The finesse by Mach-Zehnder interferometer is low and its dimension is large size as high channel spacing requires cascaded devices. Ring resonator with direct couplers or MMI couplers has a nano-functionality and the free spectrum range (FSR) is high.
Ring resonator with direct couplers is need to the smaller gap ≦ 0.8 μm. It is very different by photolithography (contact alignment machine) and dry etching the smaller gap region is a challenge. So the MMI coupler is used, the gap is bigger ≧ 1.6 μm and the dry etching is easier (the loading effect is unaffected). For PICs purpose, 1x1 60-degree multimode waveguide (MMI) turning mirror, 1x1 90-degree MMI turning mirror, 2x2 90-degree MMI turning mirror and a single ring resonator with 2x2 MMI turning mirror couplers has been achieved. The MMI turning mirror coupler with cross coupling factor (K) of 0.15 is performed by an etched facet with a correction for Goos-Hanchen shift. The advantage of the MMI turning mirror coupler is only 33% the length of conventional straight 2x2 MMI coupler with K=0.15. Moreover, the circumference of the curve waveguide in this ring resonator is decreased by 50% and the gap between 2x2 input/output waveguides is 1.6 μm for MMI width of 7.6 μm.
However, the used conventional straight MMI couplers or direct couplers are either of too large size to reduce the channel spacing, or not feasible for photolithography. This thesis mainly describes a novel design and fabrication of single-ring resonators with low-loss
multimode waveguide turning-mirror couplers.
1.4 Outline of this thesis
The PICs require a monolithic integration of active and passive components such as lasers, semiconductor optical amplifiers (SOAs), electro-absorption modulators (EAMs), ring waveguides, optical couplers, etc., to implement the circuit functionality. One of the fundamental difficulties for monolithic integration is the realization of different semiconductor bandgaps for the active/passive components within one epitaxy wafer.
This can be achieved using re-growth, selective area growth [1.19], vertical coupling [1.20] or quantum well intermixing (QWI) [1.21]. The energy bandgap is blue shifted by a typical wavelength space > 80 nm for the passive components [1.22] to reduce direct bandgap absorption. The other issue is to reduce the component dimension and to simplify the fabrication process. Ring-based waveguide interference devices such as resonators, filters are the key components in DWDM system.
The analysis and simulation of the single ring resonator with multimode waveguide turning mirrors is presented in chapter Ⅱ The novel design is developed and researched. It is . an important part of the design process.
Chapter Ⅲ describes that the composition of the quaternary III-V semiconductor compound InGaAsP or InGaAlAs lattice matched to InP are two main material systems used to fabricate long-wavelength semiconductor lasers. The material is presented the advantage, strain, p-i-n structure…etc. The fabricated process has two methods (wet and dry etching) and the experimental results are presented in chapter Ⅳ.
All of these results are summarized in chapter Ⅴ for active, passive devices and quantum well intermixing techniques. Appendix - A develops the quantum well intermixing techniques. This technique can combine the active and passive component to integrate on the chip.
Reference
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Chapter Ⅱ
Design of Multimode Waveguide Turning Mirror Couplers ---- Analysis , Simulation and Model
2.1 Introduction
Optical switches providing point-to-point and/or point-to-multipoint connections are important components for signal routing in optical communication networks and photonic integrated circuits (PICs). There has been a growing interest in the application of multimode interference (MMI) effects in PICs. [2.1-2.5] The MMI coupler is an attracting component because of its bandwidth and polarization properties and its tolerance of fabrication variations.
[2.1-2.3] Its operation has been demonstrated in Mach-Zenhnder interferometer switches, [2.5, 2.6] and ring resonators. [2.7] For example, dense wavelength division multiplexing (DWDM) systems require different kinds of wavelength selective devices which may de-/multiplex closely spaced channels. Ring resonator devices have already been used for many other DWDM applications such as wavelength filtering, routing, switching, modulation and multiplexing /de-multiplexing applications [2.8-2.11]. Optical waveguide switches provide optical connection between the branching components on the same semiconductor substrate.
If the propagation direction of the light-wave signal which spreads optical waveguide is changeable by the acute angle, the accumulation element number per unit area can be increased. The requirements for an optical switch are that it should be lossless, and has a low crosstalk. In this section, the new design of optical switches using MMI effect is demonstrated. The propagation direction can be changeable at 90 or 60 degrees. When two multimode waveguides are made to cross, it can result in significant scattering loss and cross talk due to the perturbation to the edges of the waveguide. We find the perturbation is the minimum when the crossing occurs at self-image location in a multimode waveguide. We use
a center-fold MMI waveguide with a single self-image at the center. One can reflect the incident mode into an intersecting waveguide by introducing an idea reflecting plane. For compactness, the MMI waveguides can be as narrow as twice the width of the access waveguide.
