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High-Q slow light and its localization in a photonic crystal microring

Nature Photonics volume 16, pages 66–71 (2022)Cite this article

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Abstract

We introduce a photonic crystal ring cavity that resembles an internal gear and unites photonic crystal (PhC) and whispering gallery mode (WGM) concepts. This ‘microgear’ photonic crystal ring (MPhCR) is created by applying a periodic modulation to the inside boundary of a microring resonator to open a large bandgap, as in a PhC cavity, while maintaining the ring’s circularly symmetric outside boundary and high optical quality factor (Q), as in a WGM cavity. The MPhCR targets a specific WGM to open a large PhC bandgap up to tens of free spectral ranges, compressing the mode spectrum while maintaining the high-Q, angular momenta and waveguide coupling properties of the WGM modes. In particular, near the dielectric band edge, we observe modes whose group velocity is slowed down by 10 times relative to conventional microring modes while supporting Q = (1.1 ± 0.1) × 106. This Q is around 50 times that of the previous record in slow-light devices. Using the slow-light design as a starting point, we further demonstrate the ability to localize WGMs into photonic crystal defect modes, enabling a more than 10 times reduction of mode volume compared with conventional WGMs while maintaining a high Q value of up to (5.6 ± 0.1) × 105. Importantly, this additional photonic crystal defect localization is achievable without requiring detailed electromagnetic design. Moreover, controlling their resonance frequencies and waveguide coupling is straightforward in the MPhCR, owing to its WGM heritage. In using a PhC to strongly modify the fundamental properties of WGMs, such as group velocity and localization, the MPhCR provides an exciting platform for a broad range of photonics applications, including sensing/metrology, nonlinear optics and cavity quantum electrodynamics.

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Fig. 1: MPhCR, a high-Q slow-light photonic crystal microring.
Fig. 2: Slow light in the MPhCR.
Fig. 3: Defect modes in the MPhCR.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Vahala, K. J. Optical microcavities. Nature 424, 839–846 (2003).

    Article  ADS  Google Scholar 

  2. O’Brien, J. L., Furusawa, A. & Vučković, J. Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009).

    Article  ADS  Google Scholar 

  3. Strekalov, D. V., Marquardt, C., Matsko, A. B., Schwefel, H. G. L. & Leuchs, G. Nonlinear and quantum optics with whispering gallery resonators. J. Opt. 18, 123002 (2016).

    Article  ADS  Google Scholar 

  4. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    Article  ADS  Google Scholar 

  5. Vollmer, F. & Yang, L. Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices. Nanophotonics 1, 267–291 (2012).

    Article  ADS  Google Scholar 

  6. Matsko, A. B. & Ilchenko, V. S. Optical resonators with whispering gallery modes—part I: basics. IEEE J. Sel. Top. Quantum Electron. 12, 3–14 (2006).

    Article  ADS  Google Scholar 

  7. Istrate, E. & Sargent, E. H. Photonic crystal heterostructures and interfaces. Rev. Mod. Phys. 78, 455–481 (2006).

    Article  ADS  Google Scholar 

  8. Lu, X. et al. Efficient telecom-to-visible spectral translation using silicon nanophotonics. Nat. Photon. 13, 593–601 (2019).

    Article  ADS  Google Scholar 

  9. Smith, C. J. et al. Coupled guide and cavity in a two-dimensional photonic crystal. Appl. Phys. Lett. 78, 1487–1489 (2001).

    Article  ADS  Google Scholar 

  10. Kim, S. H. et al. Two-dimensional photonic crystal hexagonal waveguide ring laser. Appl. Phys. Lett. 81, 2499–2501 (2002).

    Article  ADS  Google Scholar 

  11. Zhang, Y. et al. High-quality-factor photonic crystal ring resonator. Opt. Lett. 39, 1282–1285 (2014).

    Article  ADS  Google Scholar 

  12. Lee, J. Y. & Fauchet, P. M. Slow-light dispersion in periodically patterned silicon microring resonators. Opt. Lett. 37, 58–60 (2012).

