Abstract

We demonstrate broadband frequency comb generation in the mid-infrared (MIR) from 2.3 to 3.5 μm in a Si3N4 microresonator. We engineer the dispersion of the structure in the MIR using a Sellmeier equation we derive from experimental measurements performed on Si3N4 films from the UV to the IR. We use deposition–anneal cycling to decrease absorption losses due to vibrational transitions in the MIR and achieve a Q-factor of 1.0×106. To our knowledge, this is the highest Q reported in this wavelength range for any on-chip resonator.

© 2015 Optical Society of America

Microresonator-based parametric frequency combs are of interest for applications such as precision frequency metrology, optical clocks, and absorption spectroscopy [15] because of their narrow linewidths and precise frequency spacing. Comb generation in the mid-infrared (MIR) wavelength range (2–20 μm) is of particular interest for spectroscopy of characteristic molecular vibrational transitions and for trace-gas sensing within the Earth’s atmospheric transparency window [6]. Some MIR comb sources have been demonstrated in fiber lasers, mode-locked lasers, and optical parametric oscillators [79], but these systems are either bulky or limited in power per comb line. Microresonator-based combs, in contrast, provide compact, robust systems that require relatively low operating power, but few have been demonstrated in the MIR [1013].

The key to generating MIR combs based on microresonators is to engineer the resonator dispersion; however, this is challenging due to the low waveguide dispersion in this spectral range. The parametric four-wave mixing process that is responsible for comb generation typically requires anomalous group velocity dispersion (GVD) to enforce proper phase matching. However, most materials have strongly normal material dispersion. In telecom comb generation, anomalous GVD is typically achieved by engineering the geometry of the resonator to modify the waveguide dispersion of the resonator, which can compensate for inadequate material dispersion. It should be noted that some materials—for example, barium fluoride—have naturally anomalous material dispersion that can be further tuned with resonator geometry [14]. However, many low-loss MIR materials have low refractive indices, which results in lower index contrast. This reduces the impact of waveguide dispersion on the overall dispersion of the resonator. Because the waveguide dispersion can be geometrically tuned while other sources of dispersion are fixed by material properties, engineering overall anomalous dispersion is challenging.

We characterize the optical properties of Si3N4 in the MIR and show that it can be used as a material that can provide strong enough waveguide dispersion to generate wide spectral combs in this regime. The optical properties of Si3N4 have been characterized in the telecom wavelength range and shorter wavelengths [15,16] but not in the MIR. This is mainly because in this regime, due to lack of wide spectral sources in typical ellipsometers, the film properties are typically extrapolated from the Sellmeier coefficients derived from the (lower wavelength) measurable range of ellipsometers. Although Sellmeier equations are considered valid within the transparent region of a material, this is only true if all absorption resonances contributing to the optical properties are included in the Sellmeier equation. However, Si3N4 is known to have a strong absorption peak near 10 μm, which can strongly influence the optical properties at shorter wavelengths.

We derive a Sellmeier equation for Si3N4 for the MIR spectral range based on measured optical properties from the UV (193 nm) up to the far IR (33 μm). These results were obtained in collaboration with J.A. Woollam Co., the leading manufacturer of spectroscopic ellipsometers. The sample consisted of 340 nm Si3N4 on 3.1 μm of thermal SiO2 on silicon. In order to isolate the optical properties of the Si3N4 from the properties of the thermal oxide and silicon in this spectral range, samples consisting of uncoated silicon and a sample of 4.6 μm of thermally grown SiO2 on silicon were also measured. The Si3N4 sample was deposited via low-pressure chemical vapor deposition (LPCVD) and then annealed for 3 h at 1200°C. J.A. Woollam then measured these samples using M-2000 and IR-VASE instruments over the 193–1690 nm and 1.7–33 μm wavelength ranges, respectively. The data were fit to Lorentzian and Gaussian oscillator models (Fig. 1) and then simultaneously fit over both spectral ranges to obtain the following Sellmeier equation for Si3N4:

nSiN2=1+3.0249λ2λ2135.34062+40314λ2λ212398422.

