## Integrated photonic threshold comparator based on square-wave synthesis |

Optics Express, Vol. 21, Issue 12, pp. 14251-14261 (2013)

http://dx.doi.org/10.1364/OE.21.014251

Acrobat PDF (2336 KB)

### Abstract

A photonic threshold comparator is presented. A step-like electrical-to-optical (E/O) response is obtained by employing Fourier series synthesis in which a set of sine-wave responses of different amplitudes and phases are superimposed according to the Fourier series representation of a square-wave. The proposed comparator does not rely on optical material non-linearity; rather it consists of multimode interference (MMI) couplers and phase shifters.

© 2013 OSA

## 1. Introduction

1. H. Taylor, “An optical analog-to-digital converter–design and analysis,” IEEE J. Quantum Electron. **15**(4), 210–216, (1979) [CrossRef] .

3. Y. Peng, H. Zhang, Q. Wu, Y. Zhang, X. Fu, and M. Yao, “Experimental Demonstration of all-optical analog-to-digital conversion with balanced detection threshold scheme,” IEEE Photon. Technol. Lett. **21**(23), 1776–1778, (2009) [CrossRef] .

4. L. Loh and J. LoCicero, “Subnanosecond sampling all-optical analog-to-digital converter using symmetric self-electro-optic effect devices,” SPIE Optical Engineering (**35**)(2), 457–466 (1995) [CrossRef] .

13. A. Tait, B. Shastri, M. Fok, M. Nahmias, and P. Prucnal, “The DREAM: an integrated photonic thresholder,” J. of Lightwave Technol. **31**(8), 1263–1272, (2013) [CrossRef] .

*self-imaging*effect in waveguides [15

15. L. Soldano and E. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications”, J. of Lightwave Technol. **13**(4), 615–627 (1995) [CrossRef] .

16. J. Yu, H. Wei, X. Zhang, Q. Yan, and J. Xia, “Integrated MMI optical couplers and optical switches in silicon-on-insulator technology,” Proc. SPIE **4582**, 57–62 (2001) [CrossRef] .

17. N.S. Lagali, M.R. Paiam, R.I. MacDonald, K. Rhoff, and A. Driessen, “Analysis of generalized Mach-Zehnder interferometers for variable-ratio power splitting and optimized switching,” J. of Lightwave Technol. **17**(12), 2542–2550 (1999) [CrossRef] .

## 2. Comparator overview

*V*and

_{a}*V*, respectively. The figure provides the static transfer characteristic of an ideal comparator (dashed line) and a realistic comparator (continuous line).

_{out}*V*, and above

_{IL}*V*, generate well defined output levels, namely:

_{IH}*V*, representing logic-0; and

_{OL}*V*, representing logic-1, respectively. For input levels in the range [

_{OH}*V*,

_{IL}*V*] the comparator output state is undefined [18

_{IH}18. C. Toumazou, G. Moschytz, and B. Gilbert, *Trade-offs in analog circuit design: the designer’s companion*(Kluwer Academic Publishing2002) [CrossRef] .

*V*is continuous in nature, it is not unlikely for the output to yield values in the transition region [

_{a}*V*,

_{OL}*V*] which may be erroneously identified by the following stage.

_{OH}*gain*and

*extinction ratio*. The

*Gain*is defined as the slope of the output curve about the input value

*V*[18

_{m}18. C. Toumazou, G. Moschytz, and B. Gilbert, *Trade-offs in analog circuit design: the designer’s companion*(Kluwer Academic Publishing2002) [CrossRef] .

*V*is the input voltage for which the output voltage is

_{m}*V*= (

_{out}*V*+

_{OH}*V*)/2; this is actually the input threshold level. Note that the gain of the ideal comparator is infinite, while the gain is finite in a realistic comparator. High gain in the vicinity of the threshold point is a desirable property of a good comparator.

