Control Strategy of an Integrated Tunable Laser With a Single Intra-Cavity AMZI Filter

Asymmetric Mach-Zehnder interferometers (AMZIs) can, in principle, enable continuous wavelength tuning of a laser when used as intra-cavity filters. Their simplicity and good compatibility with generic foundry platforms are major advantages. However, the difficulty to develop a well-defined and robust control strategy is an important drawback which restricts the use-cases of these tunable lasers. Here, we make an in-depth investigation of the tunability properties of a laser including a single-stage AMZI in its cavity. We find that due to imperfections of Electro-Optic Phase Modulators (EOPMs), the dependence of the phase variation with the applied voltage is not linear. Because integrated EOPMs cannot be individually calibrated, these nonlinearities prevent a precise and independent tuning of the phase and amplitude of the AMZI transfer function, and thus continuous tuning cannot be reliably achieved. To overcome this issue, we propose a refined control strategy which allows for semi-continuous tuning. With this approach, we demonstrate a piece-wise continuous tuning of the emission wavelength by taking advantage of the coupling between amplitude and phase in the AMZI response. With our refined control strategy, we achieve tuning of the emission wavelength over the full free spectral range (FSR) of the AMZI.


I. INTRODUCTION
I NTEGRATED wavelength-tunable laser sources have become increasingly important due to their implementation in a wide variety of applications such as communication systems, spectroscopy, sensing and metrology [1], [2], [3], [4]. Precise tuning of the wavelength is required in these applications e.g., to accurately record the shape of the resonance lines in spectroscopy or precisely locate the position of the Bragg wavelength in fiber Bragg gratings (FBGs). Depending on the intended application the required precision of the wavelength tuning varies from a few MHz to a few GHz. Over the last years, several types of wavelength-tunable lasers have been developed based on different wavelength filtering mechanisms and designs such as ring resonators [5], [6], [7], [8], distributed Bragg reflectors (DBR) [9], [10], [11] and coupled cavity lasers [12], [13], [14]. Among the various concepts, wavelength-tunable lasers based on asymmetric Mach-Zehnder interferometer (AMZI) as the wavelength selective intra-cavity filter are attractive since, in principle, the AMZI enables a continuous wavelength tuning over a wide spectral range and its performance is robust to the tolerances of the fabrication processes. However, if the AMZI is the only wavelength-selective mechanism of the laser, more than one AMZI is needed to obtain single mode operation. Tunable AMZIs as wavelength filters have been employed by Latkowski et al. [15] inside the cavity of a ring laser ensuring a record tuning range of 74.3 nm around 1525 nm as well as to obtain tunable sources operating at 2 μm [16]. In these designs, three AMZIs in series [15] or two nested AMZIs [16] have been used.
Despite the wide and thus attractive tuning range, widely reported in literature, no accurate control approach has been derived yet. A precise and efficient control represents a technique through which the dependence of the filter's transfer function on the filter parameters is fully determined and accurately connected with the emission wavelength with an open loop mechanism. This issue is first tackled in Ref. [17] where attempts to exploit the serially cascaded AMZI configuration [15] for applications in optical coherence tomography (OCT) have been made. This brought the need to calibrate the response of the emission wavelength on the phase modulators voltage amplitude, in order to tune the laser in a step-wise manner with 1 GHz accuracy. A three step calibration method with progressive wavelength accuracy has been proposed [17], although the tuning of the coarse and medium AMZI alone leads to wavelength gaps within the tuning range. Moreover, the electrical cross-talk between the phase modulators limits the tuning accuracy to 8 GHz. Recently, an optimized control strategy for the wavelength calibration of an improved design configuration has been reported [18]. This strategy re-calibrates the fine filter and the cavity mode position every 24 h for every coarse and medium filter control setting configuration. A table with uniform wavelengths with 10 GHz frequency steps has been obtained. Unfortunately, a sequential selection of the longitudinal modes cannot be achieved and wavelength gaps as wide as 2.5 nm are still present. Hence, a technique giving access to the entire spectral range of an This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ AMZI-based laser with continuous wavelength tuning remains to be developed.
