Abstract

We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. D. Poularikas, Transforms and Applications Handbook, 3rd ed. (CRC Press, 2010), Chap. 7.
  2. A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, Opt. Lett. 21, 281 (1996).
    [CrossRef]
  3. C. S. Guo, Y. J. Han, J. B. Xu, and J. Ding, Opt. Lett. 31, 1394 (2006).
    [CrossRef]
  4. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, Opt. Lett. 33, 98 (2008).
    [CrossRef]
  5. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, Opt. Express 16, 13707 (2008).
    [CrossRef]
  6. Z. Li, H. Chi, X. Zhang, and J. P. Yao, IEEE Photon. Technol. Lett. 23, 1694 (2011).
    [CrossRef]
  7. Z. Li, Y. Han, H. Chi, X. Zhang, and J. P. Yao, J. Lightwave Technol. 30, 1948 (2012).
  8. X. Wang, M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of Asia-Pacific Conference on Comunication (2009), pp. 622–625.
  9. M. H. Asghari and J. Azaña, Opt. Lett. 34, 334 (2009).
    [CrossRef]
  10. M. Li and J. P. Yao, IEEE Photon. Technol. Lett. 22, 1559 (2010).
    [CrossRef]
  11. C. Sima, J. C. Gates, H. L. Rogers, P. L. Mennea, C. Holmes, M. N. Zervas, and P. G. R. Smith, Opt. Lett. 38, 727 (2013).
    [CrossRef]
  12. L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).
  13. P. Dumais, J. Lightwave Technol. 30, 906 (2012).
    [CrossRef]
  14. H. H. Yaffe, C. H. Henry, R. F. Kazarinov, and M. A. Milbrodt, J. Lightwave Technol. 12, 64 (1994).
    [CrossRef]
  15. A. Kilian, J. Kirchof, G. Przyrembel, and W. Wischmann, J. Lightwave Technol. 18, 193 (2000).
    [CrossRef]
  16. B. M. A. Rahman, N. Somasiri, and K. T. V. Grattan, IEEE Photon. Technol. Lett. 17, 1205 (2005).
    [CrossRef]
  17. H. Shahoei and J. P. Yao, IEEE Photon. Technol. Lett. 25, 2225 (2013).
    [CrossRef]
  18. A. Yariv, Electron. Lett. 36, 321 (2000).
    [CrossRef]
  19. A. Melloni, R. Costa, G. Cusmai, and F. Morichetti, Int. J. Mater. Prod. Technol. 34, 421 (2009).
    [CrossRef]
  20. G. Bourdon, G. Alibert, A. Beguin, B. Bellman, and E. Guiot, IEEE Photon. Technol. Lett. 15, 709 (2003).
    [CrossRef]
  21. P. Dumais, C. Callender, C. Blanchetiere, and C. Ledderhof, Proc. SPIE 8412, 84120 (2012).
    [CrossRef]

2013 (2)

2012 (4)

P. Dumais, J. Lightwave Technol. 30, 906 (2012).
[CrossRef]

Z. Li, Y. Han, H. Chi, X. Zhang, and J. P. Yao, J. Lightwave Technol. 30, 1948 (2012).

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).

P. Dumais, C. Callender, C. Blanchetiere, and C. Ledderhof, Proc. SPIE 8412, 84120 (2012).
[CrossRef]

2011 (1)

Z. Li, H. Chi, X. Zhang, and J. P. Yao, IEEE Photon. Technol. Lett. 23, 1694 (2011).
[CrossRef]

2010 (1)

M. Li and J. P. Yao, IEEE Photon. Technol. Lett. 22, 1559 (2010).
[CrossRef]

2009 (2)

A. Melloni, R. Costa, G. Cusmai, and F. Morichetti, Int. J. Mater. Prod. Technol. 34, 421 (2009).
[CrossRef]

M. H. Asghari and J. Azaña, Opt. Lett. 34, 334 (2009).
[CrossRef]

2008 (2)

2006 (1)

2005 (1)

B. M. A. Rahman, N. Somasiri, and K. T. V. Grattan, IEEE Photon. Technol. Lett. 17, 1205 (2005).
[CrossRef]

2003 (1)

G. Bourdon, G. Alibert, A. Beguin, B. Bellman, and E. Guiot, IEEE Photon. Technol. Lett. 15, 709 (2003).
[CrossRef]

2000 (2)

1996 (1)

1994 (1)

H. H. Yaffe, C. H. Henry, R. F. Kazarinov, and M. A. Milbrodt, J. Lightwave Technol. 12, 64 (1994).
[CrossRef]

Alibert, G.

G. Bourdon, G. Alibert, A. Beguin, B. Bellman, and E. Guiot, IEEE Photon. Technol. Lett. 15, 709 (2003).
[CrossRef]

Asghari, M. H.

Azaña, J.

Beeker, W.

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).

Beguin, A.

G. Bourdon, G. Alibert, A. Beguin, B. Bellman, and E. Guiot, IEEE Photon. Technol. Lett. 15, 709 (2003).
[CrossRef]

Bellman, B.

