## Abstract

Mode selection in square resonator semiconductor microlasers is demonstrated by adjusting the width of the output waveguide coupled to the midpoint of one side. The simulation and experimental results reveal that widely tunable single mode lasing can be realized in square resonator microlasers. Through adjusting the width of the output waveguide, the mode interval of the high-*Q* modes can reach four times of the longitudinal mode interval. Therefore, mode hopping can be efficiently avoided and the lasing wavelength can be tuned continuously by tuning the injection current. For a 17.8-μm-side-length square microlaser with a 1.4-μm-width output waveguide, mode-hopping-free single-mode operation is achieved with a continuous tuning range of 9.2 nm. As a result, the control of the lasing mode is realized for the square microlasers.

© 2015 Optical Society of America

## 1. Introduction

Wavelength-tunable semiconductor lasers are important light sources in the wavelength-division-multiplexing optical communication systems [1–9]. Based on thermal and carrier effects, varieties of continuous wavelength-tunable semiconductor lasers have been proposed and demonstrated, such as tunable distributed-feedback (DFB) lasers with film heaters [1,2], multi-section DFB lasers [3], tunable distributed amplification DFB lasers [4,5], three-electrode distributed-Bragg-reflector (DBR) lasers [6,7], and sampled grating and super-structured grating DBR lasers [8,9]. Continuous wavelength tuning range up to 22 nm was demonstrated for the three-electrode DBR laser [7]. However, complicated control of the injection currents is required for the continuous wavelength tuning.

Microlasers with a large longitudinal mode interval are a potential choice for realizing tunable semiconductor lasers [10–15]. Recently, square resonator microlasers have attracted a great attention for potential application in photonic integrated circuits and optical interconnects [12–29]. For a square resonator, the mode interval of high-*Q* confined modes will be twice of the longitudinal mode interval, which makes the square microresonator suitable for realizing single mode lasing [13,14,17,18]. However, the prediction was not observed for the square microlasers laterally confined by SiO_{2} and p-electrode layers [21,24]. Very recently, single mode operation with the side mode suppression ratio of 41 dB was realized for a square microlaser laterally confined by the bisbenzocyclobutene (BCB) layer, with a side length of 16 μm and a 2-μm-wide vertex output waveguide [28]. In addition, higher output powers were obtained for the square microlasers compared with the microdisk lasers [29].

In this paper, we demonstrate the widely and continuously tunable single-mode square semiconductor microlasers, with a midpoint-connected output waveguide for mode selection and unidirectional emission. The influences of the output waveguide on the mode behaviors are investigated numerically and experimentally. The results show that the mode selection caused by the output waveguide can result in mode-hopping-free single mode operation, through adjusting the width of the output waveguide. Therefore, the lasing wavelength can be tuned continuously by tuning the injection current. The tunable square microlaser provides wavelength tuning by injection current and it simplifies the fabrication process as well as the tuning process. For a square microlaser with the side length of 17.8 μm and the output waveguide width of 1.4 μm, single-mode operation is achieved with a continuous tuning range of 9.2 nm.

## 2. Simulation of mode selection

#### 2.1 Numerical model

The square microresonator with the side length *a* and the output waveguide width *w*, are numerically investigated by two-dimensional (2D) finite-difference time-domain (FDTD) technique. As shown in Fig. 1(a), the square microresonator is laterally confined by a 200-nm silicon nitride (SiN* _{x}*) layer and the BCB layer. The refractive indices of AlGaInAs/InP laser wafer, SiN

*and BCB layers are taken to be 3.2, 2 and 1.54, respectively. A perfectly matched layer (PML) absorbing boundary condition is used to terminate the simulation area. A uniform mesh with cell size of 20 nm is used in the simulation and the time step is fixed to be 0.0467 fs according to the Courant limit. A cosine impulse modulated by a Gaussian function*

_{x}*P*(

*t*) = exp[−(

*t*−

*t*

_{0})