In this article we investigate the performance and control mechanism of a single stage AMZI-tuned laser. The goal is to understand the tuning limitations and control challenges of an integrated intra-cavity AMZI without the influence of other intra-cavity filters. Thus, the AMZI is combined with a DBR, which eliminates the need for additional intra-cavity AMZIs. Despite its simplicity, we show that the simple tuning method of reverse biasing the phase modulators, results in wavelength gaps within the free spectral range (FSR) of the AMZI. Moreover, the comprising phase modulators have different dependencies with the applied voltage, hence, a correction is needed. Thus, we propose a control strategy that takes advantage of the phase difference between the AMZI arms and demonstrate a semicontinuous tuning covering the entire FSR of the AMZI and 89.5% of the laser's tuning range. At this point this method is shown for one stage AMZI however, we speculate that it has the potential to be implemented for cases where more intra-cavity AMZIs are employed.
The article is organized as follows. In Section II, we present details on the cavity design and the experimental results on the current-light-voltage characteristics and the spectral quality. The power spectral density of the frequency noise is determined and compared with the values reported in literature. In Section III, challenges for a simple step-wise and sequential tuning of the emission wavelength are highlighted and in Section IV, a control strategy that enables semi-continuous tuning is presented. We end the article by summarizing the main conclusions.

A. Design of an Intra-Cavity AMZI Based Tunable Laser
The AMZI is built with two 1.8 mm long electro-optic phase modulators (EOPMs), one in each arm, and two 1 × 2 multimode interference reflectors (MMIs), as splitter and coupler. The asymmetry is created by introducing an optical path length imbalance ΔL equal to 965 μm. The theoretical transmission of an individual AMZI, the blue curve in Fig. 1(a), has a periodic behavior in the frequency domain, with a cosine-squared transmission profile. The AMZI transmission maxima can be tuned by applying a reverse bias voltage in one of the EOPMs, or both EOPMs simultaneously, as shown with black in Fig. 1(a). The free spectral range (FSR), defined as the spacing between two successive transmitted optical intensity maxima or minima, of the AMZI is 83.1 GHz (0.66 nm).
The transmission of an individual AMZI in combination with the fundamental mode structure of the laser cavity is not sufficient to achieve single mode operation as there will be selected modes for every AMZI transmission maxima. For that, we use a DBR to select only one of the transmission maxima as illustrated with orange in Fig. 1(a). To choose one of the transmission maxima, in the design procedure, we made a trade-off between the ΔL of the AMZI and the width of the DBR stop-band in order to allow for only one maximum of the transmission spectrum of the AMZI within the DBR stop-band. The stop-band width of the DBR is approximately 1.2 nm which means that the cavity modes that fall at the edge and outside of this band will be greatly suppressed. On the other hand, the length choice of the DBR is a compromise between its reflectivity and stop-band since a higher stop-band theoretically will result in a higher tuning range but also lower output power of the laser. We use a 500 μm long DBR, and its reflectivity is predicted to be around 90%. The wavelength selection is thus realised by combining one AMZI with a DBR. In order to obtain a good side-mode suppression ratio (SMSR), the proposed filter should ensure a sufficient mode selectivity, at least 4% transmission difference between the selected wavelength and the other competing modes [15]. A close-up of the combined cavity mode selection in black, shown in Fig. 1(b), overlapped with the longitudinal cavity modes around the transmission peak demonstrate the analysis of the losses corresponding to the neighboring modes of the selected peak. With our set of parameters only one cavity mode will be selected.
To form the laser cavity one multimode interference reflector (MIR) is used in the rear end of the laser. The laser also includes a 500 μm semiconductor optical amplifier (SOA) which provides the optical gain, and a 500 μm long EOPM as a phase section. Reverse biasing the phase section enables in-line cavity phase adjustments and therefore the translation of the cavity modes which can aid to continuously tune the laser. The overall cavity length is approximately 4860 μm which results in a longitudinal mode spacing of ≈ 65 pm. The proposed design is shown schematically in Fig. 1(c). The laser was fabricated using a commercially available active-passive InP-based integration technology in the framework of a multi-project wafer run by Smart Photonics. A microscopic image of the laser is shown in Fig. 1(d). Its footprint is less than 4 × 0.5 mm 2 .

