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Letter
On-chip microwave signal generation based on a silicon microring modulator HAIFENG SHAO, HUI YU,* XIA LI, YAN LI, JIANFEI JIANG, HUAN WEI, GENCHENG WANG, TINGGE DAI, QIMEI CHEN, JIANYI YANG, AND XIAOQING JIANG Institute of Microelectronics and Optoelectronics, Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China *Corresponding author: [email protected] Received 15 April 2015; revised 19 June 2015; accepted 24 June 2015; posted 25 June 2015 (Doc. ID 237915); published 13 July 2015
A photonic-assisted microwave signal generator based on a silicon microring modulator is demonstrated. The microring cavity incorporates an embedded PN junction that enables a microwave signal to modulate the lightwave circling inside. The DC component of the modulated light is trapped in the cavity, while the high-order sideband components are able to exit the cavity and then generate microwave signals at new frequencies in a photodetector. In our proof-of-concept experiment, a 10 GHz microwave signal is converted to a 20 GHz signal in the optical domain with an electrical harmonic suppression ratio of 22 dB. An analytic model is also established to explain the operation mechanism, which agrees well with the measured data. © 2015 Optical Society of America OCIS codes: (060.5625) Radio frequency photonics; (130.3120) Integrated optics devices; (130.4110) Modulators. http://dx.doi.org/10.1364/OL.40.003360
Microwave photonics (MPW), which generates, transports, and processes microwave or millimeter (mm)-wave signals in the optical domain, has found many applications in wireless access networks, phase array antennas, radio-over-fiber systems, satellite communications, radio astronomy, and so on [1–4]. An essential functionality in any MPW link is to generate the microwave signal in the optical domain. The most prevailing solution so far is based on optical heterodyning with a highbandwidth photodetector (PD). This necessarily requires two stable phase-correlated optical waves with a fixed frequency difference, which can be obtained by utilizing techniques such as optical injection locking [5], an optical phase-lock loop [6], a dual-wavelength laser [7], and electro-optic (EO) modulation [8]. Among all these techniques, EO modulation has proved to be a simple and effective approach with high spectrum purity and stability. This solution uses a sinusoidal microwave signal to drive a stand-alone Mach–Zehnder modulator (MZM) or 0146-9592/15/143360-04$15/0$15.00 © 2015 Optical Society of America
cascaded multi-MZMs. Unwanted frequency sidebands in the spectra of modulated optical carriers are suppressed by setting proper bias points, cascading manners, or optical notch filters. The heterodyning of the remaining frequency components at the PD gives rise to desired microwave signals whose frequencies are integer multiples of the driving frequency [9–16]. In all these instances, MZMs are exclusively utilized largely owing to their well-understood sinusoidal modulation transfer function. Compared with MZMs, modulators based on optical resonators such as microrings could drastically enhance the interaction between the light and the driving signal, and hence have the advantages of small footprints and low power consumption. Until today, microring cavities have been investigated comprehensively to implement digital modulation for demanding optical interconnect systems [17–21]. However, we are unaware of any attempt so far to generate a microwave signal with a microring cavity. Therefore, it is worthwhile to explore the potential of microring modulators for this application. In this Letter, we demonstrate microwave signal generation with a silicon carrier-depletion-based microring modulator. With proper coupling conditions and operating wavelength, the DC component of the modulated light is trapped in the cavity. The heterodyning of untrapped sidebands then induces a microwave signal at a new frequency. Specifically, we implement a proof-of-concept experiment to convert the frequency of a RF signal from 10 to 20 GHz with a silicon ring modulator. An analytic model that agrees with the measured data and provides physical insight to the mechanism is also established. Figure 1(a) presents a schematic diagram of the silicon microring cavity under test; its radius is 10 μm. A cross section of the rib waveguide forming the ring is shown in Fig. 1(b). The rib waveguide is embedded with a lateral PN junction whose doping concentration is 1.5 × 1018 ∕cm3 . The two ohmic contact regions of the PN junction are heavily doped to 1 × 1020 ∕cm3 . The etching depth is 160 nm and the dimension of the rib waveguide accommodating the PN junction is 450 nm × 220 nm. The device can be electrically represented by the equivalent circuit shown in Fig. 1(c) [17,20,21]. C 0 represents the capacitance between contact pads, while R 1 and
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expanding ω0 and 1∕τ at the DC bias point, and keeping only the first three items, we have ω0 ωDC k 1 v pn ω1 k 2 v 2pn ω1 …;
(2)
1 1 r 1 v pn ω1 r 2 v 2pn ω1 …; τ τDC
(3)
where ωDC and 1∕τDC represent the resonance frequency and the amplitude decay rate at the DC bias point. The coefficients k1 , k 2 , r 1 , and r 2 depend on profiles of the dopants and the guide mode. Their value can be obtained through the measurement. By substituting Eqs. (2) and (3) into Eq. (1), we deduce the analytical solution of at:
Fig. 1. (a) Schematic diagram of a typical microring cavity in the microwave signal generation system. (b) Cross section of rib waveguide. (c) Equivalent circuit of the device. TL, tunable laser; PC, polarization controller; DUT, device under test; GC, grating coupler; DC, direct current; EDFA, erbium-doped fiber amplifier; ESA, electrical signal analyzer. Optical fiber is represented by solid lines and the electrical path is represented by dashed lines.
