generate tunable electromagnetically induced transmission resonances (or photonic electromagnetically induced transparency) within the band gap.
We utilize electromagnetically induced absorption (EIA) in a one-dimensional functional (active) photonic band gap structure to propose a coherently generated purely loss-coupled distributed feedback (DFB) laser. Such a laser happens when interaction of the photonic band structure with a control laser field totally removes its refractive index perturbation and replaces it with periodic regions of EIA, forming an optical dark lattice. Such a lattice does not have any stop band, but scatters light coherently at the Bragg wavelength. We also show that before the optical dark lattice happens, the photonic band gap structure can act as a coherently generated partly loss-coupled DFB laser with dominant lasing mode at the longer wavelength side of the stop band. We expect such a distinct feature makes this laser quite stable.
The resonant absorption, emission, and scattering of light are the fundamental optical processes that have been used both to probe matter and to manipulate light itself. In the last decade there has been essential progress in coherent control of both linear and nonlinear optical responses based on resonant excitation of atomic coherence in multilevel quantum systems. Some interesting and useful phenomena, resulting from coherent control of absorption and the group index, such as electromagnetically induced transparency, lasing without inversion, and ultra-slow group velocity of light have been widely studied. This work is focused on coherent control of refractive index and resonant fluorescence in multilevel medium. \n \nWe suggest two promising schemes for resonant enhancement of the refractive index with eliminated absorption and propose their implementation in transition element doped crystals with excited state absorption and in a cell of Rb atoms at natural abundance. We show how to use one of these schemes for spatial variation of the refractive index via its periodic resonant increase/decrease, remarkably keeping at the same time zero absorption/gain. It opens the way to production of transparent photonic structures (such as distributed Bragg reflectors, holey fibers, or photonic crystals) in a homogeneous resonant atomic media such as dielectrics with homogeneously distributed impurities, atomic, or molecular gases. These optically produced photonic structures could easily be controlled (including switching on/off, changing amplitude and period of modulation) and would be highly selective in frequency, naturally limited by the width of the optical resonance. \n \nWe also derive the optical fluorescence spectra of a three-level medium driven by two coherent fields at the adjacent transitions in a general case when all three transitions are allowed. We show that coherent driving can efficiently control the distribution of intensities between the fluorescent channels. In particular, the total intensity of fluorescence at the transition which is not driven by the optical fields may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. This counter-intuitive effect is due to depletion of the intermediate state via atomic interference.
We propose one-dimensional bright and dark optical lattices where Bragg scattering occurs, respectively, via periodic generation of gain without inversion and electromagnetically induced absorption in the absence of any refractive index perturbation. The absorption and gain processes are caused by quantum interference in the conduction intersubband transitions of a corrugated nnn-doped quantum well structure interacting with an intense infrared laser. The quantum well structure is embedded between two optical confinement layers, forming a periodic structure with a Bragg wavelength similar to that of the intersubband transition between the second and third conduction subbands of the quantum well. We show that in the absence of the intense infrared laser this transition is transparent, and the periodic structure forms a passive one-dimensional photonic gap generated by the background refractive index contrast of the corrugated region. In the presence of this laser, the intersubband transition is influenced by the quantum coherence effects, causing dramatic changes in the photonic band gap. We show that when one adjusts the intensity and wavelength of such a laser properly these effects can (i) destroy the one-dimensional photonic band gap, and (ii) form periodic regions of gain without inversion or electromagnetically induced loss, while the index perturbation is completely canceled out. Such bright and dark optical lattices can scatter a light at Bragg wavelength when its frequency is the same or close to that of the intersubband transition.
The phenomenon of electromagnetically induced transparency has been studied when a four-level atom is located in a photonic band gap material. Quantum interference is introduced by driving the two upper levels of the atom with a strong pump laser field. The top level and one of the ground levels are coupled by a weak probe laser field and absorption takes place between these two states. The susceptibility due to the absorption for this transition has been calculated by using the master equation method in linear response theory. Numerical simulations are performed for the real and imaginary parts of the susceptibility for a photonic band gap material whose gap-midgap ratio is 21%. It is found that when resonance frequencies lie within the band, the medium becomes transparent under the action of the strong pump laser field. More interesting results are found when one of the resonance frequencies lies at the band edge and within the band gap. When the resonance frequency lies at the band edge, the medium becomes nontransparent even under a strong pump laser field. On the other hand, when the resonance frequency lies within the band gap, the medium becomes transparent even under a weak pump laser field. In summary, we found that the medium can be transformed from the transparent state to the nontransparent state just by changing the location of the resonance frequency. We call these two effects anomalous electromagnetically induced transparency.