_{OL}*ER*) measures the distinction between the output high and low levels:

## 3. Photonic threshold comparator using square-wave synthesis

*v*and it outputs high optical power when

_{a}*v*exceeds a certain voltage level, and low optical power otherwise. This threshold behavior, which makes the device suitable as a comparator, is obtained here by using Fourier series synthesis whereby a set of sine-wave responses of appropriate amplitudes and phases are superimposed to generate a square-wave. Periodic function

_{a}*f*(

*x*) of period

*L*can be described by a complex Fourier series as: where The power of complex Fourier series of a biased (negative values are not allowed) square-wave with periodicity

*V*is: where

_{π}*P*is the optical input power,

_{in}*P*is the optical output power,

_{out}*M*and |

*m*| are odd integers, and

*C*is a constant offset.

- A coherent optical signal splits into
*N*equal components, where*N*= 2*M*+ 1. E.g., if*N*= 5, then*M*= 3 and so*m*∈ {−3, −1, 1, 3} plus a DC component,*C*, are used. - The amplitude of each component is attenuated proportionally to the corresponding Fourier coefficient.
- The phase of each signal is adjusted accordingly. The individual phases have a fixed part and a variable part, the later being proportional to the electrical input signal
*v*._{a} - The signals are recombined into a single waveguide while preserving their phases and amplitudes.
- The outcoming optical signal is transduced into an electrical voltage
*V*by means of a square-law detector._{out}

*V*(

_{out}*V*) is attained through the mathematical dependencies between between phases and amplitudes of interfering signals. A 5-arm design example for implementing Eq. (5) with

_{a}*N*= 5, is depicted in Figure 2. Optical power enters MMI-1 and equally splits into its 5 output arms. The arms serve as passive phase shifters (#1). These constant phases can be adjusted in such a way that when combined with MMI-2, produce a set of 5 optical signals whose amplitudes nearly obey the Fourier series formula. For these signals, the appropriate constant phase shifts are induced by the additional set of passive phase shifters (#2). The analog input voltage,

*v*, is simultaneously applied to the set of active phase shifters (#3) thus inducing the phases for the 5 signals as required by Eq. (5). The set of passive phase shifters (#4) together with the third coupler, MMI-3, serve as a coherent optical field combiner. In a practical design, the two passive shifters (#2 and #4), can be combined into a single one.

_{a}*L*is given by [20

20. N. Lagali, M. Paiam, and R. MacDonald, “Theory of variable-ratio power splitters using multimode interference couplers,” IEEE Photon. Technol. Lett. **11**(6), 665–667, (1999) [CrossRef] .

*N*is the number of arms of the MMI and

*L*is its beat length defined by with

_{π}*β*

_{0}and

*β*

_{1}being the propagation constants of the fundamental and first-order modes supported by the multimode region of the MMI coupler, respectively.

*N*×

*N*MMI device by

*S*. The element in row

_{MMI}*i*and column

*k*of this matrix is given by where

*a*is the field amplitude transfer coefficient from input

_{ik}*i*to output

*k*, and

*ϕ*is the associated phase. In a lossless MMI the field amplitude transfer coefficient is

_{ik}17. N.S. Lagali, M.R. Paiam, R.I. MacDonald, K. Rhoff, and A. Driessen, “Analysis of generalized Mach-Zehnder interferometers for variable-ratio power splitting and optimized switching,” J. of Lightwave Technol. **17**(12), 2542–2550 (1999) [CrossRef] .

*i*,

*k*is: The field emerging from MMI-2 can be written in matrix form as where the input field vector is meaning that optical energy enters only the center port of MMI-1.

*M*

_{ps}_{1}is an

*N*×

*N*diagonal matrix whose non-zero entries are the phase shifts The optimum values for

*θ*are found by employing the method described by Lagali [20

_{i}20. N. Lagali, M. Paiam, and R. MacDonald, “Theory of variable-ratio power splitters using multimode interference couplers,” IEEE Photon. Technol. Lett. **11**(6), 665–667, (1999) [CrossRef] .

**e**

_{out}_{2}in accordance with the Fourier series formula. Its operation can be formulated by a

*N*×

*N*diagonal matrix

*M*

_{ps}_{2}. For the 5-arm design, relative to the phase of the optical wave in the middle arm, the phases of the optical waves in the two upper arms are set to

*v*, is applied to the device through a number of electrodes of different lengths. The electrodes produce a set of phase shifts given mathematically by the diagonal matrix,

_{a}*M*

_{ps}_{3}, whose elements are given by:

*x*⌋ means rounding to nearest integer smaller than

*x*,

*n*indicates the relative electrode length, and

*V*is the half-wave voltage of the phase shifter. Note that no electrical signal is applied to the middle arm. For example, for

_{π}*N*= 5, the diagonal elements of

*M*

_{ps}_{3}are:

*M*

_{ps}_{4}are assuming that the output port of MMI-3 is in the center,

*k*= ⌊

*N*/2⌋.

