Abstract

We provide the first experimental demonstration of the impact of bias-frequency on second-order distortion in sampled analog optical links. We show proper selection of bias frequency yields >48 dB improvement in second-order distortion performance. In addition, we demonstrate that measurement of the average frequency of the optical comb may be used to determine the optimum bias frequency – without the need for involved radio-frequency distortion measurements.

© 2013 OSA

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References

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  1. J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech.59, 3249–3257 (2011).
    [CrossRef]
  2. B. C. Pile and G. W. Taylor, “Performance of subsampled analog optical links,” J. Lightwave Technol.30, 1299–1305 (2012).
    [CrossRef]
  3. B. H. Kolner and D. W. Dolfi, “Intermodulation distortion and compression in an integrated electrooptic modulator,” Appl. Opt.26, 3676–3680 (1987).
    [CrossRef] [PubMed]
  4. J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech.57, 2093–2099 (2009).
    [CrossRef]
  5. V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-haul analog photonics,” J. Lightwave Technol.29, 1182–1205 (2011).
    [CrossRef]
  6. V. J. Urick, M. N. Hutchinson, J. M. Singley, J. D. McKinney, and K. J. Williams, “Suppression of even-order photodiode distortions via predistortion linearization with a bias-shifted mach-zehnder modulator,” Opt. Express21, 14368–14376 (2013).
    [CrossRef] [PubMed]
  7. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991), 3rd ed.
  8. D. M. Pozar, Microwave Engineering (John Wiley and Sons, Inc., 2005), 3rd ed.
  9. H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Select. Topics Quantum Electron.6, 1325–1331 (2000).
    [CrossRef]
  10. R. Wu, V. R. Supradeepa, C. M. Long, D. E. Leaird, and A. M. Weiner, “Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms,” Opt. Lett.35, 3234–3236 (2010).
    [CrossRef] [PubMed]
  11. F. Rahmatian, N. A. F. Jaeger, R. James, and E. Berolo, “An ultrahigh-speed AlGaAs–GaAs polarization converter using slow-wave coplanar electrodes,” IEEE Photon. Technol. Lett.10, 675–677 (1998).
    [CrossRef]
  12. K. J. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett.25, 1242–1243 (1989).
    [CrossRef]
  13. E. Sorokin, G. Tempea, and T. Brabec, “Measurement of the root-mean-square width and the root-mean-square chirp in ultrafast optics,” J. Opt. Soc. Am. B17, 146–150 (2000).
    [CrossRef]

2013 (1)

2012 (1)

2011 (2)

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech.59, 3249–3257 (2011).
[CrossRef]

V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-haul analog photonics,” J. Lightwave Technol.29, 1182–1205 (2011).
[CrossRef]

2010 (1)

2009 (1)

J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech.57, 2093–2099 (2009).
[CrossRef]

2000 (2)

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Select. Topics Quantum Electron.6, 1325–1331 (2000).
[CrossRef]

E. Sorokin, G. Tempea, and T. Brabec, “Measurement of the root-mean-square width and the root-mean-square chirp in ultrafast optics,” J. Opt. Soc. Am. B17, 146–150 (2000).
[CrossRef]

1998 (1)

F. Rahmatian, N. A. F. Jaeger, R. James, and E. Berolo, “An ultrahigh-speed AlGaAs–GaAs polarization converter using slow-wave coplanar electrodes,” IEEE Photon. Technol. Lett.10, 675–677 (1998).
[CrossRef]

1989 (1)

K. J. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett.25, 1242–1243 (1989).
[CrossRef]

1987 (1)

Berolo, E.

F. Rahmatian, N. A. F. Jaeger, R. James, and E. Berolo, “An ultrahigh-speed AlGaAs–GaAs polarization converter using slow-wave coplanar electrodes,” IEEE Photon. Technol. Lett.10, 675–677 (1998).
[CrossRef]

Brabec, T.

Briguglio, J.

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech.59, 3249–3257 (2011).
[CrossRef]

Bucholtz, F.

Campillo, A. L.

Dagenais, M.

K. J. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett.25, 1242–1243 (1989).
[CrossRef]

Devgan, P. S.

Dexter, J. L.

Dolfi, D. W.

