Abstract

We present an analytical model that describes the limiting spectral performance of arrayed-waveguide-grating (AWG) spectrometers that incorporate slow-light methods. We show that the loss-limited spectral resolution of a slow-light grating-based spectrometer scales as the loss–group-index ratio of the waveguide array. We further show that one can achieve a spectral resolution of a few GHz using currently available slow-light photonic crystal waveguides while greatly shrinking the on-chip footprint of the spectrometer.

© 2013 OSA

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References

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  1. R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2002), (vol. 43) pp. 497–530.
    [CrossRef]
  2. C. J. Chang-Hasnain and S. L. Chuang, “Slow and fast light in semiconductor quantum-well and quantum-dot devices,” J. Lightwave Technol.24, 4642–4654 (2006).
    [CrossRef]
  3. J. B. Khurgin, “Slow light in various media: a tutorial,” Adv. Opt. Photon.2, 287–318 (2010).
    [CrossRef]
  4. T. Baba, “Slow light in photonics crystals,” Nature Photonics2, 465–473 (2008).
    [CrossRef]
  5. S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).
  6. Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett.32, 915–917 (2007).
    [CrossRef] [PubMed]
  7. G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99, 133601 (2007).
    [CrossRef] [PubMed]
  8. Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett.99, 240801 (2007).
    [CrossRef]
  9. Z. Shi and R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Amer. B25, C136–C143 (2008).
    [CrossRef]
  10. U. Bortolozzo, S. Residori, and J.-P. Huignard, “Slow-light birefringence and polarization interferometry,” Opt. Lett.35, 2076–2078 (2010).
    [CrossRef] [PubMed]
  11. M. Smit and C. Van Dam, “Phasar-based wdm-devices: Principles, design and applications,” IEEE J. Sel. Topics Quantum Electron.2, 236 –250 (1996).
    [CrossRef]
  12. O. Matos, M. Calvo, P. Cheben, S. Janz, J. Rodrigo, D.-X. Xu, and A. Delage, “Arrayed waveguide grating based on group-index modification,” J. Lightwave Technol.24, 1551 –1557 (2006).
    [CrossRef]
  13. Z. Shi and R. W. Boyd, “Slow-light enhanced spectrometers on chip,” Proceedings of SPIE8007, 80071D (2011).
    [CrossRef]
  14. L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express14, 9444–9450 (2006).
    [CrossRef] [PubMed]
  15. S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12, 104004 (2010).
    [CrossRef]
  16. L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express18, 27627–27638 (2010).
    [CrossRef]
  17. J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express16, 6227–6232 (2008).
    [CrossRef] [PubMed]
  18. W. Jiang, K. Okamoto, F. M. Soares, F. Olsson, S. Lourdudoss, and S. J. Yoo, “5 GHz channel spacing InP-based 32-channel arrayed-waveguide grating,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2009), p. OWO2.
  19. F. Wang, J. S. Jensen, J. Mørk, and O. Sigmund, “Systematic design of loss-engineered slow-light waveguides,” J. Opt. Soc. Am. A29, 2657–2666 (2012).
    [CrossRef]

2012 (1)

2011 (1)

Z. Shi and R. W. Boyd, “Slow-light enhanced spectrometers on chip,” Proceedings of SPIE8007, 80071D (2011).
[CrossRef]

2010 (4)

2008 (3)

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express16, 6227–6232 (2008).
[CrossRef] [PubMed]

T. Baba, “Slow light in photonics crystals,” Nature Photonics2, 465–473 (2008).
[CrossRef]

Z. Shi and R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Amer. B25, C136–C143 (2008).
[CrossRef]

2007 (3)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99, 133601 (2007).
[CrossRef] [PubMed]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett.99, 240801 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett.32, 915–917 (2007).
[CrossRef] [PubMed]

2006 (3)

1996 (1)

M. Smit and C. Van Dam, “Phasar-based wdm-devices: Principles, design and applications,” IEEE J. Sel. Topics Quantum Electron.2, 236 –250 (1996).
[CrossRef]

Baba, T.

T. Baba, “Slow light in photonics crystals,” Nature Photonics2, 465–473 (2008).
[CrossRef]

Beggs, D. M.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12, 104004 (2010).
[CrossRef]

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express18, 27627–27638 (2010).
[CrossRef]

Borel, P. I.

