Abstract

The vast majority of work on waveguide-coupled resonators focuses on decreasing losses in the waveguide and coupling region. Here we present fully integrated resonators based on an ultralow-loss Si3N4 waveguide platform. By tailoring the directional coupler excitation to the resonators, we are able to achieve lower loss single-mode coupling to multimode waveguide widths compared to straight bus waveguide directional couplers. This allows us to demonstrate record-high integrated waveguide coupled intrinsic quality factor (Qint) values of 81 million at a 9.65 mm bend radius, with a future direction to both stronger and lower loss waveguide–resonator coupling. This result opens up integration possibilities for narrow linewidth integrated diode lasers, low noise feedback systems, microwave photonic research, and the ultrastable timing reference community.

© 2014 Optical Society of America

The availability of fully integrable high-Q resonators, with quality factors approaching 100 million, can create a paradigm shift for the application of photonic integrated circuits (PICs) in a wide variety of applications. A monolithically integrated resonator and coupler allows for lithographic definition and control of the system, and integration with other optical devices that can greatly benefit from such narrowband filters and frequency references in the linear operation regime [1].

In the field of microwave photonics, these high-Q resonators can act as filters with a large tuning range over tens of gigahertz bandwidth. With bandpass widths of a few megahertz, such filters outperform best-in-class YIG-based microwave filters [2]. Such high-Q elements enable oscillators with lower-noise performance than oven-controlled crystal-based oscillators (OCXOs) in the microwave frequency range. Target applications include 60 GHz wireless systems where these oscillators can increase the spectral efficiency over systems based on CMOS technology, by enabling complex modulation formats, or increase the link distance by improving the signal-to-noise ratio [3]. This added energy efficiency is essential for ubiquitous implementation of future 4G and 5G wireless systems. In coherent Doppler radars, e.g., automotive, the probability of detection of, especially, small and slow-moving targets will be increased. This increase in probability can be up to 40% for 5 dB decrease in noise [4]. In the optical domain, such oscillators can be used to create combs of optical frequencies, with very accurate spacings. These combs can act as optical “rulers” for precision spectroscopy in fields such as high-resolution metrology and gas sensing, with applications to lidar and satellite positioning systems [5]. PIC-based gyroscopes based on such high-Q resonators will outperform MEMS-based gyros and become competitive with fiber-optic and ring-laser-based approaches for tactical grade gyro applications requiring resolutions of 0.1°/h [6,7].

Generally, waveguide platforms have achieved low loss using Si [8], InP [6], doped silica [9,10], or Si3N4 [1116]. In Fig. 1, we show the state of the art in resonator performance for integrable coupling schemes, typically horizontal or vertical evanescent waveguide coupling. The trade-off between quality factor and bend radius is shown in both the microring regime (20–200 μm radius) and large bend radius regime (1–10 mm radius). Recent Si3N4 results from our group are highlighted in the 1–10 mm bend radius range, with new results in this Letter showing the highest integrated Qint ever reported, to our knowledge.

 figure: Fig. 1.

Fig. 1. State-of-the-art resonator comparison of Qint versus bend radius for integrated waveguide-coupled resonators [6,816]. The propagation loss (α) and FSR are scaled assuming λ=1550nm, neff=ng=1.5, and lossless directional couplers according to Eq. (1). UCSB Si3N4 results [15,16], including this Letter, are highlighted in red triangles.

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The theoretically obtainable Qint for a given system takes into account the waveguide propagation loss, α (dB/m), directional coupler power ratio, κ, and excess directional coupler power loss per pass, γ. Equation (1) shows the obtainable Qload for a given propagation loss [17]:

Qload=2πneffLλ[κ+αL+γ]1.

The excess coupler loss adds parasitic loss and becomes important as it approaches the round-trip propagation loss αL. Parasitic losses can occur from scattering loss in the coupler as well as coupling into unwanted higher order or radiation modes as the coupling gap decreases, which occur for even high bend radius devices [18].