 

Fig. 1. Refractive index n and extinction coefficient k for the wavelength range 1.4–32 μm. Extrapolation from NIR Sellmeier equations (blue) shows no influence from the MIR absorption peak, as expected. However, the measured absorption peak near 10 μm (red) strongly influences the measured refractive index (green), and the fitted Sellmeier equation (dotted green) agrees well with the measurement in the spectral range between 1.4 and 4 μm (see inset). As shown in the inset, at shorter wavelengths, even as far as the telecom wavelength range, the refractive index is significantly influenced by the MIR absorption peak.

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This equation is valid over the wavelength range 310–5504 nm, with λ in units of nanometer. Note that this equation is significantly different from the traditional Sellmeier equation based on ellipsometry measurements in the near-infrared (NIR, see Fig. 1) [15,16]. As expected, the absorption peak near 10 μm influences the refractive index strongly as it approaches the wavelength of the absorption peak. Another Sellmeier equation was obtained for SiO2, which matched literature values well [15]. We use this equation to model the Si3N4 layer for dispersion engineering in the MIR.

In order to achieve anomalous dispersion in the MIR, we use large film thickness, well beyond the thicknesses typically limited by the intrinsic film stress. We engineer the dispersion of our resonator by choosing the height and width of the rectangular waveguide cross section to yield anomalous GVD. A waveguide height of almost a micrometer is required to sufficiently confine the optical mode of the waveguide to the core in order to achieve adequate waveguide dispersion.

We achieve the large film thicknesses required for anomalous GVD using crack isolation trenches detailed in [17]. These trenches are made using a diamond scribe prior to Si3N4 film deposition. These trenches ensure that threading dislocations are terminated well before reaching the critical device area. This technique allows us to access film thicknesses beyond the traditional limit of 750 nm [18]. For this work, we use a film thickness of 950 nm and a waveguide width of 2.7 μm.

We develop a method for estimating material absorption losses as a tool for improving material absorption for the MIR. Absorption in the MIR is critical due to the vibrational absorption transitions in this wavelength range. In particular, trapped hydrogen impurities within thin films can introduce absorption bands in the MIR. Adapting the method developed by Borselli et al. [19], we estimate the amount of absorption by measuring the resonance shift as a function of power. Because Si3N4 has negligible nonlinear losses in the MIR and no free carriers, resonance shift is dominated by thermal effects. We can therefore link this thermal resonance shift Δλth to the increase in absorbed optical power ΔPabs via the group index ng, the low power resonance wavelength λ0, the effective thermo-optic coefficient (dn/dT)eff, the thermal conductance κth, and the round-trip path length of the resonator L:

Δλthng/λ0Δn(dn/dT)eff1ΔTκthLΔPabs.

The values for Δλth and λ0 are measured experimentally, whereas ng, (dn/dT)eff, and κth are determined via simulation of the resonator cross section and known material constants. To calculate (dn/dT)eff, we weight the different thermo-optic coefficients of the different materials of the resonator cross section (in this case silicon nitride and silicon dioxide) by the optical mode confinement in that material. For the geometry used in this work, (dn/dT)eff is dominated by (dn/dT)SiN. From characterization at low optical power, we can determine the dropped power Pd, corresponding to the total amount of power lost in the resonator, from the minimum resonant transmission Tmin:

ΔPd=(1Tmin)ΔPin.

Combining Eqs. (2) and (3), we obtain an expression for the ratio of absorption loss to total loss, ηabs:

ηabs=ΔPabsΔPd=κthLngΔλthλ0(dndT)eff(1Tmin)ΔPin.

As we improve the material quality and device processing for MIR applications, we use ηabs as a tool to determine whether absorption loss, as opposed to scattering loss, is the dominant loss mechanism.