C 1 denote the resistance and the capacitance of the reversebiased PN junction, respectively. The buried SiO2 layer and the Si substrate are represented by capacitance C 2 and resistance R 2 , respectively. Supposing an external microwave signal of v 0 cosω1 t is applied to the device, the AC voltage v pn ω1 that drops across the space charge region of the PN junction is v pn ω1 v 0 f ω1 cosω1 t φω1 . Here f ω1 and φω1 denote the modulus and the phase of the frequency response of v pn ω1 . Their expressions can be obtained according to the circuit in Fig. 1(c); these expressions are not listed here for brevity but can be found in [20]. According to the mode coupling theory in the time domain [20], the amplitude at of the energy stored inside the microring satisfies d 1 αt jω0 − αt − jμAe jωt ; (1) dt τ where ω and A denote the angular frequency and the amplitude of the incident optical field, respectively. The microring resonates at angular frequency ω0. 1∕τ is the overall amplitude decay rate of the optical field inside the microring cavity. The sum of 1∕τe and 1∕τl . 1∕τe represents the amplitude decay rate caused by the coupling with the bus waveguide, while 1∕τl is owing to the beam propagation loss of the doped rib waveguide. The parameter μ represents the mutual coupling between the bus waveguide and the microring. It is calculated as μ2 2∕τe . By controlling the width of the space charge region, the voltage signal v pn ω1 can shift values of both ω0 and 1∕τ. The inherent characteristic of the PN junction determines that dependences of ω0 and 1∕τ on v pn ω1 are not linear. By Taylor
αt −jμA expjωt ∞ X k jr 1 Jn 1 v 0 f ω1 expjnω1 t φ × ω1 n−∞ ∞ X k jr 2 2 2 Jm 2 v 0 f ω1 expj2mω1 t φ · 4ω1 m−∞ ∞ X ∞ X k 1 jr 1 · Jp − v0 f ω1 ω1 p−∞ q−∞ k 2 jr 2 2 2 v f ω1 × Jq − 4ω1 0 ×
expjpω1 t φ 2jqω1 t φ ; jω − ω0 1τ − 12 jk2 − r 2 v 20 f 2 ω1 jpω1 2jqω1 (4)
where J n z is the nth Bessel function. The transmitted filed S t t in the bus waveguide can be calculated as S t t A expjωt − jμat. By the small signal approximation, we can explain qualitatively how the microwave frequency upconversion occurs. In the small signal regime, the quadratic items k2 v 2pn ω1 and r 2 v 2pn ω1 in Eqs. (2) and (3) can be neglected. Based on this premise, the solution in Eq. (4) can be greatly simplified, and thus S t t can be written as jω − ω0 1τ − τ2e S t t A expjωt jω − ω0 1τ jv μ2 k1 jr 1 f ω1 − 0 cos ω1 t jω − ω0 1τ 2 ω21
jv0 μ2 k1 jrf ω1 ω1 sin ω1 t : (5) − jω − ω0 1τ 2 ω21 jω − ω0 1τ With Eq. (5) we have investigated the small-signal frequency response of the optical amplitude modulation carried out by silicon ring modulators in [20]. The first item inside the braces of Eq. (5) represents the transmitted field of the all-pass microring cavity in the static state, which composes the DC component of S t t. The second and the third items represent the EO modulation. If the microring is critical coupled (τe τl ) and works at the resonance wavelength (ω ω0 ), the DC component of S t t is zero. Thus, S t t consists only of the 1st sidebands:
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Fig. 2. Transmission spectra of the microring cavity under various bias voltages. The inset shows dependences of Δ1∕τl and Δω0 on the bias voltage. Here, Δ1∕τl and Δω0 represent offsets of 1∕τl and ω0 with respect to their values at 0 V bias.
