Abstract

A novel, all-optical design for implementing terahertz (THz) bandwidth real-time Hilbert transformers is proposed and numerically demonstrated. An all-optical Hilbert transformer can be implemented using a uniform-period long-period grating (LPG) with a properly designed amplitude-only grating apodization profile, incorporating a single π-phase shift in the middle of the grating length. The designed LPG-based Hilbert transformers can be practically implemented using either fiber-optic or integrated-waveguide technologies. As a generalization, photonic fractional Hilbert transformers are also designed based on the same optical platform. In this general case, the resulting LPGs have multiple π-phase shifts along the grating length. Our numerical simulations confirm that all-optical Hilbert transformers capable of processing arbitrary optical signals with bandwidths well in the THz range can be implemented using feasible fiber/waveguide LPG designs.

© 2012 Optical Society of America

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References

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2011 (1)

M. Smietana, W. J. Bock, P. Mikulic, and J. Chen, Meas. Sci. Technol. 22, 015201 (2011).
[CrossRef]

2010 (2)

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

M. Li and J. Yao, Opt. Lett. 35, 223 (2010).
[CrossRef]

2009 (4)

2008 (2)

2003 (1)

J. K. Brenne and J. Skaar, J. Ligthwave Technol. 21, 254 (2003).
[CrossRef]

1997 (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

1996 (1)

Asghari, M. H.

Azaña, J.

Bock, W. J.

M. Smietana, W. J. Bock, P. Mikulic, and J. Chen, Meas. Sci. Technol. 22, 015201 (2011).
[CrossRef]

Booysen, A.

R. Kritzinger, D. Schmieder, and A. Booysen, Meas. Sci. Technol. 20, 034004 (2009).
[CrossRef]

Brenne, J. K.

J. K. Brenne and J. Skaar, J. Ligthwave Technol. 21, 254 (2003).
[CrossRef]

Bui, L. A.

Callender, C. L.

Chen, J.

M. Smietana, W. J. Bock, P. Mikulic, and J. Chen, Meas. Sci. Technol. 22, 015201 (2011).
[CrossRef]

Ding, J.

Emami, H.

Erdogan, T.

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Hahn, S. L.

S. L. Hahn, in The Transforms and Applications Handbook, 2nd ed., A. D. Poularikas, ed. (CRC Press, 2000), p. 551.

Jiang, J.

Kritzinger, R.

R. Kritzinger, D. Schmieder, and A. Booysen, Meas. Sci. Technol. 20, 034004 (2009).
[CrossRef]

Kulishov, M.

Li, M.

M. Li and J. Yao, Opt. Lett. 35, 223 (2010).
[CrossRef]

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

Lohmann, A. W.

Mendlovic, D.

Mikulic, P.

M. Smietana, W. J. Bock, P. Mikulic, and J. Chen, Meas. Sci. Technol. 22, 015201 (2011).
[CrossRef]

Mitchell, A.

Noad, J. P.

Park, Y.

Sarkhosh, N.

Schmieder, D.

R. Kritzinger, D. Schmieder, and A. Booysen, Meas. Sci. Technol. 20, 034004 (2009).
[CrossRef]

Skaar, J.

J. K. Brenne and J. Skaar, J. Ligthwave Technol. 21, 254 (2003).
[CrossRef]

Slavík, R.

Smietana, M.

M. Smietana, W. J. Bock, P. Mikulic, and J. Chen, Meas. Sci. Technol. 22, 015201 (2011).
[CrossRef]

Yao, J.

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

M. Li and J. Yao, Opt. Lett. 35, 223 (2010).
[CrossRef]

Zalevsky, Z.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

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

J. Lightwave Technol. (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

J. Ligthwave Technol. (1)

J. K. Brenne and J. Skaar, J. Ligthwave Technol. 21, 254 (2003).
[CrossRef]

Meas. Sci. Technol. (2)

R. Kritzinger, D. Schmieder, and A. Booysen, Meas. Sci. Technol. 20, 034004 (2009).
[CrossRef]

M. Smietana, W. J. Bock, P. Mikulic, and J. Chen, Meas. Sci. Technol. 22, 015201 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Other (1)

S. L. Hahn, in The Transforms and Applications Handbook, 2nd ed., A. D. Poularikas, ed. (CRC Press, 2000), p. 551.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of the spectral amplitude (|H(ω)|) and phase [Φ(ω)] responses of an ideal (green dotted lines) and a practically realizable (green solid lines) PHT/PFHT (output temporal curve corresponds to φ=π, i.e., PHT). (b) Illustration of a previously demonstrated fiber-optic approach [8] to transfer the cross-coupling signal in the fiber cladding mode to the fiber core mode by using (1) a core-mode blocker and (2) a short, strong uniform LPG.

Fig. 2.
Fig. 2.

(a) Designed apodization profile for the LPG-based PHT. (b) Spectral phase and amplitude responses of the designed LPG-based PHT (for L=11.3cm).

Fig. 3.
Fig. 3.

Temporal responses (complex envelopes) of the designed PHT to two ultrafast optical input signals, compared with the ideal HT of the input waveforms.

Fig. 4.
Fig. 4.

(a) Designed apodization profiles for the LPG-based PFHTs with three different amounts of phase shifts in the spectral phase response: φ=3π/4 (dashed–dotted curve), φ=π/2 (solid curve), and φ=π/4 (dotted curve). The number of required π-phase shifts along the grating length for the cases of φ=3π/4, π/2, and π/4 are 3, 7, and 19, respectively. The corresponding simulated spectral phase and amplitude responses for each designed PFHT are shown in (b) and the inset of (a).

Tables (1)

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Table 1. Estimated Minimum and Maximum Operation Bandwidths for Three LPG Truncation Lengths

Equations (3)

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y(t)=HT[x(t)]P.V.[x(τ)/(tτ)dτ],
Y(ω)=X(ω)×[jsgn(ω)],
H(ω)={ejφ/2forω<0,0forω=0,ande+jφ/2forω>0},

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