Abstract

We investigate the waveguide dispersion of subwavelength structures, and propose that the waveguide dispersion can be reduced by reducing the period of subwavelength structures. A 3 dB bandwidth increment of 20% has been observed by introducing this concept into previously demonstrated grating couplers. To fully exploit the bandwidth merits of the structures, gratings with interleaved subwavelength structures were designed and fabricated. Two typical types of interleaving geometries have been investigated. Both demonstrated a 1 dB bandwidth 70nm, a 3 dB bandwidth 117nm, and a peak efficiency 5.1dB at 1570 nm for transverse-electric polarized light. The simulation confirms that the dispersion engineering adds an extra 12 nm to the 1 dB bandwidth.

© 2013 Optical Society of America

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  1. M. Asghari and A. V. Krishnamoorthy, Nat. Photonics 5, 268 (2011).
    [CrossRef]
  2. M. Lipson, J. Lightwave Technol. 23, 4222 (2005).
    [CrossRef]
  3. P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D. X. Xu, A. Densmore, A. Delage, B. Lamontagne, and T. J. Hall, Opt. Lett. 35, 2526 (2010).
    [CrossRef]
  4. P. Cheben, D. X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006).
    [CrossRef]
  5. X. Chen, K. Xu, Z. Z. Cheng, C. K. Y. Fung, and H. K. Tsang, Opt. Lett. 37, 3483 (2012).
    [CrossRef]
  6. Z. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, Appl. Phys. Lett. 101, 101104 (2012).
    [CrossRef]
  7. R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernandez, Opt. Lett. 35, 3243 (2010).
    [CrossRef]
  8. R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
    [CrossRef]
  9. H. Subbaraman, X. Xu, J. Covey, and R. T. Chen, Opt. Express 20, 20659 (2012).
    [CrossRef]
  10. X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
    [CrossRef]
  11. Z. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, Opt. Lett. 37, 5181 (2012).
    [CrossRef]
  12. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, Electron. Lett. 38, 1669 (2002).
    [CrossRef]
  13. S. J. McNab, N. Moll, and Y. A. Vlasov, Opt. Express 11, 2927 (2003).
    [CrossRef]
  14. M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, Opt. Commun. 283, 3678 (2010).
    [CrossRef]
  15. V. R. Almeida, R. R. Panepucci, and M. Lipson, Opt. Lett. 28, 1302 (2003).
    [CrossRef]
  16. Z. Xiao, T. Y. Liow, J. Zhang, P. Shum, and F. Luan, Opt. Express 21, 5688 (2013).
    [CrossRef]
  17. M. Qiu, Appl. Phys. Lett. 81, 1163 (2002).
    [CrossRef]
  18. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).
  19. X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
    [CrossRef]
  20. M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

2013 (1)

2012 (7)

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
[CrossRef]

X. Chen, K. Xu, Z. Z. Cheng, C. K. Y. Fung, and H. K. Tsang, Opt. Lett. 37, 3483 (2012).
[CrossRef]

Z. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, Appl. Phys. Lett. 101, 101104 (2012).
[CrossRef]

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

H. Subbaraman, X. Xu, J. Covey, and R. T. Chen, Opt. Express 20, 20659 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
[CrossRef]

Z. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, Opt. Lett. 37, 5181 (2012).
[CrossRef]

2011 (1)

M. Asghari and A. V. Krishnamoorthy, Nat. Photonics 5, 268 (2011).
[CrossRef]

2010 (3)

2006 (1)

2005 (1)

2003 (2)

2002 (2)

M. Qiu, Appl. Phys. Lett. 81, 1163 (2002).
[CrossRef]

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, Electron. Lett. 38, 1669 (2002).
[CrossRef]

Almeida, V. R.

Asghari, M.

M. Asghari and A. V. Krishnamoorthy, Nat. Photonics 5, 268 (2011).
[CrossRef]

Bass, M.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

Bedard, D.

Bock, P. J.

Cheben, P.

Chen, R. T.

H. Subbaraman, X. Xu, J. Covey, and R. T. Chen, Opt. Express 20, 20659 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
[CrossRef]

Chen, X.

Cheng, Z. Z.

Covey, J.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
[CrossRef]

H. Subbaraman, X. Xu, J. Covey, and R. T. Chen, Opt. Express 20, 20659 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
[CrossRef]

DeCusatis, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

Delage, A.

Densmore, A.

Enoch, J.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

Fedeli, J. M.

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

Fournier, M.

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

Fung, C. K. Y.

Halir, R.

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernandez, Opt. Lett. 35, 3243 (2010).
[CrossRef]

Hall, T. J.

Hosseini, A.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
[CrossRef]

Hvam, J. M.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, Opt. Commun. 283, 3678 (2010).
[CrossRef]

Janz, S.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Krishnamoorthy, A. V.

M. Asghari and A. V. Krishnamoorthy, Nat. Photonics 5, 268 (2011).
[CrossRef]

Kwong, D.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
[CrossRef]

Lakshminarayanan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

Lamontagne, B.

