Abstract

Whispering gallery delay lines have demonstrated record propagation length on a silicon chip and can provide a way to transfer certain applications of optical fiber to wafer-based systems. Their design and fabrication requires careful control of waveguide curvature and etching conditions to minimize connection losses between elements of the delay line. Moreover, loss characterization based on optical backscatter requires normalization to account for the impact of curvature on backscatter rate. In this paper we provide details on design of Archimedean whispering-gallery spiral waveguides, their coupling into cascaded structures, as well as optical loss characterization by optical backscatter reflectometry.

© 2014 Optical Society of America

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  1. H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
    [CrossRef]
  2. H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
    [CrossRef] [PubMed]
  3. K. Takada, H. Yamada, Y. Hida, Y. Ohmori, S. Mitachi, “Rayleigh backscattering measurement of 10m long silica-based waveguides,” Electron. Lett. 32, 1665–1667 (1996).
    [CrossRef]
  4. J. F. Bauters, M. Heck, D. John, D. Dai, M. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19, 3163–3174 (2011).
    [CrossRef] [PubMed]
  5. B. Soller, D. Gifford, M. Wolfe, M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13, 666–674 (2005).
    [CrossRef] [PubMed]
  6. T. Chen, H. Lee, J. Li, K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20, 22819–22829 (2012).
    [CrossRef] [PubMed]
  7. R. Adar, M. Serbin, V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
    [CrossRef]
  8. M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
    [CrossRef] [PubMed]
  9. S. M. Splillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
    [CrossRef]
  10. H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
    [CrossRef] [PubMed]
  11. T. Chen, H. Lee, K. J. Vahala, “Thermal stress in silica-on-silicon disk resonators,” Appl. Phys. Lett. 102, 031113 (2013).
    [CrossRef]

2013 (2)

H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[CrossRef] [PubMed]

T. Chen, H. Lee, K. J. Vahala, “Thermal stress in silica-on-silicon disk resonators,” Appl. Phys. Lett. 102, 031113 (2013).
[CrossRef]

2012 (3)

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef] [PubMed]

T. Chen, H. Lee, J. Li, K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20, 22819–22829 (2012).
[CrossRef] [PubMed]

2011 (1)

2005 (1)

2003 (1)

S. M. Splillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

2000 (1)

M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef] [PubMed]

1996 (1)

K. Takada, H. Yamada, Y. Hida, Y. Ohmori, S. Mitachi, “Rayleigh backscattering measurement of 10m long silica-based waveguides,” Electron. Lett. 32, 1665–1667 (1996).
[CrossRef]

1994 (1)

R. Adar, M. Serbin, V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

Adar, R.

R. Adar, M. Serbin, V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

Barton, J. S.

Bauters, J. F.

Blumenthal, D. J.

Bowers, J. E.

Cai, M.

M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef] [PubMed]

Chen, T.

T. Chen, H. Lee, K. J. Vahala, “Thermal stress in silica-on-silicon disk resonators,” Appl. Phys. Lett. 102, 031113 (2013).
[CrossRef]

H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[CrossRef] [PubMed]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef] [PubMed]

T. Chen, H. Lee, J. Li, K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20, 22819–22829 (2012).
[CrossRef] [PubMed]

Dai, D.

Diddams, S.

H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[CrossRef] [PubMed]

Froggatt, M.

Gifford, D.

Heck, M.

Heideman, R. G.

Hida, Y.

K. Takada, H. Yamada, Y. Hida, Y. Ohmori, S. Mitachi, “Rayleigh backscattering measurement of 10m long silica-based waveguides,” Electron. Lett. 32, 1665–1667 (1996).
[CrossRef]

John, D.

Kippenberg, T. J.

S. M. Splillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Lee, H.

H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[CrossRef] [PubMed]

T. Chen, H. Lee, K. J. Vahala, “Thermal stress in silica-on-silicon disk resonators,” Appl. Phys. Lett. 102, 031113 (2013).
[CrossRef]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef] [PubMed]

T. Chen, H. Lee, J. Li, K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20, 22819–22829 (2012).
[CrossRef] [PubMed]

Leinse, A.

Li, J.

