Two-Bandpass All-Optical Filters by Tunneling Induced Transparency in a Semiconductor

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Two-bandpass all-optical filters by tunneling induced transparency in a semiconductor microcavity

Rui Zhang,Tao Wang, Xing Yu Xu, Zhong Chang Zhuo and Xue Mei Su*

(Affiliation): Key Lab of Coherent Light, Atomic and Molecular Spectroscopy, Ministry of Education, Changchun 130012, p. R. China

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Received **** 2015

Copyright © 2015 by author(s) and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

Abstract

The effects of tunneling induced transparency between intersubband transitions are investigated in a microcavity whereseveral periods of asymmetric triple-quantum wells are embedded. Two narrow dark polaritons can be created by intracavity coherent effects. The slow optical polaritons are demonstrated by group time delays. The two dark polaritons can be used for all-optical two-bandpass filters.

Keywords

Cavity electrodynamics; Quantum-well microcavity; tunneling induced transparency

1. Introduction (Heading 1)

Fano interference [1] as one of the powerfuleffects of quantum coherence was introduced in many media [2] such as quantum well structures in interband [3] and intersubband transitions [4, 5]. Fano interference can result in tunneling induced transparency (TIT) [4, 5] in asymmetricsemiconductor quantum well structures in intersubband transitions and many applications, such as ac Stark splitting [6], all-optical switch [7] and so on.

It is well known that the interactive strength can be enormously enhanced when the coherent media placed in a cavity [8].An intracavity TIT has been obtained in a quantum well-cavity system in interband transitions [3].In this paper we propose and demonstrate effects of quantum coherence in a triple quantum wellsmicrocavity to make two dark polaritons. The steep dispersions of the two dark polaritons can be applied in two-bandpass all-optical filters.

2. Theory

2.1. structure of the quantum well microcavity

Fig. 1 is a sketch of several periods of triple quantum wellsare embedded in a planar microcavity, each of which includes one deep and two shallow quantum wells separated by two thin tunneling barriers, and a ultrathin tunneling barrier connect the deep quantum well and a wide well which supplies the electronic continuum. The ground subband in the deep quantum well is initially populated by electronics whose density is , which can be changed by static doping [9], electron injection [10] and ultrafast light pumping [11]. The three discrete excitation subbands , and are dressed states resulting from the resonant coupling between the second subband in deep well and two ground subbands in the two shallow wells. There are two TIT windows created by the triple quantum well structure because of the three subbands decaying to the common continuum.

In the Ciuti-Carusotto theory [12], the electronic transitions are treated as quantum harmonic oscillatorsas the cavity mode does. The polarization direction of the electronic dipole moment is along axis which is the same as the growth direction of quantum wells. The in-plane wave vector is a conversed quantity. The fundamental mode of the cavity photons is near resonant to transitions from ground subband in deep well to the three middle subbands. The wave vectorof cavity mode is the quantized along the growth directionand is the cavity thickness.

We applyGaAs/AlxGa1-xAs materials to design the triple quantum well microcavity in Fig. 1. Electronic density is chosen ascm-2 [13]. One period of thetriple quantum well is as: one 10 nm barrier (Al0.35Ga0.65As), 6.7 nm well (Al0.15Ga0.85As), 4.2 nm barrier (Al0.35Ga0.65As), 6.7 nm (Al0.15Ga0.85As),4.2 nm barrier (Al0.35Ga0.65As), 7.9 nm (GaAs), 2.6 nm barrier (Al0.35Ga0.65As) and 160 nm electronic continuum (Al0.17Ga0.83As). The chosen length for the continuum is much longer than that of the electron coherence length (50 nm). The length of each period of triple quantum well structure is 202.3 nm. The cavity length is chosen as 2476.9nmby and thus 12 asymmetric triple quantum wells can be embedded in this microcavity.

The energies of the ground state in the deep well and the four excited states are 43.75 meV (), 165.45 meV (), 169.2 meV (), 173.76 meV () and 267.13 meV (). Other parameter are calculated as oscillation strengths , , , , , ;meV and, . The cavity mode is chosen to be resonant with transition from level |1> to level |3>.

Figure 1.Subband energy level diagram for triple quantum wells in a planar cavity.

2.2. Hamiltonian of the quantum wells-cavity system

Hamiltonian can be described as:

(1)

In equ. (1), the first four terms describe energies of the four bosonics. The fifth to seventh terms represent the interaction between the cavity photons and three electronic excitations and the eighth term stands for the interaction based on electromagneticvector potential. The ninth to twelfthterms are the anti-resonant of the fifth to eighth terms. Here is the creation operator of the cavity mode with in-plane wave vector and energy ;,, are the creation operators of the bright electronic excitation modeswith wave vector and energy ,, , respectively.is the vacuum Rabi frequency of the cavity photon and the electronic excitation (,) whose explicit expression is

(2)

where is the number of triple quantum well structure in the microcavity and is mass of free electron. is the effective length of the cavity mode depending on boundary conditions. is the oscillator strength of the corresponding transitions;is the intracavity probe photon propagation angle.

Hopfiled matrix of the system described as Equ. (4) as:

(6)

Where and

The reflectivity and transmission of the probe field are defined as:

3. Results and discussions

Transmission and reflectivity spectra are plotted as a function of the incident photon enengy in Fig. 2. From Fig. 2, four polaritons are generated in the microcavity which are resulted from linear mixing of the four quantum oscillators called as upper polariton (UP), middle-upper polariton (MUP), middle-lower polariton (MLP) and lower polariton (LP). The optical spectra of UP and LP are normal, whose position is decided by vacuum Rabi splitting in Fig. 2 (a) and Fig. 2 (b). Because of the joint influence of the cavity feedback and TIT, transmission spectra of thetwodark polaritons (MUP and MLP)are much narrower shown as in fig. 2.It is shown as two-bandpass all-optical filters by the two dark polaritons.

Figure 2.(a)Reflectivity, (b) Transmission spectra versus incident photon enengy .

The group delay is drawn in fig. 3as a function of the incident photon enengy by using the same parameters as in Fig. 2. Group time delay 2.86ps and 2.09 ps for MLP and MUP polaritons correspond to their group velocities are as slow as and where c is the light speed in the vacuum.

Figure 3.group velocity versus incident photon enengy .

4. Summary

In conclusion，we investigate quantum coherence in intersubband electronic excitations in triple asymmetric quantum wells microcavity.Four prolaritons are induced by interactions of cavity photon and three subband electronic transition oscillators. In this system two narrow middle dark polaritons can be used to enhance the interaction time of intracavity photons. An external laser can switch the two dark polaritons on or off. This semiconductor microcavity system can be used to devise quantum optical and photoelectronic devices in nanoscale at the mid-infrared regime.

Acknowledgements

We acknowledge supports from National Natural Science Foundation of China (Grant No.11174109).

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