Wavelength tunable semiconductor lasers are in great demand for high-speed, large-capacity optical communication and interconnection ^[1–3]. Distributed feedback (DFB) laser arrays ^[4,5], distributed Bragg reflector (DBR) lasers ^[6], sampled grating DBR lasers ^[7,8], superstructure grating DBR lasers ^[9,10], and digital supermode DBR lasers ^[11] were investigated for realizing wavelength tuning semiconductor lasers. In addition, coupled cavity lasers based on the Vernier effect, such as etched groove and cleaved coupled-cavity lasers ^[12], Y-branch lasers ^[13], V-coupled cavity lasers ^[14,15], and coupled-ring lasers ^[16,17] were applied for single-mode and tunable semiconductor lasers. Recently, etched-slot based lasers ^[18] and multichannel interference lasers ^[19,20] were reported to achieve a good performance in wavelength tuning range and side-mode suppression ratios (SMSRs). Furthermore, a hybrid square-rectangular laser (HSRL) as a coupled cavity consisting of a square microcavity and a Fabry–Perot (FP) cavity has been demonstrated for mode Q factor control and single-mode operation ^[21–23]. All-optical flip-flop is realized based on the optical bistability caused by saturable absorption and mode competition ^[24,25], and all-optical switch and logic gates of NOT and NOR are demonstrated by using HSRLs ^[26].

However, a coupled-mode field pattern in the FP cavity of the HSRL is a mixture of fundamental transverse mode and symmetric high-order modes, which may reduce the coupling efficiency into a single-mode fiber (SMF). For improving the performance of this kind of coupled cavity, it is necessary to optimize the mode field pattern and increase the proportion of the fundamental transverse mode in the FP cavity. In this paper, we report a hybrid square/rhombus-rectangular laser (HSRRL) composed of a square/rhombus microcavity (SRM) and an FP cavity for improving the mode field pattern in the FP cavity. The mode field distributions inside the hybrid cavity and the far-field patterns are numerically simulated for the HSRRL with an optimized SRM, which shows a near fundamental-transverse-mode distribution in the FP cavity and improved far-field patterns. The SRMs work as a wavelength selective reflector for the FP cavity, with the effective reflectivity related to the mode in the SRM. The results indicate that a properly deformed SRM has more stable mode selection properties than that with a square microcavity. HSRRLs with different sizes are fabricated, and single-mode operation is realized with an SMSR over 45.3 dB. Furthermore, the wavelength tuning is achieved by varying injection currents into the SRM and FP cavity. Finally, the direct modulation characteristics are investigated for an HSRRL, and an open-eye diagram at 35 Gb/s is demonstrated.

As shown in Fig. 1(a), an HSRRL consists of an FP cavity with a width d, a length L, and an SRM with a side length a and a deformation amplitude δ. A two-dimensional finite-difference time-domain (FDTD) method is used to investigate the reflection behaviors of the SRM as an equivalent reflector. The FDTD simulation region covers the entire SRM and part of the FP cavity, in which the end of the waveguide is embedded into the perfectly matched layer (PML) to ensure no backreflection from the waveguide facet. The practical devices are surrounded by bisbenzocyclobutene (BCB), and the effective refractive indices of the HSRRL cavity and the BCB medium are assumed to be 3.2 and 1.54, respectively. A wide-band exciting source with a Gaussian profile, is set in the FP cavity 12 μm away from the center of the SRM with tw=1.195fs, t0=3tw, and f0=193.5THz. The reflectivity is defined as the ratio of reflected energy to incident energy and is obtained from the FDTD time domain output and the Padé approximation method based on Baker’s algorithm ^[27]. The intensity detector is set at the midpoint of the FP cavity 15 μm away from the center of the SRM.

