Abstract

We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S21 response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  22. R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
    [CrossRef]
  23. L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express 19(23), 23162–23170 (2011).
    [CrossRef] [PubMed]

2012

2011

2010

2009

R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
[CrossRef]

M. H. Asghari and J. Azaña, “All-optical hilbert transformer based on a single phase-shifted fiber bragg grating: design and analysis,” Opt. Lett. 34(3), 334–336 (2009).
[CrossRef] [PubMed]

J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
[CrossRef]

2008

2007

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[CrossRef]

1996

1994

M. Lang and T. I. Laakso, “Simple and robust method for the design of allpass filters using least squares phase error criterion,” IEEE Trans. Circuits Syst. II 41(1), 40–48 (1994).
[CrossRef]

Asghari, M. H.

Ashrafi, R.

Azaña, J.

Beeker, W. P.

Bentum, M.

Bui, L. A.

Burla, J.

Burla, M.

Capmany, J.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[CrossRef]

Chevalier, L.

Chi, H.

Chu, S. T.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29) (2010).

Dekker, R.

R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
[CrossRef]

Emami, H.

Ferrera, M.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29) (2010).

Geuzebroek, D.

R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
[CrossRef]

Han, Y.

Heideman, R. G.

Hoekman, M.

Hoving, W.

R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
[CrossRef]

Huang, T. X. H.

Hulzinga,

Jorna, A.

Khan, M. R.

Klein, E.

R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
[CrossRef]

Laakso, T. I.

M. Lang and T. I. Laakso, “Simple and robust method for the design of allpass filters using least squares phase error criterion,” IEEE Trans. Circuits Syst. II 41(1), 40–48 (1994).
[CrossRef]

Lang, M.

M. Lang and T. I. Laakso, “Simple and robust method for the design of allpass filters using least squares phase error criterion,” IEEE Trans. Circuits Syst. II 41(1), 40–48 (1994).
[CrossRef]

Leimeng Zhuang, D. A. I.

Leinse, A.

Li, M.

M. Li and J. Yao, “All-fiber temporal photonic fractional hilbert transformer based on a directly designed fiber bragg grating,” Opt. Lett. 35(2), 223–225 (2010).
[CrossRef] [PubMed]

M. Li and J. Yao, “Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber bragg grating,” Photon. Technol. Letters 22(21), 1559–1561 (2010).
[CrossRef]

Li, Z.

Lin, B.

N. Q. Ngo, Y. Song, and B. Lin, “Design of Hilbert transformers with tunable THz bandwidths using a reconfigurable integrated optical FIR filter,” Opt. Commun. 284(3), 787–794 (2011).
[CrossRef]

Little, B. E.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29) (2010).

Liu, F.

Lohmann, A. W.

Marpaung, D. A. I.

Marpaung, M. J.

Meijerink, A.

Meijerink, R.

Mendlovic, D.

Minasian, R. A.

Mitchell, A.

Morandotti, R.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29) (2010).

Moss, D. J.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29) (2010).

Ngo, N. Q.

N. Q. Ngo, Y. Song, and B. Lin, “Design of Hilbert transformers with tunable THz bandwidths using a reconfigurable integrated optical FIR filter,” Opt. Commun. 284(3), 787–794 (2011).
[CrossRef]

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[CrossRef]

Park, Y.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29) (2010).

Qiang, L.

Qiu, M.

Razzari, L.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29) (2010).

Roeloffzen, C. G. H.

D. A. I. Marpaung, L. Chevalier, M. Burla, and C. G. H. Roeloffzen, “Impulse radio ultrawideband pulse shaper based on a programmable photonic chip frequency discriminator,” Opt. Express 19(25), 24838–24848 (2011).
[CrossRef] [PubMed]

L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express 19(23), 23162–23170 (2011).
[CrossRef] [PubMed]

M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express 19(22), 21475–21484 (2011).
[CrossRef] [PubMed]

A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, D. A. I. Leimeng Zhuang, M. J. Marpaung, M. Bentum, J. Burla, P. Verpoorte, A. Jorna, Hulzinga, and W. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part I: design and performance analysis,” J. Lightwave Technol. 28(1), 3–18 (2010).
[CrossRef]

D. A. I. Marpaung, C. G. H. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express 18(26), 27359–27370 (2010).
[CrossRef] [PubMed]

L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol. 28(1), 19–31 (2010).
[CrossRef]

R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
[CrossRef]

Sarkhosh, N.

Song, Y.

N. Q. Ngo, Y. Song, and B. Lin, “Design of Hilbert transformers with tunable THz bandwidths using a reconfigurable integrated optical FIR filter,” Opt. Commun. 284(3), 787–794 (2011).
[CrossRef]

Stoffer, R.

