Abstract

We propose and experimentally demonstrate an all-silicon passive optical diode with low-power consumption and high nonreciprocal transmission ratios (NTRs) based on cascaded opto-mechanical microring resonators (MRRs). As the oxide substrates of the opto-mechanical MRRs are removed, the nonlinear effects in the free-hanging waveguides could be efficiently activated by low optical powers. The operation principle of the optical diode is based on the asymmetric resonance red-shifts of the two MRRs in the forward and backward transmissions, which could be effectively induced by the nonlinear effects. In the experiment, with injecting an optical power low as 0.96 dBm, a high NTR of 33.6 dB and a relatively broad 20-dB bandwidth of 0.11 nm are achieved. The proposed passive optical diode is competent to process optical signals with dominant advantages of CMOS-compatibility, a compact footprint, low-power consumptions and high NTRs, which has significant applications for on-chip signal processing systems, such as logic gates and optical computing.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical logic devices are long-standing goal and fundamental components in optical communication systems [1–5]. Especially, passive optical diodes are highly desirable for on-chip optical signal processing [6–9], such as optical computing and logic gates. Numerous optical diodes based on the magneto-optical effect have been investigated [10–12], but the magneto-optical devices are incompatible with complementary metal-oxide semiconductor (CMOS) which increases the integration difficulty. Furthermore, indirect interband photonic transition [13], electro-absorption modulation [14], photonic crystal fiber [15] and cholesteric liquid crystals [16] are also employed to realize optical diodes. However, the device fabrication and manipulation of most schemes are relatively complex.

In recent years, silicon-on-insulator (SOI) technology is becoming the mainstay of silicon photonics, due to its advantages of high index contrast and compatibility with CMOS [17–19]. To pursue better integration and simple fabrication process, several schemes have been demonstrated based on the silicon microring resonators (MRRs) [20–23] and photonic crystal cavities [24]. Fan et al. realized all-silicon passive optical diode based on two cascaded MRRs [20,21]. However, the optical diode requires the two MRRs with identical resonances, which needs precise thermal tuning to compensate the resonance mismatch. To improve the device fabrication tolerance, Xu et al. designed a diode structure with better tolerance. A nonreciprocal transmission ratio (NTR) of 27 dB was obtained, but the required power of 8.2 dBm is relatively high [22]. In our previous work, we demonstrated an optical circulator based on thermo-optic effect in silicon MRRs. With injecting an optical power of 15 dBm, a maximum NTR of 33 dB has been realized [25]. In order to decrease the power consumption, Qiu et al. employed a racetrack MRR to realize optical diodes with an input power of 6 dBm [26], but the NTR of 12.7 dB need to be improved. Therefore, it is still highly desirable to realize a silicon energy-efficient optical diode with high NTRs [20,27].

Due to the significant combination of nanophotonics and nanomechanics, silicon opto-mechanical MRRs have attracted increasing interests and widespread attentions in the past decade [28–30]. Especially, the nonlinear effects in the opto-mechanical MRR (mainly including the thermo-optic effect and opto-mechanical effect) could be effectively activated by low pump powers [31]. In this case, the device characteristics could be manipulated with low-power consumption [32,33]. Therefore, the opto-mechanical MRRs provide a significant solution for on-chip energy-efficient signal processing.

In this paper, we experimentally demonstrate a passive optical diode based on cascaded silicon opto-mechanical MRRs, whose transmissions could be manipulated by the nonlinear effects. The radii of the two MRRs have a slight difference, so their free spectral ranges (FSRs) are different. Because of the Vernier effect, transmission spectrum of the cascaded MRRs is a series of notch bimodal distribution. The input wavelength is fixed around the right resonance of one selected bimodal distribution. As the wavelength intervals between the input wavelength and the two resonances are different, the red-shifts of the two resonances induced by the nonlinear effects are not equal. In the forward transmission, by injecting an optical power, the wavelength interval of the bimodal distribution would become larger due to the different resonance red-shifts. Thus the power transmittances between the two red-shift resonances would be high. Namely, the transmittance of the input wavelength is large and the power could transmit in the forward transmission. In the backward transmission, through controlling the input power, the two resonances of the bimodal distribution could overlap at the input wavelength to minimize the power transmittance. In this case, the NTR of the optical diode at the input wavelength could realize the maximum value. With injecting an optical power of 0.96 dBm, a maximum NTR of 33.6 dB and 20-dB bandwidth (BW) of 0.11 nm have been achieved. The compact silicon optical diode with low-power consumption and high NTRs has significant applications for on-chip signal processing systems, such as logic gates and optical computing.