Figure 2 plots Eq. (1) without the power coupling term, κ, which is usually extracted through data analysis. In the low-loss regime of 0.2dB/m and at a bend radius of 10 mm, efficient directional couplers with less than 30dB excess insertion loss are required to not add appreciable loss to the system. Such low insertion losses are not possible to simulate in commercial software packages, and in this Letter we present experimental results showing low-loss adiabatic directional couplers in 81 million Qint resonators. In our work, we target low confinement, fully monolithic Si3N4 waveguide structures that will be useful for future integration with silicon [19,20] and hybrid silicon III–V components [21]. High-quality Si3N4 is deposited via low pressure chemical vapor deposition (LPCVD) on a 15-μm-thick thermally grown SiO2 layer on a silicon substrate. For this work, a thin 40 nm film is chosen to lower the confinement factor and decrease sidewall scattering loss at the expense of a higher bend radius device. Contact lithography defines the ring resonators and directional couplers. The bus waveguide-to-ring gap is generally >1μm wide due to the low waveguide confinement and low coupling needed for high-Q resonators. The gaps in this study were chosen based on previous experimental results, and are identical on the add and drop ports. 3.1 μm of SiO2 is deposited via LPCVD in three layers, with an 1150°C anneal after each layer. The sample is then chemically mechanically polished and a 15 μm thick thermal SiO2 on Si top cladding is wafer bonded after plasma activation of the surfaces. The samples are annealed at 950°C for 3 h and diced for testing. The completed cross section is shown in Fig. 3(a), and further fabrication details can be found in [15,22].

 figure: Fig. 2.

Fig. 2. Theoretically obtainable Qint for a given directional coupler excess loss value, γ, and propagation loss, α, according to Eq. (1).

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 figure: Fig. 3.

Fig. 3. (a) Waveguide cross section and (b)–(d) all supported modes of the 11μm×40nm Si3N4 core geometry at a 9.65 mm bending radius, simulated with FIMMWAVE.

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The waveguide width now defines the number of supported modes. 7-μm-wide waveguides have produced single-mode resonators with 55 million Qint [15]. Based on our previous work on ultralow-loss delay lines, the lowest loss of (0.045±0.04dB/m) has been observed in multimode waveguide spirals [22]. Assuming directional couplers without excess loss, this mean propagation loss in a resonator corresponds to a Qint of 575 million. This low-loss core geometry of 11μm×40nm has now been implemented in add–drop ring resonators at a bending radius of 9.65 mm, consistent with a free spectral range (FSR) of 3.3 GHz near 1580 nm. Figures 3(b)3(d) present the simulated mode profiles for the three supported modes, TE0, TM0, and TE1. The low-loss mode of interest is the TE0 mode, which has an effective area of 33μm2 and core confinement factor of 3% at 1580 nm.

To study multimode resonators, care must be taken in the directional coupler design. In addition to requiring low excess coupler loss, as discussed earlier, any unwanted coupling to higher order modes will produce multiple families of resonances with different FSRs, and effectively lower the resonator Q. These corrupted spectra will produce spurious tones when filtering noise for applications such as microwave photonics. Figure 4 outlines directional coupler layouts for waveguide coupled ring resonators. Figure 4(a) is a traditional symmetric coupler that is exactly beta matched but has the strongest tapering into the coupling region. Figures 4(b) and 4(d) show the two directional coupler designs studied in this Letter. The first was a straight bus waveguide coupled to the ring resonator, or “straight” coupler. We have studied these couplers on higher contrast waveguides, and our splits show an excess loss associated with a decrease in gap, yielding inefficiencies that limit the quality factor [15]. Additionally, these couplers had appreciable coupling to higher order modes, producing corrupted resonator spectra. To overcome this, we have designed a second “weakly tapered gap” directional coupler [Fig. 4(d)]. As a first experiment, we fabricate the bus waveguide with a bend radius that is 30% larger than the resonator radius to have two effects. The first is to decrease the beta mismatch between two arms of the coupler such that more efficient excitation of the fundamental mode is achieved over higher order modes. Additionally, weakly tapering the gap will yield a more adiabatic transition region from the input bus waveguide to the coupling region than the pulley, symmetric, and straight couplers of Figs. 4(a)4(c), which we hypothesize will lower the excess loss of the coupler.

 figure: Fig. 4.

Fig. 4. Directional coupler layouts for ring resonators. The tapering of the gap is strongest for (a) symmetric coupling and identical for the (b) straight and (c) pulley couplers, while the (d) weakly tapered gap coupler smoothes the gap transition. We fabricated straight and weakly tapered gap couplers in this study.