Optical ring waveguide resonators are a useful component for wavelength filtering, multiplexing, switching and modulation. [2.17, 2.18] An optical filter is needed to provide add/drop ports to select and drop the desirable channel while letting pass-through channels unaffected. [2.1, 2.3] Ring resonator devices have also been used for many other DWDM applications such as wavelength filtering, routing, switching, modulation and multiplexing /de-multiplexing. [2.7, 2.8] Ⅲ-Ⅴcompound semiconductor optical amplifiers (SOAs) are widely used in electronic and optoelectronic devices. [2.19, 2.20] One of the fundamental difficulties for monolithic integration is the need to realize different semiconductor bandgaps within one epilayer (i-layer). This can be achieved using re-growth, selective area epitaxy [2.21], vertical coupling [2.22] or quantum well intermixing (QWI) [2.23]. Our laboratory is developing a sputtered SiO2 or argon plasma bombardment technique for QWI and a re-growth technique by MBE to modify the bandgap of Ⅲ-Ⅴ quantum-wells (QWs) so that passive and active components can be integrated monolithically. Therefore, Photonic integration is divided into two parts. One is an active component with an emission wavelength of 1.55 μm, and the other is a passive component with a bandgap wavelength blue shifted as far as possible, typically space>80nm, [2.24] so as to reduce direct bandgap absorption. This section also describes a novel design of single-ring resonators with low-loss multimode waveguide turning-mirror couplers. They are implemented in In0.53Ga0.47As/In0.53Ga0.26Al0.21As heterostructure waveguides, with bandgap wavelength (λgap)
= 1.41 μm on an InP substrate.
2.2 Analysis of Coupled Ring Resonator with MMI couplers
Ring resonators are coupled to external waveguides through 2X2 couplers. These couplers can either be of the directional coupler type or of the MMI type. We will consider the directional coupler first then the MMI coupler.
2.2.1 The transfer functions of a symmetric directional coupler
Let fr and fl be the normalized wavefunctions of the single mode in the right and left waveguides respectively when they are not coupled. We shall assume that the two uncoupled waveguides are identical. Let β be the phase constant of each of these uncoupled modes and κ the coupling constant between them in the directional coupler. According to the coupled-mode theory for weakly coupled directional couplers (see text books by Yariv, Coldren and Corzine, or Chuang), the coupling of the modes results in two super modes given by (fr ± fl )/ √2. They are approximations to the true eigen modes of the directional coupler. The phase constants of the supermodes are βs0 = β+κ, and βs1 = β-κ. If light of amplitude A enters the left input port of the directional coupler, both of the supermodes will be excited with the same amplitude of A/√2. The total field that propagates down the directional coupler is given by the field on the right and left waveguides are given respectively by
( ) { [ ] }
The cross and bar transfer functions are then given respectively by
x
Equations (4) and (5) are often given in the following form with optical loss included.
where K is the power coupling factor of the coupler, αpu is the power attenuation constant in the uncoupled waveguide, Lis the length of the coupler, nu is the effective index of the uncoupled waveguide, also being the average of the modal effective indices of the two eigen modes in the coupler, k0 is the vacuum phase constant 2π/λ0.
2.2.2 The transfer functions of MMI couplers
The light that enters an MMI from an input waveguide propagates as a combination of many modes. Each of the modes propagates with a different phase constant. The phase delay to each of the output waveguides is thus ambiguous. Definite phase delays can only be derived at the exact image locations. [2.3, 2.4]
For the 1x2 3-dB coupler, the transfer functions to both of the output ports are the same. It is given by β0 is the phase constant of the fundamental mode in the MMI waveguide (nr is the effective index of the slab waveguide from which the MMI waveguide is made and We is the effective width of the MMI waveguide) and Limage = (3/8)Lπ is the exact imaging length. For the lateral TE modes (i.e. TM in the slab), the effective width is related to the physical width of the MMI by
0i
For the general 2x2 3-dB coupler, the cross (X) and bar (B) transfer functions are given by Lπ/2. For this paired-interference case, we have
X0 0 image
which are the same as for the directional coupler.