S t t −A
jv 0
μ2 k
1 jr 1 f ω21 τ−2
ω1
× cos ω1 t ω1 τ sin ω1 t expjωt:
(6)
Since the photocurrent i PD at the receiver side is proportional to the power of the optical field jS t tj2 , the optical heterodyning between the 1st sidebands in Eq. (6) leads to a new microwave signal at the frequency of 2ω1 . However, the device does not necessarily operate in the small signal regime as it works to generate a new microwave signal. As a result, the unsimplified solution of at in Eq. (4) is used to quantitatively calculate different harmonic components in the transmitted field S t t in the following context. The experimental setup to generate the microwave signal with the silicon microring cavity is shown in Fig. 1(a). The input optical carrier of 1 mW from a tunable laser (Santec TSL510) is aligned to the resonance wavelength of the cavity at the DC bias point. A polarization controller (PC) is used to adjust the polarization state. The optical carrier is coupled from a single-mode fiber (SMF) to the device via a fiber grating coupler, which gives a ∼8 dB coupling loss. Before being sent to the device under test (DUT) by a GSG probe (Cascade Microtech), the driving microwave signal is combined with a DC bias to avoid entering the carrier-injection region of the PN junction. Two microwave powers of 13 and 7 dBm are utilized in the measurement. After being coupled out from the device by another fiber grating coupler, the modulated optical field passes through an EDFA to enhance its power, and then a tunable filter to filter out undesirable amplified spontaneous emission (ASE) noise. Finally, the modulated optical signal reaches a high-bandwidth PD whose output is fed to an electrical spectrum analyzer (ESA) (Anritsu MS2830A). Discrete data points in Fig. 2 display the measured transmission spectra of the microring at different bias voltages. Extinctions of >20 dB at the resonance wavelengths indicate that the microring cavity is close to the critical coupling.
Fig. 3. S11 parameter at 0 V bias voltage. Table 1 lists extracted values of all elements in the equivalent circuit of the device. For both figures the black solid lines are the fitted curves.
For each reverse bias voltage, we can extract values of ω0 , 1∕τe , and 1∕τl by curve fitting. Black solid lines in Fig. 2 are fitted curves, which match well with the measured data. Values of ω0 and 1∕τl are displayed in the inset of Fig. 2 as a function of the reverse bias voltage. The dependences of ω0 and 1∕τl on the reverse bias voltage can be represented by two second-order polynomial functions, which are also plotted in the inset as solid lines. Expressions of the two polynomials are ω0 1229.818 × 1012 8.373 × 108 v 2b − 2.004 × 1010 v b , and 1∕τ 4.713 × 1010 1.331 × 108 v 2b − 1.430 × 109 v b . According to them, we can calculate values of k1 , k2 , r 1 , and r 2 at any bias points by Taylor expansion. The measured microwave signal reflection coefficient of the device (the S11 parameter) is presented in Fig. 3 as discrete data points. By fitting to the measured S11 data, we extract values of all elements that make up the circuit of Fig. 1(c), which are listed in Table 1 of Fig. 3. Fitted curves are presented as black solid lines in Fig. 3. After obtaining all relevant parameters, we use Eq. (4) to calculate RF powers of different harmonic components in the output of the PD. The modeled suppression ratios (SRs) between the second- and first-order harmonic components after the PD are plotted in Figs. 4(a) and 4(b) for driving microwave powers of 7 and 13 dBm, respectively, together with the measured SR. Measured electrical spectra are presented in Figs. 4(c) and 4(d). As the modulation frequency ω1 rises, both the firstand second-harmonic components attenuate, but with different rates, which are affected by the specific driving condition. If the second harmonic consistently rolls off faster than the first harmonic, the SR will drop as ω1 increases, which is the case in Figs. 4(a) and 4(c). However, if the roll-off rate of the second harmonic is slower than that of first harmonic at the lowfrequency range, and then becomes faster at the high-frequency range, the corresponding SR would reach a peak at some frequency point, as shown in Figs. 4(b) and 4(d). We note that MZMs usually offer SRs of ∼25 dB when they carry out frequency upconversion [11], so the ring modulator here offers comparable SR values, as shown in Fig. 4(d).