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Figure 5 shows the simulated neff and ng of the waveguide geometry’s two TE modes, taking into account waveguide and bulk material chromatic dispersion [23,24]. We are mainly interested in the low-loss TE0 mode. However, excitation of higher order modes from input tapers and/or directional couplers can corrupt the spectrum through multiple families of resonance peaks that would have a difference of only 3 MHz in FSR at 1580 nm. This Vernier effect is shown schematically in Fig. 5 (inset) where the high ng mode (TE0) contains one extra resonance across a large wavelength span, termed the beat wavelength, λbeat. The relative extinction ratio (ΔER) is referenced to the high ng TE0 mode. The separation between adjacent resonances of the two transverse modes, Δλres, increases with wavelength in reference to the high ng mode. The TE0 mode will thus have m+1 FSRs in λbeat, where m is the number of TE1 FSRs. The ratio of group indices is then

ngTE0ngTE1=1+1m.

 figure: Fig. 5.

Fig. 5. Simulated TE effective and group indices for the 11μm×40nm Si3N4 multimode waveguides studied in this Letter. Due to the fundamental TE0 mode having a higher group index, there will be a relative resonance wavelength separation, Δλres and overall beat wavelength, λbeat (inset).

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Since the number of FSRs in λbeat is dependent only on the group index ratio, measuring resonators with long cavity lengths allows for the beat wavelength to be within a reasonable measurable range. For a typical wavelength sweep of 100 nm, a 9.65 mm radius resonator will have 3500 FSRs and a resolution down to 0.03% change in group index ratio. A higher ng ratio will produce multiple beat frequencies in this range. To achieve the same measurement resolution would require a setup with high thermal and mechanical stability, and kilohertz level sweep accuracy for FSR extraction, such as a RF domain measurement [25,26]. We will experimentally analyze this multimode situation in the following section and use the beat wavelength to extract the resonances of each mode.

Measurement of the add–drop high-Q resonators was done in the frequency domain using a tunable external cavity laser (Agilent 86142A). The slowest sweep speed of 0.5nm/s was used so as to avoid any ring-down effects that could occur [27]. Cleaved SMF28 fiber was used for coupling in/out of the device, and the output was coupled to a high-responsivity InGaAs detector. The photocurrent was terminated on a 1 GHz oscilloscope to enable high data rate acquisition. The wavelength regime of 1580 nm was studied for the highest Q factors, as this yields the lowest propagation loss of the platform [22]. A polarization controller was also used on the input to excite the lower loss TE polarization. The TM polarization, which has a lower confinement and higher bend loss than the TE0 mode, was not excited due to the polarizing nature of S bends on the Si3N4 platform [28]. All results are averaged over multiple closely spaced resonances within 0.5 nm.

We first analyze the relative resonant wavelengths and extinction ratios (ERs) of the two directional coupler designs in the L band. Figure 6 compares a 5 μm gap straight coupler with a 3.8 μm weakly tapered gap coupler. The beat wavelength, λbeat, is extracted from the two overlap points by curve fitting a second-order polynomial that accounts for dispersion. With the same nominal path length, the two resonators show λbeat=(73±2)nm, corresponding to 2500 resonances across this range. The ratio of ng between TE0 and TE1 is found to be 1.00039±0.00002, which matches well with our simulated ratio of 1.00040±0.00002, for an ng of 1.4674 and 1.4668, respectively, in the region of interest. Additionally, the ΔER between modes in the two directional coupler designs changes sign. Due to these observations, we conclude that we have achieved stronger coupling to the fundamental TE0 mode with the weakly tapered gap directional coupler as compared to the straight directional coupler.

 figure: Fig. 6.

Fig. 6. Relative resonance wavelengths and ERs for the TE0 and TE1 modes across the region of interest. All numbers are taken relative to the fundamental TE0 mode and averaged over multiple closely spaced resonances every 5 nm. The weakly tapered gap directional coupler resonator shows a beat wavelength of 73 nm similar to that of a straight directional coupler resonator, with an increase in absolute and relative ER.

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Next, we analyze the individual resonances near 1580 nm to extract Qint values. First, we show a comparison of straight couplers with two different waveguide–resonator bus gaps, 3.8 and 5 μm, in Figs. 7(a) and 7(b), respectively. The modes are labeled according to the previous modal analysis, and all devices are undercoupled due to the identical coupler layouts on the add and drop ports. For both straight coupler gaps, the higher order TE1 mode is coupled much stronger than the lower loss fundamental mode, as observed by the magnitude of the ER. In this regime, the TE0 mode has a maximum Qint factor of 63 million at a 5 μm gap, similar to the results of the previous generation [15]. However, using a weakly tapered gap directional coupler at a 3.8 μm minimum gap at bus radius of 12.545 mm, we couple stronger and more efficiently to the fundamental TE0 mode. This has the consequence of a higher ER than for the TE1 mode, as seen in Fig. 7(c), as well as an even higher Qint factor of 81 million, outlined in Table 1. This is the largest Qint factor for a monolithic waveguide coupled resonator system to date, to our knowledge.

 figure: Fig. 7.

