Abstract

We present a highly linear ring modulator from the bonding of ion-sliced x-cut lithium niobate onto a silicon ring resonator. The third order intermodulation distortion spurious free dynamic range is measured to be 98.1 dB Hz2/3 and 87.6 dB Hz2/3 at 1 GHz and 10 GHz, respectively. The linearity is comparable to a reference lithium niobate Mach-Zehnder interferometer modulator operating at quadrature and over an order of magnitude greater than silicon ring modulators based on plasma dispersion effect. Compact modulators for analog optical links that exploit the second order susceptibility of lithium niobate on the silicon platform are envisioned.

© 2015 Optical Society of America

1. Introduction

Microwave photonics has aroused great interest from both the academic community and the industrial sector, driven by the expanding broadband wireless access networks and the growth of fiber links directly to the home [1]. Traditional microwave photonic systems rely on discrete components that are bulky, expensive, and power hungry. The emergence of integrated microwave photonics systems based on photonic integrated circuits (PICs) provides advantages in cost, size, power consumption, and reliability [2]. Among many proposed PIC platforms, silicon photonics is especially promising for large scale electronic/photonic integration due to its large index contrast and compatibility with silicon integrated circuit manufacturing [3, 4]. Silicon photonic devices with RF photonic functionalities such as filtering and arbitrary waveform generation have already been demonstrated [5, 6].

It is challenging, however, to realize high linearity and compact modulators on silicon that are critical to achieve high dynamic range microwave photonic links [7, 8]. The linear electro-optic effect is absent in unstrained crystalline silicon due to centrosymmetry. As a result, silicon modulators commonly rely on the plasma dispersion effect in pn junctions that exhibit nonlinear phase change with applied voltage [9–11]. The pn junction has been shown to be the dominant source of nonlinearity in silicon ring modulators, as opposed to the nonlinear wavelength response of the resonator [12–14]. Spurious free dynamic range (SFDR) values of 84 dB Hz2/3 and 97 dB Hz2/3 at 1 GHz for third order intermodulation distortion (IMD3) have been achieved for a silicon ring modulator and a silicon Mach-Zehnder interferometer (MZI) modulator, respectively [12, 15].

Alternatively, lithium niobate (LiNbO3) MZI modulators based on diffused waveguides have high linearity and high SFDR [16, 17]. The large device size from relatively low index contrast limits the potential, however, for dense integration [17]. Recently, compact structures have been achieved from the hybrid integration of z-cut ion-sliced LiNbO3 thin films bonded onto silicon waveguides. Miniature RF electric field sensors, tunable filters, and high speed modulators take advantage of both the high optical confinement of silicon and the second order susceptibility of LiNbO3 [18–22]. In contrast to z-cut designs, x-cut LiNbO3 allows the implementation of co-planar, low resistivity, metal electrodes that are easier to fabricate than parallel plate designs [23].

In this work, we present a compact and highly linear hybrid silicon and LiNbO3 modulator based on thin films of x-cut LiNbO3 bonded to silicon ring resonators. The use of LiNbO3 as the electro-optic medium avoids the nonlinearity of silicon plasma dispersion effect for modulation, isolating linearity characteristics to the properties of the ring cavity. The linearity as a function of bias wavelength is characterized and compared to a reference LiNbO3 MZI modulator that is three orders of magnitude larger in footprint. At the optimal bias wavelength, the hybrid silicon and LiNbO3 ring modulator has a measured SFDR of 98.1 dB Hz2/3 and 87.6 dB Hz2/3 for IMD3 at 1 GHz and 10 GHz, respectively. The measured values are 3.4 dB higher and 1.4 dB lower than the reference LiNbO3 MZI modulator operating at quadrature. Furthermore, the hybrid Si/LiNbO3 results are over an order of magnitude greater than the measured SFDR for silicon ring modulators (84 dB Hz2/3 at 1 GHz) based on the plasma dispersion effect [12].

The paper is organized as follows. Sections two describe the concept of the device. Design and fabrication details are discussed in section three. Electro-optical measurement results are presented in section four and linearity measurements are conveyed in section five. A conclusion is given in section six.

2. Concept

We consider a general waveguide optical phase shifter under voltage control. The relationship between waveguide effective index and applied voltage is expressed by the following power series

