## Analysis of linearity of highly saturated electroabsorption modulator link due to photocurrent feedback effect

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/Hz^{2/3} has been found to be achievable with sufficiently high power.

© 2007 Optical Society of America

## 1. Introduction

*f*

_{1}and

*f*

_{2}with a small frequency offset modulate the optical carrier. The second- and third- order intermodulation (IM2 and IM3) distortion signals are measured at the link output. The widely used figure of merit, spur-free dynamic range (SFDR), is defined as the output signal to noise ratio (SNR) as the IM3 signal starts to emerge from the noise floor. SFDR not only depends on the linearity of the optical transfer curve, but also on the link gain and link noise performance.

*et al*[2

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]

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]

## 2. Analysis

*C*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

_{J}*R*and the EAM serial resistance

_{S}*R*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

_{M}*v*modulates the active layer and leads to the intensity modulation of the optical carrier, expressed as

_{S}*P*[

_{L}t_{I}t_{P}t_{O}*T*(

*V*)-

_{B}*T*(

*V*+

_{B}*v*)], where

_{M}*T*(

*V*) is the optical transfer function of the EAM;

*P*,

_{L}*t*,

_{I}*t*,

_{P}*t*,

_{O}*V*and

_{B}*v*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

_{M}*v*across load resistance

_{L}*R*. This description can be schematically shown in Fig. 2, where η

_{D}_{M}and η

_{D}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

*v*, but

_{S}*v*which is modified by the photocurrent feedback. We can easily show that

_{M}*v*satisfies the following equation:

_{M}*v*=

_{OUT}*g*(

*v*) at no feedback, we can relate

_{IN}*v*and

_{IN}*v*under feedback as follows:

_{OUT}*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:

*v*=

_{IN}*v*/2 is used to conform with the conventional definition for analog fiber-optic link gain, where the input RF power is taken with a modulator load matched to that of the RF source [3

_{S}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]

*v*is equivalent to

_{OUT}*v*, the ac voltage across the load resistance of the photodetector. It has been well established in electronic amplifier design that the negative feedback can improve the linearity of the whole system if the feedback coefficient is more linear than the transfer function of the system under no feedback [4]. When the loop voltage gain is large, the overall feedback system response is close to the inverted feedback network response. In our case,

_{L}*g*represents the transfer function at no feedback and includes optical transfer curve nonlinearities. Feedback coefficient

*f*, on the other hand, does not consist of any elements of the nonlinear optical transfer curve. When the voltage gain at no feedback (

*f*= 0) is high enough, the actual voltage gain (under feedback) can be approximated as 1/

*f*. The system linearity is hence determined mainly by

*f*, and not by the EAM transfer function. However, the EAM and photodetector responsivities involved in f can still affect the system linearity.

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]

*dT*/

*dV*is considered negative due to the fact that larger voltage causes less optical transmission in conventional quantum well designs. The denominator on the right side of Eq. (4), denoted as EAM saturation factor

_{M}*k*, becomes much larger than unity when the input optical power is high enough, which reduces the link gain:

*k*

^{4}and

*k*

^{3}compared with the no-feedback situation. The output second and third-order intercept points (OIP2 and OIP3) increases by the same factor when the gain saturates. On the other hand, the link output noise only increases linearly with optical power even when EAM shot noise dominates in the saturation case, which is approximately proportional to

*k*. Hence, in the absence of laser intensity noise (RIN), the link SFDR improves by

*k*

^{4/3}.

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]

^{2/3}.

_{M}and η

_{D}to be constants with respect to the input voltage, which is the ideal case. In practice, a complete calculation should include nonlinearities of η

_{M}and η

_{D}as well. More studies are needed for a better understanding of the dependences of η

_{M}and η

_{D}upon input voltage at high optical power before their effects on link linearity can be evaluated.

^{2/3}at 240 mW laser power [6

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]

^{4/5}. However, the multi-octave SFDR remained low. A dual-wavelength EOM scheme with optical powers of 200 mW at 1320 nm and 30 mW at 1550 mW yielded an SFDR of 121 dB/Hz

^{2/3}[7

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

## 3. Conclusions

*k*

^{3}and

*k*

^{4/3}, respectively.

## Acknowledgments

## References and Links

1. | W. B. Bridges, U. V. Cummings, and J. H. Schaffner, “Linearized modulators for analog photonic links,” in MWP ’ |

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. |

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. |

4. | T. H. Lee, |

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. |

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. |

7. | E. I. Ackerman, “Broad-band linearization of a Mach-Zehnder electrooptic modulator,” IEEE Trans. Microwave Theory Tech. |

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 |

**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

- 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.
- 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]
- 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]
- T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits (Cambridge Univ. Press, 1998), Chap. 14.
- 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]
- 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]
- E. I. Ackerman, "Broad-band linearization of a Mach-Zehnder electrooptic modulator," IEEE Trans. Microwave Theory Tech. 47, 2271-2279 (1999). [CrossRef]
- 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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