A novel design of an InP-based monolithic widely tunable laser, multi-channel interference (MCI) laser, is proposed and presented for the first time. The device is comprised of a gain section, a common phase section and a multi-channel interference section. The multi-channel interference section contains a 1x8 splitter based on cascaded 1 × 2 multi-mode interferometers (MMIs) and eight arms with unequal length difference. The rear part of each arm is integrated with a one-port multi-mode interference reflector (MIR). Mode selection of the MCI laser is realized by the constructive interference of the lights reflected back by the eight arms. Through optimizing the arm length difference, a tuning range of more than 40 nm covering the whole C band, a threshold current around 11.5 mA and an side-mode-suppression-ratio (SMSR) up to 48 dB have been predicted for this widely tunable laser. Detailed design principle and numerical simulation results are presented.
© 2015 Optical Society of America
Tunable semiconductor lasers have become one of the key devices for fiber-optic communications and the next generation optical networks . They can be used in dense wavelength division multiplexing (DWDM) systems to provide effective inventory management and rapid channel establishment with tremendous reduction in cost. Besides, they can also be used in the next generation reconfigurable optical networks to provide automatic wavelength configuration, wavelength conversion and wavelength routing. Tunable semiconductor lasers, especially monolithic widely tunable semiconductor lasers which are more compatible, reliable, compact and less-cost, have attracted worldwide attention due to their wide applications.
Lots of monolithic widely tunable semiconductor lasers have been proposed and demonstrated over the past few decades. One type of commercially available monolithic widely tunable semiconductor laser is the distributed Bragg reflector (DBR) type laser, including the sampled grating distributed Bragg reflector (SG-DBR) laser , the super-structure grating distributed Bragg reflector (SSG-DBR) laser , the modulated grating Y-branch (MGY) laser , and the digital super-mode distributed Bragg reflector (DS-DBR) laser , which can achieve tuning ranges above 40 nm, SMSRs in excess of 35 dB, output powers exceeding 10 dBm. Except for the DS-DBR laser, these lasers are based on the Vernier effect to extend the tuning range with limited refractive index change. Another type of commercially available monolithic widely tunable semiconductor laser is the thermally tuned distributed feedback (DFB) laser array . The tuning range of a single DFB laser is about 3~5 nm, which is limited by the thermal-optic coefficient of ~0.1 nm/°C. Therefore, a laser array is needed to cover the whole C band. All the above commercially available monolithic widely tunable semiconductor lasers are based on gratings to realize mode selection. However, fabrication of gratings requires extra epitaxial growth steps and expensive high-resolution processing such as electron-beam lithography (EBL). To avoid the fabrication complexity caused by utilizing embedded gratings, varieties of widely tunable laser schemes have been demonstrated, such as two-ring-resonator based widely tunable lasers [7–9 ], etched-slot based widely tunable laser , V-couple-cavity tunable laser , and widely tunable coupled cavity laser based on a Michelson interferometer . However, none of them have been reported with a performance comparable to the grating based widely tunable lasers.
In this paper, we propose a novel design of an InP-based monolithic widely tunable laser, the multi-channel interference (MCI) laser, whose mode selection scheme is fundamentally different from the widely tunable lasers mentioned above. As schematically shown in Fig. 1 , the MCI laser includes three sections, an optical gain section, a common phase section and a multi-channel interference section. The multi-channel interference section contains eight arms with unequal length difference. The rear part of each arm is integrated with a multi-mode interference reflector (MIR) , which has already been successfully utilized as a reflector in an on-chip laser  and coupled-cavity lasers [12,15 ]. There is a phase section on each arm (called arm phase section in the following) which is used to tune the phase of each channel independently. In our design, mode selection of the MCI laser is realized by the interference of the multi-channel interference section. The shape of the reflection spectrum generated from the MCI section depends on the arm length difference, so the arm length difference must be optimized in order to make the MCI laser have a good single-mode characteristic and a wide tuning range. The paper is organized as follows: section 2 introduces the operation principle of the MCI laser; section 3 explains the optimization of the arm length difference in detail; section 4 shows the numerical simulation results of the MCI laser, such as reflection spectra of the multi-channel interference section, lasing spectra, threshold currents and L-I curve.
2. Operation principle
The MCI laser is similar to the MGY laser in the sense that mode selection reflectors are on the same side of the laser cavity and mode selection is realized by the addition of reflections. However, they are still conceptually different from each other. The MGY laser is based on the additive Vernier effect to achieve a wide tuning range . The MCI laser is based on the multi-channel interference. By using eight arms with unequal length difference, reflection spectrum dominated by a single narrow reflection peak can be realized, which ensures that the MCI laser has a good single-mode performance.