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signal is obtained from a 10 GHz input signal with a 22 dB harmonic suppression ratio. Analogously to the MZM, the ring modulator can also be cascaded or combined with a notch filter to achieve higher multiplication factors. This microringbased RF signal generation technique could be a prospective candidate for future integrated MPW systems. Future works include enhancing the conversion efficiency and operation frequency with improved designs, as well as investigating stability and phase noise of the microwave signal generated by this technique.
Fig. 4. Modeled and measured suppression ratios for (a) 7 dBm and (b) 13 dBm input microwave signals. Measured electrical spectra for (c) 7 dBm and (d) 13 dBm input microwave signals.
Funding. Fundamental Research Funds for the Central Universities; National Natural Science Foundation of China (NSFC) (61177055, 61307074); Nature Basic Research Program of China (2013CB632105); Zhejiang Provincial Natural Science Foundation for Distinguished Young Scholar (LR15F050002). REFERENCES
In Figs. 4(a) and 4(b), the theoretical prediction agrees with the measurement result in the trend. The discrepancy between the model and the measurement lies in the facts that, first, as the frequency of the driving signal increases, the power of the first harmonic drops below the noise floor of the ESA, as shown in Figs. 4(c) and 4(d). As a result, the measured SR is actually limited by the signal-to-noise ratio (SNR), whose value is lower than the real SR. Second, the modeled result is based on the assumption that the laser wavelength is exactly aligned to the resonance wavelength corresponding to the DC bias point. However, it is difficult to fulfill this condition in practice owing to the susceptibility of the resonance to the ambient temperature fluctuation. The conversion efficiency from the input microwave signal to the second harmonic is limited mainly by two factors in Fig. 4: first, the slab electrically connecting the PN junction and the ohmic contact regions presents a large series resistance due to the unoptimized implantation condition. According to the circuit in Fig. 1(c), the 3 dB bandwidth of the frequency response function f ω1 is 3.5 GHz. This implies that the amplitude of a 10 GHz microwave signal has attenuated by 7.1 dB when it reaches the space charge region to implement the EO modulation. Second, the total coupling loss of the two fiber grating couplers is 16 dB. The small signal approximation in Eq. (6) indicates that the power of the generated second harmonic is proportional to P 20 f ω1 4 , where P 0 denotes the optical power collected by the PD at off-resonance wavelengths. Supposing ring modulators of reduced RC constants [17] and advanced fiber grating couplers of enhanced coupling efficiencies [22] are utilized, the conversion efficiency can be significantly boosted to be comparable with commercial LiNbO3 modulators [9–16]. Also the frequency of the generated signal can be substantially raised by reducing the RC constant. In conclusion, we demonstrate a microwave frequency generation system based on a silicon microring cavity. A 20 GHz
1. J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007). 2. P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, and A. Malacarne, Nature 507, 341 (2014). 3. C. Liu, J. Wang, L. Cheng, M. Zhu, and G.-K. Chang, J. Lightwave Technol. 32, 3452 (2014). 4. K. Xu, R. Wang, Y. Dai, F. Yin, J. Li, Y. Ji, and J. Lin, Photon. Res. 2, B54 (2014). 5. R. T. Ramos and A. J. Seeds, Electron. Lett. 28, 82 (1992). 6. B. Vidal, Opt. Lett. 37, 5055 (2012). 7. H. Shao, S. Keyvaninia, M. Vanwolleghem, G. Ducournau, X. Jiang, G. Morthier, J.-F. Lampin, and G. Roelkens, Opt. Lett. 39, 6403 (2014). 8. W. Li and J. Yao, IEEE Trans. Microwave Theory Tech. 58, 3259 (2010). 9. J. J. O’Reilly, P. M. Lane, R. Heidemann, and R. Hofstetter, Electron. Lett. 28, 2309 (1992). 10. J. J. O’Reilly and P. M. Lane, Electron. Lett. 30, 1329 (1994). 11. Y. Zhao, X. Zheng, H. Wen, and H. Zhang, Opt. Lett. 34, 3250 (2009). 12. Y. Qin, J. Sun, M. Du, and J. Liao, Opt. Commun. 315, 280 (2014). 13. J. Lin, W. Ho, Y. Chang, P. Peng, and H. Lu, Opt. Commun. 