## Abstract

Silicon photonics has emerged as the premier candidate for the photonic systems-on-chip (SoC). The scheme based on the silicon Mach-Zehnder modulator (MZM) to generate photonic ultra-wideband (UWB) signals is helpful to the integration of the UWB system with other optical networks on a single silicon-based chip. In this paper, according to the influence of the nonlinear free carrier dispersion (FCD) effect and the free carrier absorption (FCA) effect, the performance of two typical UWB generation schemes is numerically analyzed. The double side-band UWB (DSB-UWB) generation scheme needs the DC reverse bias which increases the complexity of the modulator and there is a residual chirp resulting from the FCD effect even the push-pull operation is adopted. The quasi single-sideband UWB (QSSB-UWB) generation scheme doesn’t have these problems. However there is the asymmetric amplitude peak in the generated UWB signal. The property of the large singal modulation is also investigated to improve the signal-to-noise ratio (SNR).

© 2012 OSA

## 1. Introduction

Ultra-wideband (UWB), known as one of the most promising technology in next generation wireless personal area network, has attracted lots of research interest due to its advantages including high data-rate, low cost and low power consumption [1, 2]. The restriction of low power spectral density regulated by the U.S. Federal Communication Commission (FCC) leads to a limited coverage range within tens of meters. In order to enlarge coverage and offer undisrupted service, UWB over fiber (UWBoF) system is then proposed [3]. As a result, UWB generation in the optical domain is highly desirable.

However, most of UWB generation schemes employ a combination of discrete devices and then the system becomes bulky and expensive. In the last few years, silicon photonics has emerged as the premier candidate for the photonic systems-on-chip (SoC) due to its small footprints and CMOS-compatibility [4]. The use of on-chip devices based on silicon is thus of much interest and could greatly reduce the complexity and the cost of UWB systems. It also can help integrate the UWB system with other existing wireless and wired networks on a single silicon-based chip which will have a profound effect on future UWB applications. Silicon MZM will be one of the most promising structures for the practical UWB system on chip (UWBSoC) since it is simple and has been improved with high stability and speed performance [5]. Moreover, the modulator based on Mach-Zehnder structure has been widely deployed in the commercial optical networks, so UWB generation scheme using silicon MZM will be more facile for integration with other optical networks.

Until now, there have been two reports about LiNbO_{3} MZM based UWB generations including double-side band UWB (DSB-UWB) [6] and quasi single-sideband UWB (QSSB-UWB) [7]. The two schemes are classified according to the optical spectral properties of the generated UWB pulses [8]. The influence of transmission over fiber [8] or large signal modulation [9] on UWB signals generated by MZM has also been analytically studied. However, silicon has different modulation mechanism from LiNbO_{3}, it modulates the refractive index through the free carrier dispersion effect (FCD) accompanying the free carrier absorption (FCA) [10]. The FCD is nonlinear and the FCA introduces considerable loss, both of which will result in the distortion of UWB signal. To the best of our knowledge, the impact of the silicon FCD and FCA on the performance of UWB signal is never before discussed.

In this paper, we propose the reverse-biased p-n diode based MZM with high modulation efficiency for the photonic generation of DSB-UWB and QSSB-UWB. P-n diode has an advantage on the operational speed which can meet the requirement of UWB signal modulation. Then we fully analyze the influence of the nonlinear FCD and FCA on these two types of signals and find the unique characteristics when using silicon to replace LiNbO_{3}. The paper is aimed to provide the theoretical basis about what should be considered when constructing the silicon MZM based optical UWB transmitter with compact footprints, relatively low power consumption and fabrication cost.

## 2. Theory and device structure

Figure 1(a)
shows the optical DSB-UWB monocycle generation scheme based on silicon MZM. The principle is that MZM as the intensity modulator converts an electrical UWB pulse to the optical domain. To obtain low or zero frequency chirping, two paths of electrical signal with π phase shift are applied to p-n junction waveguide phase shifters. According to the working principle of p-n junction, DC bias should be set at a proper value to make the electrical monocycle pulse’s voltage above zero as the reverse bias. Thermo-optic phase shifter (*φ*_{bias} = π/2) is used to set the operation point at the quadrature transmission.

In terms of the FCD effect in silicon, the two paths of electrical monocycle pulse will introduce the effective index change (Δ*N*_{eff}) and absorption coefficient variation (Δ*α*) by means of carrier depletion in p-n junction. The phase shift and the electric field transmission coefficient are Δ*φ* = Δ*N*_{eff}2π*L*/*λ* and *γ* = exp (*−*Δ*αL*/2) respectively (γ ≈1 for LiNbO_{3}), where *L* is the phase shifter length and *λ* is the optical wavelength of 1.55 μm. The optical field at the output of the MZM can be expressed as

*α*

_{1},

*α*

_{2}and

*φ*

_{w}_{(}

_{t}_{)},

*φ*

_{-w}_{(}

_{t}_{)}are the absorption coefficient change and phase shift induced by the drive signal

*W*(

*t*) and

*–W*(

*t*).