Esman, R. D.

K. J. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett.25, 1242–1243 (1989).
[CrossRef]

Goldberg, L.

K. J. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett.25, 1242–1243 (1989).
[CrossRef]

Hutchinson, M. N.

Jaeger, N. A. F.

F. Rahmatian, N. A. F. Jaeger, R. James, and E. Berolo, “An ultrahigh-speed AlGaAs–GaAs polarization converter using slow-wave coplanar electrodes,” IEEE Photon. Technol. Lett.10, 675–677 (1998).
[CrossRef]

James, R.

F. Rahmatian, N. A. F. Jaeger, R. James, and E. Berolo, “An ultrahigh-speed AlGaAs–GaAs polarization converter using slow-wave coplanar electrodes,” IEEE Photon. Technol. Lett.10, 675–677 (1998).
[CrossRef]

Kobayashi, T.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Select. Topics Quantum Electron.6, 1325–1331 (2000).
[CrossRef]

Kolner, B. H.

Leaird, D. E.

Long, C. M.

McKinney, J. D.

V. J. Urick, M. N. Hutchinson, J. M. Singley, J. D. McKinney, and K. J. Williams, “Suppression of even-order photodiode distortions via predistortion linearization with a bias-shifted mach-zehnder modulator,” Opt. Express21, 14368–14376 (2013).
[CrossRef] [PubMed]

V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-haul analog photonics,” J. Lightwave Technol.29, 1182–1205 (2011).
[CrossRef]

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech.59, 3249–3257 (2011).
[CrossRef]

J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech.57, 2093–2099 (2009).
[CrossRef]

Morimoto, A.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Select. Topics Quantum Electron.6, 1325–1331 (2000).
[CrossRef]

Murata, H.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Select. Topics Quantum Electron.6, 1325–1331 (2000).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991), 3rd ed.

Pile, B. C.

Pozar, D. M.

D. M. Pozar, Microwave Engineering (John Wiley and Sons, Inc., 2005), 3rd ed.

Rahmatian, F.

F. Rahmatian, N. A. F. Jaeger, R. James, and E. Berolo, “An ultrahigh-speed AlGaAs–GaAs polarization converter using slow-wave coplanar electrodes,” IEEE Photon. Technol. Lett.10, 675–677 (1998).
[CrossRef]

Singley, J. M.

Sorokin, E.

Supradeepa, V. R.

Taylor, G. W.

Tempea, G.

Urick, V. J.

Weiner, A. M.

Weller, J. F.

K. J. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett.25, 1242–1243 (1989).
[CrossRef]

Williams, K. J.

Wu, R.

Yamamoto, S.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Select. Topics Quantum Electron.6, 1325–1331 (2000).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

K. J. Williams, L. Goldberg, R. D. Esman, M. Dagenais, and J. F. Weller, “6–34 GHz offset phase-locking of Nd:YAG 1319 nm nonplanar ring lasers,” Electron. Lett.25, 1242–1243 (1989).
[CrossRef]

IEEE J. Select. Topics Quantum Electron. (1)

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Select. Topics Quantum Electron.6, 1325–1331 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

F. Rahmatian, N. A. F. Jaeger, R. James, and E. Berolo, “An ultrahigh-speed AlGaAs–GaAs polarization converter using slow-wave coplanar electrodes,” IEEE Photon. Technol. Lett.10, 675–677 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech.59, 3249–3257 (2011).
[CrossRef]

J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech.57, 2093–2099 (2009).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Other (2)

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991), 3rd ed.

D. M. Pozar, Microwave Engineering (John Wiley and Sons, Inc., 2005), 3rd ed.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the optical comb-based analog link (PMCIM: polarization mode converter-based intensity modulator; ESA: electrical spectrum analyzer). (b) Example optical comb (gray) and filtered bias frequency lines corresponding to the −10, 0, and +10 order comblines (red, black, and blue, respectively).