    Article  ADS  Google Scholar 

  13. Zhang, Y. et al. Slow-light dispersion in one-dimensional photonic crystal racetrack ring resonator. IEEE Photon. Technol. Lett. 27, 1120–1123 (2015).

    Article  ADS  Google Scholar 

  14. Gao, G. et al. Air-mode photonic crystal ring resonator on silicon-on-insulator. Sci. Rep. 6, 19999 (2016).

    Article  ADS  Google Scholar 

  15. McGarvey-Lechable, K. et al. Slow light in mass-produced, dispersion-engineered photonic crystal ring resonators. Opt. Express 25, 3916–3926 (2017).

    Article  ADS  Google Scholar 

  16. Lo, S. M., Lee, J. Y., Weiss, S. M. & Fauchet, P. M. Bloch mode selection in silicon photonic crystal microring resonators. Opt. Lett. 43, 2957–2960 (2018).

    Article  ADS  Google Scholar 

  17. Lu, X., Rogers, S., Jiang, W. C. & Lin, Q. Selective engineering of cavity resonance for frequency matching in optical parametric processes. Appl. Phys. Lett. 105, 151104 (2014).

    Article  ADS  Google Scholar 

  18. Arbabi, A., Kamali, S. M., Arbabi, E., Griffin, B. G. & Goddard, L. L. Grating integrated single mode microring laser. Opt. Express 23, 5335–5347 (2015).

    Article  ADS  Google Scholar 

  19. Yu, S. P. et al. Spontaneous pulse formation in edgeless photonic crystal resonators. Nat. Photon. 15, 461–467 (2021).

    Article  ADS  Google Scholar 

  20. Cai, X. et al. Integrated compact optical vortex beam emitters. Science 338, 363–366 (2012).

    Article  ADS  Google Scholar 

  21. Feng, L., Wong, Z. J., Ma, R.-M., Wang, Y. & Zhang, X. Single-mode laser by parity-time symmetry breaking. Science 346, 972–975 (2014).

    Article  ADS  Google Scholar 

  22. Krauss, T. F. Slow light in photonic crystal waveguides. J. Phys. D 40, 2666–2670 (2007).

    Article  ADS  Google Scholar 

  23. Yu, S. P. et al. Nanowire photonic crystal waveguides for single-atom trapping and strong light-matter interactions. Appl. Phys. Lett. 104, 111103 (2014).

    Article  ADS  Google Scholar 

  24. Baba, T. Slow light in photonic crystals. Nat. Photon. 2, 465–473 (2008).

    Article  ADS  Google Scholar 

  25. Arcari, M. et al. Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide. Phys. Rev. Lett. 113, 093603 (2014).

    Article  ADS  Google Scholar 

  26. Fujita, M. & Baba, T. Microgear laser. Appl. Phys. Lett. 80, 2051–2053 (2002).

    Article  ADS  Google Scholar 

  27. McGarvey-Lechable, K. & Bianucci, P. Maximizing slow-light enhancement in one-dimensional photonic crystal ring resonators. Opt. Express 22, 26032–26041 (2014).

    Article  ADS  Google Scholar 

  28. Shi, Z. & Boyd, R. W. Slow-light interferometry: practical limitations to spectroscopic performance. J. Opt. Soc. Am. B 25, C136–C143 (2008).

    Article  Google Scholar 

  29. Shi, Z., Boyd, R. W., Camacho, R. M., Vudyasetu, P. K. & Howell, J. C. Slow-light Fourier transform interferometer. Phys. Rev. Lett. 99, 240801 (2007).

    Article  ADS  Google Scholar 

  30. Boyd, R. W. Slow and fast light: fundamentals and applications. J. Mod. Opt. 56, 1908–1915 (2009).

    Article  MATH  ADS  Google Scholar 

  31. Vučković, J., Lončar, M., Mabuchi, H. & Scherer, A. Design of photonic crystal microcavities for cavity QED. Phys. Rev. E 65, 016608 (2001).

