Abstract

We present a heterogeneously coupled Si/SiO2/SiN waveguide structure that can achieve extremely high dispersions (> | ± 107| ps · nm−1km−1). A strong mode coupling between the Si and SiN waveguides introduces a normal dispersion to symmetric mode and an anomalous dispersion to anti-symmetric mode, and the large group velocity difference between the two waveguides results in such high dispersions. Geometric parameters of the structure control the peak dispersions and the central wavelength of the mode coupling, and these engineering capabilities are studied numerically. Analytical representations on the heterogeneously coupled waveguides are also introduced and these equations explain the effects of geometric parameters. This extremely dispersive waveguide scheme can be constructed with other material combinations as well and should be of interest in ultrafast signal processing and spectroscopic applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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S. Kim, D. A. Westly, B. J. Roxworthy, Q. Li, A. Yulaev, K. A. Srinivasan, and V. A. Aksyuk, “Photonic waveguide mode to free-space gaussian beam extreme mode converter,” Light. Sci. Appl. 7, 72 (2018).
[Crossref]

M. Hummon, S. Kang, D. Bopp, Q. Li, D. Westly, S. Kim, C. Fredrick, S. Diddmas, K. Srinivasan, V. Aksyuk, and J. Kitching, “Photonic chip for laser stabilization to an atomic vapor at a precision of 10−11,” Optica 5, 2334 (2018).
[Crossref]

G. Moille, Q. Li, S. Kim, D. Westly, and K. Srinivasan, “Phased-locked two-color single soliton microcombs in dispersion-engineered Si3N4 resonators,” Opt. Lett. 43, 2772 (2018).
[Crossref] [PubMed]

2017 (7)

Y. Dai, J. Li, Z. Zhang, F. Yin, W. Li, and K. Xu, “Real-time frequency-to-time mapping based on spectrally-discrete chromatic dispersion,” Opt. Express 25, 16660–16671 (2017).
[Crossref] [PubMed]

X. Ji, F. A. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017).
[Crossref]

X. Xue, P.-H. Wang, Y. Xuan, M. Qi, and A. M. Weiner, “Microresonator kerr frequency combs with high conversion efficiency,” Laser Photonics Rev. 11, 1600276 (2017).
[Crossref]

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotech. 12, 675 (2017).
[Crossref]

C. V. Poulton, A. Yaacobi, D. B. Cole, M. J. Byrd, M. Raval, D. Vermeulen, and M. R. Watts, “Coherent solid-state LIDAR with silicon photonic optical phased arrays,” Opt. Lett. 42, 4091 (2017).
[Crossref] [PubMed]

T. Komljenovic, R. Helkey, L. Coldren, and J. E. Bowers, “Sparse aperiodic arrays for optical beam forming and lidar,” Opt. Express 25, 2511–2528 (2017).
[Crossref]

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8, 372 (2017).
[Crossref] [PubMed]

2016 (8)

N. Ashok, Y. L. Lee, and W. Shin, “Design and study of strip-slot waveguide structure for dispersion analysis,” IEEE Photon. J. 8, 1–8 (2016).
[Crossref]

Y. Xuan, Y. Liu, L. Varghese, A. J. Metcalf, X. Xue, P.-H. Wang, K. Han, J. A. Jaramillo-Villegas, A. Alnoman, C. Wang, S. Kim, M. Teng, Y. J. Lee, B. Niu, L. Fan, J. Wang, D. E. Leaird, A. M. Weiner, and M. Qi, “High-Q silicon nitride micro-resonators exhibiting low-power frequency comb initiation,” Optica 3, 1171–1180 (2016).
[Crossref]

M. H. Pfeiffer, A. Kordts, V. Brasch, M. Zervas, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, “Photonic damascene process for integrated high-Q microresonator based nonlinear photonics,” Optica 3, 20–25 (2016).
[Crossref]

K. K. Mehta, C. D. Bruzewicz, R. McConnell, R. J. Ram, J. M. Sage, and J. Chiaverini, “Integrated optical addressing of an ion qubit,” Nat. Nanotech. 11, 1066–1070 (2016).
[Crossref]

Q. Li, M. Davanço, and K. Srinivasan, “Efficient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics,” Nat. Photon. 10, 406 (2016).
[Crossref]

S. Kim and M. Qi, “Broadband second-harmonic phase-matching in dispersion engineered slot waveguides,” Opt. Express 24, 773 (2016).
[Crossref] [PubMed]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref] [PubMed]

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316 (2016).
[Crossref]

2015 (4)

2014 (1)

2013 (3)

2012 (5)

M. Estevez, M. Alvarez, and L. Lechuga, “Integrated optical devices for lab-on-a-chip biosensing applications,” Laser & Photonics Rev. 6, 463–487 (2012).
[Crossref]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photon. 6, 84 (2012).
[Crossref]

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, and A. E. Willner, “Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation,” Opt. Express 20, 1685 (2012).
[Crossref] [PubMed]

R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, and A. L. Gaeta, “Ultrabroadband supercontinuum generation in a CMOS-compatible platform,” Opt. Lett. 37, 1685 (2012).
[Crossref] [PubMed]