2. Operation principle

The physical mechanism of the opto-mechanical MRR is based on the nonlinear effects (mainly including the thermo-optic effect and opto-mechanical effect). The opto-mechanical MRR is designed on a SOI wafer with 220-nm-thick silicon slab and 2-μm buried oxide layer. The size of the SOI chip is 1 mm × 1 mm. As shown in Fig. 1(a), the oxide substrate under half MRR is removed which results the corresponding waveguides to be free-hanging. As half of the MRR is free-hanging in the air, the effective index contrast between the MRR and the surroundings is higher. In this case, the transmission loss of the MRR would be lower which contributes to increase the quality (Q) factor of the MRR [34]. When the resonance light λr is injected into the microring, the two nonlinear effects could be effectively activated by low input powers. Because the opto-mechanical MRR is free-hanging in the air, the device heatsink and dissipation could be significantly reduced. In this case, the thermo-optic effect would cause higher temperature rise of the MRR to induce larger red-shifts. On the other hand, the gradient of the optical field is greatly enhanced in the opto-mechanical MRR which is significant to enhance the opto-mechanical effect. As shown in Fig. 1(b), the free-hanging MRR arc would be bent downwards to the substrate by the generated optical force. Due to the waveguide deformation, the effective optical path of the MRR would be changed which results in resonance red-shifts. Therefore, the nonlinear effects could be efficiently activated in the opto-mechanical MRRs to induce resonance red-shifts.

 figure: Fig. 1

Fig. 1 (a) Schematic diagram of the free-hanging MRR. (b) Cross-sectional illustration of the deflected MRR influenced by the optical force.

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The resonance red-shift δλ1 induced by the thermo-optic effect could be described by

δλ1λrngΓthkthRthPt
where λr is the resonant wavelength, ng is the group index, Γth is the effective confinement factor corresponding to the thermo-optic effect, kth is silicon thermo-optic coefficient, Rth is the thermal resistance of the silicon ring resonator, and Pt is the optical pump power for the thermo-optic effect.

On the other hand, the resonance red-shift δλ2 induced by the opto-mechanical effect can be expressed as

δλ2gom2Pm/k
where gom=neffg is the opto-mechanical tuning efficiency, neff is the effective index of the free-hanging MRR, g represents the waveguide separation between the free-hanging arc and the substrate, Pm is the circulating pump power on the ring for opto-mechanical effect, and k is the beam stiffness.

Therefore, the total resonance red-shift δλ can be determined by

δλ=δλ1+δλ2Pin
where Pin is the input power of λr which mainly consists of Pt and Pm.

As the resonance red-shifts caused by the two nonlinear effects are proportional to the input power Pin, the transmission characteristics of the opto-mechanical device could be manipulated by adjusting the input optical powers.

Figure 2(a) shows the structure of the optical diode which consists of two cascaded all-pass MRRs (i.e. R1 and R2). The radii of R1 and R2 has a slight difference which leads to different FSRs. Due to the Vernier effect, the initial transmission spectrum of the device is a series of notch bimodal distribution. The MRR waveguides in the two dashed boxes are free-hanging arcs. The gaps between the MRRs and straight waveguides (G1 and G2) are designed to induce strong coupling. As shown in Fig. 2(b), the two resonances of the selected notch bimodal distribution are λ1 and λ2 which belong to R1 and R2 respectively. To realize the maximum NTR, the operation wavelength is chosen as λ0 (the blue line) which is close to λ1. The forward and backward transmissions are from Port 1 to Port 2 and from Port 2 to Port 1, respectively. The asymmetric transmission in the optical diode is illustrated in Fig. 2(c).

 figure: Fig. 2

Fig. 2 (a) The structure of the optical diode. (b) The initial transmission spectrum of the cascaded MRRs. (c) The forward transmission (red line) and backward transmission (blue line) of the optical diode.

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The forward transmission (red solid line): the optical power of λ0 is injected from Port 1. Because the wavelength λ0 is near λ1, the input power coupling into R1 is strong. Therefore, the power accumulating in R1 is high enough to induce a large red-shift (λ3-λ1). As the optical power is attenuated by R1 and λ0 is relatively far from λ2, the remaining power is not strong enough to excite the nonlinear effects in R2. Namely, the red-shift of R2 is little (i.e. a redshift of λ4-λ2). In this case, the wavelength intervals between the red-shift resonances λ3 and λ4 is large enough to realize a high transmittance of λ0, shown as the red solid line in Fig. 2(c). Namely, the power of λ0 could transmit in the forward transmission (from Port 1 to Port 2).