neff(Vin)=ne0+αVin+βVin2+γVin3+
where Vin is the applied voltage, neff is the effective index, and ne0 is the effective index without applied voltage. For silicon phase shifters based on the plasma dispersion effect, the effective index changes nonlinearly with Vin, resulting in relatively large non-zero higher order terms in Eq. (1). For phase shifters based on the linear electro-optic effect such as in a LiNbO3 MZI modulator or in the hybrid Si/LiNbO3 ring modulator, the effective index changes more linearily with Vin. A good approximation for small signals is
neff(Vin)ne0+αVin
MZI and ring modulators based on highly linear phase shifters still exhibit nonlinearity due to their nonlinear modulation transfer functions [25]. For ring resonators at the critical coupling condition, the steady state photocurrent received as a function of the wavelength and Vin is given by
Iout(λ,Vin)=R(λ)Pout,max[111+4F2π2sin2[πLneff(λ,Vin )λ]]
where Iout and R are the detected photo current and the responsivity of the photodetector, Pout,max is the maximum optical transmission power, F is the finesse of the resonator, L is the length of the resonator, and λ is the wavelength of operation [12]. Based on the nonlinearity in Vin, we express the photocurrent in terms of a power series as
Iout(λ,Vin)=c0(λ)+c1(λ)Vin+c2(λ)(Vin)2+c3(λ)(Vin)3+
where cn is the nth order term of the series expansion [24].

With a two-tone input signal in the form of

 Vin=A1eiω1t+A1*eiω1t+A2eiω2t+A2*eiω2t
spurious signals are generated at the output due to the nonlinearity. For RF frequencies much smaller than the device bandwidth, the second harmonic distortion (SHD) terms at 2ω1 and 2ω2 and the IMD3 terms at 2ω1-ω2 and 2ω2- ω1 are

SHD:c2(λ)(A12ei2ω1t+A1*2ei2ω1t+A22ei2ω2t+A2*2ei2ω2t)
IMD3:3c3(λ)[A12A2*ei(2ω1ω2)t+A1*2A2ei(2ω1ω2)t+A22A1*ei(2ω2ω1)t+A2*2A1ei(2ω2ω1)t]

Equations (6) and (7) highlight that SHD and IMD3 depend on bias wavelength. Steady state numerical calculation shows that the Lorentzian transfer function of a ring resonator has zero third order distortion with a bias point at 0.48 optical transmission and zero second order distortion with a bias point at 0.24 optical transmission [26]. Distortion-free points are, however, absent in a silicon ring modulator based on the plasma dispersion effect, since the linearity is mainly contributed by the pn junction instead of the Lorentzian transfer function. In contrast, the hybrid Si/LiNbO3 platform can take advantage of these distortion free bias points since the voltage controlled phase shift is based on the second order susceptibility of the LiNbO3.

3. Design and fabrication

A schematic of the hybrid silicon and LiNbO3 modulator is shown in Fig. 1. The device consists of a silicon strip waveguide ring resonator and a 1 µm thick x-cut ion-sliced LiNbO3 thin film bonded via BCB [21]. The ring radius is 10 µm on the curves and is 50 µm in length on the straight sections. The cross-section of the silicon strip waveguide is 550 nm × 170 nm and the coupling gap between the bus waveguide and the ring is 180 nm. The z crystal axis of the LiNbO3 is oriented perpendicular to the propagation direction of the straight sections of the ring.

 figure: Fig. 1

Fig. 1 (a) Schematic of hybrid Si/LiNbO3 ring modulator. For clarity, the PECVD SiO2 top-cladding layer and electrical contact pads are not shown. (b) Schematic of cross-section of device along dashed line in (a).

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Metal electrodes are placed on top of the LiNbO3 thin film with a 1 µm lateral electrode gap aligned to the center of the silicon core. The electrodes are interdigitated so that the directions of the applied electric fields in the two straight waveguide sections are the same. As a result, the phase change accumulates constructively as light propagates along the racetrack ring. The configuration allows the device to access the r33 electro-optic coefficient along the straight waveguide sections for the transverse-electric (TE) optical waveguide mode (r33 = 31 pm V−1 in bulk LiNbO3) [27]. A large ratio of straight section length to curved section length around the ring is desirable because the modulation efficiency is weaker along the arcs.

Figure 2 shows the TE mode optical distribution in a straight waveguide section at 1550 nm calculated via the beam propagation method. The mode effective index is 2.45 and the fraction of the optical mode power in the LiNbO3 is 25%. Also shown is the electric field (yellow vectors) from a DC voltage applied between the top metal electrodes. The high optical confinement allows the top side metal electrodes to be placed close to each other and over the waveguide without inducing large optical absorption loss, enabling a large electric field for a given applied voltage. The capacitance per unit length of the electrode is calculated to be 0.2 pF/m based on finite element method simulations. A device capacitance of 30 fF and resistance of 30 Ω yields an RC limited bandwidth of 66 GHz in a 50 Ω system. As a result, the device speed is limited by the photon lifetime of the resonator.

 figure: Fig. 2

Fig. 2 Calculated optical TE mode distribution at 1550 nm wavelength and electric field vectors from applied DC voltage.