^{2}/

*t*

_{w}^{2}]cos(2

*πf*

_{0}

*t*) is added to

*H*at the point (

_{z}*x*,

*y*) = (1.2, −8.3) μm to excite the transverse electric (TE) modes. The pulse center

*t*

_{0}= 6.6 fs, the pulse half width

*t*

_{w}= 19.8 fs, and the pulse center frequency

*f*

_{0}= 193.5 THz are used to excite the TE modes over a wide frequency range. The time-domain outputs of

*H*at the points (

_{z}*x*,

*y*) = (8.3, 2.4), (2.5, 8.4) and (−8.3, 6.4) μm, are monitored and recorded as the FDTD outputs. The FDTD output is transformed from the time domain to the frequency domain through Padé approximation [30], and the mode wavelengths and

*Q*factors are calculated from the peak wavelength and the width by fitting the resonance peak with a Lorentzian function.

#### 2.2 Modes in square microresonator

For the square microresonator with *a* = 17.8 μm and *w =* 1.4 μm, the obtained mode intensity spectrum for the TE modes is plotted in Fig. 1(b). The mode numbers *p* and *q* for mode TE^{o}^{,(}^{p}^{,} ^{q}^{)} and TE^{e}^{,(}^{p}^{,} ^{q}^{)} are the numbers of the wave nodes along the sides of the square resonator, where the superscripts ‘*o*’ and ‘*e*’ indicate the anti-symmetry and symmetry relative to the diagonals of the square resonator [14]. As a comparison, the intensity spectrum for the TE modes in the perfect square microresonator with the same size is also calculated and plotted in Fig. 1(b) as the dashed line. To figure out the influences of the output waveguide on different modes, the high resolution spectra for modes around 1530 nm are calculated and plotted in Fig. 1(c) as the solid and dash lines for the square microresonator with and without the output waveguide. For the perfect square microresonator without the output waveguide, seven high-*Q* modes are observed around 1530 nm with the wavelengths of 1530.97, 1530.26, 1529.10, 1527.47, 1525.42, 1522.90 and 1520.06 nm. They are TE^{o}^{,(52,54)}, TE^{o}^{,(51,55)}, TE^{o}^{,(50,56)}, TE^{o}^{,(49,57)}, TE^{o}^{,(48,58)}, TE^{o}^{,(47,59)} and TE^{o}^{,(46,60)} modes with the mode *Q* factors of 1.91 × 10^{5}, 1.30 × 10^{5}, 7.89 × 10^{4}, 2.55 × 10^{4}, 2.04 × 10^{4}, 1.69 × 10^{4} and 3.05 × 10^{4}, corresponding to the fundamental,first-order, second-order, third-order, forth-order, fifth-order and sixth-order transverse modes, respectively. With the introduction of the output waveguide, the even order transverse modes TE^{o}^{,(52,54)}, TE^{o}^{,(50,56)}, TE^{o}^{,(48,58)} and TE^{o}^{,(46,60)} are suppressed, with *|p* - *q|* = 4*n* + 2 and *n* the transverse mode number [13,14], due to high coupling loss to the output waveguide.

Furthermore, the mode field distributions are simulated using a narrow-bandwidth exciting source around the resonant peak. The mode field distributions |*H _{z}*| are presented in Figs. 2(a) and 2(b) for TE

^{o}^{,(52,54)}and TE

^{o}^{,(51,55)}modes in the perfect square microresonator without the output waveguide, respectively. For TE

^{o}^{,(52,54)}mode, the mode field distribution is strong in the middle region of the square sides, and thus the midpoint-connected output waveguide leads to a large coupling loss and a small mode

*Q*factor. Similar to TE

^{o}^{,(52,54)}mode, TE

^{o}^{,(50,56)}, TE

^{o}^{,(48,58)}and TE

^{o}^{,(46,60)}modes are suppressed due to the large coupling loss caused by the output waveguide. Because of the weak mode field distribution in the midpoints of the square sides, as shown in Fig. 2(b), TE