In order to reduce absorption losses in the film, we perform multiple anneals during film deposition to allow residual hydrogen to outgas before the film can become too thick to prevent hydrogen from diffusing to the film boundaries. We hypothesize that annealing successfully drives out residual hydrogen from the silicon oxide cladding but not from the silicon nitride core, since silicon nitride is an effective diffusion barrier. Hydrogen within the silicon nitride core will be prevented from diffusing to the nitride–oxide interface, where it can then outgas from the film. We perform multiple anneals during film deposition [Fig. 2(a)] to allow residual hydrogen to outgas before the film can become too thick to prevent hydrogen from diffusing to the film boundaries. We deposit a total of 950 nm Si3N4 via LPCVD at 800°C in layers of approximately 300 nm thickness, with an anneal of 1200°C in argon atmosphere for 3 h between each deposition layer. However, when processing on single-side-polished wafers, the imbalance in film stress between the frontside and backside of the wafer leads to wafer bowing of up to 170 μm on a 4 inch wafer after the intermediate anneal step. This extreme wafer bow precludes further processing, because electron beam lithography tools cannot properly expose on wafers with large height variations. In addition, photolithography processes suffer from nonuniformity across wafers with extreme wafer bow. To prevent wafer bowing, we instead process on double-side-polished wafers. Although the films on the frontside and backside remain stressed, the stresses are balanced such that the wafer no longer bows. In order to maintain balanced stress, we must also process the backside throughout fabrication, as detailed below.

 

Fig. 2. (a) Schematic of the deposition–anneal cycling process. After the thermal oxide undercladding and trenches are formed, we deposit silicon nitride via LPCVD and then anneal at 1200°C. We deposit another silicon nitride layer, anneal, and then deposit the final layer. The final layer is annealed before cladding the devices. (b) Scanning electron microscope image of fabricated ring resonator of radius 230 μm and gap of 860 nm. We implement an adiabatic coupling region as in [20] to minimize excitation of higher order modes. (c) Schematic of resonator cross section of 950 nm tall by 2.7 μm wide.

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Using the techniques described above, we fabricate Si3N4 microring resonators (Fig. 2) with a Q of 1.0×106. We begin fabrication with double-side-polished silicon wafers and then oxidize 4.5 μm of silicon oxide. Using a diamond scribe, we define crack isolation trenches as in [17]. We then deposit a total of 950 nm Si3N4 via LPCVD and anneal cycling, as mentioned above. We then proceed with fabrication as detailed in [17]. Following deposition of 500 nm of high temperature oxide cladding, we etch the Si3N4 film on the backside of the wafer in order to balance film stress between the frontside and the backside of the wafer. This is necessary to prevent excessive wafer bowing after annealing in the next step. We anneal again in order to drive out hydrogen impurities from the third layer of Si3N4. After 2 μm deposition of silicon oxide using plasma enhanced chemical vapor deposition (PECVD), we dry oxidize the sample for 3 h and then anneal in nitrogen atmosphere for 3 h at 1200°C in order to increase the oxide quality and drive out residual hydrogen from the PECVD oxide. We measure a Q of 1.0×106 for this device at λ0=2.6μm. This is, to our knowledge, the highest Q reported in this wavelength range for any on-chip resonator.

In order to verify that multiple annealing during film deposition is necessary to enable hydrogen impurities to diffuse out of the Si3N4 film, we also measure a device fabricated using a single anneal and show that the optical quality is indeed much lower. We achieve high optical quality films in the MIR with low absorption losses using a high temperature anneal. We fabricate resonators as detailed in [17], with a cross section 910 nm tall by 2.4 μm wide and round-trip path length of 1.8 mm. For this geometry, we determine via simulation ng=2.12, (dn/dT)eff=3.5×105K1, and κth=3.7×105W/K·μm at λ0=2.6μm. From low power characterization (Fig. 3), we measure an intrinsic quality factor (Q) of 55,000. From high power characterization, we measure a resonance shift of 0.5 nm for 115 mW increase in optical power, resulting in ηabs=0.9, corresponding to absorption loss of 3.7 dB/cm, which indicates that losses are heavily dominated by absorption. This absorption may be due to residual hydrogen in the silicon nitride core and silicon oxide cladding, since hydrogen bonds are known to absorb in the MIR. We drive out this residual hydrogen by annealing the devices at 1100°C in argon atmosphere for 13 h. We repeat low power (Fig. 3) and high power characterization on the same resonator and measure a Q of 200,000 and ηabs=0.6, corresponding to absorption loss of 0.6 dB/cm. Although the increase in Q demonstrates that we have successfully improved the material quality in the MIR, ηabs reveals that losses are still dominated by absorption. This suggests that residual hydrogen impurities remain trapped within the Si3N4 film despite the long anneal. Therefore, multiple annealing during film deposition is critical for outgassing the hydrogen impurities within the film.