*W*(

*t*) is the electrical Gaussian monocycle which is the first order derivative of a Gaussian pulse and its normalized expression is given by

*W*(

*t*) = –

*t*exp(1/2)exp(

*-t*

^{2}/2

*T*

_{0}

^{2})/

*T*

_{0},

*T*

_{0}is the half-width (at 1/

*e*-intensity point) of the Gaussian pulse. In addition,

*α*

_{0}and

*φ*

_{DC}are the absorption coefficient and phase shift introduced by DC bias.

When the signal expressed by Eq. (1) is through a photo-detector (PD) for square-law detection, the photocurrent at the output of PD is

From Eqs. (1) and (2), we can see that there is some difference from that based on LiNbO_{3} MZM [8]. Firstly, the nonlinear FCD determines that the phase shift *φ _{w}*

_{(}

_{t}_{)}in silicon is not linear with the drive signal and can’t be expressed as κ∙

*W*(

*t*) like in LiNbO

_{3}, κ is the phase modulation index. Secondly, FCA leads to the power imbalance between two phase shifters (exp[

*-*(

*α*

_{1}

*+ α*

_{0})

*L*/2]

*≠*exp[

*-*(

*α*

_{2}

*+ α*

_{0})

*L*/2]) because the voltage of drive signal applied to the two phase shifters are different and then the absorption coefficient changes (

*α*

_{1},

*α*

_{2}) are different. Moreover, the FCA also results in the considerable loss at the output of PD which is nonexistent in LiNbO

_{3}MZM. Therefore, the nonlinear FCD and FCA will both cause the distortion of UWB signal.

Figure 1(b) shows the scheme for the generation of QSSB-UWB monocycle. The MZM is biased at the quadrature transmission point by thermo-optic phase shifter. Two Gaussian pulses with a time delay difference of *τ*_{0} are applied to the phase shifters of MZM. If *τ*_{0} is sufficiently short, the first-order difference can be approximated as the first-order derivative [8]. Then the pulse after a PD for square-law detection is QSSB-UWB monocycle.

The optical field at the output of MZM can be expressed as

The photocurrent at the output of PD is

*α*

_{3},

*α*

_{4}and

*φ*,

_{G(t)}*φ*

_{G(t-τ}_{0}

*are the absorption coefficient change and phase shift induced by the drive signal*

_{)}*G(t)*and

*G(t-τ*

_{0}

*)*.

*G(t)*is a normalized Gaussian pulse which is given by

*G*(

*t*)

*=*exp(

*−t*

^{2}/2

*T*

_{0}

^{2}). The distortion also comes from the nonlinearity of FCD and FCA.

As for the two schemes based on silicon MZM, device simulation is needed because there is no effective formula for the relationship between the reverse bias, phase shift and transmission coefficient. Figure 2(a)
shows the cross section of p-n diode based optical phase shifter [11]. The rib width and height are 500 nm and 220 nm with the etching depth of 70 nm. Two moderately doped slits with equal concentration of 10^{18}/cm^{3} and opposite polarities form a p-n junction inside the rib waveguide. Two heavily doped regions (10^{20}/cm^{3}) are situated 1μm apart from the rib to form ohmic contacts and the regions in the middle are lightly doped to 2 × 10^{17}/cm^{3}. The simulation model of p-n diode with incomplete ionization, concentration dependent mobility, Shockley Read Hall recombination and ohmic contact is built by using the software ATLAS [12]. The 2-D carrier distributions are calculated and then imported into a finite-difference program. At last we obtain the free-carrier-induced effective refractive index change (∆*N*_{eff}) and the optical loss which is related to absorption coefficient variation as shown in Fig. 2(b). This structure has high modulation efficiency with *V*_{π}∙*L* of 1.93 V∙cm.

## 3. Numerical simulations

To investigate the influence of nonlinear FCD and FCA on the performance of UWB photonic generation, numerical simulations are performed.

#### 3.1 DSB-UWB

We set DC reverse bias to be 1V which allows the electrical Gaussian monocycle signal has the 1V peak voltage. The length of phase shifters are 1000 μm and the key parameter *T*_{0} = 30 ps is selected. Figure 3(a)
shows that the phase shift introduced by the electrical drive signal has a small distortion compared with the ideal monocycle pulse shape. This is because the curve of ∆*N*_{eff} in Fig. 2(b) is not linear which determines that the increase of ∆*N*_{eff} between 1-2 V is smaller than that between 0-1 V. However, according to Eq. (2), the output of PD is related to the phase difference (*φ _{w(t)}− φ_{-w(t)}*) whose temporal shape is very close to the ideal monocycle as shown in the insert of Fig. 3(a). Thus the generated DSB-UWB signal after PD in Fig. 3(b) has the same positive and negative amplitude peak, this can be considered that the push-pull operation eliminates the influence of nonlinear FCD. The ideal MZM without the influence of nonlinearity of FCD and FCA is set for comparison. We can see that there is 1.9 dB loss in the amplitude peak resulting from the FCA which may result in the large optical to electrical conversion loss and low SNR [9]. This problem can be improved by increasing the peak voltage of the drive electrical monocycle signal. Because DC bias should be set above the peak voltage to ensure that the p-n diode MZM works in the reverse bias region, then according to the working principle of p-n diode, the peak voltage exceeding 5 V will result in the breakdown of p-n diode. From Fig. 3(c), we can see that the amplitude peak of the generated Gaussian monocycle increases with the peak voltage of drive signal, yet when the peak voltage is above 3 V, the increasing rate of amplitude peak becomes obviously slow, then the larger signal modulation over 3 V gets meaningless.

