Extreme Nonreciprocal Near-Field Thermal Radiation via Floquet Photonics

By using Floquet driving protocols and interlacing them with a judicious reservoir emission engineering, we achieve extreme nonreciprocal thermal radiation. We show that the latter is rooted in an interplay between a direct radiation process occurring due to temperature bias between two thermal baths and the modulation process that is responsible for pumped radiation heat. Our theoretical results are confirmed via time-domain simulations with photonic and rf circuits.

Figure 1

A photonic Floquet diode for near-field thermal radiation. The resonators $n=2$, 3 and the coupling between them are periodically modulated in time, while the $n=1$-resonator is static. (a) In the “forward” (f) configuration, the reservoir with the high (low) temperature $T_{\alpha =1}=T_H$ ($T_{\alpha =2}=T_C$) is coupled to the $n=1(n=2)$-resonator. (b) In the “backward” (b) configuration the low (high) temperature reservoir $T_{\alpha =1}=T_C(T_{\alpha =2}=T_H)$ is coupled to the $n=1(n=2)$-resonator. (c), (d) An equivalent electronic circuit. The LC resonators $n=2$, 3 and their coupling are driven by modulating the (pink) capacitors: (c) forward and (d) backward configurations. The currents are measured at the same position at the $\alpha =2$ transmission line [green transparent plane in (a),(b); bold green line in (c),(d)].

Figure 2

(a) Transmittance spectrum ${\mathcal{T}}_{\alpha ,\beta }^F(\omega )$ for the photonic circuit of Eq. (9) showing a nonreciprocal behavior around $\omega \sim 0.88{\omega }_C$. Parameters: $\mathrm{\Omega }=0.01{\omega }_C,k=0.04{\omega }_C,{\delta }_0=0.015{\omega }_C,{\gamma }_1={\gamma }_2\approx 0.004{\omega }_C$, ${\gamma }_3=0$, ${\omega }_C\approx 190\times {10}^{12}\mathrm{rad}{\mathrm{s}}^{-1}$, $T_C=T_H-\mathrm{\Delta }T=300\mathrm{K}$. The green area describes the engineered emission spectrum, Eq. (10). (b) The radiative currents Eq. (4) vs $\mathrm{\Omega }$ for three representative temperature gradients $\mathrm{\Delta }T$. (c) The rectification parameter $|\mathcal{R}|$ vs $\mathrm{\Omega }$. The dashed lines represent the function $R=(\alpha /\mathrm{\Delta }T)\times \mathrm{\Omega }$ with $\alpha =20$ from a best fit.

Figure 3

(a) The currents Eq. (4) vs $\mathrm{\Omega }$ are calculated with (filled symbols) and without (open symbols) spectral engineering (SE) for a forward and backward ${\overline{I}}_2^{(f/b)}$ configuration. (b) The rectification $\mathcal{R}$ vs $\mathrm{\Omega }$ for temperature gradient $\mathrm{\Delta }T=10\mathrm{K}$. Other parameters are as in Fig. 2. The black dashed lines indicate a function $R=\alpha \times \mathrm{\Omega }$ with best fitting values $\alpha =2(250)$ for the unfiltered (filtered) circuit.

Figure 4

Time-domain simulations for the electronic circuit of Figs. 1 and 1. (a) The radiative currents Eq. (12) vs $\mathrm{\Omega }$ are calculated with (filled symbols) and without (open symbols) spectral engineering (SE) for a forward and backward ${\overline{I}}_2^{(f/b)}$ configuration. The inset shows the transmission spectrum. (b) The rectification parameter $\mathcal{R}$ vs $\mathrm{\Omega }$. The black dashed lines indicate a function $R=\alpha \times \mathrm{\Omega }$ with $\alpha =4$ and 350 for the unfiltered and filtered circuit, respectively. Here $\kappa =0.1$, $\epsilon =0.1$, $\delta =0.05$, $T_{H(C)}=(1\pm 0.05)T_0$ with $T_0={10}^9\mathrm{K}$ [69] and ${\omega }_C\approx 0.96{\omega }_0$.