317, 34 (2014). 14. Y. Gao, A. Wen, Q. Yu, N. Li, G. Lin, S. Xiang, and L. Shang, IEEE Photon. Technol. Lett. 26, 1199 (2014). 15. Y. Zhang and S. Pan, IEEE MTT-S International Microwave Workshop Series on Millimeter Wave Wireless Technology and Applications (IEEE, 2012), pp. 1–4. 16. Y. Gao, A. Wen, H. Zhang, S. Xiang, H. Zhang, L. Zhao, and L. Shang, Opt. Commun. 321, 11 (2014). 17. X. Xiao, X. Li, H. Xu, Y. Hu, K. Xiong, Z. Li, T. Chu, J. Yu, and Y. Yu, IEEE Photon. Technol. Lett. 24, 1712 (2012). 18. J. C. Rosenberg, W. M. Green, S. Assefa, D. M. Gill, T. Barwicz, M. Yang, S. M. Shank, and Y. A. Vlasov, Opt. Express 20, 26411 (2012). 19. M. Pantouvaki, H. Yu, M. Rakowski, P. Christie, P. Verheyen, G. Lepage, N. V. Hoovels, P. Absil, and J. V. Campenhout, IEEE J. Quantum Electron. 19, 7900308 (2013). 20. H. Yu, D. Ying, M. Pantouvaki, J. V. Campenhout, P. Absil, Y. Hao, J. Yang, and X. Jiang, Opt. Express 22, 15178 (2014). 21. G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, Opt. Express 19, 20435 (2011). 22. Y. Ding, C. Peucheret, H. Ou, and K. Yvind, Opt. Lett. 39, 5348 (2014).
Vol. 40, No. 14 / July 15 2015 / Optics Letters
Letter
On-chip microwave signal generation based on a silicon microring modulator HAIFENG SHAO, HUI YU,* XIA LI, YAN LI, JIANFEI JIANG, HUAN WEI, GENCHENG WANG, TINGGE DAI, QIMEI CHEN, JIANYI YANG, AND XIAOQING JIANG Institute of Microelectronics and Optoelectronics, Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China *Corresponding author: [email protected] Received 15 April 2015; revised 19 June 2015; accepted 24 June 2015; posted 25 June 2015 (Doc. ID 237915); published 13 July 2015
A photonic-assisted microwave signal generator based on a silicon microring modulator is demonstrated. The microring cavity incorporates an embedded PN junction that enables a microwave signal to modulate the lightwave circling inside. The DC component of the modulated light is trapped in the cavity, while the high-order sideband components are able to exit the cavity and then generate microwave signals at new frequencies in a photodetector. In our proof-of-concept experiment, a 10 GHz microwave signal is converted to a 20 GHz signal in the optical domain with an electrical harmonic suppression ratio of 22 dB. An analytic model is also established to explain the operation mechanism, which agrees well with the measured data. © 2015 Optical Society of America OCIS codes: (060.5625) Radio frequency photonics; (130.3120) Integrated optics devices; (130.4110) Modulators. http://dx.doi.org/10.1364/OL.40.003360
Microwave photonics (MPW), which generates, transports, and processes microwave or millimeter (mm)-wave signals in the optical domain, has found many applications in wireless access networks, phase array antennas, radio-over-fiber systems, satellite communications, radio astronomy, and so on [1–4]. An essential functionality in any MPW link is to generate the microwave signal in the optical domain. The most prevailing solution so far is based on optical heterodyning with a highbandwidth photodetector (PD). This necessarily requires two stable phase-correlated optical waves with a fixed frequency difference, which can be obtained by utilizing techniques such as optical injection locking [5], an optical phase-lock loop [6], a dual-wavelength laser [7], and electro-optic (EO) modulation [8]. Among all these techniques, EO modulation has proved to be a simple and effective approach with high spectrum purity and stability. This solution uses a sinusoidal microwave signal to drive a stand-alone Mach–Zehnder modulator (MZM) or 0146-9592/15/143360-04$15/0$15.00 © 2015 Optical Society of America