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The fabrication process involves a silicon-on-insulator (SOI) wafer with a silicon device layer thickness of 170 nm and a buried SiO2 layer thickness of 1 μm. The silicon waveguides are patterned with hydrogen silsesquioxane (HSQ) resist using electron beam lithography and inductively coupled plasma reactive ion etching (ICP-RIE) to obtain strip waveguides of cross-section 550 nm × 170 nm [28]. To obtain LiNbO3 thin films, an x-cut LiNbO3 wafer is ion-sliced by He+ ions with an implantation energy of 380 keV and a fluence of 3.5 × 1016 ions cm−2. The LiNbO3 thin films are transferred and bonded to the silicon waveguides using a BCB bonding layer [21]. A 1 µm thick plasma-enhanced chemical vapor deposition (PECVD) silicon dioxide layer is deposited as cladding. A via hole is then etched through the SiO2 to expose the LiNbO3. The signal and ground electrodes are patterned on LiNbO3 in two lithography steps to allow accurate control of the electrode gaps. Finally, cantilever couplers are fabricated for fiber-waveguide coupling [28, 29]. A top-view optical micrograph of the fabricated device and a scanning electron micrograph (SEM) of the electrodes are shown in Fig. 3.

 figure: Fig. 3

Fig. 3 (a) Top-view optical micrograph of fabricated device; (b) SEM of electrodes.

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4. Electro-optical measurements

Figure 4(a) shows the measured TE-mode optical transmission spectrum as a function of the applied DC voltage between the electrodes. The measured quality factor is 14,400, the free spectral range is 4.05 nm, and the full width half max is 108 pm. A blue shift of resonance frequency is observed for increasingly positive voltage, indicating a decrease in refractive index with applied voltage, consistent with the orientation of the applied electric field and the LiNbO3 z axis. A linear fit of the resonance wavelength shift with voltage, shown in Fig. 4(b), indicates a tunability of 5.3 pm/V.

 figure: Fig. 4

Fig. 4 (a) Measured optical spectrum as a function of applied voltage; (b) linear fitting of the resonance wavelength shift as a function of applied voltage.

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The RF scattering parameter, S11, is measured with a 20 GHz vector network analyzer (VNA) operating in a 50 Ω system. As shown in Fig. 5, S11 is 0 dB at DC and decreases to –3.3 dB at 20 GHz. For optical wavelength biased at −3 dB optical transmission, the small-signal electrical-to-optical modulation response is obtained from the VNA and a 25 GHz photodetector by taking 1/2 of the S21 scattering parameter in dB. Ignoring for a moment the deep resonance at 7.5 GHz, the 3 dB modulation bandwidth is approximately 15 GHz. The deep resonances on the optical modulation response are a result of acousto-optic resonances [30, 31]. Compared to a hybrid silicon and LiNbO3 modulator using z-cut LiNbO3, fewer acoustic-optic resonances are excited for the x-cut design. The acoustic resonances can be suppressed by roughening the LiNbO3 top surface [32]. Alternatively, the thickness of the LiNbO3 thin film can be reduced to push the resonances to higher frequencies that exceed the bandwidth of the modulator.

 figure: Fig. 5

Fig. 5 Measured optical modulation response and the S11 magnitude.

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5. Linearity measurements

The SFDR measurement setup is shown in Fig. 6. TE polarized light from a continuous wave (CW) tunable laser is fiber coupled into the modulator through the cantilever coupler. The output light is passed through an erbium doped fiber amplifier (EDFA) to amplify the signal and filtered to suppress the amplified spontaneous emission (ASE) noise. A 25 GHz photodetector with a conversion gain of 15 V/W and a 40 GHz RF spectrum analyzer are used to detect the signals. The optical power reaching the photodetector is maintained at 1 mW for all measurements by adjusting the the EDFA current. Two tone signals from two RF sources are combined and launched to the modulator using an on-wafer RF probe. A frequency separation of 6 MHz between the two tones centered at 100 MHz, 1 GHz, 5 GHz, and 10 GHz is used. The bias wavelength is varied on the blue side of the optical resonance. The noise floor of the RF spectrum analyzer is −157 dBm/Hz at 100 MHz and 1 GHz, −150 dBm/Hz at 5 GHz, and −148 dBm/Hz at 10 GHz.

 figure: Fig. 6

Fig. 6 Test and measurement setup for characterization of linearity.

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Figure 7 shows the fundamental, SHD, and IMD3 components versus detuning wavelength from resonance. At large detuning, the fundamental power increases as the detuning is decreased because the slope of the resonator transfer function is increasing and the EDFA gain is increasing to maintain 1 mW total optical power at the photodetector. Within 10 pm of the resonance, the slope of the resonator transfer function decreases sharply, resulting in the sharp decrease in the fundamental power. The fundamental power at −54 pm resonance detuning, which is the −3 dB optical transmission wavelength, is −49.3 dBm, −49.1 dBm, −49.3 dBm, and −51.3 dBm for 100 MHz, 1 GHz, 5 GHz, and 10 GHz, respectively, consistent with the optical modulation response in Fig. 5. The fundamental power peaks at −37 dBm, −37 dBm, −39.3 dBm and −43.8 dBm for 100 MHz, 1 GHz, 5 GHz, and 10 GHz, respectively. Generally, SHD and IMD3 power increase as the wavelength is tuned closer to the resonance. In the 100 MHz case, local minima are observed for SHD and IMD3, attributed to the Lorentzian transfer function of the ring [26]. Lower distortion occurs at the local minima. At higher frequencies, the local minima no longer appear.

 figure: Fig. 7

Fig. 7 RF output power of the fundamental, SHD, and IMD3 components as a function of wavelength detuning from resonance for two RF tones centered at (a) 100 MHz, (b) 1 GHz, (c) 5 GHz, and (d) 10 GHz.