The backward transmission (blue dashed line): the optical power of λ0 is injected from Port 2. As the optical power is not attenuated before the light arrives in R2, the power coupling into R2 is much higher than the forward transmission. Thus the resonant wavelength of R2 shifts more closely to λ0 which brings stronger couplings and larger red-shifts. When the light reaches R1, the resonance red-shift of R1 could be ignored as the optical power has been largely attenuated by R2. In this case, the wavelength detuning between R1 red-shift resonance and λ0 could be negligible, so the power coupling into R1 is strong which leads to a large power attenuation. By adjusting the input power of λ0, the red-shift resonances of R1 and R2 could overlap at the wavelength of λ0. As a result, the notch depth of the synthetic waveform at λ0 could realize the maximum value, shown as the blue dashed line in Fig. 2(c). Namely, the power of λ0 could not transmit in the backward transmission (from Port 2 to Port 1). It is clear that a high NTR could be achieved at the input wavelength of λ0.

Before fabricating the silicon optical diode, we utilize the waveguide theory and finite-element mode solver to optimize the parameters of the opto-mechanical MRR. At first, as shown in Fig. 3(a), the bending loss of the MRR with different radii and widths (blue solid line: 450 nm, red dashed line: 500 nm) are calculated by the finite-difference time-domain (FDTD) method [35,36]. Considering the waveguide single-mode transmission and practical fabrication technology, the waveguide width and radius of the MRR are designed as 450 nm and 20 μm, respectively. In this case, the MRR bending loss could be ignored according to the blue solid line. Then, we use the finite-element mode solver to simulate the waveguide modes. As the silicon slab of commercial SOI wafer is 220 nm, the ridge height and slab height of the device are designed as 190 nm and 30 nm, respectively. As shown in Fig. 3(b), the effective indexes of the ridge MRR (red dashed line), the straight waveguide (blue dotted line) and the free-hanging MRR (green solid line) at 1550 nm are 2.36, 2.33 and 2.26, respectively. Namely, the differences of the waveguide effective indexes could be negligible, which benefits the signal transmission and coupling between different structures. The energy profiles of the fundamental modes in the silicon straight waveguide, ridge MRR and free-hanging MRR are shown as Figs. 3(c)-3(e), respectively.

 figure: Fig. 3

Fig. 3 (a) Calculated MRR bending loss. (b) The effective indexes of different waveguides. Energy profiles of the fundamental modes in (c) straight waveguide, (d) ridge MRR and (e) free-hanging MRR, respectively.

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In order to demonstrate the passive optical diode, we fabricated the cascaded opto-mechanical MRRs on the SOI wafer with a 220-nm-thick silicon layer and 2-μm buried oxide layer. The size of the SOI chip is 1 mm × 1 mm. The MRR free-hanging part is released by selective etching processing. Firstly, the whole device was transferred to photoresist by the first E-beam lithography (EBL, Vistec EBPG 5000 Plus) and the voltage of the EBL device is 100 kV. Then the SOI chip was etched downwards for 190 nm in an Oxford 100 inductively coupled plasma (ICP) etcher using SF6/C4F8 mixture for silicon etching. The powers of the ICP component and radio frequency (RF) are 850 W and 20 W, respectively. In this case, the device structures are ridge waveguides with a 30 nm slab layer. Secondly, half MRR waveguides which are away from the straight waveguide experienced a second EBL and ICP processing to etch another 30 nm. In this case, the structure of the above half MRR is slab waveguide whose oxide substrates are exposed in the air. Thus a corrosion window for the hydrofluoric (HF) wet etching was formed. In contrast, the other half MRR with a ridge structure has a 30 nm silicon protection layer to separate from the later HF acid. Finally, the HF acid etching was utilized to selectively undercut the oxide layer of the corrosion windows. In this case, the half MRR would be free-hanging while the other waveguides are fixed.

Figure 4(a) illustrates the scanning electron microscope (SEM) image of the cascaded opto-mechanical MRRs (i.e. R1 and R2). The radii of the two MRRs are 20.12 μm and 20 μm, respectively. The coupling gaps between the straight waveguides and R1, R2 are 210 nm and 190 nm, respectively. The zoom-in image of the free-hanging region is shown in Fig. 4(b). The widths of the whole waveguides are 450 nm to guarantee single-mode transmission. Figure 4(c) shows the side view of the opto-mechanical microring R1 whose half waveguides are free-hanging. As half of the MRR is fixed, the opto-mechanical MRR could be considered as a cantilever structure. Due to the characteristics of the waveguide material and structure, the fixed waveguides could sustain the free-hanging arc. The vertical grating couplers are employed to couple the optical signals from the fibers to the silicon chip. The period, duty cycle, total length and coupling loss for a single side of the grating coupler are 610 nm, 50%, 19 µm and 3 dB, respectively. The compact footprint of the whole optical diode is 0.4 mm × 0.1 mm.

 figure: Fig. 4

Fig. 4 (a) SEM image of the cascaded opto-mechanical MRRs. (b) The zoom-in image of the free-hanging region. (c) The side view of R1.

