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• Abstract

SECTION I

## INTRODUCTION

As a novel material platform, SOI is widely used for integrated optical circuit in recent years. High refractive index contrast between silicon and the buried oxide (BOX) layer enables ultra-compact photonic devices such as waveguides, modulators and photo-detectors to be integrated on a SOI wafer. However, integration of lasers on this platform remains a bottleneck owing to silicon indirect bandgap. Building light sources, and in particular laser sources, on integrated silicon circuits is a big challenge.

Recently, heterogeneous integration of III-V devices on silicon has been demonstrated either by direct wafer bonding techniques [1], [2], [3] or adhesive benzo-cyclo-butene (BCB) bonding [4], [5], [6]. Because of the ultrathin bonding layer between the III-V devices and silicon waveguides, light generated by III-V materials is coupled to the underneath silicon waveguides through evanescent field [7]. In order to achieve efficient coupling, coupling length requires accurate design to confirm 100% optical power coupling from III-V waveguide to silicon waveguide. Mode conversion coupling from III-V waveguide to silicon waveguide using a tapered adiabatic coupler was demonstrated [8], which lessened the accuracy requirement of coupling length. However, fabrication of this adiabatic coupler using normal UV lithography is challenging because of sub-micron scale of the taper ending. To lower the difficulty and complexity of III-V process in the fabrication of a III-V/SOI hybrid laser, researchers utilized underneath silicon Bragg grating to modulate the optical modes in the hybrid waveguide [9], fully taking advantage of silicon waveguide which is compatible with CMOS process. As in Ref. [9], using silicon distributed Bragg grating (DBR), single mode hybrid III-V/SOI laser was reported. Fujitsu Co. demonstrated a four-wavelength CWDM transmitter using silicon hybrid DBR lasers array [10].

In this paper, we proposed a novel four-wavelength III-V/SOI heterogeneous laser. By bonding a III-V active waveguide on a pair of silicon sampled Bragg grating (SBG), four wavelengths laser with 18.5 nm wavelength interval is achieved. Output wavelengths can be thermally tuned by heating the underneath silicon microring with tuning bandwidth of 2.4 nm owing to the thermo-optic effect.

SECTION II

## LASER STRUCTURE DESIGN

Schematic diagram of the laser structure is illustrated in Fig. 1. First, we fabricated the passive waveguides (two SBGs, a microring resonator (MRR) and a straight waveguide) on a SOI wafer. An active III-V ridge waveguide is then bonded to the patterned SOI wafer by BCB above the SBGs and MRR. On the other side of the MRR, a straight rectangular waveguide is close to the microring as a evanescent coupling output waveguide.

Fig. 1. Schematic diagram of the heterogeneous integrated silicon laser.

Once III-V active waveguide is pumped, stimulated emission transiting along the waveguide will be modulated by the bilateral underneath silicon SBGs. Comb reflection spectrum of bilateral hybrid SBGs only allows certain wavelengths to be remained in the cavity. The MRR is elaborately designed to have the same free spectrum range (FSR) and center filtering wavelengths with the SBGs. Optical mode satisfying phase matching condition as well as threshold condition will couple from III-V waveguide to MRR vertically and be output at two directions of the output waveguide by evanescent wave coupling laterally.

### 1. Design of the Hybrid SBGs

Fig. 2 gives the 2-D side view of right SBG (left SBG has the same structural parameters). A SOI wafer with 220 nm top silicon layer and 3 $\mu \hbox{m}$ BOX layer is used in this structure. The straight waveguide and MRR are fully etched with width of 450 nm and 500 nm to enable single mode operation. Grating period, sample period, grating number and sample number of the silicon SBG are $\Lambda$, $L_{s}$, $N_{g}$ and $N_{s}$, respectively. $L_{BCB}$, D, and $L_{g}$ are for thickness of BCB, etch depth of silicon SBG (while the sample gap is fully etched along with the straight waveguide) and grating length, respectively. The III-V ridge waveguide is 400 nm high, with etch depth of 290 nm and width of 1 $\mu\hbox{m}$.

Fig. 2. 2-D side view of right hybrid SBG.

According to Bragg condition, grating period $\Lambda = \lambda_{0}/4/n_{eff1} + \lambda_{0}/4/n_{eff2} = 288\ \hbox{nm}$, while $\lambda_{0} = 1550\ \hbox{nm}$, $n_{eff1} = 2.65$, $n_{eff2} = 2.73$ which are the center reflection wavelength and effective refractive indices of the grating (etched part and unetched part). We set grating period number $N_{g} = 10$, sample number $N_{s} = 10$ to reach high reflectivity (more than 90%). We define $s = L_{g}/L_{s}$ as sample duty cycle.