As shown in Fig. 1, the 1x8 MMI splitter is realized by cascading 1x2 MMIs. The reason to utilize 1x2 MMIs is that 1x2 MMI normally has the advantages of low insertion loss, large fabrication tolerance and wavelength independent characteristics. The incident light is separated into eight equal parts by the 1x8 MMI splitter and the lights are reflected back by the MIRs. Therefore, the MCI laser is performed by the addition of the complex reflectivities. So the aggregated complex reflection coefficient at the right side of the gain section can be expressed as
Although making the eight arms in phase can generate a narrow strong reflection peak at wavelength λ 0, the shape of the whole reflection spectrum is decided by the length difference of the eight arms. Supposing that the lengths of the eight arms are arranged increasingly, the length difference ΔLi between the i-th and (i + 1)-th arm isEq. (1) can be expressed by ΔLi as below:Eq. (4), the common phase section, the 1x8 MMI splitter and the length of the first arm can be treated as part of the resonant cavity, which is reflected in the common phase term ; the shape of the reflection spectrum is determined by the arm length difference ΔLi . Therefore, we can optimize the shape of the reflection spectrum by optimizing the arm length difference.
Once attaining an ideal reflection spectrum through optimizing the arm length difference, the lengths of the eight arms are fixed. The length difference between the other seven arms and the first arm can be calculated by the arm length difference ΔLi introduced above. Correspondingly the initial round trip phase difference can be written asEq. (5), which makes the No. 2 to 8 channels out of phase with the first channel. Thus we include an independent arm phase section on each arm to adjust the phases of the seven arms. By injecting currents into these arm phase sections, we can eliminate the phase errors so as to make the eight channels in phase. Thus a narrow main reflection peak at wavelength λ 0 can be obtained, which makes the longitudinal mode of the laser cavity around λ 0 lase. Similarly, if we want to make the longitudinal mode around a different wavelength λ 1 lase, we have to readjust the phases of the No. 2 to 8 channels to make them in phase with the first channel at wavelength λ 1. Therefore, the center wavelength of the main reflection peak will shift from wavelength λ 0 to λ 1, which tunes the lasing wavelength accordingly (coarse tuning). Thus, for the MCI laser, generation of the narrow main reflection peak and coarse tuning of the laser are achieved by adjusting the phases of any seven channels (actually any channel can be chosen as the reference channel).
After coarse tuning, we need to slightly adjust the position of the cavity longitudinal mode selected by the main reflection peak so as to realize fine tuning of the MCI laser. Fine tuning of the MCI laser can be realized in two ways: one way is to adjust the phase of the common phase section, which is similar to the fine tuning of the DBR type tunable lasers; the other way is to control all the eight arm phase sections at the same time. The second way is feasible because the first arm is actually a part of the resonant cavity. If the first arm phase is now changed, the cavity longitudinal mode position can be adjusted, the same as adjusting the common phase section. However, the other seven channels have to be adjusted accordingly to keep in phase with the first channel so that the reflection spectrum remains unchanged. So by adjusting the phases of the total eight arms, we are able to adjust only the cavity longitudinal mode position but keep the peak wavelength of the reflection spectrum unchanged, which is the same as only adjusting the phase of the common phase section. However the second way of fine tuning will make the whole tuning strategy more complex because the fine tuning will involve the adjustment of all eight channels.
3. Optimization of the arm length difference
As illustrated in section 2, the shape of the reflection spectrum generated from the multi-channel interference section is closely related to the arm length difference. The simplest case is to choose ΔLi equal to each other, which makes the eight channels generate a comb-like reflection spectrum. The FWHM (full width at half maximum) and the FSR (free spectral range) of the comb-like reflection spectrum are related to the arm length difference. Figure 2 shows the reflection spectra for two groups of equal arm length difference (In Fig. 2, and Figs. 3(a)-3(c) , in order to figure out the ratio between the main reflection peak and the other reflection peaks conveniently, reflectivity is normalized by the largest reflectivity of the spectrum). As shown in Fig. 2, if the arm length difference is larger, the reflection peaks will be narrower, but they are also more closely packed. In the MCI laser case, instead of a comb-like reflection spectrum, a reflection spectrum dominated by a single narrow reflection peak is needed. This is achieved by making the arm length difference unequal. Once the periodicity is broken, the reflection spectrum will have a lot of random reflection peaks. Then making the eight channels in phase at wavelength λ 0 can generate a narrow main reflection peak at wavelength λ 0. Figures 3(a)-3(c) shows the reflection spectra for three groups of unequal arm length difference. As can be seen, there are lots of random reflection peaks but only one narrow main reflection peak at 1530 nm where the eight channels are in phase. However, only making the arm length difference unequal is not enough, because the FWHM of the main reflection peak should be narrow enough to suppress the adjacent longitudinal modes of the laser cavity and the other random reflection peaks should be suppressed as well to leave the main reflection peak the strongest so that the MCI laser can have a good single-mode performance. Therefore, the arm length difference should be carefully optimized. In reality we use the particle swarm optimization (PSO) algorithm  to optimize the arm length difference. We find that if the arm length difference is averagely larger, the main reflection peak will be potentially narrower, which is beneficial to suppress the adjacent longitudinal modes; however the other random reflection peaks are more difficult to suppress, as shown in Fig. 3(a). On the opposite, if the arm length difference is averagely smaller, it helps to suppress the other reflection peaks but the FWHM of the main reflection will be potentially larger. This in principle agrees with the case with equal arm length difference. So practically we need to make a trade-off by adjusting the average arm length difference.