**e**

_{out}_{3}| assumes a square-like shape as a function of the input voltage,

*v*. MMI-3 also induces passive phases that need to be cancelled by shifters #2, #4.

_{a}## 4. Design considerations

**1)**use of low-loss, high contrast materials for the fabrication of an efficient MMI coupler. Materials such as Silicon, InP, GaAs are suitable;

**2)**it follows from Equation (5) that the active phase shifters must be linear so that the induced phase shift is linear with the applied voltage. Materials which posses the Pockels effect would be most suitable for this purpose.

21. G. Reed, G. Mashanovich, F. Gardes, and D. Thomson, “Silicon optical modulators,” Nature photonics **4**(8), 518–526 (2010) [CrossRef] .

23. K. Tsuzuki, T. Ishibashi, T. Ito, S. Oku, Y. Shibata, R. Iga, Y. Kondo, and Y. Tohmori, “40 Gbit/s n-i-n InP Mach-Zehnder modulator with a *π *voltage of 2.2V,” IET Electronics Letters **39**(20), 1464–1466 (2003) [CrossRef] .

*μm*is formed with a 1

*μm*thickness layer of InGaAsP on InP substrate. The refractive index of the InP is

*n*= 3.167 and that of the InGaAsP is

_{InP}*n*= 3.22. The waveguide is surrounded by air cladding. The widths of the MMI couplers are

_{InGaAsP}*W*= 40

_{MMI}*μm*, and the corresponding lengths are

*L*= 2527

_{MMI}*μm*.

## 5. Performance

*V*where

*P*= 10

_{in}*mW*.

*v*while the y-axis is the resulting optical signal intensity,

_{a}*P*, at the device output. The applied voltages,

_{out}*v*, in the figure are DC reversed biased. The horizontal bar labeled

_{a}*P*= 3.5

_{OH}*mW*, is the minimum output power-level representing logic-1, while the horizontal bar labeled

*P*= 0.35

_{OL}*mW*, is the maximum power level representing logic-0. The output levels,

*P*and

_{OH}*P*, were chosen as explained in Section 2. In a practical system, the comparator typically drives a logical stage. Therefore, one has to make sure that these output levels suitably match the specified input logic levels of the following digital stage.(for E/E response one may employ a photodetector at the device output to convert the output optical power to a corresponding voltage level.)

_{OL}### 5.1. Input dynamic range

*input dynamic range*(DR) will be defined as |

*V*−

_{IE}*V*|, where

_{IS}*V*and

_{IS}*V*are the lowest and highest voltage values allowed at the input for proper operation of the comparator. In Figure 3, it can be seen that an input voltage below

_{IE}*V*= 0.45

_{IL}*V*will output low level (not greater than

_{π}*P*) and input above

_{OL}*V*= 0.55

_{IH}*V*, will output high level (not smaller than

_{π}*P*). This, in turn, means that input voltage levels in the range

_{OH}*V*<

_{IS}*v*<

_{a}*V*produce low output power, while input voltage levels

_{IL}*V*<

_{IH}*v*<

_{a}*V*produce high output power.

_{IE}*V*,

_{IL}*V*] produce output power levels of undefined logic interpretation [18

_{IH}18. C. Toumazou, G. Moschytz, and B. Gilbert, *Trade-offs in analog circuit design: the designer’s companion*(Kluwer Academic Publishing2002) [CrossRef] .

*v*is analog, of a continuous nature, the region [

_{a}*V*,

_{IL}*V*] should clearly be minimized. It follows that a well designed comparator must present a steep transition slope, which one may refer to as gain.

_{IH}### 5.2. Comparator gain

*Gain*is measured between the input and the output of a device. Since the proposed comparator is an electro-optical device in which the input is electrical and the output is optical, the gain may be defined as the following ratio: where

*V*is the input voltage for which the output power is

_{m}*P*= (

_{out}*P*+

_{OH}*P*)/2.