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As the radii of the two MRRs have a slight difference, the device transmission spectrum is a series of notch bimodal distributions. According to the operation principle in Fig. 2, one bimodal distribution is chosen to demonstrate the optical diode, as shown in Fig. 5(a). The resonant wavelengths are 1551.658 nm (λ1) and 1551.53 nm (λ2) with a wavelength interval of 0.128 nm. To further investigate the device tuning property based on the nonlinear effects, different powers at 1551.658 nm (λ1) and 1551.698 nm (i.e. λ1 + 0.04) are injected into the device. As shown in Fig. 5(b), the red-shifts of wavelengths λ1 (red solid line) and λ1 + 0.04 (blue dashed line) both increase linearly with the input powers. In this case, the required input powers to realize the maximum NTRs could be effectively estimated which is beneficial for optimizing the tuning process and performances of the diode experiments. The measured red-shifts show that the tuning characteristics of the opto-mechanical device are energy-efficient. For example, the red-shift of λ1 could reach 0.17 nm with injecting an optical power of 1 mW. According to Eq. (3), because coupling efficiencies of the MRR resonant wavelengths are higher, the wavelength of the input light aligned at the resonances could induce stronger thermal effect and opto-mechanical interaction which would cause the larger resonance red-shifts. Therefore, the slope of λ1 + 0.04 is lower than λ1.

 figure: Fig. 5

Fig. 5 (a) One bimodal distribution of the device transmission spectrum. (b) The red-shifts of λ1 and λ1 + 0.04 under different input powers.

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3. Experimental results and discussions

In order to demonstrate the nonreciprocal transmission of the device, continuous-wave (CW) light with different wavelengths around λ1 are injected into the silicon chip. Meanwhile, a low-power amplified spontaneous emission (ASE) source is used to characterize the device transmission spectrum. The device initial transmission spectrum is shown as the green line (no CW input) in Fig. 6(a). At first, the input optical wavelength is fixed at 1551.698 nm (i.e. λ1 + 0.04). As shown in Fig. 2(c), a maximum NTR could be achieved when the red-shift resonances of the two MRRs overlap at the input wavelength in the backward transmission. By injecting an optical power of 0.96 dBm, the two red-shift resonances could overlap around 1551.698 nm in the backward transmission, shown as the blue line. In contrast, the forward transmission is shown as the red line with the same input power. Therefore, a high NTR of 33.6 dB is obtained at the input wavelength of 1551.698 nm.

 figure: Fig. 6

Fig. 6 Measured transmission of no CW light input (green line), forward input (red line) and backward input (blue line), respectively. The input optical powers are set as (a) 0.96 dBm and (b) −0.52 dBm, respectively.

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Then, the CW wavelength is tuned to 1551.678 nm (λ1 + 0.02). With injecting an optical power of −0.52 dBm, the forward and backward transmissions of the device are shown as the red line and blue line in Fig. 6(b), respectively. In this case, the NTR could realize 31.8 dB. The NTR difference between the above two wavelengths (i.e. λ1 + 0.04 and λ1 + 0.02) is described as follows. Compared with λ1 + 0.04, the coupling efficiency of λ1 + 0.02 is higher because λ1 + 0.02 is closer to the resonances λ1 and λ2. Thus the input power of λ1 + 0.02 should be reduced to −0.52 dBm to guarantee that the two red-shift resonances could overlap around λ1 + 0.02 in the backward transmission. As the input power is reduced, the resonance red-shifts in the forward transmission is lower. Compared with the red line in Fig. 6(a), the resonance interval of the red line in Fig. 6(b) is narrower. In this case, the forward transmittances between the two red-shift resonances would decrease, which leads to a lower NTR of 31.8 dB in Fig. 6(b).