For the 2x2, K = 0.85 (cos2(π/8) to be exact) coupler, they are given by
B0 0 image
If the device length derives slightly from the exact imaging length either because of a small fabrication error or a small change of the wavelength, then we write
image
L = L + Lδ (2.24)
If the deviation is only due to a deviation in the wavelength, then
i 0
MMI image MMI
i
L = L -L = -L λ λ-
δ λ (2.25)
The light propagation within the distance δL can be modeled as the propagation of a Gaussian beam. [2.14] The input and output waveguides can be characterized by the following two normalized parameters
where neio = βio/k0 is the effective index of the fundamental mode in the input/output waveguides and nc is the effective index of the lateral claddings, and
2 2
io
0 r c
V = W k n -n
2 (2.27)
where Wio is the physical width of the input/output waveguides.
The field distribution of the fundamental mode in the input and output waveguides can be well approximated by that of a Gaussian beam with a spot size of w0. This spot size is half the mode-field diameter of the waveguide. [2.15]
( )
Inside the MMI, Gaussian beam waists with spot size w0 are formed at the input/output and imaging planes. The Rayleigh range around each of the beam waist is given by zR = πw02/λ0.
Assuming that the coupling between the neighboring input/output waveguides is negligibly small, the transfer function for finite value of δL is given by
2 1/4
Let us consider the N’th racetrack formed by interconnecting couplers N and N+1 by a curved front track of length Lf and a rear track of length Lr.(As shown in Fig. 2.1) The transfer function through the length of the front track is given by
) 2
/
exp( wLf j nwk0Lf
tf = −α − ⋅ (2.31)
where αw is the average power attenuation constant in the waveguide including the bending loss, and nw is the average modal effective index in the waveguide.
The transfer function through the length of the rear track is given by r exp( w r/ 2 w )
t = −α L − ⋅j n k L0 r (2.32)
Fig. 2.1 Schematic diagram of the general racetrack ring resonator for single racetrack with MMI couplers
The transfer function for one complete loop inside the racetrack N is given by
B,N B,N+1 N
H H
N N
tl = ⋅tf ⋅ ⋅ rt (2.33)
The transfer function from input port 1 to drop port 3 is the sum of outputs from successive passes inside the racetrack
The transfer function from input port 1 to through port 2 is
For single ring resonator filter, we have obtained the transfer functions for MMI coupler and curve waveguide, so we can calculate the transmitted power at the through and drop port of the racetrack in a single ring resonator. [2.26-2.28] The average power attenuation constant (αw) in the waveguide including bending loss in the ring device is set to 0 cm-1. In these device analysis of MMI and MMI turning mirror, the general design of a single ring resonator with MMI couplers consists of two half-circles, with a radius of 260 μm, connected to two 3-dB MMI couplers or two (K=0.15) MMI couplers jointed at the short straight waveguides. However, the new design of a single ring resonator with MMI turning mirror couplers consists of two 90-degree arc 260 μm radius waveguides connected to two (K=0.15) MMI turning-mirror couplers jointed at short straight waveguides. Comparing only the 50:50 to 85:15 split ratio couplers is of interest to the single- ring resonator. The length of the 3-dB MMI coupler is (3/2)Lπ , but the 85:15 ratio requires a much longer length [3*(3/4)*Lπ]. Therefore, the resonator round-trip length using 85:15 couplers is (3/2)Lπ
longer than using 3-dB MMI couplers in the general design. Fig. 2.2 shows the through and drop port power (in dBm) for this resonator with 3-dB MMI couplers and K=0.15 MMI couplers. The free spectral range (FSR) is 0.27 nm for k=0.5 and 0.22 nm for K=0.15. The FWHM linewidth is about 0.08 nm for K=0.5 and 0.02 nm for K=0.15, and the on-off ratio for drop port is about 9.5 dB for K=0.5 and 21 dB for K=0.15. [2.27] From the simulation results, to achieve a narrow FWHM linewidth, K=0.15 MMI coupler is a better choice.
Fig. 2.2 Simulated through and drop port power of this resonator with 3-dB MMI couplers and K=0.15 MMI couplers for the TE polarization.
. When we achieve high FSR, the cavity length is smaller. The new design concept of MMI turning-mirror coupler is introduced to this resonator. The length of the MMI turning-mirror coupler (K=0.15) is (3/4)*Lπ and the curve waveguide of this resonator consists of two 90-degree arc-radius waveguides. Fig. 2.3 shows the through and drop port power for the two types of ring resonators with MMI couplers (K=0.15) and with MMI turning mirror couplers (K=0.15). FSR is 0.53 nm, the FWHM is about 0.03 nm, and the on-off ratio for the drop port is about 21dB for MMI turning mirror couplers (K=0.15).
