Digital compensation for nonlinearity in SiP modulator Chuandong Li, Zhuhong Zhang Huawei Technologies Canada, 303 Terry Fox Drive, Suite 400, Ottawa, Ontario, K2K 3J1, Canada Email:
[email protected]
Abstract: We investigate distortion in Silicon photonics modulator, and develop compensation method through digital pre-compensation. OCIS codes: (060.1660) Coherent communications, (230.4110) Modulators; (060.4080 ) Modulation;
1. Introduction Silicon photonics (SiP) is recognized for its effectiveness on cost and integration [1]. It had been widely used to make passive components until recently. Besides high insertion loss due to its physical size, the active SiP devices also suffer performance degradation because of its physics behaviour. In this paper, we investigate the intrinsic distortion caused by physics characterization of the SiP modulator, and develop digital signal processing (DSP) method to compensate these distortions. 2. Compensation for memoryless distortion In a PN-junction type modulator, the driving current would change the density of electrons and holes, and cause the refractive index varying. At the wavelength of 1550nm, Soref and Bennett experimentally measured the refractive index and absorption changes due to density of electrons and holes [2]
n 8.8 10 22 N e 8.5 10 18 N h
0.8
[1]
8.5 10 18 N e 6.0 10 18 N h
in which n and are variation of refractive index and absorption, Ne and Nh are density variation of electrons and holes as driving signal changed. Different from that in LiNbO3 modulator, there will be associated amplitude modulation combining with desired phase modulation which degrade the performance. Assuming that the electrons and holes density could follow driving current immediately, which is not always true as we will discuss in next section, we modified a conventional MZ modulator model according to Eq [1]. Fig. 1(a) shows a simulated 16QAM constellation generated from a SiP modulator model described above (with proper selection of bias). As a comparison, Fig.1 (b) is an experimental results reported by Leuthold etc in 2013[3]. The simulated constellation shows the same „twisting‟ feature as the reported one.
(a)
(b) Fig.1: 16QAM constellation
The above comparison gives us confidence about the accuracy of our simple SiP modulator model. Fig2(b) show detail distortion of the optical field with an ideal I/Q drive signal showing in Fig. 2(a). Base on this confirmation, we developed an algorithm to pre-distort drive signal as being shown in Fig.2(c), which could generate a distortion free optical signal as desired.
Fig.2: Electrical drive signal without (a) and with (c) pre-distortion, and corresponding optical filed from SiP modulator
3. Compensation for dynamic distortion As we mentioned in last section, the electrons and holes density could not always follow the driving current quick enough as being assumed, especially for high-speed signals. A SiP device designer could rely on the commercial software to investigate how the optical signal changed with the driving signal. However, this software could not help a digital designer to develop a suitable algorithm because of its black-box style interface. In this section, we will simplify a complicated model to a clear mathematical description, and develop corresponding compensation algorithm. We start with a so-called Drift-Diffusion Approach [4], which is composed of 3 equations
V p n N D N A
Poisson equation:
n 1 Jn Un Continuity Equations: t q p 1 J p U p t q
J n qnx n E x qDn
dn dt Current Density Equations: dp J p qnx p E x qD p dt
[2]
[3a] [3b]
[ 4a ] [4b]
In these equations, we are mostly interesting in 3 variables: V: driving voltage applied on the nodes of SiP modulator n & p:density of electrons and holes, whose variation corresponding to Ne & Nh in Eq. [1] The other part of equations are highly depending on devices physical and geometric parameters, such and doping density, PN junction size, etc. Using small signal approximation, we could separate holes density and electrical field as the geometric part and time varying part, i.e., p = pxpt, E = ExEt, then we could rewrite Eq [3b] & [4b] as
Pt Pt E t Pt t 2 p x x 2 p x DP P E X x pX pX
[5]
P
pN0 P pX
Eq. [5] shows a simple relationship between driving signal Et and hole density Pt, which will impact optical field through refractive index and attenuation. We can do the same simplification for electron density. With simple expression as Eq [5], we could design the algorithm to get desired density (thus modulation on optical field) by pre-distorting driving signals, as being shown in Fig. 3
Fig.3: Digital pre-distortion could drive the hole density to a desired time domain variation, thus get desired optical signal.
With controlled electrons and hole density varying as we desired, and compensated phase and amplitude response due to electrons and holes, it is not difficult to develop a DSP method to get desired optical waveform from SiP modulator by pre-distorting the driving signal. 4. Conclusion We investigate the digital way to compensate steady and dynamic distortion of silicon photonics modulator. We shows that DSP‟s could not only be able to compensate jointed phase and amplitude modulation in SiP modulator, but also be able to make holes/electrons density changing in a desired way. With combination of these two results, we believe the DSP can be used to compensate distortion from SiP modulator, and pave its way for long haul applications. We could expect expanding this approach to other devices so that the whole industry could share the benefit of rapid progress of CMOS and DSP. 5. References 1.
T.N. Nielsen, etc, “Engineering Silicon Photonics Solutions for Metro DWDM,” OFC 2014, Th3J.1
2.
Liu, D. Samara-Rubio, L. Liao, M. Paniccia, “Scaling the Modulation Bandwidth and Phase Efficiency of a Silicon Optical Modulator “, IEEE J. Selected Topics in Quan. Electron., VOL. 11, P.367, 2005
3.
J. Leuthold, etc. , “High-Speed, Low-Power Optical Modulators in Silicon”, ICTON 2013 We.D2.1.
4.
S. Selberherr, "Analysis and Simulation of Semiconductor Devices“, Springer, 1984.