 

Fig. 3. Resonance spectrum measured around λ0=2.6μm for devices fabricated with single anneal during Si3N4 film deposition but without post-fabrication annealing (blue), with post-fabrication annealing (green) and multiple annealing (red) during Si3N4 film deposition. For devices with cross section 910 nm tall by 2.4 μm wide, the Q improves from Q=55,000 with single anneal during deposition (blue) to Q=200,000 after a long post-fabrication anneal for 13 h at 1100°C (green). The resonance extinction increases as expected, since reduction in losses transitions the resonance from the undercoupled to critically coupled regime. With multiple annealing during film deposition (red, inset) of devices with cross sections 950 nm tall by 2.7 μm wide (the devices used for comb generation in this work), the Q improves to Q=1,000,000.

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We generate a frequency comb by pumping a cavity resonance of a Si3N4 microring resonator with a tunable optical parametric oscillator source based on periodically poled lithium niobate using the sample that was annealed multiple times during deposition. For this experiment, we use the microring resonator shown in Fig. 2. We use a half-wave plate to adjust input polarization and a lens to focus the pump beam onto the nanotaper coupler of the Si3N4 bus waveguide. The light then couples into a ring resonator of radius 230 μm and a cross section 950 nm tall by 2.7 μm wide. We collect the output with a lens and measure the comb spectrum with a Fourier transform infrared (FTIR) spectrometer while monitoring a portion of the output on an InGaAs photodiode. To generate the frequency comb, we gradually tune the pump wavelength into resonance, which increases the circulating power in the resonator. After tuning partially into resonance, parametric oscillation and then cascaded FWM occur. As we tune further into resonance, the remaining comb lines fill in, resulting in frequency comb generation.

We experimentally demonstrate a frequency comb spanning from 2.3 to 3.5 μm, shown in Fig. 4(a), which represents the broadest frequency comb in the MIR demonstrated in a passive microresonator platform. Although a slightly broader comb was demonstrated in [10], that comb was demonstrated in an active device, in which continuous carrier extraction was required to achieve comb generation. This comb has a free spectral range of 99 GHz, and it is generated with a 2.6 μm pump. The pump power for the generated comb is 500 mW, and we measure the threshold power to be 80 mW. The resonator has an intrinsic quality factor (Q) of 1.0×106 and an extinction ratio of 95% at the pump wavelength. Although the Q in this work is significantly higher than in [10], the lower material nonlinearity and the larger mode volume result in higher pump powers required. RF amplitude noise measurements of the comb with a fast photodiode do not show a reduction in RF noise, indicating that the comb has not transitioned to a phase-locked state. However, based on the Lugiato–Lefever model [21] [Fig. 4(b)], the comb is in the pump power range for transitioning to a phase-locked state, but this transition is sensitive to the pump power, resonance detuning, and coupling conditions between the bus waveguide and the resonator [22]. For this experiment, instability in the setup due to high optical power precluded fine adjustment of pump power and resonance detuning. In the future, optical microresonators with integrated microheaters and/or with higher optical quality factors could alleviate this constraint and enable transitions to phase-locked states. The Q may be improved with optimized etching and with thinner Si3N4 deposition-anneal cycling.

 

Fig. 4. (a) Experimentally generated frequency comb spanning 2.3 to 3.5 μm. The different noise floors are due to optical filtering necessary to overcome the limited dynamic range of the FTIR. Inset shows the dispersive wave beginning to form, as predicted by simulations in (b).

