We investigate theoretically and experimentally the effect of the physical length of gain medium on dynamic mode stability in semiconductor lasers with an intra-cavity filter. In simulation, two types of analysis models were used to examine the lasing properties and to analyze the dynamic mode stability of the external-cavity system, respectively. In experiment, two different kinds of the structures were fabricated and their spectra were analyzed. Both simulation and measurement results show clearly the length of the gain medium has a critical influence on the stability around the peak wavelength of the filter.
© 2009 Optical Society of America
Long-cavity multi-channel laser (MCL) uses an array of semiconductor optical amplifiers (SOAs) on one side or both sides of a wavelength selective element (WSE) such as arrayed waveguide grating (AWG) [1, 2] or concave grating (CG) [3, 4]. The WSE acts as an intra-cavity filter and the lasing wavelength is selected by turning on the appropriate channel in the SOA array. The channel spacing is adjusted by controlling the linear dispersion of the WSE and is typically very accurate. However, compared to the short cavity MCL such as an array of integrated DFB lasers combined with a star coupler  or a multiplexer , the modulation speed is limited by the long cavity, and moreover, since the mode spacing corresponding to the total cavity is much narrower than the WSE passband, many longitudinal modes exist within the passband width.
As for the longitudinal mode stability, the most important feature in long-cavity lasers, it has been shown experimentally stable single mode operation can be achieved even if passband width contains many modes and also theoretically reported that to maximize the stability both the cavity length and the passband width must be minimized . Still, it is practically difficult to minimize these two parameters at the same time because narrowing the passband can make the AWG larger and thus the cavity longer. Besides, since linewidth enhancement factor and internal reflection between the gain and passive sections are usually uncontrollable parameters, it is not easy to find the method for improving the mode stability further in this type of laser without the use of additional filters , .
On the other hand, a novel multi-frequency laser monolithically integrating InGaAsP gain sections with index matched amorphous silicon (a-Si) waveguide has been reported recently . It is expected to be a low-cost photonic integrated device because it can be easily implemented by using PECVD-based technology without the need for multiple epitaxial growths. However, the device seriously suffered from the mode instability and showed the multimode operation in spite of the proper design (-3 dB AWG passband width of about 0.6 nm and cavity length of about 1.2 cm), compared to the other structures -.
In order to examine the cause of this phenomenon theoretically and experimentally, we first simulated the dynamic mode stability of the device based on the external-cavity laser model with frequency-filtered feedback  and then fabricated it with some modifications in design and fabrication from its original structure. In this paper, we present some simulation and measurement results showing the large contribution to the mode stability in the long-cavity lasers with an intra-cavity filter.
2. Analysis models and simulation results
Figure 1 shows a design layout of the device which consists of InGaAsP gain sections, amorphous silicon (a-Si) waveguides (WGs), an a-Si AWG, and an a-Si Y-branch WG monolithically integrated on a single InP substrate. The laser cavity (path1) is formed between the HR-coated facets of one of the gain sections on the right (gain 1) and the common gain section (gain 2). Part of the light is branched out of the cavity (path 2) and amplified through an output amplifier (gain 3).
Two types of the structures were introduced in order to analyze the operational properties of the device as shown in Fig. 2. The first structure realistically describing the device structure in detail provides the information about lasing properties, power distributions across the cavity, and the contributions of the path 2 to the path 1. The structure was modeled by using a well-known transfer matrix method (TMM) including the carrier rate equation . The laser and a-Si waveguide parameters were extracted from the measured data  of the ridge MQW laser diodes (ridge width=2µm) for the integration, a-Si rib WGs (width=2 µm), and a-Si AWGs. Numerical simulations have been done for the  with the parameters listed in Table I. Simulation results such as L-I characteristics were good agreement with the measured data. Figure 3 shows the calculated normalized power distributions of the lasing mode with the lowest threshold gain along the path 1 under the current condition 1 (threshold, IG1/IG2/IG3=38.6/38.6/0mA, solid lines) and the condition 2 (80/60/0mA, dashed lines).