Fig. 7. Resonator spectra and fits near 1580 nm for three different directional coupler designs: (a) 5 μm straight bus waveguide, (b) 3.8 μm straight bus waveguide, and (c) 3.8 μm weakly tapered gap waveguide.

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Tables Icon

Table 1. Measured and Extracted Resonator Parameters for the Three Directional Coupler Designs Studied at 1580 nm, Assuming No Parasitic Losses (γ=0)a

We have presented results on the highest integrated resonator Qint values to date, to our knowledge, with a value of 81 million at a 9.65 mm bend radius. Using low confinement Si3N4/SiO2 waveguides, we have utilized multimode waveguide widths and spectral analysis to extract propagation losses and directional coupler information for weakly tapered coupling gaps. These weakly tapered gap directional couplers are a critical path forward to higher quality factor integrated resonators that require increasingly efficient and low-loss coupling. Improved design of beta matched weakly tapered gap couplers should help reduce the loss of directional couplers, and full utilization of the Si3N4 platform, with record propagation loss of 0.05dB/m, should be able to yield resonators with Qint values of 600 million.

FUNDING INFORMATION

Defense Advanced Research Projects Agency (DARPA) (HR0011-12-C-0006); National Science Foundation (NSF) (DGE-1144085)

ACKNOWLEDGMENTS

The authors would like to thank Josh Conway, Scott Rodgers, Dan Blumenthal, Arne Leinse, and René Heideman for helpful discussions. The devices were partially fabricated at LioniX BV.

REFERENCES

1. M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, and J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev., doi: 10.1002/lpor.201300183 (posted online March 5, 2014).

2. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, Laser Photon. Rev. 7, 506 (2013). [CrossRef]  

3. D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, and R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006). [CrossRef]  

4. J. R. Vig, “Introduction to quartz frequency standards,” Res. Dev. Tech. Rep. SLCET-TR-92-1 1 (U.S. Army Electronics Technology and Devices Laboratory, 1992).

5. P. Maddaloni, M. Bellini, and P. De Natale, Laser-Based Measurements for Time and Frequency Domain Applications (Taylor & Francis, 2013).

6. C. Ciminelli, F. Dell’Olio, M. N. Armenise, F. M. Soares, and W. Passenberg, Opt. Express 21, 556 (2013). [CrossRef]  

7. C. Ciminelli, F. Dell’Olio, and M. N. Armenise, IEEE Photon. J. 4, 1844 (2012). [CrossRef]  

8. A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, and M. R. Watts, Opt. Lett. 37, 4236 (2012). [CrossRef]  

9. R. Adar, Y. Shani, and C. Henry, Appl. Phys. Lett. 58, 444 (1991). [CrossRef]  

10. R. Adar, M. R. Serbin, and V. Mizrahi, J. Lightwave Technol. 12, 1369 (1994). [CrossRef]  

11. Q. Li, A. A. Eftekhar, M. Sodagar, Z. Xia, A. H. Atabaki, and A. Adibi, Opt. Express 21, 18236 (2013). [CrossRef]  

12. A. Gondarenko, J. S. Levy, and M. Lipson, Opt. Express 17, 11366 (2009). [CrossRef]  

13. K. Luke, A. Dutt, C. B. Poitras, and M. Lipson, Opt. Express 21, 22829 (2013). [CrossRef]  

14. L. Zhuang, D. Marpaung, M. Burla, W. Beeker, A. Leinse, and C. Roeloffzen, Opt. Express 19, 23162 (2011). [CrossRef]  

15. D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, and J. E. Bowers, in IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 141–142.

16. M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, Opt. Express 19, 13551 (2011). [CrossRef]  

17. O. Schwelb, J. Lightwave Technol. 22, 1380 (2004). [CrossRef]  

18. D. Ding, M. J. A. de Dood, J. F. Bauters, M. J. R. Heck, J. E. Bowers, and D. Bouwmeester, Opt. Express 22, 6778 (2014). [CrossRef]  

19. T. Tsuchizawa and K. Yamada, IEEE J. Sel. Top. Quantum Electron. 17, 516 (2011). [CrossRef]  

20. J. F. Bauters, M. L. Davenport, M. J. R. Heck, J. K. Doylend, A. Chen, A. W. Fang, and J. E. Bowers, Opt. Express 21, 544 (2013). [CrossRef]  