^{o}^{,(51,55)}mode can still have a high mode

*Q*factor with the introduction of the output waveguide. The mode

*Q*factors for TE

^{o}^{,(51,55)}, TE

^{o}^{,(49,57)}and TE

^{o}^{,(47,59)}modes are 3.71 × 10

^{4}, 6.18 × 10

^{3}and 4.21 × 10

^{3}, respectively, at the output waveguidewidth of 1.4 μm, with those of TE

^{o}^{,(49,57)}and TE

^{o}^{,(47,59)}by fitting with Fano-shape-like resonances [31]. The result indicates that the mode

*Q*factors for the third-order transverse mode TE

^{o}^{,(49,57)}and fifth-order transverse mode TE

^{o}^{,(47,59)}are much lower than that of the first-order transverse mode TE

^{o}^{,(51,55)}. TE

^{o}^{,(52,56)}, TE

^{o}^{,(50,54)}and TE

^{o}^{,(49,53)}modes at the mode wavelengths of 1501.32, 1560.35 and 1591.64 nm are also the high-

*Q*first-order transverse modes, as shown in Fig. 1(a). The average mode interval between the high-

*Q*first-order transverse modes is 30.1 nm, which is equal to the twice of the longitudinal mode interval. To have the high-

*Q*mode interval of 30.1 nm, we should reduce the cavity length to 12.5 μm for a Fabry-Pérot cavity.

In Table 1, the mode wavelengths and *Q* factors are summarized for TE^{o}^{,(52,56)}, TE^{e}^{,(52,55)}, TE^{o}^{,(51,55)}, TE^{e}^{,(50,55)}, TE^{o}^{,(50,54)}, TE^{e}^{,(50,53)}, TE^{o}^{,(49,53)} and TE^{e}^{,(48,53)} modes at the gain of 0 and 3.0 cm^{−1}. The threshold gain can be calculated from ${g}_{t}={n}_{g}{k}_{0}/Q$, where *k _{0}* is the wave vector in a vacuum and

*n*is the mode group index. The obtained threshold gain for the high-

_{g}*Q*first-order transverse modes is about 3.4~5.2 cm

^{−1}. The mode

*Q*factors of the symmetrical modes TE

^{e}^{,(52,55)}, TE

^{e}^{,(50,55)}, TE

^{e}^{,(50,53)}and TE

^{e}^{,(48,53)}are much smaller than those of the anti-symmetrical modes TE

^{o}^{,(52,56)}, TE

^{o}^{,(51,55)}, TE

^{o}^{,(50,54)}and TE

^{o}^{,(49,53)}, because of a large radiation loss at the vertices of the square microresonator for the symmetrical modes [13].

#### 2.3 Influences of circular corners

The fabricated square microresonators usually have round vertices after dry etching and wet chemical etching processes. Assuming the vertices to be a circular with a radius of *r* as shown in Fig. 1(a), we investigate the influences of the circular vertices on the mode characteristics. The mode wavelengths and *Q* factors are summarized in Table 2 for the high-*Q* modes at *r* = 0, 0.5 and 1 μm. At *r* = 0.5 μm, the mode intervals of the high-*Q* modes are still twice of the longitudinal mode interval as *r* = 0, with the mode *Q* factors of the anti-symmetrical modes are about five times of those of the symmetrical modes. However, the mode *Q* factors of the anti-symmetrical modes TE^{o}^{,(52,56)}, TE^{o}^{,(51,55)}, TE^{o}^{,(50,54)} and TE^{o}^{,(49,53)} are about 20% less than those of the symmetrical modes TE^{e}^{,(52,55)}, TE^{e}^{,(50,55)}, TE^{e}^{,(50,53)} and TE^{e}^{,(48,53)}, as *r* increases from 0.5 to 1 μm. The small difference of the mode *Q* factors shows that the mode interval of the high-*Q* modes reduces to the longitudinal mode interval at *r* = 1 μm. The results indicate that the square resonator with near perfect vertices is important to keep the mode interval of the high-*Q* modes twice of the longitudinal mode interval. The mode field distributions |*H _{z}*| for TE