It’s worth pointing out that the optical field at the output of silicon MZM is not chirp free. Although the push-pull operation is adopted, the nonlinear FCD made *φ _{w}*

_{(}

_{t}_{)}+

*φ*

_{-}

_{w}_{(}

_{t}_{)}≠ 0. On the other hand, the FCA leads to the power imbalance between two phase shifters of silicon MZM (exp[

*-*(

*α*

_{1}

*+ α*

_{0})

*L*/2]

*≠*exp[

*-*(

*α*

_{2}

*+ α*

_{0})

*L*/2]). These two factors are both time-varied coefficients. Figure 3(d) shows the instantaneous frequency of the optical signal at the output of MZM which is related to the frequency chirp. We can see that much optical power contains the frequency chirp. We believe this kind of residual chirp induced by silicon materials accounts for the difference in the dispersion penalty [13, 14].

#### 3.2 QSSB-UWB

The QSSB-UWB generation scheme doesn’t need DC reverse bias and the peak voltage of Gauss pulse is 1 V. The length of the phase shifter is also 1000 μm and the time delay *τ*_{0} is 20 ps. The phase distortion caused by nonlinear FCD only has a slight deviation from the ideal monocycle pulse shape as can be seen from Fig. 4(a)
, thus the influence of nonlinear FCD can be neglected. Figure 4(b) shows that the generated QSSB-UWB pulse has the asymmetric amplitude peak, the positive peak and negative peak are 0.20 and −0.15 (a.u.) respectively. This is because the two Gaussian pulses have 20 ps delay, the absorption coefficients of two phase shifters (*α*_{3}, *α*_{4}) are different and vary with time, then the DC component in Eq. (4) also has a change with time resulting in the asymmetric peak. Similarly, DSB-UWB generation scheme has this problem as well, however the push-pull operation almost eliminates that impact. From [9] we know that QSSB-UWB signal generated by LiNbO_{3} can maintain its shape even at large signal modulation. As for silicon, increasing the peak voltage of the electrical Gauss pulse will lead to a larger amplitude asymmetry between the positive peak and negative peak as shown in Fig. 4(c). Figure 4(d) shows that the length of phase shifter also has the influence on the amplitude peak. When L is above 3000 μm, the peak will decrease because increasing the length of phase shifter will result in the larger absorption loss. As thus, the length of the phase shifter and the peak voltage of electrical drive Gauss signal should be considered together when constructing the silicon MZM based QSSB-UWB generation scheme. In our simulation, the length exceeding 2000 μm will make less contribution to the increase of amplitude peak.

Furthermore, the optical field at the output of silicon MZM also has the chirp, yet the influence of nonlinear FCD is so small that can be neglected, the frequency chirp is very similar to that based on LiNbO_{3} MZM, then it will keep the same good transmission performance as analyzed in [8]. In addition, the spectrum characteristics of the generated UWB signal based on the two silicon UWB generation schemes in Fig. 1 are almost like that based on LiNbO_{3} schemes within 15 GHz, then the analysis about the spectrum performance is neglected in this paper.

## 4. Conclusion

The influence of the nonlinear FCD and the FCA on two photonic UWB generation schemes based on silicon MZM was numerically analyzed. The impacts on two schemes are different. For DSB-UWB generation scheme, DC reverse bias should be proposed according to the working principle of p-n diode. Push-pull operation can eliminate the effect of nonlinear FCD, however the nonlinearity of FCD and the power imbalance between two arms will introduce residual chirp which will lead to the signal distortion when transmitting over fiber. There is also considerable loss caused by FCA, large signal modulation but not too large signal modulation can improve the SNR and the receiver sensitivity. The QSSB-UWB generation scheme doesn’t need DC reverse bias, however the generated UWB signal has different amplitudes between the positive and negative peak mainly resulting from different transmission coefficients *γ* between two arms. The SNR can be also improved when large signal modulation is operated, yet the asymmetry between the positive and negative peak will become bigger. In addition, the length of the phase shifter will also influence the amplitude peak. In our simulation the length exceeding 2000 μm will make less contribution to the increase of the amplitude peak. The other performance like the chirp and power spectral within 0-15 GHz is similar to that based on LiNbO_{3}, so it can keep the same good transmission performance as analyzed in [8]. On the whole, the QSSB-UWB signal suffers less distortion than DSB-UWB signal when silicon material is used to replace LiNbO_{3}. The study provides the theoretical basis about what should be considered when constructing the silicon MZM based optical UWB transmitter. We believe that the UWBSoC will have a profound effect on future UWB applications

## Acknowledgments

This work is supported by the Natural Science Foundation of China (No. 6177055) and the Natural Basic Research Program of China (No. 2007CB613405).

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