Based on coupled wave theory [11], coupling coefficient $\kappa_{0}$ of a uniform Bragg grating can be described as TeX Source $$\kappa_{0} = {\pi\Delta n \over \lambda} + j{\Delta\alpha \over 2}. \eqno{\hbox{(1)}}$$

$\Delta n$ and $\Delta \alpha$ are variation of effective refractive index and propagation loss of the uniform grating.

According to SBG theory [12], SBG has comb reflection spectrum of which different reflection orders have different coupling coefficient and reflectivity. Coupling coefficient of the corresponding mth order can be described as TeX Source $$\kappa_{m} = \kappa_{0}{L_{g} \over L_{s}}{sin(\pi m{L_{g}}/{L_{s}}) \over \pi m L_{g}/L_{s}}e^{- i\pi L_{g}/L_{s}} \eqno{\hbox{(2)}}$$ where $m$ is an integer. Reflectivity of different reflection orders can be describe as TeX Source $$R_{m} = \tanh^{2}\left(\vert\kappa_{m}\vert N_{s} \times L_{s}\right).\eqno{\hbox{(3)}}$$

In accordance with Eq. (1)(3), relationship between reflectivity of different orders of SBG and the sample duty cycle (s) can be calculated. Fig. 3 shows the variation of reflectivity from primary order to ±3rd order with sample duty cycle. We choose $s = 0.152$ to obtain around 5 wavelengths (primary, ±1st, ±2nd order) with reflectivity higher than 90%. We define $R_{th}$ as threshold reflectivity, which means only wavelengths with reflectivity larger than $R_{th}$ can get stimulatively amplified as laser output. To achieve four-wavelength output, $R_{th}$ should be near 90%.

Fig. 3. Reflectivity varies with sample duty cycle at different reflection orders of the hybrid SBG.

Reflectivity of the SBG, full width at half maximum (FWHM) of the reflection peaks and center reflection wavelength are sensitive to the thickness of BCB and etch depth of silicon SBG.

FWHM of reflection peaks at different reflection orders can be described as TeX Source $$FWHM = {\lambda^{2} \over \pi n_{g}}\sqrt{\vert\kappa_{m}\vert^{2} + (\pi/N_{s} \times L_{s})^{2}}\eqno{\hbox{(4)}}$$ where $n_{g}$ is the effective refractive index of the hybrid SBG.

Using finite element method (FEM) modeling, the curves of center wavelength, reflectivity, FWHM of primary reflection order depending on the thickness of BCB and etch depth are given in Fig. 4, which shows that with thinner BCB thickness and deeper etch depth we can get higher reflectivity and wider reflection bandwidth. We finally choose etch depth $D = 180\ \hbox{nm}$, BCB thickness $L_{BCB} = 40\ \hbox{nm}$ to achieve high reflectivity and wide reflection bandwidth with FWHM of about 2.8 nm.

Fig. 4. Center wavelength (CW), reflectivity, and FWHM of primary reflection peak varies with (a) thickness of BCB (D fixed at 180 nm) and (b) etch depth of silicon SBG ($L_{BCB}$ fixed at 40 nm), which are more sensitive to the former.

### 2. Determination of Threshold Reflectivity $R_{th}$

Reflection spectrum of the hybrid SBG is shown in black line in Fig. 6. Number of the output wavelengths depends on $R_{th}$ of the hybrid SBG reflectors. $R_{th}$ should be chosen properly since high $R_{th}$ causes narrow tuning bandwidth while low $R_{th}$ results in more wavelengths being motivated. Thus we need to choose proper parameters ($t_{1}$, $k_{1}$, $t_{2}$, $k_{2}$, r in Fig. 5) to make $R_{th}$ around 90%. $t_{1}$, $k _{1}$ are transmitting coefficient and coupling coefficient between III-V waveguide and MRR while $t_{2}$, $k_{2}$ are those between MRR and the output waveguide. r is radius of the MRR.

Fig. 5. A brief 2-D top view of the laser structure for $R_{th}$ calculation.

Fig. 5 shows the 2-D top view of the laser. We define T as the single trip optical transmittance at MRRś resonant wavelength between two SBGs, which can be describe as [13] TeX Source $$T = \left({E_{t} \over E_{i}}\right)^{2} = \left({t_{1} - \alpha{t_{2}} \over 1 - \alpha t_{1} t_{2}}\right)^{2}\eqno{\hbox{(5)}}$$ where $E_{i}$, $E_{t}$ are for the input and transmission electric field, $\alpha$ is intrinsic loss factor of MRR. We assumes no phase change in the ring in Eq. (5).