To further characterize the transmission performances of the optical diode, the device operation bandwidths under different input powers are measured. The input optical wavelength ranges from 1551.56 nm to 1551.76 nm. Figure 7(a) illustrates the measured NTRs with injecting powers of 0.96 dBm (green solid line), −0.52 dBm (blue dashed line) and −1.87 dBm (red dotted line), respectively. The 20-dB BW represents the operation bandwidth with NTRs larger than 20 dB. According to the measured green line, the 20-dB BW of the optical diode could realize 0.11 nm when the input power is low as 0.96 dBm. Moreover, the relationship between the NTRs and the input powers is also investigated. For instance, when the input wavelength is fixed at 1551.698 nm, the NTRs under different input powers are shown in Fig. 7(b). As the input power is increased from −2 dBm, the device NTR accordingly becomes larger. When the input power is enhanced to 0.96 dBm, the two MRR resonances could overlap at 1551.698 nm in the backward transmission, so the NTR could realize the maximum value of 33.6 dB. If the input power is larger than 0.96 dBm, the two MRR resonances in the backward transmission would be separated around 1551.698 nm, so the NTRs gradually decrease. When the input power ranges from −1.1 dBm to 2.4 dBm, the NTRs of the optical diode are larger than 20 dB. As the input powers are relevant to the device heatsink and optical force, the power sensibility of the optical diode could be improved by optimizing the free-hanging waveguide length and the separation gap between the free-hanging waveguide and substrate. In this case, the input power range could be extended with maintaining the high NTRs.

 figure: Fig. 7

Fig. 7 (a) Measured NTRs under different input wavelengths. (b) The relationship between the NTRs and input powers at 1551.698 nm.

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Table 1 illustrates the operation principles and experimental performances of recent optical diodes based on the silicon MRRs. Three important performance parameters (the required optical powers, NTRs and 20-dB BWs) of the demonstrated diodes are compared by utilizing different nonlinear effects. Firstly, the resonances of the all-pass MRR and add-drop MRR are required to be identical [20,21] which increases the fabrication and tuning complexity. The device 20-dB BWs are both narrower than 0.1 nm. Secondly, the required optical powers of the cascaded MRRs [22] and racetrack MRR [26] are relatively high (8.2 dBm and 6 dBm) which might limit their practical applications in low-power on-chip optical systems. The NTRs (24 dB and 12.8 dB) also need to be improved. In contrast, the optical diode of this work is energy-efficient as the required power is low as 0.96 dBm. The maximum NTR could realize 33.6 dB which is sufficient for practical applications. Meanwhile, the device 20-dB BW is improved to 0.11 nm. Therefore, the proposed silicon optical diode is significant in on-chip optical communications systems with advantages of CMOS-compatibility, low-power consumptions and high NTRs.

Tables Icon

Table 1. Performance comparisons of recent silicon MRR-based optical diodes

As the characteristics of the optical diodes are mainly determined by the opto-mechanical MRRs, the device performances could be significantly improved by optimizing the MRR parameters in the future. The required optical powers could be reduced from two aspects. Firstly, by optimizing the waveguide width and separation gap between the free-hanging MRR and the oxide substrate [34,37,38], the nonlinear effects in the opto-mechanical MRR could be enhanced to reduce the required optical powers. Secondly, by employing better fabrication processing [39] and post-processing technology [40,41], such as thermal oxidation [42], the waveguide roughness could be improved to reduce the device loss. By employing the optimized MRR of 2 dB/cm transmission loss [43,44] and the optical waveguides of 0.026 dB/cm loss [45], the required optical powers could be significantly reduced. Moreover, the NTRs and operation bandwidths of the optical diode could be improved in the future. Firstly, by designing the MRRs at the critical coupling [46], the MRR extinction ratios could be larger which benefits to improve the NTRs. Secondly, the input power could be enhanced so as to increase the wavelength interval of the two red-shift resonances in the forward transmission. In this case, the NTRs would be higher because the forward transmittances between the two red-shift resonances become larger. Once the NTRs increase, the device 20-dB BW could be accordingly improved.

4. Conclusion

We have experimentally demonstrated a passive optical diode with low-power consumption on pure silicon platform. The operation principle is based on the asymmetric resonance red-shifts of the cascaded opto-mechanical MRRs which are induced by the nonlinear effects. A high NTR of 33.6 dB and a relatively broad 20-dB BW of 0.11 nm are achieved. The required input power is low as 0.96 dBm. Our experiment provides a CMOS-compatible optical diode of a compact footprint, low power consumptions and high NTRs to process optical signals in on-chip optical communication systems.

Funding

National Natural Science Foundation of China (61805215), Natural Science Foundation of Hubei Province (2018CFB167), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUG170637 and CUG2018JM15).

