Pre-compensation of Nonlinear Distortion of a
Silicon Microring Modulator Using
Back-calculation
Peng Wang, John C. Cartledge, Wai-Yip Chan
Department of Elcectrical and Computer Engineering, Queen’s University
Kingston, Canada
peng.wang@queensu.ca
Abstract—A pre-compensation scheme for nonlinear distortion
of a silicon microring modulator using back-calculation of the
modulator model is proposed. The bit error ratio performance
shows significant improvement with back-calculation for a 28
Gbaud PAM-4 signal transmitted over 15 km single mode fiber.
I. I NTRODUCTION
Silicon photonics is being widely investigated due to the
potential for integration and the compatibility with CMOS
technology [1]. Compared with silicon Mach-Zehnder mod-
ulators, silicon microring modulators (MRMs) have smaller
chip size, lower power consumption, and enhanced modulation
efficiency [2]. The modulation bandwidth is limited due to the
resonance [3] and the modulation dynamics are nonlinear due
to the Lorentzian transfer function, the nonlinear electro-optic
effect, and the electrical nonlinearity of the reverse biased PN
junction [4], [5]. Previously, a Volterra nonlinear equalizer has
been used to post-compensate for the nonlinear modulation
dynamics of an MRM [6]. In this paper, we propose a pre-
compensation scheme for the nonlinear modulation dynamics
by back-calculating the input drive signal based on governing
rate equations and a defined modulator output intensity. The
pre-compensated 28 Gbaud PAM-4 signal meets the hard
decision forward error correction (FEC) coding threshold of
4.6 × 10
-3
after transmission over 15 km single mode fiber
(SMF).
II. SIMULATION MODEL
A silicon ring modulator consists of a bus waveguide and
a closely placed micro-ring, as is shown in Fig. 1(a). When
driven by an electrical signal, the refractive index of the PN
junction changes accordingly, resulting in modulation of both
the phase and intensity of the light circulating in the ring.
The wavelength dependence of the resonance properties of
an MRM under various DC bias voltages is shown in Fig.
1(b). Changing the bias voltage from 0 V to -3 V, shifts the
wavelength of the resonance point by 68 pm, resulting in a
sensitivity of 22.7 pm/V. Assuming the working wavelength
of the laser coincides with the red line in Fig. 1(b) and the
drive voltage swings between 0 V and -3 V, the shift of the
transfer function induces intensity modulation.
(a) (b)
Fig. 1: (a) Schematic diagram of intensity modulated ring modulator. (b) Ring
resonance shift at different bias voltage.
According to coupling mode theory, the dynamic modu-
lation of an MRM can be modelled by the following rate
equations [7]:
dφ(t)
dt
=
-jω
r
(t) -
1
τ
a
(t)
-
1
τ
l
φ(t)+ j
2
τ
l
E
in
(1)
E
out
= E
in
+ j
2
τ
l
φ(t) (2)
where E
in
and E
out
are the complex-valued fields of the
input and output signals, respectively, φ(t) is the optical
signal circulating in the ring, ω
r
(t) is the angular resonance
frequency, τ
a
(t) is the decay time due to free carrier absorption
and intrinsic loss in the ring, and τ
l
is the decay time constant
due to coupling loss to the bus waveguide. ω
r
(t) and τ
a
(t)
both depend on the applied electrical signal V (t). By solving
(1) and (2), the optical output signal of the modulator can be
obtained. Importantly, the intensity and phase of a modulated
optical signal are determined by V (t).
The pre-compensation is based on predistorting the input
drive signal by back-calculation of the rate equations to
achieve a specified optical intensity at the output of the mod-
ulator. The accompanying optical phase modulation is then
determined by the back-calculated V (t). It has a direct impact
on the distortion of a propagating signal and transmission
performance due to fiber dispersion. Since the modulator
output intensity |E
out
|
2
is a function of ω
r
(t) and τ
a
(t), which
are functions of the drive signal V (t), the back-calculated
drive signal can be determined for a desired output intensity.
The predistorted drive signal compensates for the nonlinear
modulation dynamics and produces a specified output optical
intensity.
NUSOD 2019
123
978-1-7281-1647-1/19/$31.00 ©2019 IEEE