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Distributed feedback lasers comprised of a reflection section and an active section have been proposed for high direct-modulation bandwidth. The reflection section has the same core layer as the active section so butt-joint re-growth is avoided. Without current injection the reflection section will be pumped to near transparency by the emission from the laser itself so high reflection (> 0.75) can still be achieved as confirmed by the simulation. Therefore a short (150 µm) active section can be used, which enables a low threshold current (~5 mA) and a high direct modulation bandwidth (>30 GHz) as demonstrated by the simulation.
© 2016 Optical Society of America
1. Introduction
With the developing demand of communications, long distance, large capacity and high-speed optical communication system is needed. In order to meet the demands, 100G Ethernet has been achieved by 4 × 25G wavelength division multiplexing (WDM) technology [1]. Now 400G rate has become the target, which could be realized by increasing the number of channels, such as 16 × 25G. Higher single channel rate of 50G or 100G can reach 400G with less number of channels, which is beneficial if even higher rate is desired. Directly modulated laser (DML) possesses the advantages of lower power consumption and higher output power, which becomes the prior choice compared to electro-absorption modulator-integrated lasers when applying to short distance communications within 10 km or less.
There are many researches about increasing the modulation bandwidth of DMLs [2–10]. In order to meet the high requirement on bandwidth of the DML, it is essential to make its relaxation oscillation frequency as high as possible. According to the following formula:
where Γ is the optical confinement factor; D, W and L is the thickness, width and length of the active section, respectively; dg/dn is the differential gain; Ith is the threshold current of the laser, it can be seen that reducing the length of the active section can effectively improve the relaxation oscillation frequency. For standard DFB lasers, however, the shorter cavity length also means the smaller equivalent reflection, which often results in higher threshold gain and finally deteriorates the direct modulation bandwidth. Lots of methods have been proposed and demonstrated to obtain short active section lengths with reasonable threshold gain. One type is that DFB lasers integrate with passive waveguides through butt-joint regrowth and then have the cleaved facets high reflection (HR) and anti-reflection (AR) coated [5–7]. The HR coating can effectively reduce the threshold gain even when a short active section length being used. The DFB lasers realized this way have demonstrated modulation rate at 56 Gbit/s [7]. Unfortunately they usually cannot be used as integrated laser source for arrays because the phase at the HR coated facet cannot be accurately determined. DFB lasers integrated with passive DBR mirrors as called distributed reflector (DR) lasers have been demonstrated as well [8–10]. This structure obtains additional feedback from the DBR mirrors so can use a short active section length as well. Furthermore the reflection phase from the DBR mirrors can be accurately controlled during the fabrication therefore they have been successfully employed to make four laser arrays [10]. Both schemes need to integrate passive waveguides through the butt-joint regrowth technology which can significantly increase the fabrication complexity.In this paper, we propose a DFB laser structure which integrates a reflection section after the active section to obtain additional reflection so that a short active section length can be used. The reflection section has the same multiple quantum wells (MQWs) waveguide core as the active section, therefore the fabrication is expected to be much easier without the need of butt-joint regrowth. The reflection section is not current injected and the laser has only one contact. The paper is organized as follows: in section 2 the operation principle of the laser is explained; section 3 shows the numerical simulation results of the proposed laser which verify that the reflection section can generate reflectivity as anticipated; the static characteristics of the laser such as the threshold current and the slope efficiency, and the dynamic response of the laser have been demonstrated through simulation; the conclusion is give in the final section.
2. Design of the DFB lasers
As schematically shown in Fig. 1, the proposed laser contains two sections: the reflection section (with length Lr) and the active section (with length La = L1 + L2). The reflection section is integrated right behind the active section. The reflection section and the active section are loaded with the same grating, i.e. the grating period and phase is continuous across the interface between the two sections. The wafer structure of the reflection section is also the same as the active section, i.e. the same multi-quantum wells and the same upper and lower optical confinement layers. The only difference is that the reflection section has no current injection. The reflection section is assumed to be electrically isolated from the active region through an ion implanted region.