During optimization, we use the ratio between the main and the secondary reflection peaks as the figure of merit. Usually the ratio is expected to be greater than 2 so that the MCI laser can achieve an SMSR of more than 40 dB. Without any restrictions the magnitude of the random reflection peaks after optimization tends to be uniform in the wavelength range from 1520 nm to 1580 nm, as shown in Fig. 3(a), and the ratio can be greater than 2 in most cases. However, these results do not really guarantee a wide tuning range, because the gain spectrum of the gain section is not flat over the C band, as shown in Figs. 3(d)-3(f). When the lasing wavelength is far away from the gain peak, the SMSR will degrade dramatically and mode hop may occur. Therefore, normally we need to suppress the reflection peaks located around the gain peak even more so as to extend the tuning range. This can be implemented by weighting the reflection spectrum generated from the MCI section during optimization. For example, we can multiply the reflection spectrum by the round-trip gain from the gain section to exaggerate the reflection around the gain peak. The PSO algorithm tends to suppress the weighted reflection spectrum the same as before. So after optimization we find that the reflection peaks around the gain peak are additionally suppressed, as seen from Figs. 3(b) and 3(c). We presented two optimization results to show this point. The ratio between the main reflection peak and the reflection peaks around the gain peak is now more than 4. This increases the threshold modal gain of the corresponding cavity modes, as shown in Figs. 3(e) and 3(f) and helps to achieve good SMSRs and a large tuning range of the MCI laser, as demonstrated in the following section.
4. Numerical simulation results
4.1 Numerical simulation of the MCI laser
To demonstrate the feasibility of the MCI laser, we simulate the MCI laser by solving the steady-state multi-mode rate equations, as shown in Eq. (6) , where Pi is the photon number in mode i, N is the carrier density, is the spontaneous emission factor of mode i, B is the coefficient for spontaneous emission, vg is the group velocity, τpi is the photon lifetime of mode i, gi is the modal gain of mode i, I is the injection current into the gain section, η is the injection efficiency, A and C are coefficients for defect recombination and Auger recombination, Vact is the volume for carriers. The MCI laser simulated here has a deep-etched 2 µm wide ridge waveguide structure with a 400 µm long shallow-etched gain section. The active region consists of five compressively strained InGaAsP quantum wells with the gain peak around 1550 nm. The front cleaved facet is assumed to have a power reflectivity of 0.32. Reflection loss of the MIR is assumed to be 0.5 dB. The effective propagation length of the 1x8 MMI splitter is 474.59 µm. Insertion loss of the 1x2 MMI is assumed to be 0.5 dB per single pass. Propagation loss of the passive waveguide is assumed to be 10.0 dB/cm. The lengths of the eight arms are 198.00 µm, 207.94 µm, 351.91 µm, 397.13 µm, 416.08 µm, 448.99 µm, 474.56 µm, and 610.71 µm, respectively, in ascending sequence (including the length of the one-port MIR). The calculated effective length of the eight arms is 387.77 µm. So the effective length of the cavity is 1452.36 µm and the wavelength separation between two adjacent cavity modes is about 0.23 nm. The overall length from the left side of the gain section to the end of the longest arm is 1700 µm and the width of the MCI laser including the electrodes for contact is 500 µm. To make the simulation more accurate, we used practically measured gain spectra at different injection currents . The material gain spectra at different carrier densities are attained through curve fitting and interpolation, as shown in Fig. 4 . We also considered the losses induced by the currents injected into the arm phase sections. For the MCI laser, the arm phase sections only need to generate π phase change at most and the length of the arm phase sections is set as 150 µm, so the tuning current can be very small. Here we set the largest tuning current as 10 mA corresponding to 1.5 dB loss. Detailed parameters of the MCI laser used in the simulation are listed in Table 1 . Wavelength tuning of the MCI laser is realized by injecting currents into the eight arm phase sections to make the round-trip phases of the eight channels equal to integral multiples of 2π at the designated wavelength.