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To provide context for the measurements, the Si/LiNbO3 modulator is compared to a commercial LiNbO3 MZI modulator with a Vπ of 3.1 V at DC (Lucent 2623-NA). The MZI is biased at quadrature and the optical power reaching the photodetector is again maintained at 1 mW for all measurements by adjusting the the EDFA current. As shown in Fig. 8 and Fig. 9, the IMD3 SFDR of the LiNbO3 MZI modulator are 94.7 dB Hz2/3 and 89 dB Hz2/3 at 1 GHz and 10 GHz, respectively. The lower SFDR at 10 GHz is primarily due to the higher noise floor of the RF spectrum analyzer at 10 GHz. For the Si/LiNbO3 modulator, the optimal bias wavelengths for maximum IMD3 SFDR are found to be 15 pm and 40 pm on the blue side of the resonance at 1 GHz and 10 GHz, respectively. At the optimal bias, the IMD3 SFDR of the Si/LiNbO3 modulator is 98.1 dB Hz2/3 at 1 GHz, and 87.6 dB Hz2/3 at 10 GHz. The measured IMD3 SFDR is 3.4 dB higher and 1.4 dB lower than the LiNbO3 MZI at 1 GHz and 10 GHz respectively. Furthermore, at the −3 dB bias wavelength, the IMD3 SFDR are 94.2 dB Hz2/3 at 1 GHz and 86.7 dB Hz2/3 at 10 GHz, which are 0.5 dB lower and 2.3 dB lower, respectively, than the LiNbO3 MZI. For the same optical insertion loss of 3 dB, the SFDR of the Si/LiNbO3 ring is comparable to the LiNbO3 MZI, but with a footprint three orders of magnitude smaller.

 figure: Fig. 8

Fig. 8 RF output power of the fundamental and IMD3 components as a function of RF input power for the LiNbO3 MZI and the Si/LiNbO3 ring at 0.997 GHz. The noise floor is in 1 Hz bandwidth.

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 figure: Fig. 9

Fig. 9 RF output power of the fundamental and IMD3 components as a function of RF input power for the LiNbO3 MZI modulator and the hybrid silicon and LiNbO3 ring modulator at 9.997 GHz. The noise floor is in 1 Hz bandwidth.

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At 1 GHz, the demonstrated IMD3 SFDR of the Si/LiNbO3 ring is over an order of magnitude greater than silicon ring modulators based on the plasma dispersion effect (84 dB Hz2/3) [12], and is comparable to the state-of-the art silicon MZI carrier depletion modulator based on differential drive (97 dB Hz2/3) [15]. In addition, SHD SFDR values of 78.4 dB Hz1/2 and 69.8 dB Hz1/2 are measured at 1 GHz and 10 GHz, respectively. At 1GHz, the measured SHD SFDR is also over an order of magnitude greater than the silicon ring modulator based on the plasma dispersion effect (64.5 dB Hz1/2) [12].

6. Conclusion

A highly linear ring modulator is achieved from hybrid silicon and LiNbO3. The approach of bonding patterned x-cut LiNbO3 thin films to silicon waveguides exploits the second order susceptibility of LiNbO3 and the high index contrast of silicon-on-insulator. IMD3 SFDR values of 98.1 dB Hz2/3 and 87.6 dB Hz2/3 are measured at 1 GHz and 10 GHz, respectively. The measured SFDR is over an order of magnitude greater than Si ring modulators based on the plasma dispersion effect. Furthermore, the SFDR is 3.4 dB higher at 1 GHz and 1.4 dB lower at 10 GHz than a commercial LiNbO3 MZI modulator biased at quadrature. SHD SFDR values of 78.4 dB Hz1/2 and 69.8 dB Hz1/2 are measured for 1 GHz and 10 GHz, respectively. The SHD SFDR is also over an order of magnitude greater than Si ring modulators based on the plasma dispersion effect. While the IMD3 SFDR of the Si/LiNbO3 device is comparable to the LiNbO3 MZI, the footprint of the Si/LiNbO3 device is three orders of magnitude smaller. Consequently, highly linear and compact electro-optical modulators for analog optical links are enabled.

Acknowledgment

This work was supported by the Army Research Office (ARO) under grant number W911NF-12-1-0488.