21. M. Piels, J. Bauters, M. Davenport, M. Heck, and J. Bowers, J. Lightwave Technol. 32, 817 (2013). [CrossRef]  

22. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, Opt. Express 19, 24090 (2011). [CrossRef]  

23. H. R. Philipp, J. Electrochem. Soc. 120, 295 (1973). [CrossRef]  

24. T. Bååk, Appl. Opt. 21, 1069 (1982). [CrossRef]  

25. N. Uehara and K. Ueda, Appl. Phys. B 61, 9 (1995). [CrossRef]  

26. B. J. J. Slagmolen, M. B. Gray, K. G. Baigent, and D. E. McClelland, Appl. Opt. 39, 3638 (2000). [CrossRef]  

27. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 15, 6768 (2007). [CrossRef]  

28. J. F. Bauters, M. J. R. Heck, D. Dai, J. S. Barton, D. J. Blumenthal, and J. E. Bowers, IEEE Photon. J. 5, 6600207 (2013). [CrossRef]  

References

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  1. M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev., doi: 10.1002/lpor.201300183 (posted online March 5, 2014).
  2. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmany, Laser Photon. Rev. 7, 506 (2013).
    [Crossref]
  3. D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
    [Crossref]
  4. J. R. Vig, “Introduction to quartz frequency standards,” (U.S. Army Electronics Technology and Devices Laboratory, 1992).
  5. P. Maddaloni, M. Bellini, P. De Natale, Laser-Based Measurements for Time and Frequency Domain Applications (Taylor & Francis, 2013).
  6. C. Ciminelli, F. Dell’Olio, M. N. Armenise, F. M. Soares, W. Passenberg, Opt. Express 21, 556 (2013).
    [Crossref]
  7. C. Ciminelli, F. Dell’Olio, M. N. Armenise, IEEE Photon. J. 4, 1844 (2012).
    [Crossref]
  8. A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, M. R. Watts, Opt. Lett. 37, 4236 (2012).
    [Crossref]
  9. R. Adar, Y. Shani, C. Henry, Appl. Phys. Lett. 58, 444 (1991).
    [Crossref]
  10. R. Adar, M. R. Serbin, V. Mizrahi, J. Lightwave Technol. 12, 1369 (1994).
    [Crossref]
  11. Q. Li, A. A. Eftekhar, M. Sodagar, Z. Xia, A. H. Atabaki, A. Adibi, Opt. Express 21, 18236 (2013).
    [Crossref]
  12. A. Gondarenko, J. S. Levy, M. Lipson, Opt. Express 17, 11366 (2009).
    [Crossref]
  13. K. Luke, A. Dutt, C. B. Poitras, M. Lipson, Opt. Express 21, 22829 (2013).
    [Crossref]
  14. L. Zhuang, D. Marpaung, M. Burla, W. Beeker, A. Leinse, C. Roeloffzen, Opt. Express 19, 23162 (2011).
    [Crossref]
  15. D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, J. E. Bowers, in IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 141–142.
  16. M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 13551 (2011).
    [Crossref]
  17. O. Schwelb, J. Lightwave Technol. 22, 1380 (2004).
    [Crossref]
  18. D. Ding, M. J. A. de Dood, J. F. Bauters, M. J. R. Heck, J. E. Bowers, D. Bouwmeester, Opt. Express 22, 6778 (2014).
    [Crossref]
  19. T. Tsuchizawa, K. Yamada, IEEE J. Sel. Top. Quantum Electron. 17, 516 (2011).
    [Crossref]
  20. J. F. Bauters, M. L. Davenport, M. J. R. Heck, J. K. Doylend, A. Chen, A. W. Fang, J. E. Bowers, Opt. Express 21, 544 (2013).
    [Crossref]
  21. M. Piels, J. Bauters, M. Davenport, M. Heck, J. Bowers, J. Lightwave Technol. 32, 817 (2013).
    [Crossref]
  22. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 24090 (2011).
    [Crossref]
  23. H. R. Philipp, J. Electrochem. Soc. 120, 295 (1973).
    [Crossref]
  24. T. Bååk, Appl. Opt. 21, 1069 (1982).
    [Crossref]
  25. N. Uehara, K. Ueda, Appl. Phys. B 61, 9 (1995).
    [Crossref]
  26. B. J. J. Slagmolen, M. B. Gray, K. G. Baigent, D. E. McClelland, Appl. Opt. 39, 3638 (2000).
    [Crossref]
  27. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, L. Maleki, Opt. Express 15, 6768 (2007).
    [Crossref]
  28. J. F. Bauters, M. J. R. Heck, D. Dai, J. S. Barton, D. J. Blumenthal, J. E. Bowers, IEEE Photon. J. 5, 6600207 (2013).
    [Crossref]