_{OL}*V*=

_{pd}*P*·

_{out}*r*·

*R*, where

*r*is the

*responsivity*of the detector in units of

*A/W*and

*R*is the output resistance, usually 50Ω. It follows that

*V*is proportional to the output optical power, and consequently the gain given by Equation (16) is suitable for device evaluation purposes.

_{pd}### 5.3. Design examples

*N*= 5 and 9 arms. Table 1 summarizes the input power, MMI dimensions and static performance for these designs. To provide baseline for comparison, the comparators were all designed to achieve high digital output level of

*P*= 2

_{OH}*mW*.

*mW*. It follows from the discussion in previous sections that increasing the arm count leads to reduction of the peak output power and consequently

*P*. This occurs because for a larger arm count, the input optical power is distributed among a larger number of ports, and the higher Fourier components are of decreasing amplitudes. So, to compensate for that loss, and achieve the required

_{OH}*P*, the input power

_{OH}*P*must be increased. Thus, for

_{in}*N*= 5,

*P*= 5.9

_{in}*mW*, while increasing the arm count to

*N*= 9 the required input power is 10.3

*mW*.

*N*= 5 design achieves gain of 10.6

*dB*, while increasing the arm count to 9 monotonically increases the gain by additional 2.6

*dB*. For the two designs, the achieved low level output and extinction ratios, are

*P*= 0.2

_{OL}*mW*and

*ER*= −10

*dB*, respectively.

*TR*= (

*V*−

_{IH}*V*)/

_{IL}*DR*, provides a good measure for the quality of the comparator. A wider transition region implies greater error probably (undefined logic state) at the output of the comparator. Obviously, the higher is the gain, the better is the TR value. The transition region improves as

*N*increases.

17. N.S. Lagali, M.R. Paiam, R.I. MacDonald, K. Rhoff, and A. Driessen, “Analysis of generalized Mach-Zehnder interferometers for variable-ratio power splitting and optimized switching,” J. of Lightwave Technol. **17**(12), 2542–2550 (1999) [CrossRef] .

*nm*. Greater deviations from the nominal wavelength results with a distorted output.

## 6. Multi-threshold comparator for optical analog-to-digital conversion

*N*= 5 when the input voltage spans from 0

*V*to 10

*V*. The response of the (single-threshold) comparator of Figure 4(a) is duplicated 4 times.

1. H. Taylor, “An optical analog-to-digital converter–design and analysis,” IEEE J. Quantum Electron. **15**(4), 210–216, (1979) [CrossRef] .

12. G.C. Valley, “Photonic analog-to-digital converters,” Opt. Express **15**(5), 1955–1982 (2007) [CrossRef] [PubMed] .

## 7. Conclusions

## References and links

1. | H. Taylor, “An optical analog-to-digital converter–design and analysis,” IEEE J. Quantum Electron. |

2. | H. Chi and J. Yao, “A photonic analog-to-digital conversion scheme using Mach-Zehnder modulators with identical half-wave voltages,” Opt. Express |

3. | Y. Peng, H. Zhang, Q. Wu, Y. Zhang, X. Fu, and M. Yao, “Experimental Demonstration of all-optical analog-to-digital conversion with balanced detection threshold scheme,” IEEE Photon. Technol. Lett. |

4. | L. Loh and J. LoCicero, “Subnanosecond sampling all-optical analog-to-digital converter using symmetric self-electro-optic effect devices,” SPIE Optical Engineering ( |

5. | L. Brzozowski and E. Sargent, “All-optical analog-to-digital converters, hardlimiters, and logicgates,” J. of Light-wave Technol. |

6. | H. Sakata, “Photonic analog-to-digital conversion by use of nonlinear Fabry-Perot resonators,” Applied Optics |

7. | P. Parolari, L. Marazzi, M. Connen, and M. Martinelli, “SOA based all-optical threshold,” in Conference on Lasers and Electro-Optics (CLEO), 309–310 (2000). |

8. | G. Morthier, M. Zhao, B. Vanderhaegen, and R. Baets, “Experimental demonstration of an all-optical 2R regenerator with adjustable decision threshold and True regeneration characteristics,” IEEE Photon. Technol. Lett. |