References and links

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2. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7(4), 506–538 (2013). [CrossRef]  

3. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]  

4. R. A. Soref, “The past, present and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]  

5. M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010). [CrossRef]  

6. P. Dong, N.-N. Feng, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and M. Asghari, “GHz-bandwidth optical filters based on high-order silicon ring resonators,” Opt. Express 18(23), 23784–23789 (2010). [CrossRef]   [PubMed]  

7. C. H. Cox III, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006). [CrossRef]  

8. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]  

9. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]  

10. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef]   [PubMed]  

11. G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “25Gb/s 1V-driving CMOS ring modulator with integrated thermal tuning,” Opt. Express 19(21), 20435–20443 (2011). [PubMed]  

12. A. Ayazi, T. Baehr-Jones, Y. Liu, A. E.-J. Lim, and M. Hochberg, “Linearity of silicon ring modulators for analog optical links,” Opt. Express 20(12), 13115–13122 (2012). [CrossRef]   [PubMed]  

13. J. Du and J. Wang, “Experimental performance evaluation of analog signal transmission in a silicon microring resonator,” Opt. Lett. 40(7), 1181–1184 (2015). [CrossRef]   [PubMed]  

14. R. A. Cohen, O. Amrani, and S. Ruschin, “Linearized electro-optic racetrack modulator based on double injection method in silicon,” Opt. Express 23(3), 2252–2261 (2015). [CrossRef]   [PubMed]  

15. M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave Mach-Zehnder carrier depletion modulator based on differential drive,” Opt. Express 21(3), 3818–3825 (2013). [CrossRef]   [PubMed]  

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24. M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (2010). [CrossRef]  

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28. M. Wood, L. Chen, J. R. Burr, and R. M. Reano, “Optimization of electron beam patterned hydrogen silsesquioxane mask edge roughness for low-loss silicon waveguides,” J. Nanophoton. 8(1), 083098 (2014). [CrossRef]  

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References

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  • |
  • |

  1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
    [Crossref]
  2. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7(4), 506–538 (2013).
    [Crossref]
  3. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
    [Crossref]
  4. R. A. Soref, “The past, present and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
    [Crossref]
  5. M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
    [Crossref]
  6. P. Dong, N.-N. Feng, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and M. Asghari, “GHz-bandwidth optical filters based on high-order silicon ring resonators,” Opt. Express 18(23), 23784–23789 (2010).
    [Crossref] [PubMed]
  7. C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
    [Crossref]
  8. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
    [Crossref]
  9. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
    [Crossref]
  10. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
    [Crossref] [PubMed]
  11. G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “25Gb/s 1V-driving CMOS ring modulator with integrated thermal tuning,” Opt. Express 19(21), 20435–20443 (2011).
    [PubMed]
  12. A. Ayazi, T. Baehr-Jones, Y. Liu, A. E.-J. Lim, and M. Hochberg, “Linearity of silicon ring modulators for analog optical links,” Opt. Express 20(12), 13115–13122 (2012).
    [Crossref] [PubMed]
  13. J. Du and J. Wang, “Experimental performance evaluation of analog signal transmission in a silicon microring resonator,” Opt. Lett. 40(7), 1181–1184 (2015).
    [Crossref] [PubMed]
  14. R. A. Cohen, O. Amrani, and S. Ruschin, “Linearized electro-optic racetrack modulator based on double injection method in silicon,” Opt. Express 23(3), 2252–2261 (2015).
    [Crossref] [PubMed]
  15. M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, “Highly linear silicon traveling wave Mach-Zehnder carrier depletion modulator based on differential drive,” Opt. Express 21(3), 3818–3825 (2013).
    [Crossref] [PubMed]
  16. A. Karim and J. Devenport, “Noise figure reduction in externally modulated analog fiber-optic links,” IEEE Photon. Technol. Lett. 19(5), 312–314 (2007).
    [Crossref]
  17. E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
    [Crossref]
  18. Y. S. Lee, G.-D. Kim, W.-J. Kim, S.-S. Lee, W.-G. Lee, and W. H. Steier, “Hybrid Si-LiNbO₃ microring electro-optically tunable resonators for active photonic devices,” Opt. Lett. 36(7), 1119–1121 (2011).
    [Crossref] [PubMed]
  19. L. Chen and R. M. Reano, “Compact electric field sensors based on indirect bonding of lithium niobate to silicon microrings,” Opt. Express 20(4), 4032–4038 (2012).
    [Crossref] [PubMed]
  20. L. Chen, M. G. Wood, and R. M. Reano, “12.5 pm/V hybrid silicon and lithium niobate optical microring resonator with integrated electrodes,” Opt. Express 21(22), 27003–27010 (2013).
    [Crossref] [PubMed]
  21. L. Chen, Q. Xu, M. G. Wood, and R. M. Reano, “Hybrid silicon and lithium niobate electro-optical ring modulator,” Optica 1(2), 112–118 (2014).
    [Crossref]
  22. L. Chen, M. G. Wood, and R. M. Reano, “Compensating thermal drift of hybrid silicon and lithium niobate ring resonances,” Opt. Lett. 40(7), 1599–1602 (2015).
    [PubMed]
  23. P. Rabiei, J. Ma, S. Khan, J. Chiles, and S. Fathpour, “Heterogeneous lithium niobate photonics on silicon substrates,” Opt. Express 21(21), 25573–25581 (2013).
    [Crossref] [PubMed]
  24. M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (2010).
    [Crossref]
  25. W. S. C. Chang, RF Photonic Technology in Optical Fiber Links (Cambridge University, 2002).
  26. H. Tazawa and W. H. Steier, “Linearity of ring resonator-based electro-optic polymer modulator,” Electron. Lett. 41(23), 1297–1298 (2005).
    [Crossref]
  27. K. K. Wong, Properties of Lithium Niobate (INSPEC, 2002).
  28. M. Wood, L. Chen, J. R. Burr, and R. M. Reano, “Optimization of electron beam patterned hydrogen silsesquioxane mask edge roughness for low-loss silicon waveguides,” J. Nanophoton. 8(1), 083098 (2014).
    [Crossref]
  29. P. Sun and R. M. Reano, “Cantilever couplers for intra-chip coupling to silicon photonic integrated circuits,” Opt. Express 17(6), 4565–4574 (2009).
    [PubMed]
  30. J. L. Nightingale, R. A. Becker, R. C. Willis, and J. S. Vrhel, “Characterization of frequency dispersion in Ti-diffused lithium niobate optical devices,” Appl. Phys. Lett. 51(10), 716–718 (1987).
    [Crossref]
  31. R. L. Jungerman and C. A. Flory, “Low-frequency acoustic anomalies in lithium niobate Mach-Zehnder interferometers,” Appl. Phys. Lett. 53(16), 1477–1479 (1988).
    [Crossref]
  32. A. Vorobiev, J. Berge, S. Gevorgian, M. Löffler, and E. Olsson, “Effect of interface roughness on acoustic loss in tunable thin film bulk acoustic wave resonators,” J. Appl. Phys. 110(2), 024116 (2011).
    [Crossref]