B. Spectral Performance and Tuning Capability
The laser was characterized at 18 • C, where the emitted power is the highest, using a thermistor controlled via a temperature controller (Thorlabs PRO800/ITC8052). The SOA and DBR current is provided by a laser diode controller (Thorlabs PRO800/ITC8052) and the output optical power is monitored by a power meter. The two EOPMs of the AMZI are reversed biased from 0 V to −10 V and, the phase section from 0 V to −5 V using a voltage source module (NI9253). 1000 quasi-random voltage combinations are generated and applied to the EOPMs. The optical spectra are recorded for each case with a 5 MHz resolution bandwidth using an optical spectrum analyzer (APEX 2083 A).
In Fig. 2(a) the optical output power and the voltage as a function of the injection current are shown. The threshold current is about 25 mA and the output optical power reaches about 100 μW at 80 mA SOA current. This is the optical power in the lensed fibre to which we should add the coupling losses from the chip facet to the lensed fiber and which are estimated to be around 3-4 dB. In Fig. 2(b) the output optical spectrum is presented, with 5 MHz resolution bandwidth, for the volt- The closest neighboring modes to the lasing mode are barely visible above the noise floor of the instrument. The laser is single mode and the SMSR is about 51 dB. 13 optical spectra across the tuning range of the laser operated at 45 mA SOA current are shown in Fig. 2(c). The tuning range reaches up to 1.2 nm, from 1550.2 nm to 1551.4 nm defined by the DBR band-stop. From all the recorded spectra the SMSR values are extracted and are plotted in Fig. 2

C. Intrinsic Linewidth
Intrinsically, the broadening of the laser linewidth is caused by the coupling of the spontaneous emission into the oscillating mode, leading to spectrally white frequency noise and to a Lorentzian laser line shape. Typically, the frequency noise spectrum of a laser is also composed of the flicker noise and random-walk frequency noise [19]. The frequency-modulation (FM) noise spectrum contains the complete statistical characteristics of the frequency noise of the laser. The FM spectrum is obtained from the power-spectral-density (PSD) function of the instantaneous optical frequency fluctuations. If the FM-noise spectrum is recorded for a short enough time [20], the impact of flicker and random-walk frequency noise can be excluded and the intrinsic linewidth is directly proportional to the constant value of the FM noise spectrum [21].
To obtain the FM-noise spectrum and characterize the laser phase noise, we use the setup shown in Fig. 3(a). The emitted light is sent through a polarization controller (PC) and then superimposed with a local oscillator (LO) laser in an optical coupler. The LO is a high-quality external-cavity laser (ECL) (Keysight N7776 C) with an intrinsic optical linewidth smaller than 10 kHz. At the output, a photodetector (Thorlabs RXM42AF) generates a beat signal at an intermediate frequency around 2 GHz defined by the detuning of the LO and the wavelength of interest. Then the beat signal is recorded using a high definition oscilloscope (Teledyne Lecroy WavePro 804HD) which works as an analog-to-digital converter (ADC) with a sampling rate of 20 GS/s. For this experiment we have recorded 150 MSa. The frequency noise spectrum is then calculated by taking the Fourier transform of the extracted instantaneous frequency noise fluctuations and is plotted in Fig. 3(b).
The spectral density of the frequency noise becomes white approximately between 50 MHz and 200 MHz where other frequency noise effects mentioned above are neglected and the frequency noise PSD is flat. To find the frequency noise power spectral density level we average the noise level in this region which is highlighted in Fig. 3(b) and obtain 121 Hz 2 /Hz. When the level of the flat part of the single-sided frequency noise is multiplied by π we obtain the Lorentzian intrinsic linewidth of 381 kHz. The value found for the Lorentzian linewidth is in the same order of magnitude as for previously reported lasers in this integration platform [10], [22].