H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[CrossRef] [PubMed]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef] [PubMed]

T. Chen, H. Lee, J. Li, K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20, 22819–22829 (2012).
[CrossRef] [PubMed]

Mitachi, S.

K. Takada, H. Yamada, Y. Hida, Y. Ohmori, S. Mitachi, “Rayleigh backscattering measurement of 10m long silica-based waveguides,” Electron. Lett. 32, 1665–1667 (1996).
[CrossRef]

Mizrahi, V.

R. Adar, M. Serbin, V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

Ohmori, Y.

K. Takada, H. Yamada, Y. Hida, Y. Ohmori, S. Mitachi, “Rayleigh backscattering measurement of 10m long silica-based waveguides,” Electron. Lett. 32, 1665–1667 (1996).
[CrossRef]

Painter, O.

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef] [PubMed]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef] [PubMed]

Painter, O. J.

S. M. Splillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Serbin, M.

R. Adar, M. Serbin, V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

Soller, B.

Splillane, S. M.

S. M. Splillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Suh, M.

H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[CrossRef] [PubMed]

Takada, K.

K. Takada, H. Yamada, Y. Hida, Y. Ohmori, S. Mitachi, “Rayleigh backscattering measurement of 10m long silica-based waveguides,” Electron. Lett. 32, 1665–1667 (1996).
[CrossRef]

Tien, M.

Vahala, K. J.

H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[CrossRef] [PubMed]

T. Chen, H. Lee, K. J. Vahala, “Thermal stress in silica-on-silicon disk resonators,” Appl. Phys. Lett. 102, 031113 (2013).
[CrossRef]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef] [PubMed]

T. Chen, H. Lee, J. Li, K. J. Vahala, “A general design algorithm for low optical loss adiabatic connections in waveguides,” Opt. Express 20, 22819–22829 (2012).
[CrossRef] [PubMed]

S. M. Splillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef] [PubMed]

Wolfe, M.

Yamada, H.

K. Takada, H. Yamada, Y. Hida, Y. Ohmori, S. Mitachi, “Rayleigh backscattering measurement of 10m long silica-based waveguides,” Electron. Lett. 32, 1665–1667 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

T. Chen, H. Lee, K. J. Vahala, “Thermal stress in silica-on-silicon disk resonators,” Appl. Phys. Lett. 102, 031113 (2013).
[CrossRef]

Electron. Lett. (1)

K. Takada, H. Yamada, Y. Hida, Y. Ohmori, S. Mitachi, “Rayleigh backscattering measurement of 10m long silica-based waveguides,” Electron. Lett. 32, 1665–1667 (1996).
[CrossRef]

J. Lightwave Technol. (1)

R. Adar, M. Serbin, V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

Nat. Commun. (2)

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef] [PubMed]

H. Lee, M. Suh, T. Chen, J. Li, S. Diddams, K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[CrossRef] [PubMed]

Nat. Photonics (1)

H. Lee, T. Chen, J. Li, O. Painter, K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (2)

M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef] [PubMed]

S. M. Splillane, T. J. Kippenberg, O. J. Painter, K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

An example of the spiral waveguide design. (a) A MATLAB generated spiral waveguide design consisting of two, interleaved pairs of Archimedean spirals. The surrounding red stripes are buffer patterns to provide etch uniformity. (b) A zoom-in view of the center-of-spiral waveguide pattern. The red patterns in the center are buffer patterns to control the etch loading near the S-bend connection. (c) An SEM image showing a cross section of the Archimedean part of spiral waveguide. w is the width of the waveguides; g is the separation between two neighbouring waveguides; u is the silicon undercut; and p is the width of the supporting silicon pillar. Inset shows a schematic of the spiral waveguide cross section.

Fig. 2
Fig. 2

Desired silicon undercut to attain a waveguide loss less than 0.1 dB/m for oxide thicknesses 12μm (panel (a)) and 6μm (panel (b)) and wedge angles 14°, 27°, 45°.

Fig. 3
Fig. 3

Measurement and calibration of spiral waveguide attenuation using optical backscatter reflectometer (OBR) data. The simple linear fitting of optical backscatter reflectometer data in panel (a) gives an underestimated 0.05 dB/m loss. In contrast, panel (b) shows the more accurate local attenuation rate calibrated based on Eq. (7). Inset of panel (b) is a photograph of a one-way spiral with a path length of approximately 7 m.