G. Bourdon, G. Alibert, A. Beguin, B. Bellman, and E. Guiot, IEEE Photon. Technol. Lett. 15, 709 (2003).
[CrossRef]

Blanchetiere, C.

P. Dumais, C. Callender, C. Blanchetiere, and C. Ledderhof, Proc. SPIE 8412, 84120 (2012).
[CrossRef]

Bourdon, G.

G. Bourdon, G. Alibert, A. Beguin, B. Bellman, and E. Guiot, IEEE Photon. Technol. Lett. 15, 709 (2003).
[CrossRef]

Bui, L. A.

Callender, C.

P. Dumais, C. Callender, C. Blanchetiere, and C. Ledderhof, Proc. SPIE 8412, 84120 (2012).
[CrossRef]

Chi, H.

Z. Li, Y. Han, H. Chi, X. Zhang, and J. P. Yao, J. Lightwave Technol. 30, 1948 (2012).

Z. Li, H. Chi, X. Zhang, and J. P. Yao, IEEE Photon. Technol. Lett. 23, 1694 (2011).
[CrossRef]

Costa, R.

A. Melloni, R. Costa, G. Cusmai, and F. Morichetti, Int. J. Mater. Prod. Technol. 34, 421 (2009).
[CrossRef]

Cusmai, G.

A. Melloni, R. Costa, G. Cusmai, and F. Morichetti, Int. J. Mater. Prod. Technol. 34, 421 (2009).
[CrossRef]

Ding, J.

Dumais, P.

P. Dumais, J. Lightwave Technol. 30, 906 (2012).
[CrossRef]

P. Dumais, C. Callender, C. Blanchetiere, and C. Ledderhof, Proc. SPIE 8412, 84120 (2012).
[CrossRef]

Emami, H.

Gates, J. C.

Grattan, K. T. V.

B. M. A. Rahman, N. Somasiri, and K. T. V. Grattan, IEEE Photon. Technol. Lett. 17, 1205 (2005).
[CrossRef]

Guiot, E.

G. Bourdon, G. Alibert, A. Beguin, B. Bellman, and E. Guiot, IEEE Photon. Technol. Lett. 15, 709 (2003).
[CrossRef]

Guo, C. S.

Han, Y.

Han, Y. J.

Hanawa, M.

X. Wang, M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of Asia-Pacific Conference on Comunication (2009), pp. 622–625.

Heideman, R.

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).

Henry, C. H.

H. H. Yaffe, C. H. Henry, R. F. Kazarinov, and M. A. Milbrodt, J. Lightwave Technol. 12, 64 (1994).
[CrossRef]

Holmes, C.

Kazarinov, R. F.

H. H. Yaffe, C. H. Henry, R. F. Kazarinov, and M. A. Milbrodt, J. Lightwave Technol. 12, 64 (1994).
[CrossRef]

Khan, M. R.

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).

Kilian, A.

Kirchof, J.

Ledderhof, C.

P. Dumais, C. Callender, C. Blanchetiere, and C. Ledderhof, Proc. SPIE 8412, 84120 (2012).
[CrossRef]

Leinse, A.

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).

Li, M.

M. Li and J. P. Yao, IEEE Photon. Technol. Lett. 22, 1559 (2010).
[CrossRef]

Li, Z.

Z. Li, Y. Han, H. Chi, X. Zhang, and J. P. Yao, J. Lightwave Technol. 30, 1948 (2012).

Z. Li, H. Chi, X. Zhang, and J. P. Yao, IEEE Photon. Technol. Lett. 23, 1694 (2011).
[CrossRef]

Lohmann, A. W.

Melloni, A.

A. Melloni, R. Costa, G. Cusmai, and F. Morichetti, Int. J. Mater. Prod. Technol. 34, 421 (2009).
[CrossRef]

Mendlovic, D.

Mennea, P. L.

Milbrodt, M. A.

H. H. Yaffe, C. H. Henry, R. F. Kazarinov, and M. A. Milbrodt, J. Lightwave Technol. 12, 64 (1994).
[CrossRef]

Mitchell, A.

Morichetti, F.

A. Melloni, R. Costa, G. Cusmai, and F. Morichetti, Int. J. Mater. Prod. Technol. 34, 421 (2009).
[CrossRef]

Nakagawa, K.

X. Wang, M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of Asia-Pacific Conference on Comunication (2009), pp. 622–625.

Nakamura, K.

X. Wang, M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of Asia-Pacific Conference on Comunication (2009), pp. 622–625.

Poularikas, A. D.

A. D. Poularikas, Transforms and Applications Handbook, 3rd ed. (CRC Press, 2010), Chap. 7.

Przyrembel, G.

Rahman, B. M. A.

B. M. A. Rahman, N. Somasiri, and K. T. V. Grattan, IEEE Photon. Technol. Lett. 17, 1205 (2005).
[CrossRef]

Roeloffzen, C.

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).

Rogers, H. L.

Sarkhosh, N.

Shahoei, H.

H. Shahoei and J. P. Yao, IEEE Photon. Technol. Lett. 25, 2225 (2013).
[CrossRef]

Sima, C.