The device has an asymmetric structure along the path 1 but the output powers, Pout1 and Pout2, are identical regardless of the current conditions owing to the same facet reflectivity r1 2. Besides, the power distributions within the gain section 1 and 2 are symmetric under the condition 1 (solid lines) while asymmetric distributions appear under the condition 2 (dashed lines) due to the current difference between the gain sections. The feedback power ratios, rfb1 2(=Pb (z=l G1)/Pf (l G1)) and rfb2 2(=Pf (lT-lG2)/Pb (l T-l G2), l T is the total cavity length), are 8 % and 8 % for condition 1 and 4.3 % and 15.1 % for condition 2, respectively. These values will be used as the grating peak reflectivity rg 2 (Fig. 2(b)) in mode stability analysis.
Mode stability can be determined by finding the location of the poles (zeros in ) on the Laplace-plane (complex frequency=f+jσ) in the small-signal transfer function (determinant) of external-cavity system. The modes in the cavity (path 1) are found by solving the steady-state condition. The poles correspond to small-signal oscillations of the considered mode, whose imaginary part σ represents the damping. If one of the poles has a negative imaginary part, the oscillation is diverged and the mode is unstable; otherwise the mode is stable. In mode stability analysis, the first model was rather inappropriate due to the complicated structure and coupled-cavity effect  caused by at least two gain sections. Instead of it, we utilized the simplified structure shown in Fig. 2(b) under the following conditions: no light generation from the path 2 (zero injection current to gain section 3), neglect of coupled-effect between both gain sections in path 1 (the effect of individual gain section on the mode stability is treated independently), and no consideration of longitudinal spatial hole-burning and spectral gain curvature in gain section.
In order to check the stability of the modes obtained from the steady-state condition, the poles should satisfy the following equation :
where D is the system determinant, ω̃=ω-ωs is the complex angular frequency excursion from the steady-state frequency ω s, τin is the internal cavity round-time (=2l G/vg, vg is the group velocity), ωR is the relaxation angular frequency , GN=vgdg/dN/Vc, P the photon number, g is the modal gain, and Vc is the volume of the active region), ΓN is the damping rate of the carrier density (=τs -1+GNP, τs is carrier lifetime), and ΓP is the damping rate of the photon density (=-GPP, GP=vgdg/dP).
Stability was checked for all the modes near the grating peak (the grating peak reflectivity rg 2 of 8% and the bandwidth of 40 GHz) with the injection current. Figures 4(a) and 4(b) show the detuning (stable) range and the minimum damping (minimum imaginary frequency of the poles) σmin for the modes at the current of Ith+70 mA for various gain section lengths. The stable range is getting larger with the decrease of the l G. It was found that this is quite different from decreasing the passive length l P. There exists the critical length (l Gc~700 µm) which determines if the stable range can be enlarged for frequencies lower than the grating peak (zero detuning). From the result, it may be estimated that the previous structure [9, l G1(2)=1.15 mm) would be operate at unstable range. When the l G decreases, the peak of the σmin is shifted toward lower frequency (longer wavelength) and its value is increased, as shown in Fig. 4(b). This means that the increase of σmin (decrease of the gain section) can result in a higher side mode suppression ratio (SMSR). It can be explained by the fact that the damping of the poles is related to the threshold gain difference between the lasing and side modes. We have also checked the stability for the rg 2 of 4~20% according to the feedback power ratios obtained in Fig. 3. There was little significant difference in the stable range and in the damping in comparison with the Fig. 4. It was found that with the increase of the rg 2, the stable range is expanded by degree and the minimum damping is increased accordingly. We note here that for l G>l Gc, the rg 2 can have a considerable influence on the mode stability at high current and, as a result, the same feedback power ratio can be preferred to minimize the influence by the relatively smaller feedback ratio.