    Article  ADS  Google Scholar 

  32. Srinivasan, K. & Painter, O. Momentum space design of high-Q photonic crystal optical cavities. Opt. Express 10, 670–684 (2002).

    Article  ADS  Google Scholar 

  33. Englund, D., Fushman, I. & Vučković, J. General recipe for designing photonic crystal cavities. Opt. Express 13, 5961–5975 (2005).

    Article  ADS  Google Scholar 

  34. Asano, T., Song, B.-S., Akahane, Y. & Noda, S. Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs. IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).

    Article  ADS  Google Scholar 

  35. Quan, Q. & Loncar, M. Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities. Opt. Express 19, 18529–18542 (2011).

    Article  ADS  Google Scholar 

  36. Li, Q., Davanço, M. & Srinivasan, K. Efficient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics. Nat. Photon. 10, 406–414 (2016).

    Article  ADS  Google Scholar 

  37. Moille, G. et al. Broadband resonator-waveguide coupling for efficient extraction of octave-spanning microcombs. Opt. Lett. 44, 4737–4740 (2019).

    Article  ADS  Google Scholar 

  38. Lu, X. et al. Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics. Optica 6, 1535–1541 (2019).

    Article  ADS  Google Scholar 

  39. Marty, G., Combrié, S., Raineri, F. & De Rossi, A. Photonic crystal optical parametric oscillator. Nat. Photon. 15, 53–58 (2021).

    Article  ADS  Google Scholar 

  40. Lu, X., Rao, A., Moille, G., Westly, D. A. & Srinivasan, K. Universal frequency engineering for microcavity nonlinear optics: multiple selective mode splitting of whispering-gallery resonances. Photon. Res. 8, 1676–1686 (2020).

    Article  Google Scholar 

  41. Douglas, J. S. et al. Quantum many-body models with cold atoms coupled to photonic crystals. Nat. Photon. 9, 326–331 (2015).

    Article  ADS  Google Scholar 

  42. Ji, X., Roberts, S., Corato-Zanarella, M. & Lipson, M. Methods to achieve ultra-high quality factor silicon nitride resonators. APL Photon. 6, 071101 (2021).

    Article  ADS  Google Scholar 

  43. Lukin, D. M. et al. 4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics. Nat. Photon. 14, 330–334 (2020).

    Article  ADS  Google Scholar 

  44. Lodahl, P., Mahmoodian, S. & Stobbe, S. Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347–400 (2015).

    Article  MathSciNet  ADS  Google Scholar 

  45. Johnson, S. G. & Joannopoulos, J. D. Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis. Opt. Express 8, 173–190 (2001).

    Article  ADS  Google Scholar 

  46. Balram, K. C. et al. The nanolithography toolbox. J. Res. Natl Inst. Stand. Technol. 121, 464–475 (2016).

    Article  Google Scholar 

  47. Xu, Y., Li, Y., Lee, R. K. & Yariv, A. Scattering-theory analysis of waveguide-resonator coupling. Phys. Rev. E 62, 30–33 (2000).

    Article  Google Scholar 

  48. Afzal, F. O., Halimi, S. I. & Weiss, S. M. Efficient side-coupling to photonic crystal nanobeam cavities via state-space overlap. J. Opt. Soc. Am. B 36, 585–595 (2019).

    Article  ADS  Google Scholar 

  49. Kippenberg, T. J., Spillane, S. M. & Vahala, K. J. Modal coupling in traveling-wave resonators. Opt. Lett. 27, 1669–1671 (2002).

    Article  ADS  Google Scholar 

  50. Hughes, S., Ramunno, L., Young, J. F. & Sipe, J. E. Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity. Phys. Rev. Lett. 94, 033903 (2005).

    Article  ADS  Google Scholar 

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Acknowledgements

This work is supported by the DARPA SAVaNT and NIST-on-a-chip programs. X.L. acknowledges support under the Cooperative Research Agreement between the University of Maryland and NIST-PML, award no. 70NANB10H193. We thank Z. Shi and V. Aksyuk for helpful discussions.