Bortolozzo, U.

Boyd, R. W.

Z. Shi and R. W. Boyd, “Slow-light enhanced spectrometers on chip,” Proceedings of SPIE8007, 80071D (2011).
[CrossRef]

Z. Shi and R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Amer. B25, C136–C143 (2008).
[CrossRef]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett.32, 915–917 (2007).
[CrossRef] [PubMed]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett.99, 240801 (2007).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2002), (vol. 43) pp. 497–530.
[CrossRef]

Calvo, M.

Camacho, R. M.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett.99, 240801 (2007).
[CrossRef]

Cardoso, G.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

Chang-Hasnain, C. J.

Cheben, P.

Chuang, S. L.

Delage, A.

Dudley, C. C.

Fage-Pedersen, J.

Frandsen, L. H.

Gauthier, D. J.

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett.32, 915–917 (2007).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2002), (vol. 43) pp. 497–530.
[CrossRef]

Gomez-Iglesias, A.

Gopal, V.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

Howell, J. C.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett.99, 240801 (2007).
[CrossRef]

Hugonin, J. P.

Huignard, J.-P.

Janz, S.

Jensen, J. S.

Jiang, W.

W. Jiang, K. Okamoto, F. M. Soares, F. Olsson, S. Lourdudoss, and S. J. Yoo, “5 GHz channel spacing InP-based 32-channel arrayed-waveguide grating,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2009), p. OWO2.

Khurgin, J. B.

Krauss, T. F.

Kuipers, L.

Lalanne, P.

Lavrinenko, A. V.

Li, J.

Lourdudoss, S.

W. Jiang, K. Okamoto, F. M. Soares, F. Olsson, S. Lourdudoss, and S. J. Yoo, “5 GHz channel spacing InP-based 32-channel arrayed-waveguide grating,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2009), p. OWO2.

Matos, O.

Mazoyer, S.

Melloni, A.

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express18, 27627–27638 (2010).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12, 104004 (2010).
[CrossRef]

Messal, M.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

Morichetti, F.

Mørk, J.

Nair, R.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

O’Faolain, L.

Okamoto, K.

W. Jiang, K. Okamoto, F. M. Soares, F. Olsson, S. Lourdudoss, and S. J. Yoo, “5 GHz channel spacing InP-based 32-channel arrayed-waveguide grating,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2009), p. OWO2.

Olsson, F.

W. Jiang, K. Okamoto, F. M. Soares, F. Olsson, S. Lourdudoss, and S. J. Yoo, “5 GHz channel spacing InP-based 32-channel arrayed-waveguide grating,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2009), p. OWO2.

Pati, G.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

Pati, G. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99, 133601 (2007).
[CrossRef] [PubMed]

Pradhan, P.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

Residori, S.

Rodrigo, J.

Salit, K.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99, 133601 (2007).
[CrossRef] [PubMed]

Salit, M.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99, 133601 (2007).
[CrossRef] [PubMed]

Schulz, S. A.

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express18, 27627–27638 (2010).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12, 104004 (2010).
[CrossRef]

Shahriar, M. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99, 133601 (2007).
[CrossRef] [PubMed]

Shahriar, S. M.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

Shi, Z.

Z. Shi and R. W. Boyd, “Slow-light enhanced spectrometers on chip,” Proceedings of SPIE8007, 80071D (2011).
[CrossRef]

Z. Shi and R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Amer. B25, C136–C143 (2008).
[CrossRef]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett.32, 915–917 (2007).
[CrossRef] [PubMed]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett.99, 240801 (2007).
[CrossRef]

Sigmund, O.

Smit, M.

M. Smit and C. Van Dam, “Phasar-based wdm-devices: Principles, design and applications,” IEEE J. Sel. Topics Quantum Electron.2, 236 –250 (1996).
[CrossRef]

Soares, F. M.

W. Jiang, K. Okamoto, F. M. Soares, F. Olsson, S. Lourdudoss, and S. J. Yoo, “5 GHz channel spacing InP-based 32-channel arrayed-waveguide grating,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2009), p. OWO2.

Spasenovic, M.

Tripathi, R.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

Van Dam, C.