III. CHALLENGES OF A ROBUST CONTROL FOR AN AMZI-BASED LASER
As explained in Section II, the laser is designed such that the wavelength selection and hence wavelength tuning is mainly enabled by the AMZI. The asymmetry between the AMZI arms introduces a different optical path-length in each of the branches, hence a relative phase difference given by [23], [24]: where λ is the wavelength in vacuum, c is the speed of light in vacuum and n the group refractive index of the deeply etched waveguide. A change of the optical phase by 2π between the arms tunes the filter over one full FSR of the AMZI. The voltage necessary to induce this phase change between the AMZI arms is denoted as V 2π , and is experimentally estimated to be ≈ 10.4 V. The resulting electric field after the AMZI is mathematically written as: where E in is the input field amplitude and V EOPM1 and V EOPM2 the voltage applied in EOPM1 and EOPM2 respectively. Here, our intention is to define the required voltages to be applied to EOPM1 and EOPM2 in order to select consecutive longitudinal modes within the DBR stop-band with a relatively simple strategy. During this experiment the sum of the voltages V EOPM1 and V EOPM2 is kept constant in each measurement step, thus, the phase term in (2) should ideally be constant, which means that the position of the longitudinal cavity modes should remain unchanged. This would ensure that the amplified mode i.e., the emission wavelength of the laser depends solely on the filter and the selected cavity mode only on the value ΔV = V EOPM1 − V EOPM2 . Thus, we vary the voltage in each EOPM in opposite directions i.e., V EOPM1 from −10 V to −5 V and V EOPM2 from −5 V to −10 V, in steps of 5 mV using a voltage source module (NI9253). The voltage of the phase section, V Phase , is set at 0 V, and is kept unchanged throughout the experiment. The optical spectra are recorded using an optical spectrum analyzer (OSA) (APEX 2083 A) with a resolution of 1.12 pm. The emission wavelength is extracted from the OSA measurements and the results are plotted in blue in Fig. 4. Several longitudinal modes separated by Δf are selected, we identify them with black doted lines. This simple tuning approach enables a step-like wavelength tuning where the EOPM voltages are switched continuously with the conditions mentioned above. We notice some features resulting from this control approach: i) when the voltages are varied continuously and the resulting transfer function of the AMZI is in the edge of the DBR transmission, the following AMZI transmission will be on the other edge of the DBR which results in sudden wavelength jumps equal to the FSR of the AMZI, as shown with the green arrows in Fig. 4. This behavior constrains the sequential selection of all the longitudinal modes within the FSR of the AMZI. A simple way to prevent it, is to exclude the voltage combinations resulting in such sudden jumps, or alternatively fine tune the design parameters to increase the AMZI transmission period or decrease the DBR stop-band; ii) there are gaps between discrete points within the wavelength tuning range which means that not all possible cavity modes can be amplified, and the wavelength tuning resolution is also defined by the cavity mode spacing, Δf . The existence of the gaps within the tuning range is an inherent feature linked to the AMZI filter performance and this control approach. However, if more cavity modes would be present, they would potentially be selected by the AMZI filter, in turn affecting the wavelength tuning resolution. For that we shift the cavity modes by varying the voltage of the phase section (V Phase ) and then tune the AMZI in the same way as in the previous experiment. The results are plotted in Fig. 4 with red for V Phase = −4 V and with black for V Phase = −8 V. The emission wavelength changes in roughly the same trend as for the case of V Phase = 0 V. With higher voltages or a longer phase section, the wavelength range between cavity modes would be attainable enabling a continuous wavelength tuning. But, that would come at the expense of the simplicity of the control mechanism since the three distinct voltages would need to be adjusted at every step; iii) for the voltage combinations that select one cavity mode it appears that the resulting wavelength peaks follow a slope which means that the modes are slightly shifted indicating the effect of an extra phase between the AMZI arms. To determine the underlying cause of the extra phase between the AMZI arms we investigate the response of each EOPM of the AMZI with the applied voltage. For that, we select three different regions where the voltages are switched in a window of 0.5 V for different values of V EOPM1 and V EOPM2 . We record the optical spectrum for each case with a resolution of 40 fm and extract the wavelength position. The data are plotted in Fig. 5, each map represents a different wavelength interval as the applied voltages are different for each case. We identify a trend on the wavelength evolution as the (V EOPM1 , V EOPM2 ) voltage space is scanned, and remark that the slope of the color gradient varies from map to map. When the phase change is the same in both arms of the AMZI the slope should be equal to -1, unlike the slope we measure which suggests that the response of the two EOPMs with the applied voltage is different and in addition, also varies with the value of the applied voltage. This nonlinearity results in an extra phase term which slightly shifts the cavity modes, and hence the emission wavelength, as observed in the experiment. In order to successfully employ this tuning approach and correct for the extra phase, a different voltage coefficient should be applied on one EOPM to remove undesired intra-cavity phase variations. Additionally, the voltage correction should be changed approximately every 0.5 V.