Lapointe, J.

Li, G.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

Liow, T. Y.

Lipson, M.

Liu, L.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, Opt. Commun. 283, 3678 (2010).
[CrossRef]

Luan, F.

Ma, R.

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernandez, Opt. Lett. 35, 3243 (2010).
[CrossRef]

MacDonald, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

Mahajan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

McNab, S. J.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Molina-Fernandez, I.

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernandez, Opt. Lett. 35, 3243 (2010).
[CrossRef]

Moll, N.

Morita, H.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, Electron. Lett. 38, 1669 (2002).
[CrossRef]

Ortega-Monux, A.

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

Ou, H.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, Opt. Commun. 283, 3678 (2010).
[CrossRef]

Panepucci, R. R.

Pu, M.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, Opt. Commun. 283, 3678 (2010).
[CrossRef]

Qiu, M.

M. Qiu, Appl. Phys. Lett. 81, 1163 (2002).
[CrossRef]

Schmid, J. H.

Shoji, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, Electron. Lett. 38, 1669 (2002).
[CrossRef]

Shum, P.

Stryland, E. V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

Subbaraman, H.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
[CrossRef]

H. Subbaraman, X. Xu, J. Covey, and R. T. Chen, Opt. Express 20, 20659 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
[CrossRef]

Tsang, H. K.

Tsuchizawa, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, Electron. Lett. 38, 1669 (2002).
[CrossRef]

Vlasov, Y. A.

Watanabe, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, Electron. Lett. 38, 1669 (2002).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Wong, C. Y.

Z. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, Opt. Lett. 37, 5181 (2012).
[CrossRef]

Z. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, Appl. Phys. Lett. 101, 101104 (2012).
[CrossRef]

Xiao, Z.

Xu, D. X.

Xu, K.

Xu, X.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
[CrossRef]

H. Subbaraman, X. Xu, J. Covey, and R. T. Chen, Opt. Express 20, 20659 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
[CrossRef]

Yamada, K.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, Electron. Lett. 38, 1669 (2002).
[CrossRef]

Yvind, K.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, Opt. Commun. 283, 3678 (2010).
[CrossRef]

Zavargo-Peche, L.

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

Zhang, J.

Appl. Phys. Lett. (4)

Z. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, Appl. Phys. Lett. 101, 101104 (2012).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 31109 (2012).
[CrossRef]

M. Qiu, Appl. Phys. Lett. 81, 1163 (2002).
[CrossRef]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, Appl. Phys. Lett. 101, 031109 (2012).
[CrossRef]

Electron. Lett. (1)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, Electron. Lett. 38, 1669 (2002).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Photonics (1)

M. Asghari and A. V. Krishnamoorthy, Nat. Photonics 5, 268 (2011).
[CrossRef]

Opt. Commun. (1)

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, Opt. Commun. 283, 3678 (2010).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

R. Halir, L. Zavargo-Peche, D. X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Monux, I. Molina-Fernandez, M. Fournier, and J. M. Fedeli, Opt. Quantum Electron. 44, 521 (2012).
[CrossRef]

Other (2)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics (McGraw-Hill, 2009).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Fundamental modes of subwavelength structure with filling factor s of 0.1–0.5. (b) Effective index versus wavelength (red), and waveguide dispersion versus wavelength (blue), assuming fsub=0.1. The black dash line is the estimated material dispersion of subwavelength structures for fsub=0.1. (c) Waveguide dispersion versus the filling factor for Λsub=200, 250, 300, and 350 nm The red dot line is the estimated material dispersion of subwavelength structure at 1.55 μm. (d) Effective index versus filling factor (blue), and waveguide dispersion versus filling factor (red) for Λsub=200nm.

Fig. 2.
Fig. 2.

(a) SEM picture of a subwavelength grating coupler. (b)–(d) SEM pictures of subwavelength structures with Λsub=350, 300, and 250 nm.

Fig. 3.
Fig. 3.

(a) Transmission spectra of subwavelength structures with different Λsub, (b) bandwidth versus Λsub. The red dot is from [10].

Fig. 4.
Fig. 4.

(a) Schematic of the wideband grating coupler with interleaved subwavelength structures. In this paper, two different types of geometries were investigated. One is with aligned air holes between the two sets, as shown in (b), and the other is with air holes of one set shifted by half a subwavelength period Λsub, with respect to the other set, as shown in (c).

Fig. 5.
Fig. 5.

Transmission spectra for wideband grating coupler with aligned (blue) and shifted subwavelength structures (shifted). Inset: fabricated wideband grating coupler with aligned subwavelength structures (left) and shifted subwavelength structures shifted (right). The dash line is the simulated transmission spectrum.

Equations (3)

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

Δλ1dB=η1dB|nccosθ1ΛGdneff(λ)dλ|.
nsi21=10.6684293λ2λ20.3015164852+0.003043475λ2λ21.134751152+1.54133408λ2λ21104.02.
dnsubTEdλ=(fsubnsi2nair2+1fsub)1.5(1fsub)(dnsidλ).

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