Y.Zhuang et al.
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device is small, only 6
, the number of wave-
length demultiplexed is limited by the MMI structure. Other
types of hybrid demultiplexers do not have this problem,
such as an ADC–AWG type proposed by Wang [16]. It can
demultiplex four modes of 16 wavelengths, sixty-four chan-
nels in total. However, the size of the device is large, about
, which is led by the large size of AWG.
To reduce the size, Tan [17] proposed an ADC–MRR type,
which can demultiplex four modes of eight wavelengths.
The size of it is only 250
m
850
, about 1/28 of the
ADC–AWG type. However, it has a defect that its FSR is
only 27 nm. That means, this type of hybrid demultiplexer
only can be applied in dense wavelength division multiplex-
ing (DWDM) system. An ADC–PCR-type device proposed
by Ji [18] solved this problem to a certain extent. The hybrid
demultiplexer consists of square lattice of silicon rods, which
can demultiplex two modes of 1310 nm and 1550 nm. The
device has a large FSR of around 300 nm. However, PhCs
with air holes are more often used compared with silicon
rods. The method [19] utilized in silicon rods is invalid in
air holes, because total internal reflection (TIR) effect and
photonic bandgap (PBG) effect exist at the same time in the
latter one. Therefore, a proposal of mode hybridization for
PhCs with air holes needs to be proposed.
This paper presents an MDM–WDM device based on SOI
nanowires and PhC slab with air holes, which belongs to
the PCR–ADC type essentially. A narrow waveguide with
unilateral variation is introduced to the PCR-type filter. It
can reduce the influence on the resonant wavelength of the
resonator. Therefore, it is easier to design resonant cavities.
In addition, the narrow waveguide changes the resonant
wavelength of the resonant mode in the PhC waveguide.
The resonant mode is called band-edge mode, which is
excited by the connection with nanowires. When the width
of the narrow waveguide is adjusted, the band-edge mode
can be coupled with cavity mode. It not only suppresses the
crosstalk brought by the coupling of band-edge modes, but
also leads to a flat top of spectral line. Then, for the first
time, we combine the WDM device on PhC slab and the
MDM device on SOI nanowires. The MDM–WDM device
can demultiplex
modes and
modes of 1530 nm and
1550 nm simultaneously. Here, only TE modes are consid-
ered because of the transmission mechanism of PhC slab
waveguide. The insertion loss is around 2.0 dB, the channel
crosstalk is less than − 25 dB. The size of the whole device
is about
.
2 Theoretical model andanalysis
The theoretical model of the device presented is drafted in
Fig.1. It is composed of five parts (namely, A–E). Among
them, A–C constitute the ADC-type MDM module, while D
and E constitute the PCR-type WDM module. In the MDM
module, A is a multi-mode area. Here,
modes and
modes of
(blue) and
(red) transmit in the waveguide at the
same time. The phase-matching area is labelled as B, where
the
mode transmitting in the multi-mode waveguide will
be coupled to the single-mode waveguide, and at the same
time converted to
mode due to phase-matching. However,
the
mode transmitting in the multi-mode waveguide still
remains the form of fundamental mode. C is a transitional area,
where there is no coupling. The only change is that the field of
mode in the upper waveguide is narrowed compared to the
original one. In the WDM module, heterostructures [20, 21]
are employed. Therefore, the filters in D and E can download
different wavelength of light. When the wavelength of inci-
dent light is consistent with the resonant wavelength of cavities
(marked by circles), incident light will be tunneled to different
downloading waveguides. In the following section, we focus
on the principle of the PCR-type filter mentioned above.
The principle of the filter in Fig.2 is as follows.
-like
mode is input from Port
. When the wavelength of incident
light is consistent with the resonant wavelength of the cavity,
the incident light will be trapped by the cavity and tunneled to
the drop waveguide, then output from Port
. In Fig.2, the
waveguides marked by deep blue represent PhC narrow wave-
guides. They reflect a specific range of light [22]. The width
of narrow waveguides is adjusted, so that incident light can
be reflected. Hence, the original model of the filter in Fig.2a
can be simplified to a waveguide–cavity–waveguide model, as
illustrated in Fig.2b.
and
represent the amplitudes of
inputting and outputting waves, respectively. a is the amplitude
of the cavity mode.
denotes damping factor. Assume that
(i = 1, 2) because of symmetry. The resonant frequency
is
. Based on coupled mode theory (CMT), the equations for
the evolution of the cavity mode in time and the amplitudes of
the waveguide modes at all ports are given by [8]:
(1)
=i𝜔
0
a − 2𝛾 a +
2𝛾 (S
+1
+ S
+2
)
Phase-matching
area
TE
0
TE
1
0000
0001
0010
0011
0
0
0000 0001
TE
0
0010
TE
0
0011
Photoniccrystal
area
MDMWDM
Demultiplexingprocess
Transitional
area
Fig. 1 Theoretical model of the ADC–PCR-type MDM–WDM
demultiplexer