The reflectivity spectra of the transverse-electric (TE) modes for the SRMs are shown in Figs. 2(a) and 2(b), where the black solid and red dotted lines correspond to reflectivity at the gain of 0 and 8cm−1 in the SRM, respectively. For the SRM with a=10μm and δ=0.15μm, two maximums, α1 and α4, appear at 1541.5 and 1594.8 nm, with an interval of 53.3 nm, as shown in Fig. 2(a), which is equal to 2 times the free spectral range of the four-bounced whispering-gallery modes in the SRM with a=10μm. The reflectivities of the modes α1 and α2 are higher than those of other modes. Compared with the hybrid square-rectangle laser in Ref. ^[22], the reflectivity peaks of modes α1 and α4 are much wider, and the peak values are insensitive to the gain at low gain level, because of the low-mode Q factors for the SRM. Figure 2(b) shows the reflection characteristics for an SRM with a=15μm and d=2μm. Selective reflection is also observed with the maximums β1 and β2 at 1530.5 and 1565.2 nm, with an interval of 34.7 nm. The reflectivity changes of the SRM with a=15μm are more obvious than that of the SRM with a=10μm under the same gain conditions, owing to higher-mode Q factors in the larger cavities. Some peaks have the reflectivity larger than unity without gain, as shown in Fig. 2(b), because the reflected fields in the waveguide contain not only the fundamental waveguide mode but also symmetric higher-order modes, which will result in overestimation of the reflectivity under the simplified calculated method ^[22]. The optical reflection from a waveguide directly connected to a high-Q silicon microdisk was applied in monitoring nanoparticles and ambient changes ^[28] where the waveguide was a single-mode waveguide.

Taking into account the reflectivity of the SRM and the confined mode in the FP cavity, we select the deformation and the size of the HSRRL. The proportion of the fundamental transverse mode in the FP cavity η is defined by where Hz is the simulated z-direction magnetic field in the FP cavity of an HSRRL, and HFP is the fundamental transverse mode in the slab waveguide of the corresponding FP cavity. The reflectivity for the modes α1, α2, α3, and η for the mode α1 versus δ are plotted as solid lines and a dashed line in Fig. 2(c) for an HSRRL with a=10μm, d=2μm, and L=300μm. The deformation δ=0.15μm is chosen with the near highest values of the reflectivity and η for the mode α1.

Mode field patterns of the z-direction magnetic field Hz are simulated for an HSRRL with a=15μm, δ=0.25μm, d=2μm, and L=300μm and plotted in Fig. 3(a) for TE mode at 1541.5 nm, and detailed distributions in the SRM and the FP cavity are illustrated in Figs. 3(b) and 3(c), respectively. Moreover, the far-field distributions are calculated from the complex near-field mode distributions ^[29] with a far-field angle of about 28°, as shown in Fig. 3(d). The deformation induces an additional wave vector along the coupled waveguide x axis for the mode light rays reflected from the two deviated sides of the SRM, which forces the transfer of the mode field pattern inside the SRM from the higher-order transverse mode to the fundamental mode in the FP cavity, as shown in Fig. 3(b), because of the reduction of the y-direction propagation constant with the increase of the x-direction propagation constant.

The numerical result of η is 0.906 for the hybrid mode in Fig. 3. Owing to the mode field pattern in the FP cavity, there is a mixture of the fundamental transverse mode and symmetric high-order modes; the mode field patterns are different in the FP cavity with different FP cavity lengths L. Mode field patterns Hz near the output facet are shown in Figs. 4(a)–4(c) for coupled cavities with L=280, 290, and 310 μm, where η can stay above 90% for the HSRRLs, as shown in Fig. 4. The simulated far-field intensity profiles out of the output facet of the HSRRLs are also shown in Figs. 4(a)–4(c), where the integral is along an arbitrary right perimeter of the external region surrounding the coupled cavity. Compared with the far-field patterns for HSRLs with the same FP cavity length, as shown in Figs. 4(d)–4(f), we can optimize the mode field pattern and enhance the proportion of the fundamental transverse mode in the FP cavity, which would make the coupled mode stabler.