cascaded multi-MZMs. Unwanted frequency sidebands in the spectra of modulated optical carriers are suppressed by setting proper bias points, cascading manners, or optical notch filters. The heterodyning of the remaining frequency components at the PD gives rise to desired microwave signals whose frequencies are integer multiples of the driving frequency [9–16]. In all these instances, MZMs are exclusively utilized largely owing to their well-understood sinusoidal modulation transfer function. Compared with MZMs, modulators based on optical resonators such as microrings could drastically enhance the interaction between the light and the driving signal, and hence have the advantages of small footprints and low power consumption. Until today, microring cavities have been investigated comprehensively to implement digital modulation for demanding optical interconnect systems [17–21]. However, we are unaware of any attempt so far to generate a microwave signal with a microring cavity. Therefore, it is worthwhile to explore the potential of microring modulators for this application. In this Letter, we demonstrate microwave signal generation with a silicon carrier-depletion-based microring modulator. With proper coupling conditions and operating wavelength, the DC component of the modulated light is trapped in the cavity. The heterodyning of untrapped sidebands then induces a microwave signal at a new frequency. Specifically, we implement a proof-of-concept experiment to convert the frequency of a RF signal from 10 to 20 GHz with a silicon ring modulator. An analytic model that agrees with the measured data and provides physical insight to the mechanism is also established. Figure 1(a) presents a schematic diagram of the silicon microring cavity under test; its radius is 10 μm. A cross section of the rib waveguide forming the ring is shown in Fig. 1(b). The rib waveguide is embedded with a lateral PN junction whose doping concentration is 1.5 × 1018 ∕cm3 . The two ohmic contact regions of the PN junction are heavily doped to 1 × 1020 ∕cm3 . The etching depth is 160 nm and the dimension of the rib waveguide accommodating the PN junction is 450 nm × 220 nm. The device can be electrically represented by the equivalent circuit shown in Fig. 1(c) [17,20,21]. C 0 represents the capacitance between contact pads, while R 1 and
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expanding ω0 and 1∕τ at the DC bias point, and keeping only the first three items, we have ω0 ωDC k 1 v pn ω1 k 2 v 2pn ω1 …;
(2)
1 1 r 1 v pn ω1 r 2 v 2pn ω1 …; τ τDC
(3)
where ωDC and 1∕τDC represent the resonance frequency and the amplitude decay rate at the DC bias point. The coefficients k1 , k 2 , r 1 , and r 2 depend on profiles of the dopants and the guide mode. Their value can be obtained through the measurement. By substituting Eqs. (2) and (3) into Eq. (1), we deduce the analytical solution of at:
Fig. 1. (a) Schematic diagram of a typical microring cavity in the microwave signal generation system. (b) Cross section of rib waveguide. (c) Equivalent circuit of the device. TL, tunable laser; PC, polarization controller; DUT, device under test; GC, grating coupler; DC, direct current; EDFA, erbium-doped fiber amplifier; ESA, electrical signal analyzer. Optical fiber is represented by solid lines and the electrical path is represented by dashed lines.
C 1 denote the resistance and the capacitance of the reversebiased PN junction, respectively. The buried SiO2 layer and the Si substrate are represented by capacitance C 2 and resistance R 2 , respectively. Supposing an external microwave signal of v 0 cosω1 t is applied to the device, the AC voltage v pn ω1 that drops across the space charge region of the PN junction is v pn ω1 v 0 f ω1 cosω1 t φω1 . Here f ω1 and φω1 denote the modulus and the phase of the frequency response of v pn ω1 . Their expressions can be obtained according to the circuit in Fig. 1(c); these expressions are not listed here for brevity but can be found in [20]. According to the mode coupling theory in the time domain [20], the amplitude at of the energy stored inside the microring satisfies d 1 αt jω0 − αt − jμAe jωt ; (1) dt τ where ω and A denote the angular frequency and the amplitude of the incident optical field, respectively. The microring resonates at angular frequency ω0. 1∕τ is the overall amplitude decay rate of the optical field inside the microring cavity. The sum of 1∕τe and 1∕τl . 1∕τe represents the amplitude decay rate caused by the coupling with the bus waveguide, while 1∕τl is owing to the beam propagation loss of the doped rib waveguide. The parameter μ represents the mutual coupling between the bus waveguide and the microring. It is calculated as μ2 2∕τe . By controlling the width of the space charge region, the voltage signal v pn ω1 can shift values of both ω0 and 1∕τ. The inherent characteristic of the PN junction determines that dependences of ω0 and 1∕τ on v pn ω1 are not linear. By Taylor
