Unidirectional photonic circuit with a phase-change Fano resonator

We demonstrate that the integration of a phase-change material (PCM) in one of the two microresonators of a photonic circuit, coupled to a bus waveguide, can lead to unidirectional Fano resonances and to the emergence of a unidirectional transmission window. The phase change is caused by light-induced heating and is accompanied by an abrupt increase in the extinction coefficient of the PCM resonator. Due to the photonic circuit asymmetry, the critical value of the input light intensity triggering the phase change is strongly dependent on the input light direction. The latter determines the unidirectional nature of the emerging transmission window. This effect can be utilized in on-chip magnetic-free isolators and $Q$ switches.

Figure 1

(a) A density plot of left-right spectral transmittance asymmetry $T_L-T_R$ (in dBs) versus frequency $\nu$ ($x$ axis) of the incident CW, for various values of its irradiance $\mathcal{I}$ ($y$ axis). (b) A density plot of the scattering field intensity inside the circuit when it is illuminated with a CW signal from the left (right) direction. The frequency of the incident CW is at the Fano resonant frequency $\nu \approx 28.58\text{THz}$ and its irradiance is $18.843{\text{kW/cm}}^2$. (c) The dependence [Eq. (1)] of the imaginary part of the index of refraction $n^{″}$ of the PCM from the temperature $\theta$. The red highlighted area indicates the temperature regime where the $Q$ factor of the PCM resonator is spoiled, leading to a destruction of the Fano mechanism.

Figure 2

(a) Transmittance $T_{L/R}$, (b) transmission phase ${\varphi }_{L/R}$, and (c) temperature ${\theta }_{L/R}$ versus the frequency $\nu$ of an incident CW with irradiance $\mathcal{I}\approx 4.4{\mathrm{kW}/\mathrm{cm}}^2$. Left (solid black lines) and right (dashed red lines) incident CW is indicated with the subindex $L$ and $R$, respectively. The red highlighted area in (c) indicates the temperature domain where the variation of $n_{\mathrm{PCM}}^{″}$ is approximately one order higher than its value in the dielectric phase. When the PCM temperature is in this range, the Fano resonance is typically destroyed.

Figure 3

(a) Left $T_L$ (solid black lines) and right $T_R$ (dashed red lines) transmittances for a CW entering a photonic circuit (see inset) consisting of two coupled resonators with the left resonator made by a PCM material (${\mathrm{VO}}_2$). (b) Transmission phase for a left ${\varphi }_L$ and right ${\varphi }_R$ incident wave versus the incident frequency $\nu$, and (c) associated temperature ${\theta }_L$ (${\theta }_R$) for a left (right) incident CW wave versus the incident frequency $\nu$. In the inset we show the variation of the imaginary part of the refractive index $n^{″}$ versus the temperature $\theta$ of the PCM. The red highlighted area indicates the regime for which Fano resonances have been destroyed. The bold black dashed line indicates the value of $\theta \approx 318$ K associated with ${\theta }_L$ [see main panel of Fig. 3]. In all cases, the irradiance of the incident CW is $\mathcal{I}\approx 18.843{\mathrm{kW}/\mathrm{cm}}^2$.

Figure 4

Mechanical oscillator analog of the photonic circuit of Fig. 1. Two coupled oscillators, one of which has temperature-dependent friction (red), are side coupled to an infinite array (lead) of identical masses coupled with identical springs.

Figure 5

Transport properties of the toy model of Eqs. (3a)–(3c). Left column: (a) transmittance $T_{L/R}$, (b) transmission phase ${\varphi }_{L/R}$, and (c) temperature ${\theta }_{L/R}$ spectra for a CW wave with field amplitude 0.5. Left (solid black lines) and right (dashed red lines) incident signal is indicated with the subindex $L/R$. (d) $T_{L/R}$, (e) ${\varphi }_{L/R}$, and (f) ${\theta }_{L/R}$ for an incident wave with field amplitude 3. The transport behavior is in one-to-one relation with the results from the photonic circuit (see Figs. 2 and 3).