Fig. 4
Fig. 4

Backscatter reflectometer study of optical waveguide loss in a cascaded spiral waveguide structure having length in excess of 27 meters. (a) Optical backscatter reflectometer data measured by coupling light at the upper left input waveguide in panel (b). The red lines show the corresponding uncorrected waveguide loss rates that do not account for variation of backscattering using Eq. (7). (b) Photograph of a cascaded, four-spiral waveguide having a physical path length of 27 m. Each spiral is approximately 4 cm in diameter (Originally appearing in [2]). Input and output coupling occur in the upper left and upper right sides of the chip. (c) The calibrated local attenuation rate in spiral 3 of Fig. 4(b) (see spiral in lower right) calibrated using Eq. (7). This should be compared to the uncorrected, simple linear fit (red line) in Fig. 4(a).

Fig. 5
Fig. 5

An example of the S-bend waveguide connection used to connect clockwise and counter-clockwise Archimedean spiral waveguides. (a) A microscope image of of the S-bend connection. Also apparent in the image is tapering of the Archimedean spiral waveguide width as it approaches the S-bend connection near the center of spiral. (b) A plot shows the width of the Archimedean spiral waveguide in the tapering region (see discussion in Sec. 3.1).

Fig. 6
Fig. 6

Loss measurement results for an S-bend connection with various tapering rates (d). The structure measured has A = 500μm, while the d parameter in the Hill function is varied from 0.5π to π. The data show an average loss value measured from 3 – 5 devices, and the error bars gives the standard deviation. The fluctuation mainly comes from fabrication imperfection.

Fig. 7
Fig. 7

An example showing connection of cascaded spirals. The blue curves outline two identical individual spirals to be connected. The red waveguide starts at (x0, y0) and ends at (x1, y1). The black curve starts at (2x1x0, y0) and ends at (x1, y1).

Fig. 8
Fig. 8

(a) An optical micrograph of a resonator formed from two S-bend connections with schematic plot of a taper fiber coupler. This resonator has a round trip length of 1.5 cm. Buffer patterns are introduced to improve the etching uniformity. (b) A spectral scan for the resonator in panel (a) having of a Q factor of 8 × 106.

Fig. 9
Fig. 9

Resonator-based insertion loss measurements of the S-bend connection with various size parameters (A). The inset is a microscope image of the S-bend connection with the scale bar indicating 500μm.

Equations (12)

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{ x c ( θ ) = ( R 0 + A θ ) sin ( θ ) y c ( θ ) = ( R 0 + A θ ) cos ( θ )
{ x in ( θ ) = x c ( θ ) n x ( θ ) w in ( θ ) y in ( θ ) = y c ( θ ) n y ( θ ) w in ( θ )
{ x out ( θ ) = x c ( θ ) + n x ( θ ) w out ( θ ) y out ( θ ) = y c ( θ ) + n y ( θ ) w out ( θ )
d P ( z ) d z = α ( z ) P ( z )
β ( z ) = C ( z ) α ( z )
B ( z ) = e 0 z α ( s ) d s β ( z ) P ( z )
1 B ( z ) d B ( z ) d z = [ 2 α ( z ) 1 α ( z ) d α ( z ) d z ]
f ( 0 ) = w 1 f ( x ) w 2 as x f ( 0 ) = f ( 0 ) = 0
H n , d ( x ) = ( x d ) n 1 + ( x d ) n
w ( θ ) = w 1 + ( w 2 w 1 ) ( θ d ) n 1 + ( θ d ) n
κ ( s ) = a 0 + a 1 s + a 2 s 2 + a 3 s 3 .
{ a 0 = κ 0 θ 1 = θ 0 + 0 s 1 κ ( s ) d s = θ 0 + 0 s 1 a 0 + a 1 s + a 2 s 2 + a 3 s 3 d s κ 1 = a 0 + a 1 s + a 2 s 2 + a 3 s 3 | s = s 1 ( x 1 , i y 1 ) = ( x 0 , i y 0 ) + 0 s 1 exp ( i θ ( s ) ) d s

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