^{o}^{,(51,55)}and TE

^{e}^{,(50,55)}are presented in Figs. 3(a)-3(d) at

*r*= 0 and 1 μm, respectively. The large radiation loss caused by the round vertices is responsible for the low

*Q*factor for TE

^{o}^{,(51,55)}at

*r*= 1 μm. For TE

^{e}^{,(50,55)}, the radiation loss induced by the round corners increases but the coupling loss caused by the output waveguide decreases, as

*r*increases from 0 to 1 μm. Therefore, different to the anti-symmetrical mode, the mode

*Q*factor for TE

^{e}^{,(50,55)}at

*r*= 1 μm is only slightly lower than that at

*r*= 0.

#### 2.4 Influences of the output waveguide width

Finally, we investigate the influences of the output waveguide width on the mode *Q* factors for the square resonator with perfect vertices, i.e., *r* = 0. The mode *Q* factors versus the waveguide width *w* are plotted in Figs. 4(a) and 4(b) for the high-*Q* modes TE^{o}^{,(52,56)}, TE^{o}^{,(51,55)}, TE^{o}^{,(50,54)} and TE^{o}^{,(49,53)} at *g* = 0 and *g* = 2 cm^{−1}. The gain is taken to be 2 cm^{−1} due to the threshold gain of TE^{o}^{,(52,56)} is only 2.1 cm^{−1} as *w* = 1 μm. The mode field distributions of TE^{o}^{,(52,56)} and TE^{o}^{,(50,54)} modes are symmetrical to the middle line of the output waveguide while those of TE^{o}^{,(51,55)} and TE^{o}^{,(49,53)} modes are anti-symmetrical, due to the even and odd mode numbers. The mode *Q* factors of the symmetrical and anti-symmetrical modes degrade with the increase of the waveguide width at different rates. For *g* = 0, the mode *Q* factors of the symmetrical modes decrease more quickly with the increase of *w* than the anti-symmetrical modes as *w* < 1.4 μm. The symmetrical modes have higher *Q* factors as *w* < 1.2 μm, but the anti-symmetrical modes have higher *Q* factors as 1.2 μm < *w* < 1.47 μm. As 1.6 μm < *w* < 1.8 μm, the mode *Q* factors of the symmetrical modes are slightly higher than those of the anti-symmetrical modes. As taking the gain into consideration, the change of the mode *Q* factors are almost the same as *g* = 0, as shown in Fig. 4(b). Therefore, by adjusting the output waveguide width, we can even have the high *Q* symmetrical or anti-symmetrical modes with the wavelength interval as four times as the longitudinal mode interval, which is important for the square microlaser with a wide continuous wavelength tuning range. In the following section, we fabricate square microlasers based on the simulated results.

## 3. Fabrication process and experimental results

#### 3. 1 Fabrication process

The square microlasers are fabricated using AlGaInAs/InP laser wafer with the active region consisted of six compressively strained quantum wells (QWs) with 6-nm-thick wells and 9-nm-thick barriers. The photoluminescence wavelength of the QWs is about 1520 nm at room temperature and the bandgap wavelength of the barrier layer is 1.2 μm. The square resonators are etched with the depth of 4 μm by inductively coupled plasma etching process using the SiO_{2} layer as the mask. After the removal of the mask, a 200-nm SiN* _{x}* layer is deposited using the plasma-enhanced chemical vapor deposition for increasing the adhesion of the BCB layer. Subsequently, the BCB layer is spin-coated twice to create a planar surface, followed by the annealing process in the N

_{2}atmosphere. After that, the BCB layer is etched by reactive-ion-etching process without any mask to expose the microresonators. Finally, a contact window is etched on the top of each microresontor for the current injection and the Ti/Pt/Au is deposited by electron-beam evaporation as the p-contact electrode. Finally, the Au/Ge/Ni n-contact electrode is deposited by electron-beam evaporation after lapping down the wafer to about 120 μm. In order to avoid the deformed vertices, no wet etching is used in the fabrication process.