K. H. Nam, I. H. Park, and S. H. Ko, “Patterning by controlled cracking,” Nature 485, 221–224 (2012).
[Crossref] [PubMed]

2011 (4)

J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19, 3163 (2011).
[Crossref] [PubMed]

L. Zhang, Y. Yan, Y. Yue, Q. Lin, O. Painter, R. G. Beausoleil, and A. E. Willner, “On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses,” Opt. Express 19, 11584 (2011).
[Crossref] [PubMed]

V. Rastogi, N. Ashok, and A. Kumar, “Design and analysis of large-core high-GVD planar optical waveguide for dispersion compensation,” Appl. Phys. B Lasers Opt. 105, 821–824 (2011).
[Crossref]

M. S. Luchansky and R. C. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. chemistry 84, 793–821 (2011).
[Crossref]

2010 (3)

2009 (2)

L. Zhang, Y. Yue, Y. Xiao-Li, R. G. Beausoleil, and A. E. Willner, “Highly dispersive slot waveguides,” Opt. Express 17, 7095–7101 (2009).
[Crossref] [PubMed]

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on-chip group velocity dispersion engineering,” Appl. Phys. Lett. 95, 141109 (2009).
[Crossref]

2008 (2)

D. Tan, K. Ikeda, R. Saperstein, B. Slutsky, and Y. Fainman, “Chip-scale dispersion engineering using chirped vertical gratings,” Opt. Lett. 33, 3013–3015 (2008).
[Crossref] [PubMed]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[Crossref] [PubMed]

2004 (1)

O. Wada, “Femtosecond all-optical devices for ultrafast communication and signal processing,” New J. Phys. 6, 1–35 (2004).
[Crossref]

2001 (1)

I. Walmsley, L. Waxer, and C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instruments 72, 1 (2001).
[Crossref]

2000 (1)

D. Stegall and T. Erdogan, “Dispersion control with use of long-period fiber gratings,” JOSA A 17, 304–312 (2000).
[Crossref] [PubMed]

1995 (1)

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67, 2111–2113 (1995).
[Crossref]

Adibi, A.

Agarwal, A. M.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotech. 12, 675 (2017).
[Crossref]

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photon. 6, 84 (2012).
[Crossref]

Aksyuk, V.

M. Hummon, S. Kang, D. Bopp, Q. Li, D. Westly, S. Kim, C. Fredrick, S. Diddmas, K. Srinivasan, V. Aksyuk, and J. Kitching, “Photonic chip for laser stabilization to an atomic vapor at a precision of 10−11,” Optica 5, 2334 (2018).
[Crossref]

Aksyuk, V. A.

S. Kim, D. A. Westly, B. J. Roxworthy, Q. Li, A. Yulaev, K. A. Srinivasan, and V. A. Aksyuk, “Photonic waveguide mode to free-space gaussian beam extreme mode converter,” Light. Sci. Appl. 7, 72 (2018).
[Crossref]

Alnoman, A.

Alvarez, M.

M. Estevez, M. Alvarez, and L. Lechuga, “Integrated optical devices for lab-on-a-chip biosensing applications,” Laser & Photonics Rev. 6, 463–487 (2012).
[Crossref]

Ashok, N.

N. Ashok, Y. L. Lee, and W. Shin, “Design and study of strip-slot waveguide structure for dispersion analysis,” IEEE Photon. J. 8, 1–8 (2016).
[Crossref]

V. Rastogi, N. Ashok, and A. Kumar, “Design and analysis of large-core high-GVD planar optical waveguide for dispersion compensation,” Appl. Phys. B Lasers Opt. 105, 821–824 (2011).
[Crossref]

Atabaki, A. H.

Atkinson, J.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, “Controlling evanescent waves using silicon photonic all-dielectric metamaterials for dense integration,” Nat. Commun. 9, 1893 (2018).
[Crossref] [PubMed]

Bailey, R. C.

M. S. Luchansky and R. C. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. chemistry 84, 793–821 (2011).
[Crossref]

Bao, C.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8, 372 (2017).
[Crossref] [PubMed]

Barbosa, F. A.

Barton, J. S.

Bauters, J. F.

Beausoleil, R. G.

Beha, K.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316 (2016).
[Crossref]

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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref] [PubMed]

Other (5)

H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).

A. Yariv and A. Yariv, Optical electronics in modern communications (Oxford University, 1997).

L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University, 2015).
[Crossref]

A. M. Weiner, Ultrafast optics (Wiley, 2009).
[Crossref]

Lumerical Mode solution, http://www.lumerical.com/ .