Author information

Authors and Affiliations

  1. Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA

    Xiyuan Lu & Kartik Srinivasan

  2. Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD, USA

    Xiyuan Lu

  3. Department of Electrical and Computer Engineering, University of Massachusetts Amherst, Amherst, MA, USA

    Andrew McClung

  4. Joint Quantum Institute, NIST/University of Maryland, College Park, MD, USA

    Kartik Srinivasan

Authors
  1. Xiyuan Lu
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  2. Andrew McClung
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Contributions

X.L. led the design, fabrication and measurement of the MPhCR devices. A.M. led the simulation with help from X.L., and all authors participated in the analysis and discussion of the results. X.L. and K.S. wrote the manuscript with assistance from A.M., and K.S. supervised the project.

Corresponding authors

Correspondence to Xiyuan Lu or Kartik Srinivasan.

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Competing interests

NIST has filed a provisional patent application, with X.L. and K.S. listed as inventors, related to the work presented in this article.

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Peer review information Nature Photonics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Simulated band diagrams and mode profiles of MPhCR devices.

a, Simulated photonic bands for the MPhCR devices experimentally studied in Fig. 2e, with A varying from 550 nm (darker blue) to 1150 nm (purple), as well as the control device (grey). The solid black lines correspond to the light cone with n = 1.44, the refractive index of the silica substrate. The slow light modes at the air band-edge (a0) and dielectric band-edge (s0) of the device with A = 550 nm (blue) are highlighted by open circles. b-e, Finite-element method (FEM) simulations of a unit cell for the a0 and s0 modes, displayed from a top view (b,d) over one period of the optical field as well as in a cross-section view (c,e). Both modes have dominant electric fields in the radial (horizontal) direction. The resonance frequencies are 193.9 THz and 191.1 THz, within 1 THz of the experimental data (Fig. 2e,g). These a0 and s0 modes have unit cell mode volumes of V = 0.29(λ/n)3 and V = 0.35(λ/n)3 with confinement factors of η = 71 % and η = 84 %, respectively. The mode volumes for a0 and s0, containing 162 cells, are 47(λ/n)3 and 56(λ/n)3. See Methods for more details on the simulations and definition of mode volume and confinement factor.

Extended Data Fig. 2 Simulated mode profiles and mode volumes for the unit cell and the photonic crystal defect modes build on this cell.

a,b, Top view and cross-section view of s0 FEM-simulated mode profiles in a unit cell with m = 162 and A = 1150 nm. The calculated resonance frequency is 191.0 THz, within 1 THz of the experimental data (Fig. 2e). The mode volume for a unit cell is 0.20 μm3, that is, 0.40(λ/n)3, with η = 86 % confinement factor in Si3N4. The mode volume of s0 over the whole ring is 64(λ/n)3. c, Photonic crystal (PhC) defects can be built based on (a). Such dPhC cavity modes are created by a reduction in A (Δ) by 10 % (magenta) to 30 % (black) at the defect center, and a quadratic grading in A over N cells is shown. The mode volumes can be further optimized by using a larger Δ and an optimized N, or using material stacks with larger refractive index contrasts, for example, silicon on insulator (SOI). d,e, Two examples of the dPhC mode (g) with {N, Δ} = {16, 30 %} and {48, 10 %}, with mode volumes of 3.3(λ/n)3 and 5.5(λ/n)3, respectively.