2015 (3)

2014 (2)

L. Chen, Q. Xu, M. G. Wood, and R. M. Reano, “Hybrid silicon and lithium niobate electro-optical ring modulator,” Optica 1(2), 112–118 (2014).
[Crossref]

M. Wood, L. Chen, J. R. Burr, and R. M. Reano, “Optimization of electron beam patterned hydrogen silsesquioxane mask edge roughness for low-loss silicon waveguides,” J. Nanophoton. 8(1), 083098 (2014).
[Crossref]

2013 (4)

2012 (2)

2011 (3)

2010 (3)

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (2010).
[Crossref]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

P. Dong, N.-N. Feng, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and M. Asghari, “GHz-bandwidth optical filters based on high-order silicon ring resonators,” Opt. Express 18(23), 23784–23789 (2010).
[Crossref] [PubMed]

2009 (2)

2007 (2)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

A. Karim and J. Devenport, “Noise figure reduction in externally modulated analog fiber-optic links,” IEEE Photon. Technol. Lett. 19(5), 312–314 (2007).
[Crossref]

2006 (3)

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
[Crossref]

R. A. Soref, “The past, present and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

2005 (2)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

H. Tazawa and W. H. Steier, “Linearity of ring resonator-based electro-optic polymer modulator,” Electron. Lett. 41(23), 1297–1298 (2005).
[Crossref]

2000 (1)

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

1988 (1)

R. L. Jungerman and C. A. Flory, “Low-frequency acoustic anomalies in lithium niobate Mach-Zehnder interferometers,” Appl. Phys. Lett. 53(16), 1477–1479 (1988).
[Crossref]

1987 (2)

J. L. Nightingale, R. A. Becker, R. C. Willis, and J. S. Vrhel, “Characterization of frequency dispersion in Ti-diffused lithium niobate optical devices,” Appl. Phys. Lett. 51(10), 716–718 (1987).
[Crossref]

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Ackerman, E. I.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

Agarwal, A.

Amrani, O.

Asghari, M.

Attanasio, D. V.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Ayazi, A.

Baehr-Jones, T.

Banwell, T.

Beausoleil, R. G.

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (2010).
[Crossref]

Becker, R. A.

J. L. Nightingale, R. A. Becker, R. C. Willis, and J. S. Vrhel, “Characterization of frequency dispersion in Ti-diffused lithium niobate optical devices,” Appl. Phys. Lett. 51(10), 716–718 (1987).
[Crossref]

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Berge, J.

A. Vorobiev, J. Berge, S. Gevorgian, M. Löffler, and E. Olsson, “Effect of interface roughness on acoustic loss in tunable thin film bulk acoustic wave resonators,” J. Appl. Phys. 110(2), 024116 (2011).
[Crossref]

Betts, G. E.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

Bossi, D. E.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Burr, J. R.