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We have experimentally demonstrated the broadest frequency comb in the MIR generated in a passive microresonator platform. Using deposition–anneal cycling and crack isolation trenches, we overcome material loss and dispersion limitations that have previously prevented MIR comb generation in Si3N4. This work could provide a platform for spectroscopy and gas sensing in the MIR wavelength range.

Funding

Defense Advanced Research Projects Agency (DARPA) (BAA-AFOSR-2012-02, W31P4Q-13-1-0016, W911NF-11-1-0202); National Science Foundation (NSF) (DGE-0903653).

Acknowledgment

We thank Ron Synowicki from J.A. Woollam Co. for his help with measurement and data analysis for optical characterization in the MIR.

REFERENCES

1. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011). [CrossRef]  

2. T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002). [CrossRef]  

3. H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, Optica 1, 396 (2014). [CrossRef]  

4. S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015). [CrossRef]  

5. S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007). [CrossRef]  

6. A. Schliesser, N. Picqué, and T. W. Hänsch, Nat. Photonics 6, 440 (2012). [CrossRef]  

7. P. Maddaloni, P. Malara, G. Gagliardi, and P. D. Natale, New J. Phys. 8, 262 (2006). [CrossRef]  

8. E. Sorokin, I. T. Sorokina, J. Mandon, G. Guelachvili, and N. Picqué, Opt. Express 15, 16540 (2007). [CrossRef]  

9. F. Adler, K. C. Cossel, M. J. Thorpe, I. Hartl, M. E. Fermann, and J. Ye, Opt. Lett. 34, 1330 (2009). [CrossRef]  

10. A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015). [CrossRef]  

11. C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013). [CrossRef]  

12. C. Lecaplain, C. Javerzac-Galy, E. Lucas, J. D. Jost, and T. J. Kippenberg, “Quantum cascade laser Kerr frequency comb,” arXiv: 1506.00626 (2015).

13. A. A. Savchenkov, V. S. Ilchenko, F. Di Teodoro, P. M. Belden, W. T. Lotshaw, A. B. Matsko, and L. Maleki, Opt. Lett. 40, 3468 (2015). [CrossRef]  

14. G. Lin and Y. K. Chembo, Opt. Express 23, 1594 (2015). [CrossRef]  

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

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

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

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

19. M. Borselli, T. J. Johnson, and O. Painter, Opt. Express 13, 1515 (2005). [CrossRef]  

20. D. T. Spencer, J. F. Bauters, M. J. R. Heck, and J. E. Bowers, Optica 1, 153 (2014). [CrossRef]  

21. M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, Opt. Lett. 38, 3478 (2013). [CrossRef]  

22. A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2845 (2011). [CrossRef]  

References

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  1. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
    [Crossref]
  2. T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
    [Crossref]
  3. H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, Optica 1, 396 (2014).
    [Crossref]
  4. S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
    [Crossref]
  5. S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
    [Crossref]
  6. A. Schliesser, N. Picqué, and T. W. Hänsch, Nat. Photonics 6, 440 (2012).
    [Crossref]
  7. P. Maddaloni, P. Malara, G. Gagliardi, and P. D. Natale, New J. Phys. 8, 262 (2006).
    [Crossref]
  8. E. Sorokin, I. T. Sorokina, J. Mandon, G. Guelachvili, and N. Picqué, Opt. Express 15, 16540 (2007).
    [Crossref]
  9. F. Adler, K. C. Cossel, M. J. Thorpe, I. Hartl, M. E. Fermann, and J. Ye, Opt. Lett. 34, 1330 (2009).
    [Crossref]
  10. A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
    [Crossref]
  11. C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
    [Crossref]
  12. C. Lecaplain, C. Javerzac-Galy, E. Lucas, J. D. Jost, and T. J. Kippenberg, “Quantum cascade laser Kerr frequency comb,” arXiv: 1506.00626 (2015).
  13. A. A. Savchenkov, V. S. Ilchenko, F. Di Teodoro, P. M. Belden, W. T. Lotshaw, A. B. Matsko, and L. Maleki, Opt. Lett. 40, 3468 (2015).
    [Crossref]
  14. G. Lin and Y. K. Chembo, Opt. Express 23, 1594 (2015).
    [Crossref]
  15. T. Bååk, Appl. Opt. 21, 1069 (1982).
    [Crossref]
  16. H. R. Philipp, J. Electrochem. Soc. 120, 295 (1973).
    [Crossref]
  17. K. Luke, A. Dutt, C. B. Poitras, and M. Lipson, Opt. Express 21, 22829 (2013).
    [Crossref]
  18. A. Gondarenko, J. S. Levy, and M. Lipson, Opt. Express 17, 11366 (2009).
    [Crossref]
  19. M. Borselli, T. J. Johnson, and O. Painter, Opt. Express 13, 1515 (2005).
    [Crossref]
  20. D. T. Spencer, J. F. Bauters, M. J. R. Heck, and J. E. Bowers, Optica 1, 153 (2014).
    [Crossref]
  21. M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, Opt. Lett. 38, 3478 (2013).
    [Crossref]
  22. A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2845 (2011).
    [Crossref]