Total loss of the laser should be equal to the modal gain, which can be describe as TeX Source $$\alpha_{total} = \alpha_{i} + {1 \over 2L_{eff}}ln{1 \over {T^{2} R_{th}^{2}}} = G.\eqno{\hbox{(6)}}$$

$\alpha_{total}$, $\alpha_{i}$, G, $L_{eff}$ are total loss of the laser, intrinsic loss in III-V waveguide, optical gain of the active area and effective length between the two SBGs, while $L_{eff}$ can be described as TeX Source $$L_{eff} = 2\sum_{N = 1}^{10}NL_{s}{R_{N} - R_{N - 1} \over R} + L_{c}.\eqno{\hbox{(7)}}$$

$R_{N}$ is reflectivity of the first N sample periods $(R_{0} = 0)$ while $L_{c}$ is the optical path length between the two SBGs. R is reflectivity of the whole SBG. We choose $L_{c} = L_{s}$ to satisfy phase matching conditions in the cavity.

We've got an InGaAsP MQWs with a planar optical gain spectrum from 1526 nm to 1579nm with $G = 30 \pm 3\ \hbox{dB/cm}$. $t_{1} = 0.91$ since $L_{BCB}$ is chosen as 40 nm, while $r = 6.21\ \mu\hbox{m}$ to confirm MRR could have the same FSR with the hybrid SBGs. $t_{2}$ can be adjusted by changing the gap between MRR and the output waveguide. $\alpha = 0.95$ which can be obtain by FEM simulation. We finally find out $L_{eff} = 110\ \mu\hbox{m}$, $\alpha_{i} = 1.75\ \hbox{dB/cm}$, $T = 0.15$ ($t_{2} = 0.66$ with $\hbox{gap} = 95\ \hbox{nm}$ between output waveguide and the MRR) to achieve $R_{th} = 0.9$.

SECTION III

## SIMULATION RESULTS AND DISCUSSION

Applying a planar wave at the port of hybrid SBG as light source, we obtained the reflective optical spectrum of the SBG using 0.1 nm wavelength resolution ranging from 1500 nm to 1600 nm. Four reflection peaks of which reflectivity larger than 90% are achieved with 18.5 nm wavelength interval, which is illustrated in Fig. 6. Optical spectrum of MRR calculated with transmission matrix method is shown in Fig. 6 in red line. Distribution of electric field intensity at different positions of the SBG is illustrated in Fig. 7. Fig. 7(a) shows the distribution of electric field intensity at low reflection wavelength. Optical mode transit from the 1st sample period to the 9th period with almost no intensity decay while opposite situation is illustrated in Fig. 7(b) at high reflection wavelength.

Fig. 6. Reflection spectrum of hybrid SBG and transmission spectrum of MRR. Four wavelengths can be obtained as output with thermal tuning bandwidth of 2.4 nm.
Fig. 7. Distribution of electric field intensity at different positions of the hybrid SBG. (a) $\hbox{Reflectivity} = 2\%$ at 1537.6 nm. (b) $\hbox{Reflectivity} = 96\%$ at 1544.4 nm. Light propagation direction is from left to right as Fig. 2 shows.

In order to tune the output wavelength, a micro $\hbox{Ti/SiO}_{2}$ heater can be added on the silicon MRR. Due to thermo-optic effect of silicon material which is determined by $\hbox{dn/dT} = 1.85 \times 10^{- 4}/\hbox{K}$, the resonant wavelength of the MRR could be thermally tuned. By changing the heater temperature, thermal tuning bandwidth of 2.4 nm is achieved according to the minimum 2.4 nm bandwidth of the four reflection peaks at $R_{th}$.

SECTION IV

## CONCLUSION

In summary, a four-wavelength III-V/SOI heterogeneous integrated laser for CWDM is proposed for the first time. By bonding a III-V active waveguide on a pair of silicon SBGs with optimized structural parameters design, four wavelengths laser with 18.5 nm wavelength interval is achieved. Output wavelengths can be thermally tuned by heating the underneath silicon microring with tuning bandwidth of 2.4 nm. We believe this novel hybrid laser structure could have potential applications in future chip-scale photonic integrated circuits.

## Footnotes

This work was supported in part by the National Basic Research Program under Grants 2012CB922103, 2013CB933303, and 2013CB632104; by the National Scientific Foundation of China under Grants 60806016 and 61177049; and by the Fundamental Research Funds for the Central Universities under HUST Grant 2012QN102. Corresponding author: Y. Wang (e-mail: ywangwnlo@mail.hust.edu.cn).

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