Generally the absorption of the quantum wells in the reflection section can generate loss which will deteriorate the corresponding reflection. However the electrical circuit of the reflection section is left open, the photon-generated carriers will mainly been removed through radiation recombination at a relatively low rate. So the carriers will accumulate to reduce the absorption. Finally an equilibrium can be reached that the generation rate by absorbing the laser emission equals to the recombination rate which is mainly determined by radiation recombination. The radiation recombination rate is proportional to the square of the carrier density which is pretty low, so it is expected that the reflection section will be pumped by the laser emission to a state slightly below transparency (no gain no aborption). The waveguide loss in the reflection section left would be mainly the inner loss of the active waveguide. The above understanding is based on our previous experience. As shown in [11], Q. Lu et al demonstrated a 190-micrometer long semiconductor optical amplifier (SOA) integrated in front of an all-active DBR laser, where the SOA shares the same active layer structure as the laser. With the SOA unbiased, the laser outputs close to 10 mW optical power and the slope efficiency is in agreement with the simulation when the SOA is assumed to be transparent. Taking this into account, the reflection section is expected to generate reasonably high reflection because the waveguide loss in the reflection section at transparency is usually around 20 cm−1 which is far less than the coupling coefficient of the grating, usually above 150 cm−1 when the active section length is around 150 micrometers. The reflection spectrum of the reflection section with different lengths, has been calculated by assuming that the waveguide loss is 20 cm−1 and the coupling coefficient of the grating is 150 cm−1. Results show that when the reflection section length is 37, 75 and 150 micrometers the power reflection at the Bragg wavelength can reach 0.25, 0.6, and 0.85, respectively. This reflection is expected to increase the output power and reduce the threshold gain of the laser, which helps the laser to work with short active section lengths.
AR coatings are assumed on both facets to eliminate the reflection from facets with uncertain positions relative to the gratings. To obtain a high single-mode yield, a quarter wavelength (λ/4) phase shift can be used in the active section. As has been pointed out before, the asymmetric grating structure with λ/4-phase shift does not necessarily yield a high side-mode suppression-ratio (SMSR) [12]. Our structure with the reflection section is asymmetric in nature, so the position of the λ/4-phase shift needs to be optimized in order to obtain a high SMSR. The normal λ/4-phase shifted DFB lasers have the phase shift located in the center where the photon density is symmetric around it. Similarly in the new structure it is expected that it would better to place the λ/4-phase shift at the symmetry position of the photon density distribution, which obviously will not be the center of the active section anymore.
3. Numerical simulation
3.1 Numerical simulation of the DFB laser
Split-step time domain dynamic modeling is used to simulate the DFB lasers [13, 14], as schematically shown in Fig. 2. DFB lasers with reflection section and active section are simulated; each section is treated generally as having its own coupling coefficient, length and injection current. The optical field inside the DFB laser can be written as:
where F(z, t) and R(z, t) is the envelope of the forward and backward propagating waves, respectively; ω0 is the reference frequency corresponding to the Bragg wavelength; β0 is the propagation constant at the Bragg wavelength λ0; ϕ(x, y) is the modal distribution in the transverse section of the laser waveguide.The coupled wave equations derived from Maxwell's equations can be written as:
where cg is the group velocity; G and δ denote the modal amplitude gain and detuning factor; K is the coupling coefficient including both index and gain coupling coefficient; spontaneous emission noise sf(z, t) and sr(z, t) are the driving source of the laser, which is set to be Gaussian and their phases are assumed to be randomly distributed between 0 and 2π.Based on Taylor expansion, F(z, t) and R(z, t) can be solved by the matrix form as:
where Δz is the step length assumed to be short enough; γ = (KK*)1/2, and in this paper we only consider index coupling.The optical gain takes the logarithmic form:
where a is the gain coefficient; N0 is the transparency carrier density; ε is the gain suppression coefficient; α is the inner waveguide loss due to scattering and intervalence-band absorption, etc; and P is the photon density given by |F(z,t)|2 + |R(z,t)|2.The detuning factor δ is related to the refractive index change as seen from the following equation. The refractive index change is related to the gain variation through the linewidth enhancement factor.
therefore neff,0 is the effective index of the waveguide at transparency and at the Bragg wavelength, Λ is the period of the Bragg grating and αm is the material linewidth enhancement factor.The photon and carrier densities along the cavity are coupled through the carrier density equation as follows:
where J is the current density, dact is the thickness of the active layer, A is the linear recombination coefficient, B is the spontaneous recombination coefficient and C is the Auger recombination coefficient.The boundary condition for the forward and backward propagating waves at the facets can be written as:
where rL and rR are the facet reflectivities at z = 0 and z = L, respectively.We assume that perfect AR coatings are applied at both facets with zero reflectivities in the simulation. A 90° phase shift is inserted into the active section. The AlGaInAs multiple quantum wells are assumed to provide the gain because it can provide better confinement for electrons, which increases the differential gain and have better performance at high temperatures. The MQWs consists of eight wells and nine barriers with thicknesses of 6 nm and 10 nm, respectively. In the simulation, gain parameters extracted from measured data are used, which are obtained this way: gain spectra at different current injections below threshold are measured from simple Fabry-Pérot lasers with cleared facets and the same active layer structure [15]; then the material gain spectra at different carrier densities are calculated based on the measured gain spectra, the A, B, C coefficients, the injection efficiency and the optical confinement factor as listed in Table 1; through curve fitting the relationship between the material gain and the carrier density is established at a specific wavelength, which is reflected into two parameters: the transparent carrier density and the gain coefficient, as demonstrated in Eq. (5) and listed in Table 1. The other parameters of the DFB laser used in the simulation are listed in Table 1 as well.
