approach, wavelength-dependent athermalization for the
asymmetric approach, and inefficient utilization of bandwidth
for the cascaded approach. In summary, the thermo-optic-
related energy consumption of MZI-based devices can be to-
tally eliminated with three passive approaches to choose from
according to the requirements of the applications.
B. Temperature-Independent Microring Resonators
Figure 6 illustrates the schematic of a microring resonator,
which is another typical optical-length-based device because
the resonance condition is expressed as
OL
Z
L
n
eff
T;λ;ldl mλ
r
m 1; 2; …; (5)
where OL is the round-trip optical length, the integral path L is
the propagation path for one round-trip in the microring, and
λ
r
is the resource wavelength. Based on Eq. (5), the temper-
ature dependence of λ
r
can be derived as
dλ
r
dT
λ
r
R
L
n
g
T;λ;ldl
·
Z
L
∂n
eff
T;λ;l
∂T
dl; (6)
where n
g
is the group refractive index, n
g
n
eff
− λ · ∂n
eff
∕∂λ.
The effective TOC (∂n
eff
∕∂T) can be approximately ex-
pressed as
∂n
eff
∂T
Γ
core
∂n
corn
∂T
Γ
clad
∂n
clad
∂T
Γ
sub
∂n
sub
∂T
; (7)
where Γ (and ∂n∕∂T) with subscripts of core, clad, and
sub represent the confinement factors (material TOCs)
for the core, cladding, and substrate, as specified in [25].
According to Eq. (7), ∂n
eff
∕∂T>0 for the basic wave-
guide, silica-clad SOI waveguide (∂n
Si
∕∂T ∼ 1.86 × 10
−4
K
−1
,
∂n
SiO
2
∕∂T ∼ 1 × 10
−5
K
−1
), in silicon photonics. Taking this
into Eq. (6), we note that the resonance wavelength will shift
with temperature variation for such silicon microrings. Prior
work has aimed at eliminating or reducing the thermal affec-
tion to the microring resonators, which will be discussed in
three groups according to their working principles.
1. Special Structure Design
Two kinds of special structures are reported for reducing the
temperature dependence of the microring, as demonstrated in
Fig. 7, where Fig. 7(a) shows the asymmetric MZI coupled mi-
croring [26], and Fig. 7(b) shows the dual-ring structure with
resonance splitting [27]. Both schemes are capable of reduc-
ing the temperature dependence of the microring resonator.
Nevertheless, both of them cannot achieve athermal micro-
ring (dλ
r
∕dT 0), which can be concluded from Eqs. (5)–(7).
No matter how the microring structure has been designed, the
resonance wavelength should satisfy Eq. (5), and its temper-
ature dependence can be expressed as Eq. (6). Without intro-
ducing a negative thermo-optic material, ∂n
eff
∕∂T and n
g
are
greater than zero everywhere in the microring, which will
cause dλ
r
∕dT>0 in Eq. (6).
2. Negative Thermo-Optic Material Cladding
The method of negative thermo-optic material cladding was
proposed by Kokubun et al. in 1993 [28] and introduced
into a SOI microring in 2007 [29]. Significant progress has
been achieved since then. The basic configuration of this ap-
proach is illustrated in Fig. 8 where negative thermo-optic
material acts as the upcladding for the SOI waveguide. This
configuration can achieve an athermal microring if the con-
finement factors and the TOCs are well matched according
to Eq. (7) to make ∂n
eff
∕∂T 0. However, two problems
exist in this method and have not been solved. First, the
TOC required for the upcladding material is as high as
−7.8 × 10
−4
K
−1
for an athermal SOI single-mode waveguide
with a dimension of 200 nm × 500 nm because the SOI
waveguide has a strong confinement for light (Γ
core
> 75%
for TE-polarized fundamental mode) [30], but, currently, all
the reported TOC of negative thermo-optic materials is in
the range of −1–3 × 10
−4
K
−1
. To solve this problem, signifi-
cant efforts have been made for the athermal SOI microring
by means of decreasing the confinement factor of the core
with a narrowed waveguide [31–34], slot waveguide [35],
or TM-polarized guided mode [25,29] These are capable
methods for athermal microrings while they suffer from
higher propagation loss and larger bending radius induced
by the low confinement. Second, most of the reported nega-
tive TOC materials (polymer) are still not compatible with
the standard CMOS fabrication process, even though some
Fig. 6. Schematic of a microring resonator.
Fig. 7. Construction of (a) asymmetric MZI coupled microring and
(b) dual-ring structure.
Fig. 8. Schematic of negative TOC material cladding SOI waveguide
in cross-section view.
Zhou et al. Vol. 3, No. 5 / October 2015 / Photon. Res. B31