Million-<i>Q</i> integrated Fabry-Perot cavity using ultralow-loss multimode retroreflectors

Fig. 1. Conceptual illustration of the FP cavity. (a) 3D view of the FP cavity; (b) schematic configuration of the FP cavity with key parameters labeled. The side coupling is accomplished by using an ADC. The cavity is terminated by a pair of retroreflectors at each end. (c) Illustration of loss mechanisms in the FP cavity; (d) working principle of the retroreflector. Other types of reflectors are also illustrated for comparison. The guided mode in a wide waveguide can be modeled by treating it as a cluster of rays. Each ray will bounce off at mirrors A and A′ via TIR. The corner scattering at the point B contributes the greatest to reflection losses. (e) Calculated electric field profiles of TE0 and TE1 modes; for TE1, the field intensity is zero at the central position, thereby depressing the corner scattering completely. (f) Calculated light propagation profiles for the retroreflector when TE0 and TE1 modes are launched. The image contrast is enhanced to clearly show the scattering wave. The scattering loss is significantly mitigated when the TE1 mode is injected.

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Fig. 2. Analysis and optimization of the retroreflector. (a) Calculated TE1 effective indices (neff,TE1) with varying waveguide widths (Wwg). The dashed line represents the effective index of the slab mode (nslab). The inset shows the waveguide cross section. (b) Calculated TIR angles (θTIR) with varying wavelengths; (c) calculated reflectance (Rref,TE0,Rref,TE1) with varying retroreflector widths (Wref). The inset shows the structural top view. The near-unity reflectance can be achieved for TE1. (d) Calculated light propagation profile for the optimized retroreflector. The arrow shows the side-scattering effect. (e) Calculated Rref,TE1 with varying sidewall tilt angles (θtilt). The inset shows the waveguide cross section. (f) Calculated TE1-reflection-loss (RLTE1) spectrum for the optimized retroreflector. The dashed line shows the calculated TE0 reflection losses (RLTE0).

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Fig. 3. Analysis and optimization of the ADC. (a) Calculated TE0 and TE1 effective indices (neff,TE0,neff,TE1) with varying waveguide widths (Wwg); the dashed lines show the phase matching between TE0 and TE1 modes. Calculated coupling-loss (CL) spectra with different (b) widths (Wacc) and (c) bending radii (racc) of the accessing waveguide; (d) calculated TE1 coupling ratio (TCRO,TE1) with varying coupling lengths (Lc). The inset shows the structural top view. (e) Calculated TCRO,TE1 spectra with different Lc; (f) calculated light propagation profile for the optimized ADC; (g)–(i) calculated intermodal cross talk (XTTE0, XTTE2, XTTE3) and extinction-ratio (ERTE0, ERTE2, ERTE3) spectra for the optimized ADC.

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Fig. 4. Analysis and optimization of the FP cavity. (a) Calculated TE1 propagation losses (αTE1) with varying waveguide widths (Wwg) under different mean deviations of sidewall roughness (σ); (b) calculated transmission efficiencies (Ttp,TEi) with varying taper lengths (Ltp); the inset shows the structural top view. (c) Calculated light propagation profile for the tapered waveguide with Ltp=1.5 mm; (d) calculated TE1 effective indices (neff,TE1) as a two-dimensional map in terms of Wwg and wavelengths; calculated (e) mean effective indices (n˜eff,TE1) and (f) mean group indices (n˜g,TE1) of the TE1 mode with varying wavelengths; (g) calculated transmittance (TFP) and reflectance (RFP) spectra for the FP cavity with Ltp=1.5 mm; (h) zoom-in view of the TFP spectrum in the vicinity of a single resonance. The red arrow indicates the corresponding spectral position in (g). (i) Calculated loaded Q factors (Qload) with varying Ltp; the dashed line represents the intrinsic Q factor (Qi). An ultrahigh intrinsic Q factor of Qi≈4.1×106 is attained.

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Fig. 5. Experimental results for the fabricated FP cavities. (a), (b) Microscopic images of the fabricated devices; the scale bars represent 350 and 200 μm, respectively. (c) Schematic configuration of the measurement setup; (d) measured transmittance (Ttp) spectra with varying taper lengths (Ltp). For clarity, a progressive shift is applied on the plotted spectra. Zoom-in views of the Ttp spectra in the vicinity of a single resonance with (e) Ltp=1.5 mm and (f) 4.0 mm; (g) measured loaded Q factors (Qload) with varying Ltp; (h) reconstructed reflectance (Rref,TE1) and mean-propagation-loss (α˜TE1) spectra; (i) measured TFP spectra at different ambient temperatures (t); (j) measured thermo-optical responses with varying electric power (P) applied. PC, polarization controller; TEC, thermo-electric cooler; DUT, device under test.

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Fig. 6. Calculated TE1-coupling ratio (TCRO,TE1) and coupling-loss (CL) spectra with parameter deviations.

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Fig. 7. Measured transmittance (TFP) spectra at different wavelength bands (λ≈1.51, 1.55, and 1.59 μm) with taper lengths of (a) Ltp=1.5 mm and (b) 4.0 mm; measured (c) extinction ratios (ERres) and (d) free spectral ranges (FSRs) with varying Ltp; (e) reconstructed TE1 coupling-ratio (TCRO,TE1) spectrum.

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Table 1. Performance Comparison of On-Chip FP Cavities

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Table 1. Performance Comparison of On-Chip FP Cavities

Reference	Platform	Reflector Type	RL [dB]	BW [nm]	FSR [nm]	$α$ [dB/cm]	$Q_{load}$	$Q_{i}$	$F$
[8]	SNOI	DBR	/	$\approx 7$	1.39	0.33	$4.8 \times 10^{5}$	/	430
[10]	SOI	DBR	/	$\approx 1$	/	10.3	$3.4 \times 10^{4}$	/	/
[11]	SOI	Loop	/	$> 4$	1.3	$5 − 8$	$2.3 \times 10^{4}$	/	19
[15]	SOI	DBR	0.22	80	31.3	/	$1.3 \times 10^{3}$	$2.6 \times 10^{4}$	26
[19]	SOI	DBR	0.32	$> 80$	30	/	$1.4 \times 10^{4}$	/	270
[20]	Bulk Si	DBR	0.03	$> 200$	29.4	1.32	$2.7 \times 10^{4}$	/	500
[21]	SOI	Metallic mirror	0.97	200	21	/	$3.6 \times 10^{2}$	$9.0 \times 10^{2}$	5
[22]	SOI	Inverse design	0.71	200	$\approx 10$	/	$2.0 \times 10^{3}$	$4.1 \times 10^{3}$	13
This work	SOI	Retroreflector	0.05	$> 100$	$< 0.16$	0.18	$2.1 \times 10^{6}$	$3.4 \times 10^{6}$	$> 100$

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Hongnan Xu, Yue Qin, Gaolei Hu, Hon Ki Tsang, "Million-Q integrated Fabry-Perot cavity using ultralow-loss multimode retroreflectors," Photonics Res. 10, 2549 (2022)

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