2014 (1)

2013 (7)

2012 (2)

C. Ciminelli, F. Dell’Olio, M. N. Armenise, IEEE Photon. J. 4, 1844 (2012).
[Crossref]

A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, M. R. Watts, Opt. Lett. 37, 4236 (2012).
[Crossref]

2011 (4)

2009 (1)

2007 (1)

2006 (1)

D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
[Crossref]

2004 (1)

2000 (1)

1995 (1)

N. Uehara, K. Ueda, Appl. Phys. B 61, 9 (1995).
[Crossref]

1994 (1)

R. Adar, M. R. Serbin, V. Mizrahi, J. Lightwave Technol. 12, 1369 (1994).
[Crossref]

1991 (1)

R. Adar, Y. Shani, C. Henry, Appl. Phys. Lett. 58, 444 (1991).
[Crossref]

1982 (1)

1973 (1)

H. R. Philipp, J. Electrochem. Soc. 120, 295 (1973).
[Crossref]

Adar, R.

R. Adar, M. R. Serbin, V. Mizrahi, J. Lightwave Technol. 12, 1369 (1994).
[Crossref]

R. Adar, Y. Shani, C. Henry, Appl. Phys. Lett. 58, 444 (1991).
[Crossref]

Adibi, A.

Armenise, M. N.

Atabaki, A. H.

Bååk, T.

Baigent, K. G.

Barton, J. S.

Bauters, J.

Bauters, J. F.

D. Ding, M. J. A. de Dood, J. F. Bauters, M. J. R. Heck, J. E. Bowers, D. Bouwmeester, Opt. Express 22, 6778 (2014).
[Crossref]

J. F. Bauters, M. L. Davenport, M. J. R. Heck, J. K. Doylend, A. Chen, A. W. Fang, J. E. Bowers, Opt. Express 21, 544 (2013).
[Crossref]

J. F. Bauters, M. J. R. Heck, D. Dai, J. S. Barton, D. J. Blumenthal, J. E. Bowers, IEEE Photon. J. 5, 6600207 (2013).
[Crossref]

J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 24090 (2011).
[Crossref]

M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 13551 (2011).
[Crossref]

D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, J. E. Bowers, in IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 141–142.

M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev., doi: 10.1002/lpor.201300183 (posted online March 5, 2014).

Beeker, W.

Bellini, M.

P. Maddaloni, M. Bellini, P. De Natale, Laser-Based Measurements for Time and Frequency Domain Applications (Taylor & Francis, 2013).

Biberman, A.

Blumenthal, D. J.

Bouwmeester, D.

Bowers, J.

Bowers, J. E.

D. Ding, M. J. A. de Dood, J. F. Bauters, M. J. R. Heck, J. E. Bowers, D. Bouwmeester, Opt. Express 22, 6778 (2014).
[Crossref]

J. F. Bauters, M. L. Davenport, M. J. R. Heck, J. K. Doylend, A. Chen, A. W. Fang, J. E. Bowers, Opt. Express 21, 544 (2013).
[Crossref]

J. F. Bauters, M. J. R. Heck, D. Dai, J. S. Barton, D. J. Blumenthal, J. E. Bowers, IEEE Photon. J. 5, 6600207 (2013).
[Crossref]

J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 24090 (2011).
[Crossref]

M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 13551 (2011).
[Crossref]

D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, J. E. Bowers, in IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 141–142.

M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev., doi: 10.1002/lpor.201300183 (posted online March 5, 2014).

Brodersen, R. W.

D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
[Crossref]

Bruinink, C. M.

Burla, M.

Cabric, D.

D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
[Crossref]

Capmany, J.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Chen, A.

Chen, M. S. W.

D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
[Crossref]

Ciminelli, C.

Dai, D.

J. F. Bauters, M. J. R. Heck, D. Dai, J. S. Barton, D. J. Blumenthal, J. E. Bowers, IEEE Photon. J. 5, 6600207 (2013).
[Crossref]

Davenport, M.

Davenport, M. L.

J. F. Bauters, M. L. Davenport, M. J. R. Heck, J. K. Doylend, A. Chen, A. W. Fang, J. E. Bowers, Opt. Express 21, 544 (2013).
[Crossref]

M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev., doi: 10.1002/lpor.201300183 (posted online March 5, 2014).

de Dood, M. J. A.