M. Wood, L. Chen, J. R. Burr, and R. M. Reano, “Optimization of electron beam patterned hydrogen silsesquioxane mask edge roughness for low-loss silicon waveguides,” J. Nanophoton. 8(1), 083098 (2014).
[Crossref]

Capmany, J.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7(4), 506–538 (2013).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Chen, L.

Chiles, J.

Cohen, R. A.

Cox, C. H.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

Cunningham, J. E.

Devenport, J.

A. Karim and J. Devenport, “Noise figure reduction in externally modulated analog fiber-optic links,” IEEE Photon. Technol. Lett. 19(5), 312–314 (2007).
[Crossref]

Dong, P.

Du, J.

Fathpour, S.

Feng, D.

Feng, N.-N.

Flory, C. A.

R. L. Jungerman and C. A. Flory, “Low-frequency acoustic anomalies in lithium niobate Mach-Zehnder interferometers,” Appl. Phys. Lett. 53(16), 1477–1479 (1988).
[Crossref]

Fritz, D. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Gevorgian, S.

A. Vorobiev, J. Berge, S. Gevorgian, M. Löffler, and E. Olsson, “Effect of interface roughness on acoustic loss in tunable thin film bulk acoustic wave resonators,” J. Appl. Phys. 110(2), 024116 (2011).
[Crossref]

Hallemeier, P. F.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Heideman, R.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7(4), 506–538 (2013).
[Crossref]

Hochberg, M.

Jalali, B.

Jungerman, R. L.

R. L. Jungerman and C. A. Flory, “Low-frequency acoustic anomalies in lithium niobate Mach-Zehnder interferometers,” Appl. Phys. Lett. 53(16), 1477–1479 (1988).
[Crossref]

Karim, A.

A. Karim and J. Devenport, “Noise figure reduction in externally modulated analog fiber-optic links,” IEEE Photon. Technol. Lett. 19(5), 312–314 (2007).
[Crossref]

Khan, M. H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Khan, S.

Kim, G.-D.

Kim, W.-J.

Kissa, K. M.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Krishnamoorthy, A. V.

Lafaw, D. A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Leaird, D. E.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Lee, D. C.

Lee, S.-S.

Lee, W.-G.

Lee, Y. S.

Leinse, A.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7(4), 506–538 (2013).
[Crossref]

Li, G.

Liang, H.

Lim, A. E.-J.

Lipson, M.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Liu, Y.

Lo, G.-Q.

Löffler, M.

A. Vorobiev, J. Berge, S. Gevorgian, M. Löffler, and E. Olsson, “Effect of interface roughness on acoustic loss in tunable thin film bulk acoustic wave resonators,” J. Appl. Phys. 110(2), 024116 (2011).
[Crossref]

Luff, B. J.

Luo, Y.

Ma, J.

Maack, D.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Marpaung, D.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7(4), 506–538 (2013).
[Crossref]

McBrien, G. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Menendez, R.

Murphy, E. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Nightingale, J. L.

J. L. Nightingale, R. A. Becker, R. C. Willis, and J. S. Vrhel, “Characterization of frequency dispersion in Ti-diffused lithium niobate optical devices,” Appl. Phys. Lett. 51(10), 716–718 (1987).
[Crossref]

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Olsson, E.

A. Vorobiev, J. Berge, S. Gevorgian, M. Löffler, and E. Olsson, “Effect of interface roughness on acoustic loss in tunable thin film bulk acoustic wave resonators,” J. Appl. Phys. 110(2), 024116 (2011).
[Crossref]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Prince, J. L.

C. H. Cox, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech. 54(2), 906–920 (2006).
[Crossref]

Qi, M.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Qian, W.

Rabiei, P.

Raj, K.

Reano, R. M.

Roeloffzen, C.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7(4), 506–538 (2013).
[Crossref]

Ruschin, S.

Sales, S.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7(4), 506–538 (2013).
[Crossref]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Shen, H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Shubin, I.

Song, M.

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (2010).
[Crossref]

Soref, R. A.

R. A. Soref, “The past, present and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Steier, W. H.

Streshinsky, M.

Sun, P.

Tazawa, H.

H. Tazawa and W. H. Steier, “Linearity of ring resonator-based electro-optic polymer modulator,” Electron. Lett. 41(23), 1297–1298 (2005).
[Crossref]

Thacker, H.

Toliver, P.

Vorobiev, A.

A. Vorobiev, J. Berge, S. Gevorgian, M. Löffler, and E. Olsson, “Effect of interface roughness on acoustic loss in tunable thin film bulk acoustic wave resonators,” J. Appl. Phys. 110(2), 024116 (2011).
[Crossref]

Vrhel, J. S.