Table 1. Parameters of the DFB laser used in the simulation.
3.2 Static characteristics of the DFB laser
In the simulation we set the product of the coupling coefficient and the active section length, KL, as 2.25. The injection current into the active section is assumed to be 40 mA first, and 1 μA current is assumed to be injected into the reflection section, which is used to avoid the Logarithm gain calculation going to infinity. The length of the reflection section is set to be 150 µm, which would achieve the maximum reflectivity around 0.85 according to the predication given above. Figures 3(a) and 3(b) show the longitudinal distribution of the photon and carrier density for both the active section and the reflection section. Different positions of the λ/4-phase shift are considered, where the position is represented by the ratio rp defined as rp = L1/(L1 + L2). Figure 3(a) shows that the carrier density in the reflection section close to the interface between the two sections is slightly below transparency, which means that the absorption of the multi-quantum wells would be small and the loss of the reflection section in this region would be close to the inner waveguide loss according to Eq. (5). The simulated L-I curves are shown in Fig. 4(a). The emission spectra at the injection current of 80 mA are shown in Fig. 4(b), which are calculated by using the probability-amplitude transfer matrix method [16].
Fig. 3 Longitudinal distribution of the carrier (a) and photon (b) density for various values of the λ/4-phase shift position as represented by rp.
Fig. 4 L-I curve (a) and emission spectra (b) of the λ/4-phase shifted two-section DFB laser at the injection current of 80 mA.
As seen from Fig. 4(a), the output power increases slightly when the phase shift position moves toward the front facet. This can also be seen from the carrier density and photon density distributions as shown in Figs. 3(a) and 3(b). However the SMSR deteriorates rapidly when rp is larger than 0.45 as seen from Fig. 4(b). When the phase shift position moves towards the reflection section, the carrier density in the reflection section get increased, which increases the reflection slightly. However the output power actually get decreased. We take the value of rp equal to 0.4 for an overall consideration of the output power, SMSR, and the reflectivity from the reflection section. rp equal to 0.4 also means that the phase shift position is nearly the symmetry point of the carrier density and photon density distributions in the active section, which is similar to normal λ/4-phase shifted DFB lasers.
With rp = 0.4, the threshold current of the λ/4-phase shifted two-section DFB laser is about 5 mA; the slope efficiency of the output from the front facet is around 0.4 mW/mA; the laser could maintain a high SMSR even at high injection currents. In the following simulations rp = 0.4 is taken.
Figure 5 shows the peak reflectivity with different lengths of the reflection section. It is seen that the reflectivity increases with longer reflection sections. The maximum reflectivity about 0.75 can be achieved at the length of 150 µm, which is very close to previous results obtained by simply assuming that the reflection section reaches transparency with the loss being close to the inner loss. As the injection current into the active section is increased, the reflectivity slightly increases as well for the same length of the reflection section. This is due to the fact that the photon density in the reflection section has been increased which makes the reflection section closer to transparency.
Fig. 5 Peak reflectivity of the reflection section with different lengths for different currents injected into the active section.
3.3 Dynamic characteristics of the DFB laser
We simulated EO response of the λ/4-phase shifted two-section DFB laser under different driving currents with the results shown in Fig. 6. It is seen that the 3-dB modulation bandwidth of the λ/4-phase shifted laser could reach 30 GHz at 80 mA current.
Fig. 6 EO response of the λ/4-phase shifted two-section DFB laser under different current injections.
Figure 7 shows the simulated 25 Gb/s and 40 Gb/s eye diagrams of the λ/4-phase shifted two-section DFB laser. The eye diagram shows that the 40 Gb/s modulation rate can be achieved and the extinction ratio is over 5 dB with the swing current of 50 mA from 30 mA to 80 mA.
4. Conclusion
We have demonstrated through simulation that the reflection section of a λ/4-phase shifted two-section DFB laser can provide enough feedback for the DFB laser to work with 150 µm gain section length even when the reflection section shares the same MQW structure as the gain section but has no current injected. The reflectivity of the reflection section can reach 0.75. The DFB laser with 150 µm gain section length has demonstrated over 30 GHz modulation bandwidth and ~5 mA threshold current and 0.4 mW/mA slope efficiency.
Acknowledgment
This work was supported by the National High-tech R&D Program of China (Gant No.2015AA017101).
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