The calculated reflection spectra at the right side of the gain section at different center wavelengths are showed in Fig. 5 . The FWHM of the main reflection peak is about 0.65 nm. The ratio between the main reflection peak and the reflection peaks around the gain peak is about 4. Peak power reflectivity of the reflection spectra is about 0.23. The loss mainly comes from the propagation loss of the passive waveguide, the 1x2 MMIs and the currents injected into the arm phase sections.
Figure 6 shows the solutions to the steady-state multi-mode rate equations. The superimposed lasing spectra at different lasing wavelengths are shown in Fig. 6(a). From the results, we can see that the MCI laser has a very even output power across the range of 40 nm covering the whole C band (more than 13dBm). The output power difference is in the range of 0.5 dB. Figure 6(b) shows the SMSRs at different lasing wavelengths, which are more than 48 dB across the tuning range. The limitation of SMSR mainly comes from the adjacent cavity modes. The device also has very low threshold currents, which are shown in Fig. 6(c). The threshold currents are around 11.5 mA. The fluctuations within the curves are due to the losses induced by the currents injected into the arm phase sections.
The calculated L-I curve at 1550 nm is presented in Fig. 6(d). The L-I curve is linear above threshold and the threshold current is around 10.5 mA as seen from the curve. The slope efficiency is 0.174 mW/mA.
4.2 Characterization of the MCI laser
Numerical simulations reveal that the MCI laser could have a good single-mode performance and a large tuning range, but characterizing the laser would be a great challenge due to eight phase sections being used. Normally other monolithic widely tunable lasers only need to control three phase tuning sections at most, such as the DBR-type tunable lasers. Characterization of these lasers is normally implemented by sweeping currents injected into the phase sections so as to generate tuning maps. Such a tuning map generation process is normally time-consuming. However, generating tuning maps by sweeping currents injected into the phase sections would be infeasible for the MCI laser. In order to overcome the problem, we propose to find the current settings for the phase sections by using optimization algorithms to maximize the output power from the MCI laser for a series of designated wavelengths. In this initial study we test the idea by optimizing the reflectivity from the multi-channel interference section, instead of maximizing the output power.
In section 2, we explained that coarse tuning of the MCI laser is realized by adjusting the currents injected into the No. 2 to 8 arm phase sections to make the phases of the eight channels in phase at the designated wavelength. In actual simulation, we set eight random initial phases for the eight channels and seven random initial currents for the No. 2 to 8 arm phase sections. Then we use the hill-climb algorithm to optimize these seven currents to search for the largest reflectivity at the designated wavelength. To do so, first the currents injected into the No. 3 to 8 arm phase sections are fixed at the initial currents and the current injected into the No. 2 arm phase section is treated as a center current. Then another four currents are selected around the center current with equal separation, reflectivities at the designated wavelength and the five currents are calculated. Next we used a parabolic function to fit the calculated reflectivities to determine the new center current for the No. 2 arm phase section. We call the above process as a searching step. The searching step is repeated for the currents injected into the No. 3 to 8 arm phase sections. After all the seven currents being searched (we call it a searching loop), we restart the searching step for the current injected into the No. 2 arm phase section until the reflectivity at the designated wavelength is maximized. During optimization, the searching scope should be adjusted in order to maximize the reflectivity accurately and fast. Averagely the reflectivity can reach maximum after about 20 loops. We record the best value of the reflectivity at the designated wavelength for each searching step. When the reflectivity is maximized, we can expect that the eight channels are nearly in phase. Currents injected into the seven arm phase sections are set in the range from 1 mA to 10 mA, which can realize a phase change more than π. Internal loss of the passive waveguides, insertion loss of the 1x2 MMIs, reflection loss of the one-port MIR and losses induced by the currents injection into the arm phase sections are considered in the simulation.
