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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 14 — Jul. 9, 2007
  • pp: 8713–8718
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Analysis of linearity of highly saturated electroabsorption modulator link due to photocurrent feedback effect

X. B. Xie, I. Shubin, W. S. C. Chang, and P. K. L. Yu  »View Author Affiliations


Optics Express, Vol. 15, Issue 14, pp. 8713-8718 (2007)
http://dx.doi.org/10.1364/OE.15.008713


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Abstract

We have analyzed the linearity performance of analog fiber-optic links based on electroabsorption modulators (EAM) operating at high optical power. The negative feedback caused by photocurrent generation improves the modulator linearity in the gain saturation regime. In the absence of laser relative intensity noise (RIN), the link spur-free dynamic range (SFDR) increases with the power of four-thirds of the input optical power after gain saturation occurs. A multi-octave SFDR of more than 135 dB/Hz2/3 has been found to be achievable with sufficiently high power.

© 2007 Optical Society of America

1. Introduction

Fig. 1. An equivalent circuit model of EAM used in an analog fiber-optic link.

2. Analysis

The small signal circuit model of the EAM can be represented similarly as in [1

1. W. B. Bridges, U. V. Cummings, and J. H. Schaffner, “Linearized modulators for analog photonic links,” in MWP ’96 Technical Digest, International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, , New York, 1996), pp. 61–64.

] which is shown here in Fig. 1, along with the optical signal transmission from the optical modulator to the photodetector. To simplify the equation derivation without loss of generality, the modulator termination resistance is not included here. The junction capacitance CJ is omitted in the following analysis for low frequency operation. As the input optical power is increased, both dc and ac photocurrent generation increase. This increases the portion of the voltage drop on the source resistance RS and the EAM serial resistance RM relative to the total source voltage, leaving a smaller portion on the modulator layer. From a feedback point of view, what happens at the EAM parallels a negative feedback system. The incoming voltage vS modulates the active layer and leads to the intensity modulation of the optical carrier, expressed as PLtItPtO[T(VB)-T(VB+vM)], where T(V) is the optical transfer function of the EAM; PL, tI, tP, tO, VB and vM are the input laser power, EAM input coupling coefficient, EAM propagation loss, EAM output coupling coefficient, the dc bias voltage, and the effective ac voltage across the modulation layer, respectively. At the same time the modulated light generates ac photocurrent which effectively reduces the voltage across the junction. At steady state, it becomes a negative feedback system, the output of which is coupled into the photodetector and generates output voltage vL across load resistance RD. This description can be schematically shown in Fig. 2, where ηM and ηD denote the responsivity of EAM and photodetector, respectively. With a low input optical power to the EAM, the photocurrent feedback can be ignored and the linearity of the electro-to-optical conversion is mainly determined by that of the optical transfer function T(V). When the optical power increases, the effective voltage across the EAM junction is no longer vS, but vM which is modified by the photocurrent feedback. We can easily show that vM satisfies the following equation:

Fig. 2. Negative feedback system formed by the effect of photo-generated current on EAM circuit in an analog fiber-optic link configuration. The black and orange lines correspond to electrical and optical transmissions, respectively.
vM=vS(RS+RM)ηMPLtItP[T(VB)T(VB+vM)]
(1)

Using a voltage gain function vOUT = g(vIN) at no feedback, we can relate vIN and vOUT under feedback as follows:

g(vINfvOUT)=vOUT
(2)

where g is a function that includes the nonlinear harmonics caused by the optical transfer curve T(V) and f is the negative feedback coefficient as described by:

f=(RS+RM)ηM2ηDRDtO
(3)

dTedVIN=2dTdVM1PLtItPηM(RS+RM)dTdVM
(4)
d2TedVIN2=4d2TdVM2(1PLtItPηM(RS+RM)dTdVM)3
(5)
d3TedVIN3=8d3TdVM3(1PLtItPηM(RS+RM)dTdVM)+24PLtItPηM(RS+RM)(d2TdVM2)2(1PLtItPηM(RS+RM)dTdVM)5
(6)

k=11PLtItPηM(RS+RM)dTdVM=1+1PLtItPηM(RS+RM)π2Vπ
(7)

IIP2(dTdVd2TdV2)2andIIP3dTdVd3TdV3
(8)

Fig. 3. Calculated link output noise floor and multi-octave IIP3 as a function of input optical power. Laser RIN noise is not included. Low power EAM IIP3 of 20 dBm is assumed.
Additional optical loss of 3 dB is caused by dc bias . Other parameters used in the calculation are: tI = tO = -3 dB, tP = -1 dB, RS = RD = 50 Ω, RM = 5 Ω, ηM = ηD = 1 A/W, Vπ = 1.5 V.
Fig. 4. Calculated RF link gain, multi-octave link OIP3 and SFDR dependence on input optical power. Conditions and parameter values in the calculation are the same as Fig. 3.