2015 (4)

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
[Crossref]

G. Lin and Y. K. Chembo, Opt. Express 23, 1594 (2015).
[Crossref]

A. A. Savchenkov, V. S. Ilchenko, F. Di Teodoro, P. M. Belden, W. T. Lotshaw, A. B. Matsko, and L. Maleki, Opt. Lett. 40, 3468 (2015).
[Crossref]

S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

2014 (2)

2013 (3)

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, Opt. Lett. 38, 3478 (2013).
[Crossref]

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

2012 (1)

A. Schliesser, N. Picqué, and T. W. Hänsch, Nat. Photonics 6, 440 (2012).
[Crossref]

2011 (2)

2009 (2)

2007 (2)

2006 (1)

P. Maddaloni, P. Malara, G. Gagliardi, and P. D. Natale, New J. Phys. 8, 262 (2006).
[Crossref]

2005 (1)

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[Crossref]

1982 (1)

1973 (1)

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

Adler, F.

Bååk, T.

Bauters, J. F.

Belden, P. M.

Borselli, M.

Bowers, J. E.

Cardenas, J.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
[Crossref]

Chembo, Y. K.

Cossel, K. C.

Del’Haye, P.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

Di Teodoro, F.

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[Crossref]

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[Crossref]

Dutt, A.

Fain, R.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
[Crossref]

Fermann, M. E.

Fischer, D.

Gaeta, A. L.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
[Crossref]

M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, Opt. Lett. 38, 3478 (2013).
[Crossref]

Gagliardi, G.

P. Maddaloni, P. Malara, G. Gagliardi, and P. D. Natale, New J. Phys. 8, 262 (2006).
[Crossref]

Gondarenko, A.

Griffith, A. G.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
[Crossref]

Guelachvili, G.

Guo, X.

Hänsch, T. W.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

A. Schliesser, N. Picqué, and T. W. Hänsch, Nat. Photonics 6, 440 (2012).
[Crossref]

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C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
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Jost, J. D.

C. Lecaplain, C. Javerzac-Galy, E. Lucas, J. D. Jost, and T. J. Kippenberg, “Quantum cascade laser Kerr frequency comb,” arXiv: 1506.00626 (2015).

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Kippenberg, T. J.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
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C. Lecaplain, C. Javerzac-Galy, E. Lucas, J. D. Jost, and T. J. Kippenberg, “Quantum cascade laser Kerr frequency comb,” arXiv: 1506.00626 (2015).

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S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
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Lau, R. K. W.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
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C. Lecaplain, C. Javerzac-Galy, E. Lucas, J. D. Jost, and T. J. Kippenberg, “Quantum cascade laser Kerr frequency comb,” arXiv: 1506.00626 (2015).

Lee, Y. H. D.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
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Liang, W.

Lin, G.

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C. Lecaplain, C. Javerzac-Galy, E. Lucas, J. D. Jost, and T. J. Kippenberg, “Quantum cascade laser Kerr frequency comb,” arXiv: 1506.00626 (2015).