The HSRRLs are fabricated by standard contact photolithography and inductively coupled plasma (ICP) techniques, as in Ref. ^[21]. After deep etching by ICP, the coupled cavity is confined by a 200-nm SiNx layer and a BCB layer for planarization. A 250-nm-SiO2 layer is grown by plasma-enhanced chemical vapor deposition (PECVD) and utilized as the hard mask to form the electrical isolation trench between the SRM cavity and FP cavity. The lasers are cleaved with the FP cavity length L about 300 μm and mounted P-side up on an AlN submount for controlling the temperature. Figure 5 shows a microscopic image of an HSRRL with a=15μm, δ=0.25μm, and d=2μm, after the deposition of two patterned p-electrodes and an n-type backside electrode. Two patterned p-type electrodes are used for current injection into the hybrid square/rhombus and FP cavities separately. Based on the simulation results and technology experiences, the side length of the square microcavity was chosen at 10–20 μm to avoid a large vertical radiation loss for a smaller microcavity and multiple-mode operation for a larger microcavity. The width of the FP cavity was chosen at 1.5–3 μm, much larger than the single-mode waveguide, which is limited by the contacting photolithography and the deep dry etching.

Output powers coupled into an SMF versus IFP at ISRM=0, 1, 5, and 30 mA are measured and plotted in Fig. 6(a) for an HSRRL with a=10μm, δ=0.15μm, and d=2μm. The threshold current is about 15 mA under different ISRM, which is in agreement with the numerical results in Fig. 2(a), where the reflectivity is little affected by the gain at a=10μm. The maximum power is about 2.6 mW, with nearly the same output power at ISRM=0, 1, and 5 mA. The output power is even lower at ISRM=30mA owing to the thermal cross talk between two cavities. For an HSRRL with a=15μm, δ=0.25μm, and d=2μm, the output powers collected by an SMF versus IFP are measured and plotted in Fig. 6(b) at ISRM=0, 10, and 25 mA. The threshold current Ith reduced from 17 to 13 mA when ISRM was increased from 0 to 25 mA, as shown in Fig. 6(b), due to the improvement of equivalent reflectivity, as shown in Fig. 2(b). The maximum output power collected by the SMF is 6.14 mW. The slope efficiencies are estimated to be about 0.06 and 0.13 W/A before the saturation for the HSRRLs with a=10 and 15 μm, respectively.

Then, the lasing spectra are measured for the HSRRLs under different injection currents. As shown in the inset of Fig. 7(a), the laser operates in stable single mode at 1574.27 nm with an SMSR of 45.3 dB, as IFP=57mA and ISRM=40mA for the HSRRL with a=15μm, δ=0.25μm, d=2μm, and L=300μm, which verifies the excellent mode selection capacity for HSRRLs. Lasing spectra versus ISRM are shown in Fig. 7(a) at IFP=64mA. The lasing mode wavelength redshifts from 1567.7 to 1589.8 nm as ISRM increases from 8 to 80 mA. The lasing wavelengths and corresponding SMSRs are plotted in Fig. 7(c), and the interval between every two lasing modes is about 1.4 nm. Similarly, the lasing spectra, lasing mode wavelengths, and SMSRs versus IFP are plotted in Figs. 7(b) and 7(d) at ISRM=20mA. The wavelength can shift over 2.5 nm with high SMSR by changing IFP. So, the lasing mode wavelength can be continuously tuned in a wide range by varying ISRM and adjusting IFP slightly. The shift of the wavelength is mainly due to the change in refractive index caused by the thermal effect when changing the injection currents of the SRM and the FP cavity. Continuous wavelength tuning ranges over 21 and 29 nm are demonstrated, as shown in Figs. 8(a) and 8(b), for the HSRRLs by adjusting the ISRM and IFP simultaneously. Their corresponding SMSRs and peak powers obtained from the spectra are plotted in Figs. 8(c) and 8(d). The SMSR is larger than 40 dB over 18 nm for the HSRRL with a=15μm in Fig. 8(c), because of the higher reflectivity and better heat conducting of the SRM. In Fig. 8(d), most SMSRs are larger than 30 dB in the tuning range. Increasing the mode Q factor and enhancing the mode reflectivity by coating the SRM with a metal layer can improve the performance of the HSRRLs, as in Ref. ^[30]. For the HSRL in Ref. ^[21], the lasing mode is easy to jump to another coupled mode of different microcavity mode with the injection current due to the redshift of gain spectrum, because the reflectivity of the square microcavity is sensitive to the mode gain. The deformed SRM has more stable mode selection properties because the reflectivity of the SRM is little affected by the practical gain value, and a large wavelength tunable range is achieved for the HSRRL. Furthermore, the far-field profiles are measured with the full width at half-maximum of 44° and 43° in the in-plane and out-of-plane directions for an HSRRL, which are similar to the HSRL in Ref. ^[21]. In fact, high-order transverse modes in the HSRL are even-order transverse modes, which mainly affect the detailed pattern instead of the width of the far-field pattern, as shown in Fig. 4. The near-symmetric output pattern leads to a high coupling efficiency to an SMF.

