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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 23695–23705
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Bias-dependent distortion in optical comb-based analog optical links

Jason D. McKinney, Vincent J. Urick, and Alexander S. Hastings  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 23695-23705 (2013)
http://dx.doi.org/10.1364/OE.21.023695


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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

1. Introduction

2. Theory

3. Experiment

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).

To illustrate the bias frequency dependence of the second-harmonic distortion (generally, all even-order distortion), we measure the RF power of the composite fundamental, second-harmonic, and third-harmonic as the bias frequency is varied discretely across the symmetric comb. For this measurement, an individual combline is selected as the bias frequency and its second-harmonic is minimized by adjusting the DC bias voltage of the modulator. The measured fundamental, second- and third-harmonic RF powers are shown in Fig. 2(a) versus the bias frequency offset from the laser center frequency. Here, the measured powers show excellent agreement with the theoretical values calculated from Eqs. (21)(23) for an average photocurrent of Iavg = 0.58 mA (shown by the solid green, black, and gray curves). Using the measured average photocurrent the derivative of the bias phase with respect to frequency is determined to be b/df = 0.63 mrad/GHz and the bias frequency corresponding to minimum second-harmonic distortion is found to be fbfo ≈ 5.02 GHz from a numerical fit of Eq. (22) to the measured second-harmonic data. The dashed black line shows the minimum measured second-harmonic power achieved through fine adjustment of the bias voltage – this value is attributed to photodiode-induced second-harmonic distortion and agrees well with the value predicted by the measured photodiode nonlinearity (to be discussed further below). From the data it is clearly seen that the second-harmonic power varies dramatically (ΔP2h > 48 dB) as the bias frequency is varied across the comb. In contrast, the fundamental and third-harmonic powers remain fixed at their “quadrature” values indicating the total variation in bias phase is quite small (the small-angle approximation to the change in bias phase is justified).

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.

In terms of the output intercept points, the measured variation in second-harmonic power translates directly to an improvement in the second-harmonic output intercept point OIP2h (dB-for-dB). This is shown in Fig. 2(b). The third-harmonic output intercept (blue circles) remains fixed at OIP3h ∼ −14 dBm as determined from the average photocurrent and the fixed fundamental and third-harmonic powers as shown in Fig. 2(a). The second-harmonic OIP (red circles), however, varies by more than 48 dB (2.17 < OIP2h < 50.6 dBm) as the bias frequency is varied. Once again, the maximum intercept point of OIP2h = 50.6 dBm (dashed black line) is believed to be set by the nonlinearity of the photodiode used in our measurement. This is supported by a laser heterodyne measurement of the photodiode distortion using a pair of phase-locked Nd:YAG lasers [12

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]

] in which the second-harmonic intercept was measured to be OIP2h,pd = 49 dBm at 1310 nm. The solid black, solid gray, and dashed gray curves illustrate the second-harmonic, third-harmonic, and third-order IMD intercept points calculated from Eqs. (25)(27). Note, the second-harmonic intercept is maximized (nonlinearity is minimized) near the laser center frequency given that the comb is nearly symmetric.

As the optical comb deviates from symmetry about the laser center frequency, for example due to a temporal misalignment of the amplitude and phase modulation in the comb generator or due to an asymmetric modelocked laser spectrum, the second-order linearity will again be optimized at the average frequency of the optical comb. To illustrate this, the comb generator is intentionally misaligned to produced combs with average frequencies lower and higher than that of the symmetric comb and the RF powers are once again measured as a function of bias frequency. Figure 3 shows the second-harmonic power (top row) normalized to the maximum value achieved either at high- or low-bias (ϕb = 0, π) and the corresponding optical comb (bottom row) as the comb is tuned to have a (a) low-frequency weighting, (b) near optimum symmetry, and (c) a high-frequency weighting. Here, the measured second-harmonic data are shown by the red circles and the calculated powers are shown by the solid black lines. The dashed red lines show the measured average comb frequency, calculated from the measured comb spectra via Eq. (19). In each case, the second-harmonic power is (optimally) minimized to the level determined by the photodiode near the comb average frequency. The frequency corresponding to minimum second-harmonic distortion is determined again from a numerical fit of Eq. (11). Comparisons of the calculated minimum distortion frequency (fbfo) determined from the measured second-harmonic data and the corresponding average frequency (favgfo) determined from the optical comb are given in Table 1. The error is defined as Error = 100 × |favgfb|/Δfrms, where Δfrms is the full root-mean-square bandwidth of the optical comb [13

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. B 17, 146–150 (2000). [CrossRef]

]. We see excellent agreement between the ideal bias frequency calculated from the measured second-harmonic distortion data and the comb average frequency, with errors less than 0.5% in all cases.

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)

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.

table-icon
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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).

4. Conclusion

5. Appendix

References and links

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. Express 21, 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. B 17, 146–150 (2000). [CrossRef]

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(350.4010) Other areas of optics : Microwaves

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: August 12, 2013
Revised Manuscript: September 9, 2013
Manuscript Accepted: September 9, 2013
Published: September 27, 2013

Citation
Jason D. McKinney, Vincent J. Urick, and Alexander S. Hastings, "Bias-dependent distortion in optical comb-based analog optical links," Opt. Express 21, 23695-23705 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23695


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References

  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]

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