#### 3. 2 Experimental results

The square microlasers are tested by bonding with p-side up on the heat sink, which is mounted on the thermoelectric cooler (TEC) for temperature control. For a square microlaser with the side length of 17.8 μm and the output waveguide width of 1.8 μm, the output powers coupled into a multi-mode fiber versus the continuous-wave (CW) injection current are plotted in Fig. 5(a) at the TEC temperature of 291 and 298 K as the solid and dash lines, respectively. The threshold currents are 4.5 and 5.5 mA at 291 and 298 K with the corresponding threshold current densities of 1.4 and 1.7 KA/cm^{2}, respectively. A series resistor of 24 Ω is estimated from the *I-V* curve in Fig. 5(a) at the threshold current. Due to the temperature rise with the injection current, the output power decreases as the CW injection current is larger than 40 mA at 298 K. The lasing spectra of the square microlaser are measured by an optical spectrum analyzer at a resolution of 0.06 nm and presented in Fig. 5(b) at 298 K and *I* = 6, 15, 20, 30, 40, 50 and 58 mA, where the adjacent spectra are relatively shifted by 10 dB for clarity. Evident resonance peaks at 1516.48, 1529.39, 1542.37 and 1555.54 nm are observed at 6 mA and marked by A, B, C and D in Fig. 5(b). The wavelength intervals 12.91, 13.01 and 13.17 nm can be fitted by the longitudinal mode interval ${\lambda}^{2}/2\sqrt{2}a{n}_{g}$ with the group index *n _{g}* ranged from 3.57 to 3.62. As the current increases from 15 to 20 mA, the lasing mode jumps 26.75 nm over two longitudinal mode intervals to mode D. This indicates that mode D has a higher mode

*Q*factor than mode C and the mode interval between the high

*Q*modes is twice of the longitudinal mode interval, which is in well agreement with the simulation results in Fig. 1. Furthermore, the coupling efficiency to the single-mode fiber

*η*is measured, which is defined as the power coupled to the single-mode fiber to that measured by a 5-mm-diameter detector 2 mm away from the cleaved facet. The measured coupling efficiency is about 5.9% as

*I*< 10 mA and 21% as

*I*> 20 mA. Based on the simulated and experimental results, the increase of the coupling efficiency is corresponding to the transition of the lasing mode from the anti-symmetrical mode to the symmetrical mode relative to the output waveguide. Considering the higher mode

*Q*factors for modes B and D than those of modes A and C, we can assign the modes B and D as the high-

*Q*first-order transverse modes. Since mode B is anti-symmetrical relative to the output waveguide while mode D is symmetrical, modes B and D may be corresponding to modes TE

^{o}^{,(51,55)}and TE

^{o}^{,(50,54)}in Fig. 1(b), respectively. The third-order and fifth-order transverse modes are not observed due to the low mode

*Q*factors. The lasing mode wavelength and the side-mode suppression ratio (SMSR) versus the CW injection current are summarized in Fig. 5(c) from 20 to 58 mA at the TEC temperature of 298 K. Single-mode operation with the SMSR > 36 dB is obtained with continuous wavelength tuning range of 6.4 nm as 20 mA <

*I*< 55 mA. The SMSR decreases to 29 dB due to the low output power caused by the heating effect at 58 mA.

The lasing modes with double longitudinal mode interval are also observed for the square microlasers with the side length of 17.8 μm and the output waveguide width *w* of 1.6 and 2 μm, as shown in Fig. 6 (a) and (b), respectively.