Finally, high-speed experiments at room temperature are conducted for the HSRRL with a=15μm, δ=0.25μm, d=2μm, and L=300μm by mounting the HSRRL onto an AlN submount. Considering the series resistor of the lasers, we chose a resistor of 40 Ω on the AlN submount to reduce the electrical return loss. The modulation signal together with the DC injection current IFP is fed into the FP cavity using a 40-GHz bias-tee and a 40-GHz radio-frequency probe. The output power is coupled into a tapered SMF, and then converted into electrical signals through a 28-GHz high-speed photodetector. The small signal modulation responses measured by a 40-GHz-bandwidth network analyzer are plotted in Fig. 9(a), where 3-dB bandwidth increases from 9.5 to 14.1 GHz, and the corresponding resonance peak decreases from 4.46 to 0.94 dB as IFP increases from 30 to 70 mA. The response curves are fitted by the modulation transfer function ^[31] as solid lines in Fig. 9(a). The fitted resonance frequency fR and 3-dB bandwidth are plotted as functions of (IFP−Ith)1/2 in Fig. 9(b). Based on this, we get the D factor ^[32] and modulation current efficiency factor of 2.04 and 2.15GHz/mA1/2. The saturation of the resonance frequency and 3-dB bandwidths is mainly caused by the thermal effect.

Utilizing a 64 Gb/s pulse-pattern generator to supply the modulation current, we perform large-signal modulation measurement using a high-speed photodetector with 70-GHz bandwidth and a 90-GHz digital sampling oscilloscope. Figures 10(a) and 10(b) show the 25-Gb/s and 35-Gb/s eye diagrams for back-to-back (BTB) configuration with a nonreturn-to-zero (NRZ) pseudo-random binary sequence (PRBS) of 231−1 input into the FP cavity. The wavelength of the laser was 1571 nm. The bias current was 68 mA for the FP cavity, and the modulation voltage was 1.5 V peak-to-peak.

In conclusion, we have proposed and demonstrated a hybrid square/rhombus-rectangular structure for realizing stable single-mode operation with a wide wavelength tuning range. Stable single-mode lasing with the SMSRs larger than 45.3 dB is realized, and a continuous single-mode wavelength tuning range over 29 nm is obtained. A 3-dB small-signal modulation bandwidth of 14.1 GHz is demonstrated with clear eye diagrams at 35 Gb/s. Compared with the traditional DFB and DBR tunable lasers, the coupled cavity with a microcavity is a simple, compact, and potentially low-cost technique for realizing single-mode lasers. The directly connected coupled cavity is also simpler than an evanescently coupled cavity with a gap of 100–200 nm between a microdisk and a waveguide and has stabler single-mode operation than a traditional two-section coupled cavity because of a soft transition region. However, the obtained wavelength tuning is based on the thermal effect of the injection current, which limits the output power and SMSR. We expect that more reliable tunable lasers can be realized by a coupled cavity with two microcavities using the Vernier effect, and have great application prospects in optical communication systems and photonic integrated circuits.