IV. CONTROL STRATEGY FOR A SEMI-CONTINUOUS WAVELENGTH TUNING
To avoid the issues discussed in the previous section, we investigate another approach on controlling the AMZI and tuning the emission wavelength of the laser. Here, instead of correcting for the phase change between the AMZI arms, our goal is to take advantage of the phase difference and shift the selected cavity mode rather then keeping them fixed. For that we identify regions of the parameter space in which the wavelength can be tuned continuously.
To find the regions where the wavelength changes continuously, we build a map with the wavelength positions obtained from all the voltage combinations when the two EOPMs are switched from −10 V to 0 V in steps of 0.3 V while the voltage of the phase section is kept constant at 0 V. The optical spectra are recorded with 1.12 pm resolution and the results are plotted in Fig. 6(a). Each color in the map correspond to a different cavity mode and within each color region we notice a gradient, i.e., a wavelength variation, resulting from the phase difference. In the map we locate the sections where the wavelength changes continuously and that reach as many wavelengths as possible. 10 different segments with length in the order of tens of pm are identified, all these segments together can cover the entire FSR range of the AMZI and 89.5% of the tuning range of the laser. Each of the selected segments are shown in the map with red lines, their slope changes slightly from one color region to another, as discussed in the previous section. For each of the selected segments we extract the values of the voltages for each EOPM at the start and at the end of the segment. In between these values the voltages are switched continuously which leads to a continuous shift of the selected mode. The position of the emission wavelength variation as a function of the applied voltage is shown in Fig. 6(b) for V EOPM1 . A similar plot can be build for the V EOPM2 . We notice that there are two regions, highlighted with red in Fig. 6(b) (1550.476 nm-1550.530 nm and 1551.266 nm-1551.327 nm) that are not covered by our tuning method. We can however extend the laser tuning range by employing the phase section. With black in Fig. 6(b) it is shown how the continuous wavelength segments are shifted when −5 V is applied on the phase section. We notice that applying a voltage on the phase section can bridge the gap between two consecutive segments as highlighted with green in Fig. 6(b). For the regions highlighted with red the voltage applied on the phase section narrows the gaps but is not sufficient to completely close them. Further increasing the bias voltage applied on the phase section can potentially narrow the gaps even more.
There are two aspect of this control mechanism that should be considered, the tuning resolution and the measurement reproducibility.
Wavelength tuning resolution. Since within the selected segments the control voltages are varied continuously, the wavelength tuning resolution will be determined by the step of the voltage variation. In the experiment, we change the voltage with a precise increment of 1 mV. To estimate the wavelength resolution when the voltage changes each step by 1 mV, we measure the variations in the beating frequency between the lasers output and the output of a high-quality reference laser (Keysight N7776 C) via a signal analyzer (Keysight N9021B). We found that the wavelength resolution for this control mechanism is 0.1 pm when the control voltages are switched by 1 mV. In principle, this tuning mechanism could allow for even higher wavelength resolutions than 0.1 pm if the control voltages are switched by steps smaller than 1 mV and the noise impact is absent. Ideally, for a voltage step of ΔV , the wavelength change corresponds to Δλ = (λ/mV 2π )ΔV , where m denotes the mode number, the anticipated change in the laser's emitted wavelength amounts to 0.033 pm/mV.