3. Conclusions

Acknowledgments

The authors acknowledge the funding support of Defense Advanced Research Projects Agency via Photonic Systems Inc., AFRL at Rome location, and Lockheed Martin at Newtown, Penn.

References and Links

1.

W. B. Bridges, U. V. Cummings, and J. H. Schaffner, “Linearized modulators for analog photonic links,” in MWP ’96 Technical Digest, International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, , New York, 1996), pp. 61–64.

2.

G. E. Betts, X. B. Xie, I. Shubin, W. S. C. Chang, and P. K. L. Yu, “Gain limit in analog links using electroabsorption modulators,” IEEE Photon. Technol. Lett. 18, 2065–2067 (2006). [CrossRef]

3.

C. H. Cox III, E. I. Ackerman, G. E. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microwave Theory Tech. 52, 906–920 (2006). [CrossRef]

4.

T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits (Cambridge Univ. Press, 1998), Chap. 14.

5.

R. B. Welstand, S. A. Pappert, C. K. Sun, J. T. Zhu, Y. Z. Liu, and P. K. L. Yu, “Dual-function electroabsorption waveguide modulator/detector for optoelectronic transceiver applications,” IEEE Photon. Technol. Lett. 8, 1540–1542 (1996). [CrossRef]

6.

K. J. Williams, L. T. Nichols, and R. D. Esman, “Photodetector nonlinearity limitations on a high-dynamic range 3 GHz fiber optic link,” IEEE J. Lightwave Technol. 16, 192–199 (1998). [CrossRef]

7.

E. I. Ackerman, “Broad-band linearization of a Mach-Zehnder electrooptic modulator,” IEEE Trans. Microwave Theory Tech. 47, 2271–2279 (1999). [CrossRef]

8.

P. K. L. Yu, I. Shubin, X. B. Xie, Y. Zhuang, A. J. X. Chen, and W. S. C. Chang, “Transparent ROF link using EA modulators,” in MWP ’05 Technical Digest, International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, Seoul, 2005), pp. 21–24.

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(130.5990) Integrated optics : Semiconductors
(250.7360) Optoelectronics : Waveguide modulators
(350.4010) Other areas of optics : Microwaves

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 26, 2007
Revised Manuscript: June 21, 2007
Manuscript Accepted: June 25, 2007
Published: June 27, 2007

Citation
X. B. Xie, I. Shubin, W. S. C. Chang, and P. K. L. Yu, "Analysis of linearity of highly saturated electroabsorption modulator link due to photocurrent feedback effect," Opt. Express 15, 8713-8718 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-8713


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References

  1. W. B. Bridges, U. V. Cummings, and J. H. Schaffner, "Linearized modulators for analog photonic links," in MWP ’96 Technical Digest, International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 61-64.
  2. G. E. Betts, X. B. Xie, I. Shubin, W. S. C. Chang, and P. K. L. Yu, "Gain limit in analog links using electroabsorption modulators," IEEE Photon. Technol. Lett. 18, 2065-2067 (2006). [CrossRef]
  3. C. H. CoxIII, E. I. Ackerman, G. E. Betts, and J. L. Prince, "Limits on the performance of RF-over-fiber links and their impact on device design," IEEE Trans. Microwave Theory Tech. 52, 906-920 (2006). [CrossRef]
  4. T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits (Cambridge Univ. Press, 1998), Chap. 14.
  5. R. B. Welstand, S. A. Pappert, C. K. Sun, J. T. Zhu, Y. Z. Liu, and P. K. L. Yu, "Dual-function electroabsorption waveguide modulator/detector for optoelectronic transceiver applications," IEEE Photon. Technol. Lett. 8, 1540-1542 (1996). [CrossRef]
  6. K. J. Williams, L. T. Nichols, and R. D. Esman, "Photodetector nonlinearity limitations on a high-dynamic range 3 GHz fiber optic link," IEEE J. Lightwave Technol. 16, 192-199 (1998). [CrossRef]
  7. E. I. Ackerman, "Broad-band linearization of a Mach-Zehnder electrooptic modulator," IEEE Trans. Microwave Theory Tech. 47, 2271-2279 (1999). [CrossRef]
  8. P. K. L. Yu, I. Shubin, X. B. Xie, Y. Zhuang, A. J. X. Chen, and W. S. C. Chang, "Transparent ROF link using EA modulators," in MWP ’05 Technical Digest, International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, Seoul, 2005), pp. 21-24.

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