R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
[CrossRef]

Su, Y.

van Etten, W.

Verpoorte, P.

Wang, T.

Yao, J.

Ye, T.

Yi, X.

Zalevsky, Z.

Zhang, X.

Zhang, Z.

Zhuang, L.

IEEE Trans. Circuits Syst. II

M. Lang and T. I. Laakso, “Simple and robust method for the design of allpass filters using least squares phase error criterion,” IEEE Trans. Circuits Syst. II 41(1), 40–48 (1994).
[CrossRef]

J. Lightwave Technol.

Nat. Commun.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29) (2010).

Nat. Photonics

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[CrossRef]

Opt. Commun.

N. Q. Ngo, Y. Song, and B. Lin, “Design of Hilbert transformers with tunable THz bandwidths using a reconfigurable integrated optical FIR filter,” Opt. Commun. 284(3), 787–794 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Photon. Technol. Letters

M. Li and J. Yao, “Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber bragg grating,” Photon. Technol. Letters 22(21), 1559–1561 (2010).
[CrossRef]

Proc. SPIE

R. G. Heideman, A. Leinse, W. Hoving, R. Dekker, D. Geuzebroek, E. Klein, R. Stoffer, C. G. H. Roeloffzen, L. Zhuang, and A. Meijerink, “Large-scale integrated optics using TriPleX waveguide technology:from UV to IR,” Proc. SPIE 7221, 72210R, 72210R-15 (2009).
[CrossRef]

Other

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley, 1999).

S. L. Hahn, Transforms and Applications Handbook (CRC Press, 2010).

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Figures (10)

Fig. 1
Fig. 1

(a) frequency and (b) corresponding discrete-time impulse responses of a theoretical and a delay-modified FHT.

Fig. 2
Fig. 2

(a) architecture of an ORR based on an MZI; (b) profile of its impulse response.

Fig. 3
Fig. 3

(a)-(e) calculated phase responses of an ORR which are optimized to fit modified FHT specification for different values of fractional order ρ; (f) the corresponding power transmissions of the ORR with r = 0.97 (inset: close-by view around resonance frequency).

Fig. 4
Fig. 4

FHT operation bandwidth related to phase ripple tolerance for different values of ρ.

Fig. 5
Fig. 5

(a) phase responses and (b) corresponding power transmissions of a cascade of two ORRs (black) and a single ORR (grey) for ρ = 2 and r = 0.97.

Fig. 6
Fig. 6

Simulated temporal responses of an ORR with an FSR of 15 GHz versus those of a theoretical FHT: (a) sinusoidal signals of 5 and 10 GHz are used as the inputs; (b)-(d) first-order Hermit-Gaussian pulses derived from a transform-limited Gaussian pulse with FWHM duration of 100 ps are used as the inputs for different values of ρ (the loss and delay effects of the ORR are removed from the simulation results).

Fig. 7
Fig. 7

(a) measured RF phase responses of a waveguide realization of an ORR for different values of power coupling coefficient κ and the curve-fittings to the target FHT specifications; (b) demonstration of the resulting FHT phase shift by removing the delay effect (linear phase) from the measured phase responses.

Fig. 8
Fig. 8

Illustration of the phase control functionality of the proposed FHT for optical generation of microwave signals using optical heterodyning: (a) with the phase responses of the FHT for θ = 0 and (b) for θ = π (fORR denotes the resonance frequency of the ORR).

Fig. 9
Fig. 9

Setup for experimental demonstration of on-chip phase control of microwave signals generated by optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals (inset: an example of the frequency positioning of the two lasers and the optical phase responses of the two channels where the delay effects of the two channels are equalized).

Fig.
       10
Fig. 10

Demonstrations of two functionalities achieved using the FHT for optical generation of microwave signals by means of optical heterodyning: (a) microwave phase control with a full 2π phase changing range and (b) simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range.

Equations (5)

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

H FHT (Ω)=| H FHT (Ω) | e jΨ(Ω) ={ e jϕ, 0Ω<π e jϕ, -πΩ<0
h FHT (nT)={ cos(ϕ), n = 0 sin(ϕ) 2 sin 2 (nπ/2) nπ ,n0 }
G a,N (z)= a N + a N1 z 1 ......+ a 1 z N+1 + z N 1+ a 1 z 1 +........+ a N1 z N+1 + a N z N
Ψ ORR (Ω)=arctan[ rsin(Ω) crcos(Ω) ][ crsin(Ω) 1crcos(Ω) ], respectively,
Η C,N (Ω)=| H C,N (Ω) | e j Ψ C,N (Ω) = n=1 N H ORR,n (Ω)= n=1 N | H ORR,n (Ω) | e j n=1 N Ψ ORR,n (Ω)

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