M. Smit and C. Van Dam, “Phasar-based wdm-devices: Principles, design and applications,” IEEE J. Sel. Topics Quantum Electron.2, 236 –250 (1996).
[CrossRef]

Vudyasetu, P. K.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett.99, 240801 (2007).
[CrossRef]

Wang, F.

White, T. P.

Xu, D.-X.

Yoo, S. J.

W. Jiang, K. Okamoto, F. M. Soares, F. Olsson, S. Lourdudoss, and S. J. Yoo, “5 GHz channel spacing InP-based 32-channel arrayed-waveguide grating,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2009), p. OWO2.

Adv. Opt. Photon. (1)

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

M. Smit and C. Van Dam, “Phasar-based wdm-devices: Principles, design and applications,” IEEE J. Sel. Topics Quantum Electron.2, 236 –250 (1996).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. (1)

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12, 104004 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Amer. B (1)

Z. Shi and R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Amer. B25, C136–C143 (2008).
[CrossRef]

Nature Photonics (1)

T. Baba, “Slow light in photonics crystals,” Nature Photonics2, 465–473 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99, 133601 (2007).
[CrossRef] [PubMed]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett.99, 240801 (2007).
[CrossRef]

Proceedings of SPIE (1)

Z. Shi and R. W. Boyd, “Slow-light enhanced spectrometers on chip,” Proceedings of SPIE8007, 80071D (2011).
[CrossRef]

Other (3)

W. Jiang, K. Okamoto, F. M. Soares, F. Olsson, S. Lourdudoss, and S. J. Yoo, “5 GHz channel spacing InP-based 32-channel arrayed-waveguide grating,” in “Optical Fiber Communication Conference,” (Optical Society of America, 2009), p. OWO2.

S. M. Shahriar, G. Pati, V. Gopal, R. Tripathi, G. Cardoso, P. Pradhan, M. Messal, and R. Nair, “Precision rotation sensing and interferometry using slow light,” in “Quantum Electronics and Laser Science Conference (QELS),” (paper JWB97, 2005).

R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2002), (vol. 43) pp. 497–530.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a slow-light arrayed-waveguide-grating spectrometer.

Fig. 2
Fig. 2

The envelope function A(x) at the output plane of the waveguide arrays when the waveguides are (a) lossless and (b) with associated loss.

Fig. 3
Fig. 3

Minimum achievable spectral resolution of a slow-light AWG defined by Eq. (12) as a function of the group index ng and loss coefficient α of the waveguides.

Equations (12)

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

n eff Δ l + n s Λ ( sin θ inc + sin θ d ) = m λ ,
d θ d d ω n g Δ l n s ω Λ cos θ d = 2 π c n g m n s n eff ω 2 Λ cos θ d .
E ( x ) [ comb ( x Λ ) Rect ( x N Λ ) A ( x ) ] * E wg ( x ) ,
A ( x ) exp ( 0.5 x 2 / w 2 ) ,
E I ( u ) = E ( x ) e i 2 π ζ u x d x = c 1 [ comb ( Λ ζ u ) * sinc ( N Λ ζ u ) * e ( 2 π w ζ u ) 2 2 ] × e ( 2 π σ ζ u ) 2 2 ,
δ u I = 1 N Λ ζ = f λ N Λ n s cos θ d .
δ ω I = δ u I d ω d u = δ u I f d ω d θ = f λ N Λ n s cos θ d n s n eff ω 2 Λ cos θ d 2 π c n g m f = n eff ω 0 N m n g ,
FSR = n eff ω 0 n g m .
A ( x ) = exp ( 1 2 x 2 / w 2 ) exp [ 1 2 α ( x + N Λ / 2 ) ] ,
E L ( u ) = E ( x ) e i 2 π ζ u x d x = c 2 [ comb ( Λ ζ u ) * sinc ( N Λ ζ u ) * e ( 2 π w ζ u ) 2 2 * e i π N Λ ζ u u 2 + ( α 2 π ζ ) 2 ] × e ( 2 π σ ζ u ) 2 2 ,
δ u L = α 2 π ζ = α Δ l f λ 2 π Λ n s cos θ d .
δ ω L = δ u L d ω d u = δ u L f d ω d θ = α Δ l f λ 2 π Λ n s cos θ d n s n eff ω 2 Λ cos θ d 2 π c n g m f = c α n g .

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