J. L. Nightingale, R. A. Becker, R. C. Willis, and J. S. Vrhel, “Characterization of frequency dispersion in Ti-diffused lithium niobate optical devices,” Appl. Phys. Lett. 51(10), 716–718 (1987).
[Crossref]

Wang, J.

Weiner, A. M.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Willis, R. C.

J. L. Nightingale, R. A. Becker, R. C. Willis, and J. S. Vrhel, “Characterization of frequency dispersion in Ti-diffused lithium niobate optical devices,” Appl. Phys. Lett. 51(10), 716–718 (1987).
[Crossref]

Willner, A. E.

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (2010).
[Crossref]

Wood, M.

M. Wood, L. Chen, J. R. Burr, and R. M. Reano, “Optimization of electron beam patterned hydrogen silsesquioxane mask edge roughness for low-loss silicon waveguides,” J. Nanophoton. 8(1), 083098 (2014).
[Crossref]

Wood, M. G.

Woodward, T. K.

Wooten, E. L.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Xiao, S.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Xu, Q.

L. Chen, Q. Xu, M. G. Wood, and R. M. Reano, “Hybrid silicon and lithium niobate electro-optical ring modulator,” Optica 1(2), 112–118 (2014).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Xuan, Y.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Xuan, Z.

Yao, J.

Yi-Yan, A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Zhang, L.

M. Song, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Nonlinear distortion in a silicon microring-based electro-optic modulator for analog optical links,” IEEE J. Sel. Top. Quantum Electron. 16(1), 185–191 (2010).
[Crossref]

Zhao, L.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Zheng, X.

Appl. Phys. Lett. (2)

J. L. Nightingale, R. A. Becker, R. C. Willis, and J. S. Vrhel, “Characterization of frequency dispersion in Ti-diffused lithium niobate optical devices,” Appl. Phys. Lett. 51(10), 716–718 (1987).
[Crossref]

R. L. Jungerman and C. A. Flory, “Low-frequency acoustic anomalies in lithium niobate Mach-Zehnder interferometers,” Appl. Phys. Lett. 53(16), 1477–1479 (1988).
[Crossref]

Electron. Lett. (1)

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic of hybrid Si/LiNbO3 ring modulator. For clarity, the PECVD SiO2 top-cladding layer and electrical contact pads are not shown. (b) Schematic of cross-section of device along dashed line in (a).
Fig. 2
Fig. 2 Calculated optical TE mode distribution at 1550 nm wavelength and electric field vectors from applied DC voltage.
Fig. 3
Fig. 3 (a) Top-view optical micrograph of fabricated device; (b) SEM of electrodes.
Fig. 4
Fig. 4 (a) Measured optical spectrum as a function of applied voltage; (b) linear fitting of the resonance wavelength shift as a function of applied voltage.
Fig. 5
Fig. 5 Measured optical modulation response and the S11 magnitude.
Fig. 6
Fig. 6 Test and measurement setup for characterization of linearity.
Fig. 7
Fig. 7 RF output power of the fundamental, SHD, and IMD3 components as a function of wavelength detuning from resonance for two RF tones centered at (a) 100 MHz, (b) 1 GHz, (c) 5 GHz, and (d) 10 GHz.
Fig. 8
Fig. 8 RF output power of the fundamental and IMD3 components as a function of RF input power for the LiNbO3 MZI and the Si/LiNbO3 ring at 0.997 GHz. The noise floor is in 1 Hz bandwidth.
Fig. 9
Fig. 9 RF output power of the fundamental and IMD3 components as a function of RF input power for the LiNbO3 MZI modulator and the hybrid silicon and LiNbO3 ring modulator at 9.997 GHz. The noise floor is in 1 Hz bandwidth.

Equations (7)

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n eff ( V in )= n e0 +α V in +β V in 2 +γ V in 3 +
n eff ( V in ) n e0 +α V in
I out ( λ, V in )=R(λ) P out,max [ 1 1 1+ 4 F 2 π 2 sin 2 [ πL n eff ( λ, V in  ) λ ] ]
I out ( λ, V in )= c 0 ( λ )+ c 1 ( λ ) V in + c 2 ( λ ) ( V in ) 2 + c 3 ( λ ) ( V in ) 3 +
  V in = A 1 e i ω 1 t + A 1 * e i ω 1 t + A 2 e i ω 2 t + A 2 * e i ω 2 t
SHD: c 2 (λ)( A 1 2 e i2 ω 1 t + A 1 *2 e i2 ω 1 t + A 2 2 e i2 ω 2 t + A 2 *2 e i2 ω 2 t )
IMD3:3 c 3 ( λ )[ A 1 2 A 2 * e i( 2 ω 1 ω 2 )t + A 1 *2 A 2 e i( 2 ω 1 ω 2 )t + A 2 2 A 1 * e i( 2 ω 2 ω 1 )t + A 2 *2 A 1 e i( 2 ω 2 ω 1 )t ]

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