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33. L. Liu, Z. Chen, X. Jin, Y. Yang, Z. Yu, J. Zhang, L. Zhang, and H. Wang, “Low-power all-optical microwave filter with tunable central frequency and bandwidth based on cascaded opto-mechanical microring resonators,” Opt. Express 25(15), 17329–17342 (2017). [CrossRef]   [PubMed]  

34. W. C. Jiang, J. Zhang, and Q. Lin, “Compact suspended silicon microring resonators with ultrahigh quality,” Opt. Express 22(1), 1187–1192 (2014). [CrossRef]   [PubMed]  

35. Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009). [CrossRef]  

36. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Modeling and measurement of losses in silicon-on-insulator resonators and bends,” Opt. Express 15(17), 10553–10561 (2007). [CrossRef]   [PubMed]  

37. A. Vasiliev, A. Malik, M. Muneeb, B. Kuyken, R. Baets, and G. Roelkens, “On-chip mid-infrared photothermal spectroscopy using suspended silicon-on-insulator microring resonators,” ACS Sens. 1(11), 1301–1307 (2016). [CrossRef]  

38. L. Martinez and M. Lipson, “High confinement suspended micro-ring resonators in silicon-on-insulator,” Opt. Express 14(13), 6259–6263 (2006). [CrossRef]   [PubMed]  

39. A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, and M. R. Watts, “Ultralow-loss silicon ring resonators,” Opt. Lett. 37(20), 4236–4238 (2012). [CrossRef]   [PubMed]  

40. C. Manfletti and G. Kroupa, “Laser ignition of a cryogenic thruster using a miniaturised Nd:YAG laser,” Opt. Express 21(Suppl 6), A1126–A1139 (2013). [CrossRef]   [PubMed]  

41. S. Lorenz, M. Bärwinkel, P. Heinz, S. Lehmann, W. Mühlbauer, and D. Brüggemann, “Characterization of energy transfer for passively Q-switched laser ignition,” Opt. Express 23(3), 2647–2659 (2015). [CrossRef]   [PubMed]  

42. A. Griffith, J. Cardenas, C. B. Poitras, and M. Lipson, “High quality factor and high confinement silicon resonators using etchless process,” Opt. Express 20(19), 21341–21345 (2012). [CrossRef]   [PubMed]  

43. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express 15(22), 14467–14475 (2007). [CrossRef]   [PubMed]  

44. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express 15(22), 14765–14771 (2007). [CrossRef]   [PubMed]  

45. G. Li, J. Yao, H. Thacker, A. Mekis, X. Zheng, I. Shubin, Y. Luo, J. H. Lee, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow-loss, high-density SOI optical waveguide routing for macrochip interconnects,” Opt. Express 20(11), 12035–12039 (2012). [CrossRef]   [PubMed]  

46. V. M. Menon, W. Tong, and S. R. Forrest, “Control of quality factor and critical coupling in microring resonators through integration of a semiconductor optical amplifier,” IEEE Photonics Technol. Lett. 16(5), 1343–1345 (2004). [CrossRef]  

References

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  30. D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
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    [Crossref]
  32. J. Tao, J. Wu, H. Cai, Q. Zhang, J. M. Tsai, J. Lin, and A. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett. 100(11), 113104 (2012).
    [Crossref]
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  34. W. C. Jiang, J. Zhang, and Q. Lin, “Compact suspended silicon microring resonators with ultrahigh quality,” Opt. Express 22(1), 1187–1192 (2014).
    [Crossref] [PubMed]
  35. Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
    [Crossref]
  36. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Modeling and measurement of losses in silicon-on-insulator resonators and bends,” Opt. Express 15(17), 10553–10561 (2007).
    [Crossref] [PubMed]
  37. A. Vasiliev, A. Malik, M. Muneeb, B. Kuyken, R. Baets, and G. Roelkens, “On-chip mid-infrared photothermal spectroscopy using suspended silicon-on-insulator microring resonators,” ACS Sens. 1(11), 1301–1307 (2016).
    [Crossref]
  38. L. Martinez and M. Lipson, “High confinement suspended micro-ring resonators in silicon-on-insulator,” Opt. Express 14(13), 6259–6263 (2006).
    [Crossref] [PubMed]
  39. A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, and M. R. Watts, “Ultralow-loss silicon ring resonators,” Opt. Lett. 37(20), 4236–4238 (2012).
    [Crossref] [PubMed]
  40. C. Manfletti and G. Kroupa, “Laser ignition of a cryogenic thruster using a miniaturised Nd:YAG laser,” Opt. Express 21(Suppl 6), A1126–A1139 (2013).
    [Crossref] [PubMed]
  41. S. Lorenz, M. Bärwinkel, P. Heinz, S. Lehmann, W. Mühlbauer, and D. Brüggemann, “Characterization of energy transfer for passively Q-switched laser ignition,” Opt. Express 23(3), 2647–2659 (2015).
    [Crossref] [PubMed]
  42. A. Griffith, J. Cardenas, C. B. Poitras, and M. Lipson, “High quality factor and high confinement silicon resonators using etchless process,” Opt. Express 20(19), 21341–21345 (2012).
    [Crossref] [PubMed]
  43. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express 15(22), 14467–14475 (2007).
    [Crossref] [PubMed]
  44. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express 15(22), 14765–14771 (2007).
    [Crossref] [PubMed]
  45. G. Li, J. Yao, H. Thacker, A. Mekis, X. Zheng, I. Shubin, Y. Luo, J. H. Lee, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow-loss, high-density SOI optical waveguide routing for macrochip interconnects,” Opt. Express 20(11), 12035–12039 (2012).
    [Crossref] [PubMed]
  46. V. M. Menon, W. Tong, and S. R. Forrest, “Control of quality factor and critical coupling in microring resonators through integration of a semiconductor optical amplifier,” IEEE Photonics Technol. Lett. 16(5), 1343–1345 (2004).
    [Crossref]