Wavelength tuning reproducibility. To examine the reproducibility of the measurements we select a set of 24 voltage combinations in the different continuous segments and measure the resulting emission wavelength every 24 h across different days. The differences of the emission wavelength measured each day with the wavelength measured on the first day are plotted in Fig. 7 for four consecutive days. We notice that the wavelength varies slightly from day to day and the change in the wavelength is in the range of ≈ ±0.02 nm. In addition, in some days the wavelength jumps by the FSR of the AMZI, as shown with the dashed red arrows in Fig. 7. We speculate that the main reason for the degradation of the calibration might come due to the changes in the room temperature at the time of the measurement for the different days. Moreover, it is possible that the temperature distribution over the chip is non-uniform which could lead to changes in the response of the intra-cavity filter resulting in wavelength drifts as big as the FSR of the AMZI [18]. Nevertheless, the accuracy of 0.02 nm is relatively high considering that this is an open-loop control for a monolithically integrated laser.
Altogether, using this control strategy the FSR wavelength jumps are avoided, and the resolution of the wavelength tuning is determined by the voltage setting and not by the filtering mechanism and is able to reach the sub-pm range. The gaps are still present even if they can be reduced when the phase section is used. In contrast with the previous method where the value of the V Phase should be precisely defined in each step, here, the V Phase is linearly increased until the following continuous region is reached, as illustrated with green in Fig. 6(b). All that is required are the start and end values of the voltages for each of the continuous segments which can be identified by a relatively simple calibration step. After the values of the voltages for each segment are correctly set from a look-up table, the wavelength can be tuned continuously over the entire FSR of the AMZI, on what we refer to as a semi-continuous wavelength tuning.

V. CONCLUSION
We have presented experimental results of the dependence of the emission wavelength of a tunable laser on the tuning of an intra-cavity AMZI. The proposed design, combining one AMZI with a DBR, allows for the thorough study of the filtering properties of the integrated AMZI without the impact of other intracavity filters that are usually necessary to enable single-mode operation. Hence, we can advantageously tackle the challenges related to the robust control of its filtering mechanism. The laser considered in this work features a tuning range of about 1.2 nm with a SMSR over 20 dB over the whole range and an intrinsic linewidth of 381 kHz.
We have investigated the control efficiency of the EOPMs comprising the AMZI and we found that the performance of the EOPMs on the same chip varies and the phase shift of the EOPMs exhibits a nonlinear behavior with the applied voltage resulting in an extra phase between the AMZI arms. Hence, selecting consecutive longitudinal modes by simply linearly changing the voltages applied to the EOPMs becomes rather challenging. Instead, we propose a control strategy that translates continuously the cavity modes in a certain range rather then selecting consecutively the cavity modes. For this strategy the voltage combinations that select specific cavity modes within the tuning range are necessary and could be found by a calibration step in order to obtain coverage of the entire FSR of the AMZI, thus, we refer to this strategy as a semi-continuous wavelength tuning. In this way the wavelength resolution on the proposed control strategy depends on the accuracy of the voltage setting, and we confirmed sub-pm precision capability. This work represents an incremental understanding on the control of integrated AMZIs in the InP platform and wavelength tunability of AMZI-based integrated lasers with potential to expand this method to control more then one intra-cavity AMZI which can in turn enable a wide and controllable wavelength tuning. Moreover, although the practical advantage of this design is on the study of the tuning performance of one AMZI, our laser can be used in applications where the high resolution and precise wavelength control are required despite the limited tuning range such as spectroscopic methods and FBG sensing.