De Natale, P.

P. Maddaloni, M. Bellini, P. De Natale, Laser-Based Measurements for Time and Frequency Domain Applications (Taylor & Francis, 2013).

Dell’Olio, F.

Ding, D.

Doylend, J. K.

Dutt, A.

Eftekhar, A. A.

Fang, A. W.

Gondarenko, A.

Gray, M. B.

Heck, M.

Heck, M. J. R.

D. Ding, M. J. A. de Dood, J. F. Bauters, M. J. R. Heck, J. E. Bowers, D. Bouwmeester, Opt. Express 22, 6778 (2014).
[Crossref]

J. F. Bauters, M. L. Davenport, M. J. R. Heck, J. K. Doylend, A. Chen, A. W. Fang, J. E. Bowers, Opt. Express 21, 544 (2013).
[Crossref]

J. F. Bauters, M. J. R. Heck, D. Dai, J. S. Barton, D. J. Blumenthal, J. E. Bowers, IEEE Photon. J. 5, 6600207 (2013).
[Crossref]

J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 24090 (2011).
[Crossref]

M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 13551 (2011).
[Crossref]

D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, J. E. Bowers, in IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 141–142.

M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev., doi: 10.1002/lpor.201300183 (posted online March 5, 2014).

Heideman, R.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Heideman, R. G.

Henry, C.

R. Adar, Y. Shani, C. Henry, Appl. Phys. Lett. 58, 444 (1991).
[Crossref]

Ilchenko, V. S.

John, D. D.

Leinse, A.

Levy, J. S.

Li, Q.

Lipson, M.

Luke, K.

Maddaloni, P.

P. Maddaloni, M. Bellini, P. De Natale, Laser-Based Measurements for Time and Frequency Domain Applications (Taylor & Francis, 2013).

Maleki, L.

Marpaung, D.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

L. Zhuang, D. Marpaung, M. Burla, W. Beeker, A. Leinse, C. Roeloffzen, Opt. Express 19, 23162 (2011).
[Crossref]

Matsko, A. B.

McClelland, D. E.

Mizrahi, V.

R. Adar, M. R. Serbin, V. Mizrahi, J. Lightwave Technol. 12, 1369 (1994).
[Crossref]

Passenberg, W.

Philipp, H. R.

H. R. Philipp, J. Electrochem. Soc. 120, 295 (1973).
[Crossref]

Piels, M.

Poitras, C. B.

Roeloffzen, C.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

L. Zhuang, D. Marpaung, M. Burla, W. Beeker, A. Leinse, C. Roeloffzen, Opt. Express 19, 23162 (2011).
[Crossref]

Sales, S.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Savchenkov, A. A.

Schwelb, O.

Serbin, M. R.

R. Adar, M. R. Serbin, V. Mizrahi, J. Lightwave Technol. 12, 1369 (1994).
[Crossref]

Shani, Y.

R. Adar, Y. Shani, C. Henry, Appl. Phys. Lett. 58, 444 (1991).
[Crossref]

Shaw, M. J.

Slagmolen, B. J. J.

Soares, F. M.

Sobel, D. A.

D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
[Crossref]

Sodagar, M.

Spencer, D. T.

M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, J. E. Bowers, Opt. Express 19, 13551 (2011).
[Crossref]

D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, J. E. Bowers, in IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 141–142.

M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev., doi: 10.1002/lpor.201300183 (posted online March 5, 2014).

Tang, Y.

D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, J. E. Bowers, in IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 141–142.

Tien, M.-C.

Timurdogan, E.

Tsuchizawa, T.

T. Tsuchizawa, K. Yamada, IEEE J. Sel. Top. Quantum Electron. 17, 516 (2011).
[Crossref]

Ueda, K.

N. Uehara, K. Ueda, Appl. Phys. B 61, 9 (1995).
[Crossref]

Uehara, N.

N. Uehara, K. Ueda, Appl. Phys. B 61, 9 (1995).
[Crossref]

Vig, J. R.

J. R. Vig, “Introduction to quartz frequency standards,” (U.S. Army Electronics Technology and Devices Laboratory, 1992).

Wang, S.

D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
[Crossref]

Watts, M. R.

Wright, J. B.

Xia, Z.

Yamada, K.

T. Tsuchizawa, K. Yamada, IEEE J. Sel. Top. Quantum Electron. 17, 516 (2011).
[Crossref]

Yang, J.

D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
[Crossref]

Zhuang, L.