Finally, the lasing characteristics are studied for a square microlaser with the side length of 17.8 μm and the output waveguide width of 1.4 μm. The output powers versus the CW injection current are plotted in Fig. 7 (a) at the TEC temperature of 291 and 298 K as the solidand dash lines, respectively. The threshold currents are 3.5 and 4.5 mA with the corresponding threshold current densities of 1.1 and 1.4 KA/cm^{2} at 291 and 298 K, respectively. The lasing spectra at *I* = 5, 15, 25, 35, 45, 55 and 65mA are presented in Fig. 7(b) at the TEC temperature of 291 K, where the adjacent spectra are relatively shifted by 10 dB for clarity. Three evident peaks at 1519.33, 1532.06 and 1544.95 nm are observed at *I* = 5 mA, and marked as A, B and C in Fig. 7(b). The dominant lasing mode keeps constant at the mode B with the increase of the injection current, which indicates mode B has a higher mode *Q* factor than modes A and C. Based on the simulation results in Figs. 1 and 4, mode B is the high-*Q* first-order transverse mode and the mode number may be TE^{o}^{,(51,55)}, while modes A and C are the low-*Q* modes. The measured coupling efficiency to the single-mode fiber is only 5.86%, so the lasing mode is anti-symmetrical mode relative to the output waveguide, which agrees well with the simulation results in Fig. 4 as the output waveguide width is 1.4 μm. The lasing wavelength and the SMSR versus the CW injection current are summarized in Fig. 7(c) at 291 K, which shows a continuous wavelength tuning range of 9.26 nm with the SMSR > 26 dB from 5 to 65 mA. From the *I-V* curve in Fig. 7(a) and the lasing wavelength under different injection current in Fig. 7(c), the tuning rate of 0.068 nm/mW is calculated. Under a pulsed current with a pulse duty of 1% and a pulse width of 10 ns, the mode wavelength redshift rate of 0.114 nm/K is obtained by varying the TEC temperature. Based on the redshift rate, the temperature rise of 81 K is obtained from 5 to 65 mA and the practical laser temperature is about 379 K at 65 mA. Furthermore, the lasing spectra are measured under different TEC temperatures and presented in Fig. 8(a), and the wavelength of the dominant lasing mode and the corresponding SMSR are summarized in Fig. 8(b). As the TEC temperature increases from 286 to 319 K, no mode hopping is observed and the wavelength of the dominant lasing mode increases from1532.20 to 1536.00 nm with the wavelength redshift of 3.8 nm. The SMSR is lower than 15 dB as the TEC temperature is higher than 319 K due to the low output power caused by the high temperature.

## 4. Conclusion

In conclusion, the mode selection in the square microlasers with a midpoint output waveguide has been investigated numerically and experimentally, for realizing wide and continuous wavelength-tunable single mode lasing. The numerical results reveal that the output waveguide can make the mode interval of the high-*Q* modes as large as four times of the longitudinal mode interval by choosing the proper width of the output waveguide. Therefore, single-mode operation without mode hopping can be achieved and the lasing wavelength can be tuned continuously by tuning the injection current. The square resonator microlasers with the side length of 17.8 μm are fabricated by dry etching technique without a wet chemical etching smooth process, which can keep near perfect vertices of the square microresonator. At the output waveguide width of 1.4 μm, mode-hopping-free single mode operation with a continuous tuning range of 9.2 nm is achieved by tuning the injection current. As the output waveguide width is 1.8 μm, single mode operation with continuous tuning range of 6.4 nm is obtained. The results reveal the possibility for the precise control of lasing mode in the square microlasers. With the simple fabrication process and the compact size, the square resonator microlaser can offer compact tunable light source for photonic integrated circuits and optical interconnects.

## Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants 61235004, 61321063, and 61376048, and the Beijing Natural Science Foundation under Grant 4142052.

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