9. | S. Pereira, P. Chak, J. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photonics and Nanostructures-Fundamentals and Applications , |

10. | B. Maes, P. Bienstman, and R. Baets, “Switching in coupled nonlinear photonic-crystal resonators,” J. Opt. Soc. Am. B , /textbf |

11. | K. Ikeda, J. Abdul, H. Tobioka, T. Inoue, S. Namiki, and K. Kitayama, “Design considerations of all-optical A/D conversion: nonlinear fiber-optic Sagnac-loop unterferometer-based optical quantizing and coding,” J. of Lightwave Technol. |

12. | G.C. Valley, “Photonic analog-to-digital converters,” Opt. Express |

13. | A. Tait, B. Shastri, M. Fok, M. Nahmias, and P. Prucnal, “The DREAM: an integrated photonic thresholder,” J. of Lightwave Technol. |

14. | Y. Ehrlichman, O. Amrani, and S. Ruschin, “Photonic comparator by square-wave synthesis,” in |

15. | L. Soldano and E. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications”, J. of Lightwave Technol. |

16. | J. Yu, H. Wei, X. Zhang, Q. Yan, and J. Xia, “Integrated MMI optical couplers and optical switches in silicon-on-insulator technology,” Proc. SPIE |

17. | N.S. Lagali, M.R. Paiam, R.I. MacDonald, K. Rhoff, and A. Driessen, “Analysis of generalized Mach-Zehnder interferometers for variable-ratio power splitting and optimized switching,” J. of Lightwave Technol. |

18. | C. Toumazou, G. Moschytz, and B. Gilbert, |

19. | M. Madhavilatha, G.L. Madhumati, and K.R.K. Rao, “Design of CMOS comparator for flash ADC,” International Journal of Electronics Engineering , |

20. | N. Lagali, M. Paiam, and R. MacDonald, “Theory of variable-ratio power splitters using multimode interference couplers,” IEEE Photon. Technol. Lett. |

21. | G. Reed, G. Mashanovich, F. Gardes, and D. Thomson, “Silicon optical modulators,” Nature photonics |

22. | S. Niwa, S. Matsuo, T. Kakitsuka, and K. Kitayama, “Experimental demonstration of 1×4 InP/InGAsP optical integrated multimode interference waveguide switch,” in |

23. | K. Tsuzuki, T. Ishibashi, T. Ito, S. Oku, Y. Shibata, R. Iga, Y. Kondo, and Y. Tohmori, “40 Gbit/s n-i-n InP Mach-Zehnder modulator with a |

**OCIS Codes**

(070.1170) Fourier optics and signal processing : Analog optical signal processing

(130.3120) Integrated optics : Integrated optics devices

(190.1450) Nonlinear optics : Bistability

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: March 14, 2013

Revised Manuscript: April 18, 2013

Manuscript Accepted: April 19, 2013

Published: June 7, 2013

**Citation**

Yossef Ehrlichman, Ofer Amrani, and Shlomo Ruschin, "Integrated photonic threshold comparator based on square-wave synthesis," Opt. Express **21**, 14251-14261 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14251