Appl. Opt. (2)

Appl. Phys. B (1)

N. Uehara, K. Ueda, Appl. Phys. B 61, 9 (1995).
[Crossref]

Appl. Phys. Lett. (1)

R. Adar, Y. Shani, C. Henry, Appl. Phys. Lett. 58, 444 (1991).
[Crossref]

EURASIP J. Wirel. Commun. Netw. (1)

D. Cabric, M. S. W. Chen, D. A. Sobel, S. Wang, J. Yang, R. W. Brodersen, EURASIP J. Wirel. Commun. Netw. 2006, 1 (2006).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Tsuchizawa, K. Yamada, IEEE J. Sel. Top. Quantum Electron. 17, 516 (2011).
[Crossref]

IEEE Photon. J. (2)

C. Ciminelli, F. Dell’Olio, M. N. Armenise, IEEE Photon. J. 4, 1844 (2012).
[Crossref]

J. F. Bauters, M. J. R. Heck, D. Dai, J. S. Barton, D. J. Blumenthal, J. E. Bowers, IEEE Photon. J. 5, 6600207 (2013).
[Crossref]

J. Electrochem. Soc. (1)

H. R. Philipp, J. Electrochem. Soc. 120, 295 (1973).
[Crossref]

J. Lightwave Technol. (3)

Laser Photon. Rev. (1)

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmany, Laser Photon. Rev. 7, 506 (2013).
[Crossref]

Opt. Express (10)

Opt. Lett. (1)

Other (4)

D. T. Spencer, Y. Tang, J. F. Bauters, M. J. R. Heck, J. E. Bowers, in IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 141–142.

M. J. R. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, J. E. Bowers, “Ultra-low loss waveguide platform and its integration with silicon photonics,” Laser Photon. Rev., doi: 10.1002/lpor.201300183 (posted online March 5, 2014).

J. R. Vig, “Introduction to quartz frequency standards,” (U.S. Army Electronics Technology and Devices Laboratory, 1992).

P. Maddaloni, M. Bellini, P. De Natale, Laser-Based Measurements for Time and Frequency Domain Applications (Taylor & Francis, 2013).

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Figures (7)

Fig. 1.
Fig. 1. State-of-the-art resonator comparison of Qint versus bend radius for integrated waveguide-coupled resonators [6,816]. The propagation loss (α) and FSR are scaled assuming λ=1550nm, neff=ng=1.5, and lossless directional couplers according to Eq. (1). UCSB Si3N4 results [15,16], including this Letter, are highlighted in red triangles.
Fig. 2.
Fig. 2. Theoretically obtainable Qint for a given directional coupler excess loss value, γ, and propagation loss, α, according to Eq. (1).
Fig. 3.
Fig. 3. (a) Waveguide cross section and (b)–(d) all supported modes of the 11μm×40nm Si3N4 core geometry at a 9.65 mm bending radius, simulated with FIMMWAVE.
Fig. 4.
Fig. 4. Directional coupler layouts for ring resonators. The tapering of the gap is strongest for (a) symmetric coupling and identical for the (b) straight and (c) pulley couplers, while the (d) weakly tapered gap coupler smoothes the gap transition. We fabricated straight and weakly tapered gap couplers in this study.
Fig. 5.
Fig. 5. Simulated TE effective and group indices for the 11μm×40nm Si3N4 multimode waveguides studied in this Letter. Due to the fundamental TE0 mode having a higher group index, there will be a relative resonance wavelength separation, Δλres and overall beat wavelength, λbeat (inset).
Fig. 6.
Fig. 6. Relative resonance wavelengths and ERs for the TE0 and TE1 modes across the region of interest. All numbers are taken relative to the fundamental TE0 mode and averaged over multiple closely spaced resonances every 5 nm. The weakly tapered gap directional coupler resonator shows a beat wavelength of 73 nm similar to that of a straight directional coupler resonator, with an increase in absolute and relative ER.
Fig. 7.
Fig. 7. Resonator spectra and fits near 1580 nm for three different directional coupler designs: (a) 5 μm straight bus waveguide, (b) 3.8 μm straight bus waveguide, and (c) 3.8 μm weakly tapered gap waveguide.

Tables (1)

Tables Icon

Table 1. Measured and Extracted Resonator Parameters for the Three Directional Coupler Designs Studied at 1580 nm, Assuming No Parasitic Losses (γ=0)a

Equations (2)

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Qload=2πneffLλ[κ+αL+γ]1.
ngTE0ngTE1=1+1m.

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