Practically, the calculated l Gc and σmin can be changed by the variation of the parameters assumed in this simulation such as dg/dP, α-parameter, and filter bandwidth. Besides, they may be reduced or distorted by the consideration of the neglected effects including the residual reflections.
3. Experimental results
The whole configuration of the fabricated devices, as shown in Fig. 1, is similar to that of  but there are some differences in AWG design (free spectral range of 52 nm, channel spacing of 3.2 nm), structures of the gain section (six 7 nm-thick strained quantum wells and 2.5 µm-wide ridge waveguide) and a-Si waveguides (core refractive index of 3.36), and fabrication techniques (stepper process and dry-etching, etc.). The device size is 4.5×5.5 mm2. By measuring individual components, propagation loss of 3~4 dB/cm was obtained for 3 µm-wide a-Si ridge waveguides deposited on thermally oxidized Si wafer, and -3 dB passband width of 0.6 nm and the crosstalk level of about 28 dB for a-Si AWG with the width of 2 µm. For a-Si waveguides deposited on InP substrates, however, propagation losses of more than 5 dB and additional bending losses of about 1.5 dB were obtained. We think this is mainly due to the a-Si film blisters.
In order to examine the effect of the length of gain section for path 1 on the mode stability, we have used two different kinds of structures: for the sample 1, the l G1 and l G2 are 800 µm and 800µm and, for the sample 2, 600 µm and 350 µm, respectively. The uncoated samples were measured at the facet of the gain section 2 without the current of gain section 3 in order to remove the effect of the path 2. Figure 5 shows the measured output spectra of both samples under the same conditions.
Although they both have the same AWG passband, their spectra are quietly different. It is clearly shown that the spectral width of the sample 2 is narrower than that of the sample 1. We also confirmed the same result by reducing the gain part of the chip by step. Therefore, these experiment results show that the spectral width is highly dependent on the length of the gain medium. It can be thought that the spectral narrowness is mainly attributed to the increase of side-mode damping which results in a higher SMSR according to Fig. 4. However, since the mode suppression between the central mode and the adjacent modes is still low for both samples, there is little significant difference between them in SMSR. For this result, we think both samples may have not enough stability (σmin) to suppress the adjacent modes (see Fig. 3 in , in complex frequency curve the lower curve of the coupled side modes is changed U-shape to double W-shape as the stability becomes improved). This can be explained that in external-cavity system the relatively high passive waveguide loss reduces the feedback power from the grating, and therefore, this power reduction makes weakened the side-mode damping originated from the gain saturation effect. Since this high passive loss can be somewhat compensated by reducing the mirror loss, the sample 2 was measured again after the HR coating. The improvement of about 10dB in SMSR at the same condition was obtained as expected. Figure 6 shows the measured output powers of (a) the sample 2 after the HR-AR coatings and (b) the packaged MFL chip of which structure is the same as the  (provided by Novatronix co).
A single mode with the SMSR of more than 22 dB (black line) appears for sample 2 while a multi-mode with a wide spectral width for the packaged chip. In sample 2, there was no difference between AR- and HR-coated facets in spectra except the power value. The SMSR was changed 15 dB to 30 dB with the combination of the operation current. It appeared that the maximum SMSR can be obtained when the current densities (=I/l G1(2)) of the gain 1 and 2 are identical as shown in red-line of Fig. 6(a). This results from the same feedback power ratios.
We have demonstrated theoretically and experimentally that the dynamic mode stability can be significantly improved by simply reducing the length of the gain section in long-cavity lasers with an intra-cavity filter. Besides, we have implemented the monolithically integrated lasers with a-Si AWG with improved mode stability compared to its original device. This type laser can be used as a low cost OLT (optical line terminal) source in WDM-PON by modifying the schematics. Additional improvements for the low a-Si WG losses, the multiple operation, and small-size are the subject of the current investigations. These works realizing the structure with the improved performances are ongoing.
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