2018 (2)

K. Xu, “Monolithically integrated Si gate-controlled light-emitting device: science and properties,” J. Opt. 20(2), 024014 (2018).
[Crossref]

K. Xu, L. Huang, Z. Zhang, J. Zhao, Z. Zhang, L. W. Snyman, and J. W. Swart, “Light emission from a poly-silicon device with carrier injection engineering,” Mater. Sci. Eng. B 231, 28–31 (2018).
[Crossref]

2017 (4)

2016 (3)

2015 (4)

2014 (2)

2013 (4)

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, A. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett. 102(2), 023103 (2013).
[Crossref]

L. Fan, L. T. Varghese, J. Wang, Y. Xuan, A. M. Weiner, and M. Qi, “Silicon optical diode with 40 dB nonreciprocal transmission,” Opt. Lett. 38(8), 1259–1261 (2013).
[Crossref] [PubMed]

M. Xu, J. Wu, T. Wang, X. Hu, X. Jiang, and Y. Su, “Push–pull optical nonreciprocal transmission in cascaded silicon microring resonators,” IEEE Photonics J. 5(1), 2200307 (2013).
[Crossref]

C. Manfletti and G. Kroupa, “Laser ignition of a cryogenic thruster using a miniaturised Nd:YAG laser,” Opt. Express 21(Suppl 6), A1126–A1139 (2013).
[Crossref] [PubMed]

2012 (7)

2011 (3)

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5(9), 549–553 (2011).
[Crossref]

C. Lu, X. Hu, H. Yang, and Q. Gong, “Ultrahigh-contrast and wideband nanoscale photonic crystal all-optical diode,” Opt. Lett. 36(23), 4668–4670 (2011).
[Crossref] [PubMed]

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

2010 (5)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
[Crossref]

L. Snyman, M. du Plessis, and E. Bellotti, “Photonic transistion (1.4 eV–2.8 eV) in silicon p + np + injection-avalanche CMOS LEDs as function of depletion layer profiling and defect engineering,” IEEE J. Quantum Electron. 46(6), 906–919 (2010).
[Crossref]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

D. A. B. Miller, “Are optical transistors the logical next step?” Nat. Photonics 4(1), 3–5 (2010).
[Crossref]

2009 (2)

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94(17), 171116 (2009).
[Crossref]

Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
[Crossref]

2007 (3)

2006 (3)

2005 (2)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, “Electro-tunable optical diode based on photonic bandgap liquid-crystal heterojunctions,” Nat. Mater. 4(5), 383–387 (2005).
[Crossref] [PubMed]

Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystals,” Opt. Lett. 30(15), 1989–1991 (2005).
[Crossref] [PubMed]

2004 (1)

V. M. Menon, W. Tong, and S. R. Forrest, “Control of quality factor and critical coupling in microring resonators through integration of a semiconductor optical amplifier,” IEEE Photonics Technol. Lett. 16(5), 1343–1345 (2004).
[Crossref]

1998 (1)

E. A. Fitzgerald and L. C. Kimerling, “Silicon-based microphotonics and integrated optoelectronics,” MRS Bull. 23(4), 39–47 (1998).
[Crossref]

Baets, R.

A. Vasiliev, A. Malik, M. Muneeb, B. Kuyken, R. Baets, and G. Roelkens, “On-chip mid-infrared photothermal spectroscopy using suspended silicon-on-insulator microring resonators,” ACS Sens. 1(11), 1301–1307 (2016).
[Crossref]

S. Ghosh, S. Keyvavinia, W. Van Roy, T. Mizumoto, G. Roelkens, and R. Baets, “Ce:YIG/Silicon-on-Insulator waveguide optical isolator realized by adhesive bonding,” Opt. Express 20(2), 1839–1848 (2012).
[Crossref] [PubMed]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Bärwinkel, M.

Bellotti, E.

