Physical Review A

All-optical modulation and amplification resulting from population inversion in two-level systems using a photonic-crystal cavity

Hiroyuki Takeda

Published Jul 3, 2012• 6 citations

Abstract

I theoretically demonstrate all-optical modulation and amplification in a one-dimensional photonic-crystal (PC) cavity with a large number of two-level quantum dots (QD's). Populations in the ground and excited states of two-level QD's with large transition dipole moments are greatly changed by an external laser, and this affects the electrical susceptibility of the QD's. In other words, all-optical modulation, in which light (the signal light) is modulated by light (the external laser), becomes possible. Moreover, a large contrast of the electromagnetic local densities of states in the PC cavity enables steady-state population inversion in two-level systems, which is generally considered impossible. The output signal power is more than twice as large as the input power at certain frequencies.

DOI: 10.1103/physreva.86.013803

Related papers

Semiclassical analysis of two-level collective population inversion using photonic crystals in three-dimensional systems

Hiroyuki Takeda

I theoretically demonstrate the population inversion of collective two-level atoms using photonic crystals in three-dimensional (3D) systems by self-consistent solution of the semiclassical Maxwell-Bloch equations. In the semiclassical theory, while electrons are quantized to ground and excited states, electromagnetic fields are treated classically. For control of spontaneous emission and steady-state population inversion of two-level atoms driven by an external laser which is generally considered impossible, large contrasts of electromagnetic local densities of states (EM LDOS’s) are necessary. When a large number of two-level atoms are coherently excited (Dicke model), the above properties can be recaptured by the Maxwell-Bloch equations based on the first-principle calculation. In this paper, I focus on the realistic 1D PC’s with finite structures perpendicular to periodic directions in 3D systems. In such structures, there appear pseudo photonic band gaps (PBG’s) in which light leaks into air regions, unlike complete PBG’s. Nevertheless, these pseudo PBG’s provide large contrasts of EM LDOS’s in the vicinity of the upper photonic band edges. I show that the realistic 1D PC’s in 3D systems enable the control of spontaneous emission and population inversion of collective two-level atoms driven by an external laser. This finding facilitates experimental fabrication and realization.

Optics ExpressJul 12, 20121 citation

Interference effects in a cavity for optical amplification

David A. Cardimona, Paul M. Alsing

In space situational awareness scenarios, the objects needed to be characterized and identified are usually quite far away and quite dim. Thus, optical detectors need to be able to sense these very dim optical signals. Quantum interference in a three-level system can lead to amplification of optical signals. If we put a three-level system into a cavity tuned to the frequency of an incoming optical signal, we anticipate the amplification possibilities should be increased proportional to the quality factor of the cavity. Our vision is to utilize quantum dots in photonic crystal cavities, but as a stepping stone we first investigate a simple three-level system in a free-space optical cavity. We investigate quantum interference and classical interference effects when a three-level system interacts with both a cavity field mode and an external driving field mode. We find that under certain circumstances the cavity field evolves to be equal in magnitude to, but 180° out-of-phase with the external pump field when the pump field frequency equals the cavity frequency. At this point the resonance fluorescence from the atom in the cavity goes to zero due to a purely classical interference effect between the two out-of-phase fields. This is quite different from the quantum interference that occurs under the right circumstances, when the state populations are coherently driven into a linear combination that is decoupled from any applied field - and population is trapped in the excited states, thus allowing for a population inversion and an amplification of incoming optical signals.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEAug 20, 20092 citations

Collective quantum dot inversion and amplification of photon and phonon waves

Sumanta Das, Mihai Macovei

The possibility of steady-state population inversion in a small sample of strongly driven two-level emitters such as quantum dots (QDs) in microcavities, and its utilization towards amplification of light and acoustic waves, is investigated theoretically. We find that inversion and absorption spectra of photons and phonons crucially depend on the interplay between the intrinsic vacuum and phonon environments. The absorption profiles of photons and phonons show marked novel features such as gain instead of transparency and absorption reversed to gain, respectively. Furthermore, we report collectivity-induced substantial enhancement of inversion and pronounced gain in the photon and phonon absorption spectra for a subwavelength-sized QD ensemble.