αt −jμA expjωt ∞ X k jr 1 Jn 1 v 0 f ω1 expjnω1 t φ × ω1 n−∞ ∞ X k jr 2 2 2 Jm 2 v 0 f ω1 expj2mω1 t φ · 4ω1 m−∞ ∞ X ∞ X k 1 jr 1 · Jp − v0 f ω1 ω1 p−∞ q−∞ k 2 jr 2 2 2 v f ω1 × Jq − 4ω1 0 ×
expjpω1 t φ 2jqω1 t φ ; jω − ω0 1τ − 12 jk2 − r 2 v 20 f 2 ω1 jpω1 2jqω1 (4)
where J n z is the nth Bessel function. The transmitted filed S t t in the bus waveguide can be calculated as S t t A expjωt − jμat. By the small signal approximation, we can explain qualitatively how the microwave frequency upconversion occurs. In the small signal regime, the quadratic items k2 v 2pn ω1 and r 2 v 2pn ω1 in Eqs. (2) and (3) can be neglected. Based on this premise, the solution in Eq. (4) can be greatly simplified, and thus S t t can be written as jω − ω0 1τ − τ2e S t t A expjωt jω − ω0 1τ jv μ2 k1 jr 1 f ω1 − 0 cos ω1 t jω − ω0 1τ 2 ω21
jv0 μ2 k1 jrf ω1 ω1 sin ω1 t : (5) − jω − ω0 1τ 2 ω21 jω − ω0 1τ With Eq. (5) we have investigated the small-signal frequency response of the optical amplitude modulation carried out by silicon ring modulators in [20]. The first item inside the braces of Eq. (5) represents the transmitted field of the all-pass microring cavity in the static state, which composes the DC component of S t t. The second and the third items represent the EO modulation. If the microring is critical coupled (τe τl ) and works at the resonance wavelength (ω ω0 ), the DC component of S t t is zero. Thus, S t t consists only of the 1st sidebands:
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Fig. 2. Transmission spectra of the microring cavity under various bias voltages. The inset shows dependences of Δ1∕τl and Δω0 on the bias voltage. Here, Δ1∕τl and Δω0 represent offsets of 1∕τl and ω0 with respect to their values at 0 V bias.
S t t −A
jv 0
μ2 k
1 jr 1 f ω21 τ−2
ω1
× cos ω1 t ω1 τ sin ω1 t expjωt:
(6)
Since the photocurrent i PD at the receiver side is proportional to the power of the optical field jS t tj2 , the optical heterodyning between the 1st sidebands in Eq. (6) leads to a new microwave signal at the frequency of 2ω1 . However, the device does not necessarily operate in the small signal regime as it works to generate a new microwave signal. As a result, the unsimplified solution of at in Eq. (4) is used to quantitatively calculate different harmonic components in the transmitted field S t t in the following context. The experimental setup to generate the microwave signal with the silicon microring cavity is shown in Fig. 1(a). The input optical carrier of 1 mW from a tunable laser (Santec TSL510) is aligned to the resonance wavelength of the cavity at the DC bias point. A polarization controller (PC) is used to adjust the polarization state. The optical carrier is coupled from a single-mode fiber (SMF) to the device via a fiber grating coupler, which gives a ∼8 dB coupling loss. Before being sent to the device under test (DUT) by a GSG probe (Cascade Microtech), the driving microwave signal is combined with a DC bias to avoid entering the carrier-injection region of the PN junction. Two microwave powers of 13 and 7 dBm are utilized in the measurement. After being coupled out from the device by another fiber grating coupler, the modulated optical field passes through an EDFA to enhance its power, and then a tunable filter to filter out undesirable amplified spontaneous emission (ASE) noise. Finally, the modulated optical signal reaches a high-bandwidth PD whose output is fed to an electrical spectrum analyzer (ESA) (Anritsu MS2830A). Discrete data points in Fig. 2 display the measured transmission spectra of the microring at different bias voltages. Extinctions of >20 dB at the resonance wavelengths indicate that the microring cavity is close to the critical coupling.
Fig. 3. S11 parameter at 0 V bias voltage. Table 1 lists extracted values of all elements in the equivalent circuit of the device. For both figures the black solid lines are the fitted curves.
