Electromagnetically-induced-transparency plasmonics: Quantum-interference-assisted tunable surface-plasmon-polariton resonance and excitation

An experimentally feasible configuration of a prism coupler with an electromagnetically-induced-transparency (EIT) medium layer, e.g., a semiconductor-quantum-dot (SQD) medium, deposited upon its prism base is suggested for generating tunable surface-plasmon-polariton resonance. Such surface-plasmon-polariton resonance and optical excitation of a surface plasmon wave can be manipulated by switchable quantum interference among SQD multilevel transitions driven by two external control fields. When an incident probe field is coupled into a surface plasmon wave excitation mode, the surface-plasmon-polariton (SPP) resonance at the interface between the SQD medium layer and the substrate will arise, and the quantum-coherently controllable reflection spectrum of the probe field on the prism base can be achieved. In this process, destructive and constructive quantum interference (determined by the intensity ratio of the two external control fields) in the SQD multilevel system plays a key role for achieving the tunable reflection spectrum. The EIT-based surface-plasmon-polariton resonance presented here will have three characteristics (some of them would be attractive): (i) switchable quantum interference exhibited by surface plasmon wave excitation, (ii) quantum-coherently controllable surface plasmon polaritons by external optical fields, (iii) surface wave sensitive to dispersion of the SQD quantum coherent medium. Such an effect of controllable optical response based on the quantum-interference switchable surface-plasmon-polariton resonance in the EIT-prism coupler may find some potential applications in design of new photonic and quantum optical devices.

Figure 1

The schematic diagrams of an EIT-prism coupler (a) and a four-level quantum coherent (EIT) system driven by two strong control fields and one weak probe field (b). (a) The probe wave (denoted by $A_2$) is incident and then reflected on the prism base, i.e., the interface (at $x=d$) between the prism dielectric and a thin EIT layer (e.g., a quantum-dot thin film). (b) The two control fields excite the $|c\rangle \text{−}|a\rangle$ and $|c^{\prime }\rangle \text{−}|a\rangle$ transitions, respectively. The $|b\rangle \text{−}|a\rangle$ transition (driven by the probe wave) can be controllably manipulated via the destructive and constructive quantum interference between the $|c\rangle \text{−}|a\rangle$ and $|c^{\prime }\rangle \text{−}|a\rangle$ transitions. If the destructive quantum interference between the $|c\rangle \text{−}|a\rangle$ and $|c^{\prime }\rangle \text{−}|a\rangle$ transitions occurs, the two levels $|c\rangle$ and $|c^{\prime }\rangle$ seem to be absent, and then the four-level system $\left\{\right|a\rangle ,|b\rangle ,|c\rangle ,|c^{\prime }\rangle \}$ will be equivalent to a two-level one $\left\{\right|a\rangle ,|b\rangle \}$.

Figure 2

The real and imaginary parts of the electric permittivity of the EIT layer depending upon the frequency detuning ${\delta }_{\mathrm{p}}$ of the incident probe light and the Rabi frequency ${\Omega }_{\mathrm{c}}$ of the control field. ${\Omega }_c={\Omega }_{c^{\prime }} \left({\Omega }_c={\Omega }_{c^{\prime }}/5\right)$ corresponds to the case of destructive (constructive) quantum interference between $|c\rangle \text{−}|a\rangle$ and $|c^{\prime }\rangle \text{−}|a\rangle$ transitions.

Figure 3

The tunable behavior of dispersion in the real part of the electric permittivity of the EIT medium layer.

Figure 4

The tunable behavior of dispersion in the imaginary part of the electric permittivity of the EIT medium layer.

Figure 5

The tunable reflection spectrum (i.e., the dimensionless reflectance $R$ depending on the incidence angle $\theta$) due to destructive $\left({\Omega }_c={\Omega }_{c^{\prime }}\right)$ and constructive $\left({\Omega }_c={\Omega }_{c^{\prime }}/5\right)$ quantum interference in the EIT-prism coupling system. The unit of the incidence angle $\theta$ is degree $\left({}^{\circ }\right)$. The detuning frequencies of the three optical fields are chosen as ${\delta }_p=2.0{\gamma }_{ab},{\delta }_{c^{\prime }}=-0.4{\gamma }_{ab}$, and ${\delta }_c=1.2{\gamma }_{ab}$. The switchable permittivity ${\varepsilon }_1$ of the quantum coherent (EIT) medium layer is $-14.9+16.5i$ (when ${\Omega }_c={\Omega }_{c^{\prime }}$ for destructive quantum interference) and $-2.52+0.31i$ (when ${\Omega }_c={\Omega }_{c^{\prime }}/5$ for constructive quantum interference).

Figure 6

The phase constant ${\beta }_{\mathrm{spw}}$ of the surface plasmon polaritons excited on the EIT layer surface corresponding to the two cases of destructive and constructive quantum interference between $|c\rangle \text{−}|a\rangle$ and $|c^{\prime }\rangle \text{−}|a\rangle$ transitions. The parameter for normalizing the phase constant ${\beta }_{\mathrm{spw}}$ is $k_0=\omega /c$ with $\omega$ the probe frequency ${\omega }_{\mathrm{p}}$. The variable $d$ denotes the EIT layer thickness (in units of $c/\omega$).

Figure 7

The spatial profile of the magnetic field $H_y$ of the TM wave in the prism coupler corresponding to ${\varepsilon }_1=-2.52+0.31i$ (i.e., constructive quantum interference with ${\Omega }_{\mathrm{c}}={\Omega }_{{\mathrm{c}}^{\prime }}/5$). The $x$ and $z$ are the coordinate axes (in units of $c/\omega$) that are normal and parallel, respectively, to the flat surface of the EIT layer in the present prism coupler (seen in Fig. 1). When the angle of incidence $\theta$ is $40\sim 45$ degrees, the amplitude of the excited surface wave at the plane of $x=0$ will be larger than that of the incident (illuminating) light (propagating in the region of $x>0$), which excites the surface wave at $x=0$.

Figure 8

Optical excitation of the magnetic field $H_y$ of the surface plasmon wave (in the region of $x\le 0$) corresponding to the case of constructive quantum interference. The $x$ and $z$ are the coordinate axes (in units of $c/\omega$) that are normal and parallel, respectively, to the flat surface of the EIT layer in the present prism coupler (seen in Fig. 1). The angle of incidence of the probe light is $\theta =41$–44 degrees. The amplitude of the excited surface plasmon wave (at the plane of $x=0$) is larger than that of the incident probe light (in the region of $x>0$).

Figure 9

The spatial profile of the magnetic field $H_y$ of the TM wave in the prism coupler corresponding to ${\varepsilon }_1=-14.9+16.5i$ (i.e., destructive quantum interference with ${\Omega }_{\mathrm{c}}={\Omega }_{{\mathrm{c}}^{\prime }}$). The $x$ and $z$ are the coordinate axes (in units of $c/\omega$) in the present prism coupler.

Figure 10

The spatial profile of the magnetic field $H_y$ of the TM wave in the prism coupler corresponding to ${\varepsilon }_1=-14.9+16.5i$ (i.e., destructive quantum interference with ${\Omega }_{\mathrm{c}}={\Omega }_{{\mathrm{c}}^{\prime }}$). The $x$ and $z$ are the coordinate axes (in units of $c/\omega$) in the present prism coupler.