arXiv:1303.5826Physical Review BSep 13, 201313 citations

Interference effects in a photonic crystal cavity

David A. Cardimona, Paul M. Alsing

We investigate quantum interference and classical interference effects when a three-level system interacts with both a cavity field mode and an external driving field mode, within the confines of a photonic crystal material. In freespace, we found that under certain circumstances the cavity field evolves to be equal in magnitude to, but 180° out-of- phase with the external pump field when the pump field frequency equals the cavity frequency. The better the cavity, the quicker this build-up occurs. When the cavity field reaches this out-of-phase condition, the resonance fluorescence from the atom in the cavity goes to zero. This is a purely classical interference effect between the two out-of-phase fields, with the resonance fluorescence going to zero at the same time as the two excited state populations go to zero. This is quite different from the quantum interference that occurs under the right circumstances, when the state populations are coherently driven into a linear combination that is decoupled from any applied field - and population is trapped in the excited states, thus allowing for a population inversion and an amplification of incoming optical signals. In this paper, we investigate the additional effects due to the presence of the altered photon density of states in a photonic crystal.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEJan 7, 20101 citation

Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals

Hiroyuki Takeda, Sajeev John

We theoretically demonstrate the population switching of quantum dots (QD's), modeled as two-level atoms in idealized one-dimensional (1D) and two-dimensional (2D) photonic crystals (PC's) by self-consistent solution of the Maxwell-Bloch equations. In our semiclassical theory, energy states of the electron are quantized, and electron dynamics is described by the atomic Bloch equation, while electromagnetic waves satisfy the classical Maxwell equations. Near a waveguide cutoff in a photonic band gap, the local electromagnetic density of states (LDOS) and spontaneous emission rates exhibit abrupt changes with frequency, enabling large QD population inversion driven by both continuous and pulsed optical fields. We recapture and generalize this ultrafast population switching using the Maxwell-Bloch equations. Radiative emission from the QD is obtained directly from the surrounding PC geometry using finite-difference time-domain simulation of the electromagnetic field. The atomic Bloch equations provide a source term for the electromagnetic field. The total electromagnetic field, consisting of the external input and radiated field, drives the polarization components of the atomic Bloch vector. We also include a microscopic model for phonon dephasing of the atomic polarization and nonradiative decay caused by damped phonons. Our self-consistent theory captures stimulated emission and coherent feedback effects of the atomic Mollow sidebands, neglected in earlier treatments. This leads to remarkable high-contrast QD-population switching with relatively modest (factor of 10) jump discontinuities in the electromagnetic LDOS. Switching is demonstrated in three separate models of QD's placed (i) in the vicinity of a band edge of a 1D PC, (ii) near a cutoff frequency in a bimodal waveguide channel of a 2D PC, and (iii) in the vicinity of a localized defect mode side coupled to a single-mode waveguide channel in a 2D PC.

Physical Review AMay 9, 201119 citations

Coupling of QD-based PhC nanocavity with two mechanical modes: an approach to tunable optical switching and sensing applications

Sajia Yeasmin, Sabur A. Barbhuiya, Aranya B. Bhattacherjee +1 more

Abstract We theoretically study the dynamical change in the amplification of the output probe field spectra of a hybrid optomechanical system consisting of double mechanical modes coupled to a photonic crystal (PhC) nanocavity. The PhC cavity is also embedded with a quantum dot (QD) (two-level system) and simultaneously driven by an external pump and a probe field. We show that multiple number of transparency windows that appear can be controlled by the QD-cavity coupling strength and also the Fano profiles are directly measured by the resonant frequency of the mechanical mode. We also show the optical transition from bistability to tristability/multistability by adjusting the switching threshold of the system parameters. These results can also be used to study frequency optical nonreciprocity and all-optical switches in multi-resonator photonic devices.

Journal of OpticsMay 23, 20232 citations