Speaker
Description
Graphene-based photonic structures make it possible to control terahertz waves with an electric voltage. In this work, we study a symmetric one-dimensional photonic microcavity made of two mirror-image Bragg reflectors, $\mathrm{PC}_{1} = (AB)^{5}$ and $\mathrm{PC}_{2} = (BA)^{5}$, with a stack of $s$ graphene layers at their junction. Layer A has a refractive index $n_{A} = 2.35 + 0.0014i$ and a thickness of $4\,\mu\mathrm{m}$, and layer B has $n_{B} = 3.61$ and a thickness of $2\,\mu\mathrm{m}$. We do not use an ordinary dielectric defect layer. Instead, we use the mirror symmetry of the structure itself, which supports a localized mode at the central interface even without graphene.
We calculate the optical response at normal incidence in the terahertz range using the transfer matrix method. The conductivity of graphene is described by the Kubo model and converted into an effective permittivity of a thin homogeneous layer. The chemical potential is controlled by the gate voltage through $\mu_{c} = \hbar v_{F} \sqrt{\pi a_{0} V_{g}}$.
The two mirrors share a common band gap from about 7.8 to 10.2 THz, and their reflectances differ by less than 0.02. Inside this gap we find two interface modes. The first is a geometric mode at 9.33 THz with a transmittance of about 0.93. It comes from the mirror symmetry and shifts by only about 0.01 THz when graphene is added, so it is almost independent of graphene. The second is a graphene mode, which appears only when enough graphene layers are present. For $s = 10$ and $V_{g} = 10$ V, it is located at 8.19 THz with a transmittance of 0.96.
The graphene mode can be tuned in two ways. First, it appears for $s = 7$ at 7.90 THz and moves to 8.70 THz at $s = 20$, a total shift of about 0.8 THz. The shift caused by each added layer becomes smaller as $s$ grows. Second, for $s = 10$, raising $V_{g}$ from 5 V to 120 V moves the mode from 7.91 THz to 8.98 THz, a shift of about 1.07 THz. This shift is strong at low voltages and saturates at high voltages, which is expected because $\mu_{c}$ grows as $\sqrt{V_{g}}$. In both cases the peak transmittance stays above 0.94.
These results show that the number of graphene layers is a necessary condition for effective electrical tunability, while the geometric mode stays almost fixed. The structure may be useful for electrically tunable terahertz filters.
Keywords: photonic crystal, interface mode, graphene, electrical tunability, transfer matrix method
| Type of presence | Presence online |
|---|---|
| Figure caption | Reflectance of the whole structure for $s = 0$ (blue) and $s = 10$ (red, dashed) with $V_{g} = 10$ V. The shaded area marks the common gap of $\mathrm{PC}_{1}$ and $\mathrm{PC}_{2}$. |