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P. Maddaloni, P. Malara, G. Gagliardi, and P. D. Natale, New J. Phys. 8, 262 (2006).
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S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
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P. Maddaloni, P. Malara, G. Gagliardi, and P. D. Natale, New J. Phys. 8, 262 (2006).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
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C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
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A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
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C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
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Wang, C. Y.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

Wong, C. W.

S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Yang, J.

S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Ye, J.

Yu, M.

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
[Crossref]

S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Zhou, H.

S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
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Appl. Opt. (1)

J. Electrochem. Soc. (1)

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

Nat. Commun. (2)

A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, Nat. Commun. 6, 6299 (2015).
[Crossref]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, Nat. Commun. 4, 1345 (2013).
[Crossref]

Nat. Photonics (1)

A. Schliesser, N. Picqué, and T. W. Hänsch, Nat. Photonics 6, 440 (2012).
[Crossref]

Nature (2)

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[Crossref]

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[Crossref]

New J. Phys. (1)

P. Maddaloni, P. Malara, G. Gagliardi, and P. D. Natale, New J. Phys. 8, 262 (2006).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Optica (2)

Phys. Rev. Lett. (1)

S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

Science (1)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[Crossref]

Other (1)

C. Lecaplain, C. Javerzac-Galy, E. Lucas, J. D. Jost, and T. J. Kippenberg, “Quantum cascade laser Kerr frequency comb,” arXiv: 1506.00626 (2015).

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Figures (4)

Fig. 1.
Fig. 1. Refractive index n and extinction coefficient k for the wavelength range 1.4–32 μm. Extrapolation from NIR Sellmeier equations (blue) shows no influence from the MIR absorption peak, as expected. However, the measured absorption peak near 10 μm (red) strongly influences the measured refractive index (green), and the fitted Sellmeier equation (dotted green) agrees well with the measurement in the spectral range between 1.4 and 4 μm (see inset). As shown in the inset, at shorter wavelengths, even as far as the telecom wavelength range, the refractive index is significantly influenced by the MIR absorption peak.
Fig. 2.
Fig. 2. (a) Schematic of the deposition–anneal cycling process. After the thermal oxide undercladding and trenches are formed, we deposit silicon nitride via LPCVD and then anneal at 1200°C. We deposit another silicon nitride layer, anneal, and then deposit the final layer. The final layer is annealed before cladding the devices. (b) Scanning electron microscope image of fabricated ring resonator of radius 230 μm and gap of 860 nm. We implement an adiabatic coupling region as in [20] to minimize excitation of higher order modes. (c) Schematic of resonator cross section of 950 nm tall by 2.7 μm wide.
Fig. 3.
Fig. 3. Resonance spectrum measured around λ 0 = 2.6 μm for devices fabricated with single anneal during Si 3 N 4 film deposition but without post-fabrication annealing (blue), with post-fabrication annealing (green) and multiple annealing (red) during Si 3 N 4 film deposition. For devices with cross section 910 nm tall by 2.4 μm wide, the Q improves from Q = 55,000 with single anneal during deposition (blue) to Q = 200,000 after a long post-fabrication anneal for 13 h at 1100°C (green). The resonance extinction increases as expected, since reduction in losses transitions the resonance from the undercoupled to critically coupled regime. With multiple annealing during film deposition (red, inset) of devices with cross sections 950 nm tall by 2.7 μm wide (the devices used for comb generation in this work), the Q improves to Q = 1,000,000 .
Fig. 4.
Fig. 4. (a) Experimentally generated frequency comb spanning 2.3 to 3.5 μm. The different noise floors are due to optical filtering necessary to overcome the limited dynamic range of the FTIR. Inset shows the dispersive wave beginning to form, as predicted by simulations in (b).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

n SiN 2 = 1 + 3.0249 λ 2 λ 2 135.3406 2 + 40314 λ 2 λ 2 1239842 2 .
Δ λ th n g / λ 0 Δ n ( d n / d T ) eff 1 Δ T κ th L Δ P abs .
Δ P d = ( 1 T min ) Δ P in .
η abs = Δ P abs Δ P d = κ th L n g Δ λ th λ 0 ( d n d T ) eff ( 1 T min ) Δ P in .

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