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oea-2020-0028 Shaohao Wang Supplementary Information |
(a) The cavity resonance of MRRs can be linearly tuned by varying the chip temperature δT or nonlinearly tuned by controlling the intra-cavity pump energy Ip through nonlinear TO effects. (b) In the wavelength domain, when δT increases, the cold-cavity resonance wavelengths of the TH mode (in red dot line) and the pump mode (in blue dot line) will linearly redshift ∆λTL and ∆λTLp, respectively. When up sweeping the CW input pump wavelength λp and δT are fixed, the corresponding Ip will induce nonlinear redshift ∆λTNL and ∆λTNLp to the resonance wavelengths of the TH and pump modes, respectively. For the pump mode, when λp is fixed, the trace of blue open circles determines τp which is the ratio between δT and Ip. Similarly, the trace of red open circles in the upper part of (b) gives the ratio τp. The overall effects of ∆λTL and ∆λTNL determine the effective TDWS of the TH mode which becomes a δT-λp relationship by mapping the trace of red open squares to the lower part of (b). For the pump mode, its TDWS is only related the linear TO redshift ∆λTLp whose trace was shown as blue open squares plotted in the δT-λp diagram. (c – e) The thermal mismatch between τp and τt will determine the effective TDWS of the TH mode, which leads to (c) a positive TDWS when τp < τt and (d) a zero TDWS when τp ≈ τt and (e) a negative TDWS when τp > τt in the δT-λp diagram.
(a) The relationship between the normalized pump detuning α and the intra-cavity pump power ρ when the input pump power F2 is fixed. The existence of stable athermal TH modes were shown in blue (F2 = 1.6) and green (F2 = 1.9) solid lines when |α| >
(a) Measured pump wavelength corresponding to the peak resonances of three types of TM TH modes. The calibrated cold-cavity resonance wavelengths were obtained by subtracted ΩTNL which are shown in plus center symbols. The calibrated TDWS of Type Ⅰ (green lines) and Type Ⅱ (purple lines) TH modes are also shown. (b) Measured third harmonic photon counts (THPC) on the resonance peaks of the TH modes as a function of Ip showing the cubic TH-pump relationship. The solid lines show the cubic TH-pump relationship for comparison. (c – d) The measured Ip (upper) and filter response (lower) of corresponding type Ⅰ TH modes as functions of Ωt in the devices of R-1 (c) and R-2 (d) respectively. The Q-factor of TH modes QTH can be indirectly determined by using Θt = 2.55×109 rad/pJ into Eq. (4). The corresponding fitted curves using estimated QTH are also shown in (c) – (d). Here, the symbols of the measured data in (b) – (d) are the same as those in (a).
(a – b) Measured spectra of all the TE athermal TH modes in MRRs of R-1 (a) and R-2 (b) that are thermal matched, i.e. ∆τ ≈ 0. In (a) and (b), the measured wavelengths of the resonance peak of TH modes at different T are shown in open diamonds. The corresponding fitted TDWS of TH modes are shown in grey dashed lines. (c) The measured photon count on the peak of different athermal TH modes as a function of Ip. The solid lines show the cubic TH-pump relationship for (a) – (b) as well as Figs. 5(c) and 5(e) for comparison. The data and fitting curves for R-1, R-2, R-3 are shown in blue, red, and green, respectively.
(a) Thermal mismatch ∆τ < 0, with a TM pump generated a TM TH mode with a TDWS of 3dTH = 7.05 pm/℃. (b) Thermal mismatch ∆τ > 0, with a TE pump generated a TE TH mode with 3dTH = −8.53 pm/℃. (c, f) When thermal mismatch ∆τ ≈ 0, with a TM pump generated TE TH mode with 3dTH = 0.14 pm/℃ (c) as well as 3dTH = −0.27 pm/℃ (f). (d, g) The extracted Q-factor of TE TH modes by using the data in (c) at 26 ℃ and in (f) at 46 ℃, with Eq. (4) is used to generate the fitted lines. (e, h) The temperature dependence of the athermal TH mode resonance fluctuation with fixed ∆τ and F2 for the TH modes shown in (c) and (f), with the measured values in gray squares. In (a – c) and (f), the measured wavelengths of the resonance peak of TH modes at different T are shown in open diamonds. The corresponding fitted TDWS of TH modes are shown in grey dashed lines.