Abstract

We present an analytical expression for the transfer function of an optically-filtered radio frequency photonic link using phase modulation and coherent detection. This solution is applicable to quadrature passband signals and is significant for evaluating the distortion and consequently improving the linearity of such electrical-optical-electrical links. We show that the nonlinearity appears as an envelope distortion and discuss linearization techniques along with experimental validation.

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References

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  1. C. Cox, Analog Optical Links, (Cambridge University Press, Cambridge, U.K., 2004).
  2. W. S. C. Chang, RF photonic technology in optical fiber links, (Cambridge University Press, Cambridge, U.K., 2002).
  3. M. Nazarathy, J. Berger, A. J. Ley, I. M. Levi, and Y. Kagan, “Progress in externally modulated AM CATV transmission systems,” J. Lightwave Technol. 11(1), 82–105 (1993).
    [CrossRef]
  4. G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog links,” IEEE Trans. Microw. Theory Tech. 42(12), 2642–2649 (1994).
    [CrossRef]
  5. L. M. Johnson and H. V. Roussell, “Reduction of intermodulation distortion in interferometric optical modulators,” Opt. Lett. 13(10), 928–930 (1988).
    [CrossRef] [PubMed]
  6. J. Zhang, and T. E. Darcie, “Two-tone analysis of distortion suppression in microwave photonic links using phase modulation and fiber-Bragg grating filters,” International Symposium on Signals, Systems and Electronics, Montreal, Quebec, 2007.
  7. A. Ramaswamy, L. A. Johansson, J. Klamkin, H.-F. Chou, C. Sheldon, M. J. Rodwell, L. A. Coldren, and J. E. Bowers, “Integrated coherent receivers for high-linearity microwave photonic links,” J. Lightwave Technol. 26(1), 209–216 (2008).
    [CrossRef]
  8. T. R. Clark and M. L. Dennis, “Coherent optical phase modulation link,” IEEE Photon. Technol. Lett. 19(16), 1206–1208 (2007).
    [CrossRef]
  9. I. S. Gradshteyn, and I. M. Ryzhik, Table of Integral Series and Products, (Academic Press, San Diego, Calif., 1994), pp. 979.
  10. A. Agarwal, T. Banwell, J. Jackel, P. Toliver, and T. K. Woodward, “Multiscale Sampling for Wide Dynamic Range Electro-optic Receivers,” Optical Fiber Communication, (Optical Society of America, San Diego, USA, 2009), OMI3.

2008 (1)

2007 (1)

T. R. Clark and M. L. Dennis, “Coherent optical phase modulation link,” IEEE Photon. Technol. Lett. 19(16), 1206–1208 (2007).
[CrossRef]

1994 (1)

G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog links,” IEEE Trans. Microw. Theory Tech. 42(12), 2642–2649 (1994).
[CrossRef]

1993 (1)

M. Nazarathy, J. Berger, A. J. Ley, I. M. Levi, and Y. Kagan, “Progress in externally modulated AM CATV transmission systems,” J. Lightwave Technol. 11(1), 82–105 (1993).
[CrossRef]

1988 (1)

Berger, J.

M. Nazarathy, J. Berger, A. J. Ley, I. M. Levi, and Y. Kagan, “Progress in externally modulated AM CATV transmission systems,” J. Lightwave Technol. 11(1), 82–105 (1993).
[CrossRef]

Betts, G. E.

G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog links,” IEEE Trans. Microw. Theory Tech. 42(12), 2642–2649 (1994).
[CrossRef]

Bowers, J. E.

Chou, H.-F.

Clark, T. R.

T. R. Clark and M. L. Dennis, “Coherent optical phase modulation link,” IEEE Photon. Technol. Lett. 19(16), 1206–1208 (2007).
[CrossRef]

Coldren, L. A.

Dennis, M. L.

T. R. Clark and M. L. Dennis, “Coherent optical phase modulation link,” IEEE Photon. Technol. Lett. 19(16), 1206–1208 (2007).
[CrossRef]

Johansson, L. A.

Johnson, L. M.

Kagan, Y.

M. Nazarathy, J. Berger, A. J. Ley, I. M. Levi, and Y. Kagan, “Progress in externally modulated AM CATV transmission systems,” J. Lightwave Technol. 11(1), 82–105 (1993).
[CrossRef]

Klamkin, J.

Levi, I. M.

M. Nazarathy, J. Berger, A. J. Ley, I. M. Levi, and Y. Kagan, “Progress in externally modulated AM CATV transmission systems,” J. Lightwave Technol. 11(1), 82–105 (1993).
[CrossRef]

Ley, A. J.