Extended Data Fig. 3 Supporting data for slow light MPhCR.

a, Characterization of a slow light device with A = 550 nm modulation. This modulation opens up a 29 nm separation between modes in the middle of the spectrum. Comparing this device to the bare microring (Fig. 2c), we see that the air band and dielectric band are symmetrically located, which is atypical to most photonic crystal designs. The dielectric band, for example, shows a singlet resonance at the band-edge (s0), and doublet resonances for all other slow light modes (s1 and s2 shown here). The s0 mode in this device has a SR of 4.29 ± 0.01 (uncertainty propagated from the FSR between s0 and s1±, see Methods for details) and Q0 = (4.4 ± 0.1) × 105 (uncertainty from one-standard deviation in nonlinear fitting). b, Extraction of SR for devices with A from 550 nm (darker blue) to 1150 nm (purple) using free spectral ranges (see Methods). Dashed lines are for guidance in viewing. The red vertical dashed line at Δm = 0.5 is used to estimate the SR of s0 mode, whose values are shown versus A in the inset (red). The SR is closely related to the ‘hyperbolic’ index ζ, the parameter describing the curvature of the dielectric band (blue). See Methods for the equation for ζ. c,Q analysis of the s0 modes of slow light devices for control devices (A = 0 nm) and MPhCR devices with A from 550 nm to 1150 nm. Devices with two waveguide-ring coupling gaps (Gs) are shown with G = 500 nm (blue) and G = 650 nm (red). In general, there seems to exist parasitic loss for MPhCR devices, that is, extra loss (reduced Q0 effectively) induced by coupling, in G = 500 nm cases.

Extended Data Fig. 4 Supporting data on improving Q of the MPhCR.

a, A slow-light device after optimization shows SR = 10 ± 2 for s0 and s1 modes. b, The s0 mode has an intrinsic optical Q of 1.1 million.

Extended Data Fig. 5 Supporting data on frequency control and coupling of dPhC modes in the MPhCR.

a-c, Control of the frequency of the g defect mode by a number of means besides varying the base modulation amplitude A (as in Fig. 3c), including varying m (the targeted azimuthal mode number), N (the number of periods comprising the potential), and Δ (the modulation depth of the potential), from left to right, respectively. Nominal parameters are {m, N, Δ} = {162, 48, 10 %}. The MPhCR has a unique tuning mechanism, in which the modulation period is varied to target different azimuthal mode numbers, for example, m = 162 (blue) and m = 164 (purple) in (a), while the characteristics of the defect (Δ,G,and N) are unchanged. This changes the location of the band-edge, but not the curvature of the dielectric band and the relative frequency of the g mode. This characteristic of the g mode is particularly convenient considering the relation of the MPhCR to control microrings (grey). Otherwise, tuning of the g mode frequency by control of N and Δ results in a largely unchanged dielectric band curvature, with its frequency shifted by < 1 THz, while the g mode frequency is tuned by as much as 2 THz. d-e, Coupling of the MPhCR devices and fitting of the g modes for centered and rotated PhC defects. This series of transmission spectra shows the control of Qc from a regime of deep coupling (Qc ≈ 104, Q0 ≈ 105, K ≈ 10) to one that is strongly undercoupled (Qc ≈ 2 × 107, Q0 ≈ 5 × 105, K ≈ 0.025). We note that the g modes have on-resonance transmission values close to 0 when K ≫ 1, unlike conventional coupling of microring traveling wave modes (see Methods).

Extended Data Table 1 Comparison to previous works in combing a PhC and a microring. Previous works fall into two categories, referred to as photonic crystal rings (PhCRs) and photonic crystal disk/ring resonators (PCDRs/PCRRs) in the literature, whose structures are based on microrings and 2D PhCs, respectively. The original work in a PhCR and a PCRR are in bold. PhCRs typically support multiple modes in a WGM fashion, and therefore have SRs listed. PCRRs only have single or few modes and SRs are not analyzed. Although not listed here, PCRRs typically have much smaller mode volumes than PhCRs. We note that reference 15 has Q and SR reported in different devices. Overall, we find that the MPhCR has the highest ng/α, which is an important metric for slow light application (see Methods
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Lu, X., McClung, A. & Srinivasan, K. High-Q slow light and its localization in a photonic crystal microring. Nat. Photon. 16, 66–71 (2022). https://doi.org/10.1038/s41566-021-00912-w

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