L. Snyman, M. du Plessis, and E. Bellotti, “Photonic transistion (1.4 eV–2.8 eV) in silicon p + np + injection-avalanche CMOS LEDs as function of depletion layer profiling and defect engineering,” IEEE J. Quantum Electron. 46(6), 906–919 (2010).
[Crossref]

Bi, L.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Biberman, A.

Brüggemann, D.

Butsch, A.

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5(9), 549–553 (2011).
[Crossref]

Cai, H.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, A. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett. 102(2), 023103 (2013).
[Crossref]

J. Tao, J. Wu, H. Cai, Q. Zhang, J. M. Tsai, J. Lin, and A. Liu, “A nanomachined optical logic gate driven by gradient optical force,” Appl. Phys. Lett. 100(11), 113104 (2012).
[Crossref]

Cardenas, J.

Chen, Z.

Cunningham, J. E.

Dai, D.

Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
[Crossref]

de Vries, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Ding, L.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, A. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett. 102(2), 023103 (2013).
[Crossref]

Dionne, G. F.

L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, “On-chip optical isolation in monolithically integrated non-reciprocal optical resonators,” Nat. Photonics 5(12), 758–762 (2011).
[Crossref]

Dong, B.

H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, A. Q. Liu, and D. L. Kwong, “A nanoelectromechanical systems optical switch driven by optical gradient force,” Appl. Phys. Lett. 102(2), 023103 (2013).
[Crossref]

Dong, J.

du Plessis, M.

L. Snyman, M. du Plessis, and E. Bellotti, “Photonic transistion (1.4 eV–2.8 eV) in silicon p + np + injection-avalanche CMOS LEDs as function of depletion layer profiling and defect engineering,” IEEE J. Quantum Electron. 46(6), 906–919 (2010).
[Crossref]

Fan, L.

L. Fan, L. T. Varghese, J. Wang, Y. Xuan, A. M. Weiner, and M. Qi, “Silicon optical diode with 40 dB nonreciprocal transmission,” Opt. Lett. 38(8), 1259–1261 (2013).
[Crossref] [PubMed]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref] [PubMed]

Fan, S.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109(3), 033901 (2012).
[Crossref] [PubMed]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94(17), 171116 (2009).
[Crossref]

Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystals,” Opt. Lett. 30(15), 1989–1991 (2005).
[Crossref] [PubMed]

Fathpour, S.

Fitzgerald, E. A.

E. A. Fitzgerald and L. C. Kimerling, “Silicon-based microphotonics and integrated optoelectronics,” MRS Bull. 23(4), 39–47 (1998).
[Crossref]

Forrest, S. R.

V. M. Menon, W. Tong, and S. R. Forrest, “Control of quality factor and critical coupling in microring resonators through integration of a semiconductor optical amplifier,” IEEE Photonics Technol. Lett. 16(5), 1343–1345 (2004).
[Crossref]

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

Gao, D.

L. Liu, J. Dong, D. Gao, A. Zheng, and X. Zhang, “On-chip passive three-port circuit of all-optical ordered-route transmission,” Sci. Rep. 5(1), 10190 (2015).
[Crossref] [PubMed]

Geluk, E.-J.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
[Crossref]

Ghosh, S.

Gong, Q.

Griffith, A.

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic diagram of the free-hanging MRR. (b) Cross-sectional illustration of the deflected MRR influenced by the optical force.
Fig. 2
Fig. 2 (a) The structure of the optical diode. (b) The initial transmission spectrum of the cascaded MRRs. (c) The forward transmission (red line) and backward transmission (blue line) of the optical diode.
Fig. 3
Fig. 3 (a) Calculated MRR bending loss. (b) The effective indexes of different waveguides. Energy profiles of the fundamental modes in (c) straight waveguide, (d) ridge MRR and (e) free-hanging MRR, respectively.
Fig. 4
Fig. 4 (a) SEM image of the cascaded opto-mechanical MRRs. (b) The zoom-in image of the free-hanging region. (c) The side view of R1.
Fig. 5
Fig. 5 (a) One bimodal distribution of the device transmission spectrum. (b) The red-shifts of λ1 and λ1 + 0.04 under different input powers.
Fig. 6
Fig. 6 Measured transmission of no CW light input (green line), forward input (red line) and backward input (blue line), respectively. The input optical powers are set as (a) 0.96 dBm and (b) −0.52 dBm, respectively.
Fig. 7
Fig. 7 (a) Measured NTRs under different input wavelengths. (b) The relationship between the NTRs and input powers at 1551.698 nm.

Tables (1)

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Table 1 Performance comparisons of recent silicon MRR-based optical diodes

Equations (3)

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δ λ 1 λ r n g Γ th k th R th P t
δ λ 2 g om 2 P m /k
δλ=δ λ 1 +δ λ 2 P in

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