M. Nazarathy, J. Berger, A. J. Ley, I. M. Levi, and Y. Kagan, “Progress in externally modulated AM CATV transmission systems,” J. Lightwave Technol. 11(1), 82–105 (1993).
[CrossRef]

Nazarathy, M.

M. Nazarathy, J. Berger, A. J. Ley, I. M. Levi, and Y. Kagan, “Progress in externally modulated AM CATV transmission systems,” J. Lightwave Technol. 11(1), 82–105 (1993).
[CrossRef]

Ramaswamy, A.

Rodwell, M. J.

Roussell, H. V.

Sheldon, C.

IEEE Photon. Technol. Lett. (1)

T. R. Clark and M. L. Dennis, “Coherent optical phase modulation link,” IEEE Photon. Technol. Lett. 19(16), 1206–1208 (2007).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog links,” IEEE Trans. Microw. Theory Tech. 42(12), 2642–2649 (1994).
[CrossRef]

J. Lightwave Technol. (2)

M. Nazarathy, J. Berger, A. J. Ley, I. M. Levi, and Y. Kagan, “Progress in externally modulated AM CATV transmission systems,” J. Lightwave Technol. 11(1), 82–105 (1993).
[CrossRef]

A. Ramaswamy, L. A. Johansson, J. Klamkin, H.-F. Chou, C. Sheldon, M. J. Rodwell, L. A. Coldren, and J. E. Bowers, “Integrated coherent receivers for high-linearity microwave photonic links,” J. Lightwave Technol. 26(1), 209–216 (2008).
[CrossRef]

Opt. Lett. (1)

Other (5)

J. Zhang, and T. E. Darcie, “Two-tone analysis of distortion suppression in microwave photonic links using phase modulation and fiber-Bragg grating filters,” International Symposium on Signals, Systems and Electronics, Montreal, Quebec, 2007.

C. Cox, Analog Optical Links, (Cambridge University Press, Cambridge, U.K., 2004).

W. S. C. Chang, RF photonic technology in optical fiber links, (Cambridge University Press, Cambridge, U.K., 2002).

I. S. Gradshteyn, and I. M. Ryzhik, Table of Integral Series and Products, (Academic Press, San Diego, Calif., 1994), pp. 979.

A. Agarwal, T. Banwell, J. Jackel, P. Toliver, and T. K. Woodward, “Multiscale Sampling for Wide Dynamic Range Electro-optic Receivers,” Optical Fiber Communication, (Optical Society of America, San Diego, USA, 2009), OMI3.

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Figures (2)

Fig. 1
Fig. 1

Optically filtered analog photonic link.

Fig. 2
Fig. 2

Two-tone experimental data (a) Time-domain waveform along with a fit of the envelope. (b) Fundamental and TOI before and after post-processing.

Tables (1)

Tables Icon

Table 1 Quadrature representation of some common RF waveforms

Equations (16)

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z(t)   =   x(t)sin(ωRFt)+y(t)cos(ωRFt)
z(t)=ρ(t)sin(ωRFt+ϑ(t))
EM(t)E0ejβz(t)ejΩt
ejβρ(t)sin(ωRFt+ϑ(t))=k=+Jk(βρ(t))ejk(ωRFt+ϑ(t))
S(t)      J1(βρ(t))ejϑ(t)ej(ωRFωLO)t
ejβx(t)sinθ=k=+Jk(βx(t))ejkθ
ejβx(t)cosθ=k=+Jk(βx(t))ikejkθ
S(t)      ej(ωRFωLO)tpipJ1p(βx(t))Jp(βy(t))
p=+ipJ1p(βρ(t)cosϑ(t))Jp(βρ(t)sinϑ(t))   =   J1(βρ(t))eiϑ(t)
J1(βρ(t))12βρ(t)      1      18(βρ(t))2   +   1192(βρ(t))4
z(t)=x0sin(ωRF+ωm)t       =x0sin(ωRFt)cos(ωmt)+x0cos(ωRFt)sin(ωmt)
z(t)=2x0cos(ωmt)sin(ωRFt)
S(t)   =   J1(2βx0cos(ωmt))ei(ωRFωLO)t
J1(2βx0cos(ωmt))   =   k=(1)kJk(βx0)Jk+1(βx0)ei(2k+1)ωmt
S2(t)=A12J12(βρ(t))
ρ(t)=1βJ11(SA1)

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