Smith, P. G. R.

Somasiri, N.

B. M. A. Rahman, N. Somasiri, and K. T. V. Grattan, IEEE Photon. Technol. Lett. 17, 1205 (2005).
[CrossRef]

Takano, K.

X. Wang, M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of Asia-Pacific Conference on Comunication (2009), pp. 622–625.

Wang, X.

X. Wang, M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of Asia-Pacific Conference on Comunication (2009), pp. 622–625.

Wischmann, W.

Xu, J. B.

Yaffe, H. H.

H. H. Yaffe, C. H. Henry, R. F. Kazarinov, and M. A. Milbrodt, J. Lightwave Technol. 12, 64 (1994).
[CrossRef]

Yao, J. P.

H. Shahoei and J. P. Yao, IEEE Photon. Technol. Lett. 25, 2225 (2013).
[CrossRef]

Z. Li, Y. Han, H. Chi, X. Zhang, and J. P. Yao, J. Lightwave Technol. 30, 1948 (2012).

Z. Li, H. Chi, X. Zhang, and J. P. Yao, IEEE Photon. Technol. Lett. 23, 1694 (2011).
[CrossRef]

M. Li and J. P. Yao, IEEE Photon. Technol. Lett. 22, 1559 (2010).
[CrossRef]

Yariv, A.

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

Zalevsky, Z.

Zervas, M. N.

Zhang, X.

Z. Li, Y. Han, H. Chi, X. Zhang, and J. P. Yao, J. Lightwave Technol. 30, 1948 (2012).

Z. Li, H. Chi, X. Zhang, and J. P. Yao, IEEE Photon. Technol. Lett. 23, 1694 (2011).
[CrossRef]

Zhuang, L.

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).

Electron. Lett. (1)

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

B. M. A. Rahman, N. Somasiri, and K. T. V. Grattan, IEEE Photon. Technol. Lett. 17, 1205 (2005).
[CrossRef]

H. Shahoei and J. P. Yao, IEEE Photon. Technol. Lett. 25, 2225 (2013).
[CrossRef]

Z. Li, H. Chi, X. Zhang, and J. P. Yao, IEEE Photon. Technol. Lett. 23, 1694 (2011).
[CrossRef]

M. Li and J. P. Yao, IEEE Photon. Technol. Lett. 22, 1559 (2010).
[CrossRef]

G. Bourdon, G. Alibert, A. Beguin, B. Bellman, and E. Guiot, IEEE Photon. Technol. Lett. 15, 709 (2003).
[CrossRef]

Int. J. Mater. Prod. Technol. (1)

A. Melloni, R. Costa, G. Cusmai, and F. Morichetti, Int. J. Mater. Prod. Technol. 34, 421 (2009).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Express (2)

H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, Opt. Express 16, 13707 (2008).
[CrossRef]

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, Opt. Express 20, 26449 (2012).

Opt. Lett. (5)

Proc. SPIE (1)

P. Dumais, C. Callender, C. Blanchetiere, and C. Ledderhof, Proc. SPIE 8412, 84120 (2012).
[CrossRef]

Other (2)

X. Wang, M. Hanawa, K. Nakamura, K. Takano, and K. Nakagawa, in Proceedings of Asia-Pacific Conference on Comunication (2009), pp. 622–625.

A. D. Poularikas, Transforms and Applications Handbook, 3rd ed. (CRC Press, 2010), Chap. 7.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the waveguide cross-section and (b) transmission magnitude response of the MRR at different light polarization directions.

Fig. 2.
Fig. 2.

(a) Transmission magnitude responses and (b) phase responses of the fabricated high-contrast SOS MRR for an input light wave with four different polarization directions.

Fig. 3.
Fig. 3.

Fractional Hilbert transform of a Gaussian pulse by using the spectral response of the MRR for four different polarization directions shown in Fig. 2 (solid lines). FHT orders corresponding to the polarization directions are (a) 0.53, (b) 0.82, (c) 1.14, and (d) 1.32. Fractional Hilbert transforms of an ideal Gaussian pulse with the same orders also are shown for comparison (dashed lines).

Fig. 4.
Fig. 4.

Experimental setup. TLS, tunable laser source, MZM, Mach–Zehnder modulator, EDFA, erbium-doped fiber amplifier, PC, polarization controller, PD, photodetector, OSC, oscilloscope.

Fig. 5.
Fig. 5.

(a) Experimentally generated Gaussian pulse (solid line) with a temporal FWHM of 80 ps. An ideal Gaussian pulse (dashed line) also is shown for comparison. The fractional Hilbert-transformed pulses (solid lines) with different orders of (b) 1, (c) 0.85, (d) 0.95, (e) 1.05, and (f) 1.13. Fractional Hilbert transforms of an ideal Gaussian pulse with an ideal FHT at the same orders are also shown for comparison (dashed lines).

Equations (2)

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

HFHT(ω)={ejφ,ω>0cos(φ),ω=0e+jφ,ω<0,
T=αc[ttαejθ1αt2ejθ],

Metrics