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic cross-section of the heterogeneously coupled SiN/SiO2/Si waveguides with geometric parameters; h1, h2, and h3 are the heights of Si, SiO2, and SiN layers, respectively, and w0 is the width of the waveguide. (b) Normalized electric fields (Ey) of the coupled symmetric (Sym, upper) and anti-symmetric (Anti, lower) modes at the wavelengths of λ < λc, λ = λc, and λ > λc, where λc is the mode crossing wavelength. (c) Effective refractive indices (neff) of the symmetric (orange solid line) and anti-symmetric (blue solid line) modes. Orange and blue dashed lines are the neff of the fundamental TM modes at Si and SiN, respectively, when they are isolated without coupling. (d) Second-order dispersion and (e) Third-order dispersion (TOD) profiles of symmetric (orange) and anti-symmetric (blue) modes through the mode coupling. The black dashed line in (e) indicates the mode coupling wavelength (ω = ω0). Geometric parameters are h1 = 200 nm, h2 = 1200 nm, h3 = 1050 nm, and w0 = 1000 nm.
Fig. 2
Fig. 2 Analytical evaluations on the heterogeneously coupled waveguides. (a) Numerically calculated coupling coefficient |κ| between the Si and SiN waveguides. Equation (5) is used with the same geometric parameters as in Fig. 1. (b) Dispersion profiles of the symmetric (orange) and anti-symmetric (blue) modes using Eqs. (6) and (7), and the |κ| of (a). (c) The full-width-half-maximum (FWHM) bandwidth (blue) and the peak dispersion wavelength (orange) for different |κ|. (d) Dispersion peaks (maximum/minimum) of the symmetric (orange) and anti-symmetric (blue) modes as a function of |κ|.
Fig. 3
Fig. 3 Numerical analysis on the heterogeneously coupled waveguides. (a) Simulated dispersion peaks (blue: anti-symmetric, orange: symmetric) of the heterogeneously coupled waveguides with different heights of SiO2 spacer h2. Other parameters are the same as in Fig. 1. (b) Simulated full-width-half-maximum (FWHM) bandwidth (blue) and the peak dispersion wavelength (orange) as a function of h2. The wavelength of the peak dispersions is almost constant at ≈ 1553 nm.
Fig. 4
Fig. 4 (a) Simulated effective refractive indices (neff) of the isolated Si and SiN waveguides for different thicknesses (dashed lines: neff of Si waveguide for different h1, solid lines: neff of SiN waveguide for different h3). The mode coupling wavelength can be estimated by tracking the crossing point of dashed (neff of Si waveguide) and solid (neff of SiN waveguide) lines. (b) Mode crossing wavelength for different thicknesses. Blue and orange lines are the tracked mode crossing wavelengths from (a), for different h1 (while fixing the h3 = 1050 nm) and h3 (while fixing the h1 = 200 nm), respectively. Blue circles and orange crosses are the mode coupling wavelengths (or the wavelengths of peak dispersions) from the full modal simulations (other geometric parameters: h2 = 1500 nm and w0 = 1000 nm).
Fig. 5
Fig. 5 Numerically simulated peak dispersions of anti-symmetric (blue) and symmetric (orange) modes while varying (a) h1 (h3 is fixed at 1050 nm) and (b) h3 (h1 fixed at 200 nm). Other parameters are set to be h2 = 1500 nm and w0 = 1000 nm. Simulated group indices (ng) of isolated (c) Si and (d) SiN waveguides for different heights of h1 and h3, respectively. The black dashed arrow guides the increase of each thickness.
Fig. 6
Fig. 6 (a) Peak dispersions of the anti-symmetric (blue) and symmetric (orange) modes for different waveguide width w0. (b) Full-width-half-maximum (FWHM) bandwidth (blue) and central wavelengths of the dispersion peaks (orange) for different w0. Other parameters are set to be h1 = 200 nm, h2 = 1500 nm and h3 = 1050 nm.

Equations (11)

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β ( ω ) β ( ω 0 ) + ω ω 0 ν + D ω 2 ( ω ω 0 ) 2
ν = ( β ω ) 1
D ω = GVD = ω ( 1 ν ) = 2 β ω 2
β ± = 1 2 ( β 1 + β 2 ) ± 1 4 ( β 1 β 2 ) 2 + | κ | 2
κ = ω ε 0 4 Δ ε ( x , y ) E 1 ( x , y ) E 2 * ( x , y ) d x d y
D ω ± = 2 β ± ω 2 = 1 2 ( D ω 1 + D ω 2 ) ± 1 4 | κ | [ ( 1 ν 1 1 ν 2 ) + ( D ω 1 D ω 2 ) ( ω ω 0 ) ] 2 ( ω ˜ 2 + 1 ) 3 2 ± 1 4 | κ | ( D ω 1 D ω 2 ) ω ˜ ( ω ˜ 2 + 1 ) 1 2
δ ω = 2 | κ | | ( 1 ν 1 1 ν 2 ) + ( D ω 1 D ω 2 ) 2 ( ω ω 0 ) | 1
D ω ± = 2 β ± ω 2 D ω 0 ± 1 4 | κ | ( 1 ν 1 1 ν 2 ) 2 ( ω ˜ 2 + 1 ) 3 2
δ ω = 2 | κ | | 1 ν 1 1 ν 2 | 1
D ω , max ± = D ω 0 ± 1 4 | κ | ( 1 ν 1 1 ν 2 ) 2 = D ω 0 ± ( n g 1 n g 2 ) 2 4 | κ | c 2
D λ = λ c 2 n eff λ 2 = 2 π c λ 2 D ω

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