For each reverse bias voltage, we can extract values of ω0 , 1∕τe , and 1∕τl by curve fitting. Black solid lines in Fig. 2 are fitted curves, which match well with the measured data. Values of ω0 and 1∕τl are displayed in the inset of Fig. 2 as a function of the reverse bias voltage. The dependences of ω0 and 1∕τl on the reverse bias voltage can be represented by two second-order polynomial functions, which are also plotted in the inset as solid lines. Expressions of the two polynomials are ω0 1229.818 × 1012 8.373 × 108 v 2b − 2.004 × 1010 v b , and 1∕τ 4.713 × 1010 1.331 × 108 v 2b − 1.430 × 109 v b . According to them, we can calculate values of k1 , k2 , r 1 , and r 2 at any bias points by Taylor expansion. The measured microwave signal reflection coefficient of the device (the S11 parameter) is presented in Fig. 3 as discrete data points. By fitting to the measured S11 data, we extract values of all elements that make up the circuit of Fig. 1(c), which are listed in Table 1 of Fig. 3. Fitted curves are presented as black solid lines in Fig. 3. After obtaining all relevant parameters, we use Eq. (4) to calculate RF powers of different harmonic components in the output of the PD. The modeled suppression ratios (SRs) between the second- and first-order harmonic components after the PD are plotted in Figs. 4(a) and 4(b) for driving microwave powers of 7 and 13 dBm, respectively, together with the measured SR. Measured electrical spectra are presented in Figs. 4(c) and 4(d). As the modulation frequency ω1 rises, both the firstand second-harmonic components attenuate, but with different rates, which are affected by the specific driving condition. If the second harmonic consistently rolls off faster than the first harmonic, the SR will drop as ω1 increases, which is the case in Figs. 4(a) and 4(c). However, if the roll-off rate of the second harmonic is slower than that of first harmonic at the lowfrequency range, and then becomes faster at the high-frequency range, the corresponding SR would reach a peak at some frequency point, as shown in Figs. 4(b) and 4(d). We note that MZMs usually offer SRs of ∼25 dB when they carry out frequency upconversion [11], so the ring modulator here offers comparable SR values, as shown in Fig. 4(d).
Letter
Vol. 40, No. 14 / July 15 2015 / Optics Letters
3363
signal is obtained from a 10 GHz input signal with a 22 dB harmonic suppression ratio. Analogously to the MZM, the ring modulator can also be cascaded or combined with a notch filter to achieve higher multiplication factors. This microringbased RF signal generation technique could be a prospective candidate for future integrated MPW systems. Future works include enhancing the conversion efficiency and operation frequency with improved designs, as well as investigating stability and phase noise of the microwave signal generated by this technique.
Fig. 4. Modeled and measured suppression ratios for (a) 7 dBm and (b) 13 dBm input microwave signals. Measured electrical spectra for (c) 7 dBm and (d) 13 dBm input microwave signals.
Funding. Fundamental Research Funds for the Central Universities; National Natural Science Foundation of China (NSFC) (61177055, 61307074); Nature Basic Research Program of China (2013CB632105); Zhejiang Provincial Natural Science Foundation for Distinguished Young Scholar (LR15F050002). REFERENCES
In Figs. 4(a) and 4(b), the theoretical prediction agrees with the measurement result in the trend. The discrepancy between the model and the measurement lies in the facts that, first, as the frequency of the driving signal increases, the power of the first harmonic drops below the noise floor of the ESA, as shown in Figs. 4(c) and 4(d). As a result, the measured SR is actually limited by the signal-to-noise ratio (SNR), whose value is lower than the real SR. Second, the modeled result is based on the assumption that the laser wavelength is exactly aligned to the resonance wavelength corresponding to the DC bias point. However, it is difficult to fulfill this condition in practice owing to the susceptibility of the resonance to the ambient temperature fluctuation. The conversion efficiency from the input microwave signal to the second harmonic is limited mainly by two factors in Fig. 4: first, the slab electrically connecting the PN junction and the ohmic contact regions presents a large series resistance due to the unoptimized implantation condition. According to the circuit in Fig. 1(c), the 3 dB bandwidth of the frequency response function f ω1 is 3.5 GHz. This implies that the amplitude of a 10 GHz microwave signal has attenuated by 7.1 dB when it reaches the space charge region to implement the EO modulation. Second, the total coupling loss of the two fiber grating couplers is 16 dB. The small signal approximation in Eq. (6) indicates that the power of the generated second harmonic is proportional to P 20 f ω1 4 , where P 0 denotes the optical power collected by the PD at off-resonance wavelengths. Supposing ring modulators of reduced RC constants [17] and advanced fiber grating couplers of enhanced coupling efficiencies [22] are utilized, the conversion efficiency can be significantly boosted to be comparable with commercial LiNbO3 modulators [9–16]. Also the frequency of the generated signal can be substantially raised by reducing the RC constant. In conclusion, we demonstrate a microwave frequency generation system based on a silicon microring cavity. A 20 GHz
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