Figure 7(a) shows the change of reflectivity at wavelength 1550 nm during optimization. We can see that the searching process converges very quickly. To verify the accuracy of the results, we also calculate the reflection spectrum with the final current values from the searching process to check whether the center wavelength of the main reflection peak matches the wavelength set in the simulation. The calculated reflection spectrum is shown in Fig. 7(b) and the center wavelength of the main reflection peak is the same as the set value. Figures 7(c)-7(i) show the seven current values found by the optimization algorithm change with the center wavelength of the main reflection peak. We can see that the current changes are periodical and currents decrease with the wavelength increasing. As explained above, during coarse tuning, the phase of the first channel is chosen as a reference, so we only need to compensate for the phase difference between the other seven channels and the first channel caused by wavelength changes. The phase difference equalsEq. (7), the phase difference is proportional to the length difference . So the larger the length difference is, the faster the phase has to be tuned with the injected current. That’s why the change of the current injected into the No. 2 channel is the slowest while the No. 8 channel has the fastest change. In Fig. 7(c), the current change is fluctuant, because the phase difference between the second channel and the first channel is very small and the reflectivity is insensitive to a small change of phase.
As introduced above, the MCI laser works based on the interference of eight arms. The phase of each arm is essentially controlled by injecting current into the corresponding arm phase section. However, the phase may deviate from the ideal value due to factors such as errors with the current settings on the arm phase sections. The deviations of the arm phase will influence the reflection spectrum generated from the multi-channel interference section and will finally influence the behavior of the laser. To study the tolerance of the current settings on the arm phase sections, we did the following simulations with a statistical method. We added a current deviation δIi to each current Ii (i = 1, 2, 3…7) on No. 2 to 8 arms. The current settings Ii are the accurate values needed to make the eight channels in phase, with which the laser can work at 1550 nm with an SMSR about 49.5 dB. Each δIi is generated in the form of a normal distribution with zero average. Standard deviation of δIi is set to be the same on each arm, which is expressed as δ. δIi on different arms are not correlated to each other. Figures 8(a)-8(c) show the peak reflectivity, peak wavelength of the reflection spectrum and the corresponding laser SMSR for totally 200 samples of the ensemble of δIi with the standard deviation δ equal to 0.1 mA. From the 200 samples it is seen that with the level of 0.1 mA fluctuations on the current settings, the peak reflectivity shows less than 2.2% variation; the peak wavelength variation is less than 0.06 nm (7.5 GHz); the SMSR variation is less than 2.5 dB. Figures 8(d)-8(f) show the average value and standard deviation of the peak reflectivity, peak wavelength and SMSR versus the standard deviation of the current fluctuations δIi. The peak reflectivity and SMSR deteriorate with the increase of the standard deviation of δIi. The results show that as long as the standard deviation of the current settings is less than 0.2 mA, the variations on the peak wavelength, peak reflectivity and the laser SMSR are reasonably acceptable. The standard deviations of the peak reflectivity, peak wavelength and SMSR are about 0.005, 0.03 nm and 1.3 dB, respectively. When the standard deviation of the current fluctuations δIi reaches 0.5 mA, we did see mode hops due to the large influence on the reflection spectrum.
Numerical simulation predicts that the MCI laser could have a good single-mode performance and a wide tuning range, which is comparable to other commercially available monolithic widely tunable semiconductor lasers. Besides, the MCI laser has some potential advantages which make it more competitive. For the MCI laser, all the reflections comes in parallel, so the loss in each arm phase section only deteriorates the reflection from that channel. The overall loss is thus reduced. Furthermore, not all arms having the highest current at the same time, this effectively reduces loss as well. Therefore it is expected that the laser performance will not dramatically deteriorate when tuning, which actually has been confirmed by the simulation. Also for the proposed MCI laser, the phase tuning section on each arm needs to generate only π phase change at most and the length of the arm phase section can be pretty long. This dramatically reduces the requirement on the capability of the arm phase section for phase shift generations. This means that some simple quantum well structures can be used to generate the phase change, which will potentially simplify the integration of the laser with modulators. Also the current density required for the phase sections will be dramatically lower which means lower thermal effect, so it is expected that the tuning speed of the laser will be faster.
For the phase sections, normally no more than 10 mA is needed to generate π phase shift from our experience. For the MCI laser, not all the injection currents into the eight phase sections will be the largest at the same time as seen from our simulations, so the total current injected into all the phase sections will not exceed 80 mA, indicating that no more than 0.12 W will be required to tune the MCI laser (assuming that 1.5 V is needed for the 10 mA current injection on each phase section). So although totally eight phase sections are employed to tune the laser, the actual power needed to operate them is not a big burden.
The biggest challenge for the MCI laser concept is that the laser characterization will be more complex because now there are eight phase sections that need to be controlled simultaneously. However, coarse tuning of the MCI laser is predictable. In our previous work, it has been shown that the control of multiple phase shifters can be dramatically simplified if they can be characterized on-site . The characterization and control of the laser will certainly be very different from the DBR based widely tunable lasers and will be dealt with in detail in the future.
The authors would like to acknowledge the support from the 1000 talented youth plan sponsored by the Chinese government.
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