Fig. 2
Fig. 2

(a) Measured RF power in the fundamental (f1 = 500 MHz, black), second-harmonic (2f1 = 1000 MHz, red) and third-harmonic (3f1 = 1500 MHz) as the bias frequency is varied across a symmetric optical comb [bottom, Fig. 3 (b)]. The dashed black line shows the minimum second-harmonic power obtained by optimizing the bias voltage (∼ −112 dBm) and the solid green, black, and gray lines show the theoretical values calculated from Eqs. (21)(23). (b) Output intercept points (OIP2h: red, OIP3h: blue) corresponding to the measured RF powers in (a). The solid black, solid gray, and dashed gray curves show the theoretical values calculated from Eqs. (25)(27). The dashed black line shows the maximum OIP2h = 50.6 dBm achieved by optimizing the bias voltage.

Fig. 3
Fig. 3

Top row: Normalized second-harmonic power as a function of bias frequency. The measured data are shown in red, calculated values [Eq. (11)] are shown by the black lines. Bottom row: Optical combs corresponding to data in the top row. Here, the average frequency favg is shown by the dashed red line. (a) Asymmetric comb weighted toward low offset frequencies (favgfo ≈ −108.64 GHz). (b) Symmetric comb (favgfo ≈ +5.16 GHz). Asymmetric comb weighted toward high offset frequencies (favgfo ≈ +111.57 GHz)

Fig. 4
Fig. 4

Contours of fixed dynamic range (labeled in blue) for an intrinsic link as a function average current and receiver bandwidth. The maximum allowable bias frequency offset to maintain a given dynamic range is shown in red. The dashed black line marks the operating current for this work (Iavg = 0.58 mA).

Tables (1)

Tables Icon

Table 1 Comparison of minimum second-harmonic distortion frequencies (relative to the laser center frequency) determined from the measured second-harmonic powers (bias frequency) and the measured optical combs (average frequency) shown in Fig. 3.

Equations (32)

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P ( ω ) = δ ( ω ω o ) * n = 0 N 1 P n δ ( ω n ω rep )
i total ( t ) = n = 0 N 1 i n ( t ) .
i ( t ) = p ( t ) * α pd h pd ( t )
d t h pd ( t ) = α pd .
i fund , n = α pd P n ( π V o V π ) | sin ϕ b | ,
i 2 h , n = α pd P n 1 4 ( π V o V π ) 2 | cos ϕ b | ,
i 3 h , n = α pd P n 1 24 ( π V o V π ) 3 | sin ϕ b |
i 3 imd , n = α pd P n 1 8 ( π V o V π ) 3 | sin ϕ b | .
Δ ϕ b , n = ( f n f b ) d ϕ b d f | f = f b .
i fund , n = α pd P n ( π V o V π ) ,
i 2 h , n = α pd P n 1 4 ( π V o V π ) 2 | Δ ϕ b , n | ,
i 3 h , n = α pd P n 1 24 ( π V o V π ) 3
i 3 imd , n = α pd P n 1 8 ( π V o V π ) 3 .
i fund = I avg ( π V o V π ) ,
i 3 h = I avg 1 24 ( π V o V π ) 3
i 3 imd = I avg 1 8 ( π V o V π ) 3 ,
I avg = α pd n = 0 N 1 P n .
i 2 h = I avg 1 4 ( π V o V π ) 2 | ( f b f avg ) d ϕ b d f | ,
f avg = n = 0 N 1 f n P n n = 0 N 1 P n .
OIP k = ( P fund k P k ) 1 / ( k 1 ) .
P fund = 1 8 I avg 2 R o ( π V o V π ) 2 ,
P 2 h = 1 128 I avg 2 R o ( π V o V π ) 4 | ( f b f avg ) d ϕ b d f | 2 ,
P 3 h = 1 4608 I avg 2 R o ( π V o V π ) 6
P 3 imd = 1 512 I avg 2 R o ( π V o V π ) 6 .
OIP 2 h = 2 I avg 2 R o | ( f b f avg ) d ϕ b d f | 2 ,
OIP 3 h = 3 I avg 2 R o ,
OIP 3 imd = I avg 2 R o .
SFDR = ( OIP k N o × B e ) ( k 1 ) / k .
| Δ f | < 2 ( SFDR 3 imd ) 1 / 4 × | d ϕ b d f | 1 .
N o = N sh + ( 1 + G ) N th .
N sh = 1 4 × 2 q I avg R o
G = 1 4 × ( π I avg V π ) 2 R o R i ,

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