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### References

- H. Taylor, “An optical analog-to-digital converter–design and analysis,” IEEE J. Quantum Electron.15(4), 210–216, (1979). [CrossRef]
- H. Chi and J. Yao, “A photonic analog-to-digital conversion scheme using Mach-Zehnder modulators with identical half-wave voltages,” Opt. Express16(2), 567–572 (2008). [CrossRef] [PubMed]
- Y. Peng, H. Zhang, Q. Wu, Y. Zhang, X. Fu, and M. Yao, “Experimental Demonstration of all-optical analog-to-digital conversion with balanced detection threshold scheme,” IEEE Photon. Technol. Lett.21(23), 1776–1778, (2009). [CrossRef]
- L. Loh and J. LoCicero, “Subnanosecond sampling all-optical analog-to-digital converter using symmetric self-electro-optic effect devices,” SPIE Optical Engineering(35)(2), 457–466 (1995). [CrossRef]
- L. Brzozowski and E. Sargent, “All-optical analog-to-digital converters, hardlimiters, and logicgates,” J. of Light-wave Technol.19(1), 114–119, (2001). [CrossRef]
- H. Sakata, “Photonic analog-to-digital conversion by use of nonlinear Fabry-Perot resonators,” Applied Optics40(2), 240–248, 2001. [CrossRef]
- P. Parolari, L. Marazzi, M. Connen, and M. Martinelli, “SOA based all-optical threshold,” in Conference on Lasers and Electro-Optics (CLEO), 309–310 (2000).
- G. Morthier, M. Zhao, B. Vanderhaegen, and R. Baets, “Experimental demonstration of an all-optical 2R regenerator with adjustable decision threshold and True regeneration characteristics,” IEEE Photon. Technol. Lett.12(11), 1516–1518 (2002). [CrossRef]
- S. Pereira, P. Chak, J. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized Kerr nonlinear microresonator system,” Photonics and Nanostructures-Fundamentals and Applications, 2(3), 181–190 (2004). [CrossRef]
- B. Maes, P. Bienstman, and R. Baets, “Switching in coupled nonlinear photonic-crystal resonators,” J. Opt. Soc. Am. B, /textbf22(8), 1778–1784 (2005). [CrossRef]
- K. Ikeda, J. Abdul, H. Tobioka, T. Inoue, S. Namiki, and K. Kitayama, “Design considerations of all-optical A/D conversion: nonlinear fiber-optic Sagnac-loop unterferometer-based optical quantizing and coding,” J. of Lightwave Technol.24(7), 2618–2628, (2006). [CrossRef]
- G.C. Valley, “Photonic analog-to-digital converters,” Opt. Express15(5), 1955–1982 (2007). [CrossRef] [PubMed]
- A. Tait, B. Shastri, M. Fok, M. Nahmias, and P. Prucnal, “The DREAM: an integrated photonic thresholder,” J. of Lightwave Technol.31(8), 1263–1272, (2013). [CrossRef]
- Y. Ehrlichman, O. Amrani, and S. Ruschin, “Photonic comparator by square-wave synthesis,” in Proceedings of 26th Convention of Electrical and Electronics Engineers in Israel (IEEEI)(IEEE2010), pp. 395–397.
- L. Soldano and E. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications”, J. of Lightwave Technol.13(4), 615–627 (1995). [CrossRef]
- J. Yu, H. Wei, X. Zhang, Q. Yan, and J. Xia, “Integrated MMI optical couplers and optical switches in silicon-on-insulator technology,” Proc. SPIE4582, 57–62 (2001). [CrossRef]
- N.S. Lagali, M.R. Paiam, R.I. MacDonald, K. Rhoff, and A. Driessen, “Analysis of generalized Mach-Zehnder interferometers for variable-ratio power splitting and optimized switching,” J. of Lightwave Technol.17(12), 2542–2550 (1999). [CrossRef]
- C. Toumazou, G. Moschytz, and B. Gilbert, Trade-offs in analog circuit design: the designer’s companion(Kluwer Academic Publishing2002). [CrossRef]
- M. Madhavilatha, G.L. Madhumati, and K.R.K. Rao, “Design of CMOS comparator for flash ADC,” International Journal of Electronics Engineering, 1(1), 53–57 (2009).
- N. Lagali, M. Paiam, and R. MacDonald, “Theory of variable-ratio power splitters using multimode interference couplers,” IEEE Photon. Technol. Lett.11(6), 665–667, (1999). [CrossRef]
- G. Reed, G. Mashanovich, F. Gardes, and D. Thomson, “Silicon optical modulators,” Nature photonics4(8), 518–526 (2010). [CrossRef]
- S. Niwa, S. Matsuo, T. Kakitsuka, and K. Kitayama, “Experimental demonstration of 1×4 InP/InGAsP optical integrated multimode interference waveguide switch,” in 20th International Conference on Indium Phosphide and Related Materials (IPRM)(IEEE2008), pp. 1–4.
- K. Tsuzuki, T. Ishibashi, T. Ito, S. Oku, Y. Shibata, R. Iga, Y. Kondo, and Y. Tohmori, “40 Gbit/s n-i-n InP Mach-Zehnder modulator with a π voltage of 2.2V,” IET Electronics Letters39(20), 1464–1466 (2003). [CrossRef]

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