Fig. 2.3 Simulated through and drop port power of this resonator with MMI couplers (K=0.15) and with MMI turning mirror couplers (K=0.15) for the TE polarization.
2.2.4 Transfer functions for a double racetrack
Now let us consider the transfer functions for a double racetrack structure made up of racetracks N-1 and N. This is the same problem as the single racetrack problem if we replace the role of the coupler N+1 in the previous problem by the racetrack N. (As shown in Fig. 2.4) The transfer function from the input port 1 to the drop port 3 is now given by
X,N-1 1 , 1
1, 1
1,N
H .
1
N N N
N N
N
tf td
td tl
−
− +
−
⋅ ⋅ +
= − (2.36)
where the new loop transfer function tlN-1,N involves the participation by the N-th ring. It is given by
-1,N HB,N-1 -1 ttN,N+1 N-1
N N
tl = ⋅tf ⋅ ⋅ rt (2.37)
The transfer function from the input port 1 to the through port 2 is given by
2 2
Fig. 2.4 Schematic diagram of the general racetrack ring resonator for double racetrack with MMI couplers
2.2.5 Transfer functions for a triple racetrack
The scheme described above can be used repeatedly to obtain the transfer functions for any coupled multiple-racetrack unit. We shall now discuss the case of a coupled triple racetrack for illustrative purpose.
First, td3,4 and tt3,4 are calculated according to equations (2.34) and (2.35). Then, td2,4, tl2,3 and tt2,4 are calculated according to equations (2.36), (2.37) and (2.38). The same
equations are now used to calculate td1,4, tl1,3, and tt1,4 with the tdN,N+1 and ttN,N+1 in the equations replaced by td2,4 and tt2,4.
The transfer functions are for field amplitudes. To obtain the power transferred, take the absolute value of the transfer function squared.
TABLE 2.1 The layer sequence of the devices
Function Composition Thickness (nm)
p-contact layer In0.53Ga0.47As 60
i-region SCH/etch-stop In0.53Ga0.26Al0.21As 45 n-side depletion layer In0.53Ga0.26Al0.21As 4.5
The low-loss multimode waveguide crossings and turning mirror couplers were implemented in In0.53Ga0.47As/In0.53Ga0.26Al0.21As heterostructures. The wafer was of p-i-n structure and grown on n-type InP substrate by solid-source molecular beam epitaxy (MBE).
The epi-layer sequence is depicted in Table 2.1. The epitaxial structure has a 54.2-nm thick core layer of InGaAlAs/InGaAs multiple quantum wells (MQWs), which is sandwiched with 1.79-μm top-cladding layer and 0.18-μm bottom-cladding layer (almost InAlAs).
2.3.1 1x1 MMI waveguides of 4.4 μm-wide and 5 μm-wide model
To realize passive components in optical wavelength (λ) = 1.55 μm, the band gap wavelength (λgap) is 1.41 μm for the MQWs to avoid absorption loss. The numerical simulation for the TE-polarized optical wave propagation in the waveguide crossings was carried out by using 3-D beam propagation method (BPM) software. First, the optical transmission at λ = 1.55 μm for the MMI waveguides was studied. The 1x1 MMI waveguides with a width of 5 μm and 4.4 μm were simulated, respectively. The 1x1 MMI waveguide has an in/output single-mode waveguide of 2.2 μm in width. The in/output single-mode waveguide is located at the lateral center of the MMI waveguide, as shown in Fig. 2.5(a). Fig.
2.5(b) shows that the 5-μm-wide MMI waveguide has an output power of 0.98 at the length (Lmmi) of 112 μm, which is equal to the theoretical value of (3/2)Lπ. Here Lπ is the beat length of the two lowest-order modes in the MMI waveguides [2.1]. For the 4.4-μm-wide MMI waveguide, the output power is 0.94 at Lmmi = 88 μm, as shown in Fig. 2.5(c).
Fig. 2.5 (a) 1x1 MMI waveguide model (b) 1x1 MMI waveguide: width of 5 μm, Lmmi= (3/2)Lπ= 112 μm and the output power is 0.98; (c) 1x1 MMI waveguide: width of 4.4 μm , Lmmi= (3/2)Lπ= 88 μm, and the output power is 0.94.
2.3.2 90-degree MMI waveguide crossing and turning mirror model
From the simulations, at the middle Lmmi /2 of the 1x1 MMI waveguides, a self image
From the simulations, at the middle Lmmi /2 of the 1x1 MMI waveguides, a self image