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Abstract
We experimentally demonstrate that single-mode operation of an SOA-based random fiber laser is only possible in pulsed regime at driving currents close to the threshold, whereas multimode regime dominates under higher SOA currents. Theoretical simulations support random frequency spacing of the laser modes to be due to residual stress on the optical fiber. Pulsed regime is shown to be due to randomly driven Q-switching induced by a scintillation effect in the Rayleigh backscattered light, which effectively translates as a time-varying cavity loss. Mode lifetimes of ∼1 ms and narrow linewidths ranging from 4 to 7 kHz were experimentally observed.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Random Lasers have been attracting special interest in recent studies, mainly because of the simple required technology combined with remarkable features and promising applications [1,2], such as phase-sensitive time-domain reflectometry, high-resolution spectroscopy and low-phase noise microwave generation [3,4,5]. In the same way that common lasers operate, the requirements of an optical gain medium and an optical feedback are also part of random lasers, but whereas the modes in standard lasers are defined by the cavity length and are equally spaced, in random lasers they are determined by multiple scattering events and are randomly distributed. Random feedback lasers were presented using either distributed or localized gain combined with Rayleigh backscattering in single mode fibers. Distributed gain random fiber lasers have been achieved with Raman effect [6,7,8,9], Brillouin gain [3,10,11] and erbium doped fiber amplifiers (EDFAs) [12,13,14], while random fiber lasers with localized gain were achieved with semiconductor optical amplifiers (SOAs) [15,16,17,18,19,30].
Although the mode structure was not discussed in detail, single longitudinal mode (SLM) operation with narrow linewidth has been claimed in SOA-based lasers [15,16,17,18]. However, experimental results of an SOA-based random feedback fiber laser [19] support the conclusion of single and multimode operation, depending on the SOA driving current. In this work, spectral and temporal measurements in an SOA-based random feedback fiber laser are presented, showing that single longitudinal mode operation is only possible in pulsed operation close to the threshold current, whereas multimode operation dominates the emission when the SOA current is increased. A theoretical model is developed, attributing the chaotic pulsed behavior, usually found in random fiber lasers, to time-varying coherent reflectivity peaks of the fiber. The mode spacing distribution is shown, via simulations, to be a consequence of the refractive index variations along the optical fiber due to residual stress.
2. Theoretical model
It is well known that coherent backscattered light in an optical fiber presents strong random fluctuations generated by the interference of the backscattered light from different parts of the fiber within the coherence length of the light pulse. These fluctuations are usually referred to as Coherent Rayleigh Noise (CRN) in OTDR [20], and are very sensitive to local fiber perturbations such as temperature, vibration or stress/strain [21,22,23]. In order to understand the effect of the feedback generated by the backscattered light of a single mode fiber in a random feedback fiber laser, we consider the coherent Rayleigh backscattered light generated in a single mode fiber by a continuous laser tone whose coherence length is greater than twice the fiber length. The optical field backscattered by a section dz at position z is proportional to the forward propagating field at this point as well as to the number of scattering centers at that section:
where E0 is the launched field, α is the power attenuation coefficient of the fiber, k is the vacuum propagation constant and n is the refractive index. C is a field backscattering coefficient including the density of scattering centers as well as the capture of the scattered wave into the fundamental mode of the fiber, and A is the mode field effective area. The amplitude of the total backscattered optical field at the launching point will be the coherent sum of the contributions of all sections of the fiber back propagated to the origin: Calculation of Eq. (2) is straightforward assuming uniform parameters, resulting in a complex field reflectivity r, given by the ratio Eb(0)/E0 $\propto \textrm{sinc}({nkL} )$. However, uniform parameters are unreasonable for long fibers, so that the calculation must be performed with position-dependent parameters. Although C, A and $\alpha $ may present small variations along the fiber, they affect the magnitude of r, so that their minor fluctuations with position, which may arrive from uneven concentration of dopant gases during the preform manufacturing process, will not translate into significant changes on the reflectivity, thus, we assume them to be constants. On the other hand, the refractive index is part of a phase term multiplied by the wavenumber and fiber length, thus minor fluctuations of n could lead to significant changes on $r$. Residual stresses along optical fibers, originating from fluctuations in the fiber drawing process, can induce permanent changes on the fiber’s refractive index. As will be evident soon, these stresses can be treated as a random variable, resulting in minor fluctuations of the refractive index, which is henceforth written as position dependent, $n(z )$, assuming random values for each position z.In order to calculate r we need to estimate the amount of random variations of n as well as the typical length between random variations due to residual stress. Residual stresses and strains in optical fibers are said to be those that exist in the absence of externally applied forces. The impact of residual stresses and strains on fiber’s refractive index has been widely studied, and an extensive review is presented in [24]. One of the causes of residual stress is the draw tension applied during the fiber’s drawing process. A linear relation between the change in refractive index and the drawing tension is reported in [24], where a slope coefficient of ${\sim} 5 \times {10^{ - 3}}/g$ was found, and index changes as large as $1 \times {10^{ - 3}}$ were measured for 200 g draw tension.
In the manufacturing process of optical fibers, the draw tension is proportional to the speed of the capstan pulley, which is the controlled parameter used to adjust the fiber’s diameter. For standard single mode fibers, product specifications require an outside diameter of 125 µm (controller set point) with an accuracy of ± 1 µm. To accomplish such specification, an accuracy of ± 0.1 µm is tolerable in the design [25]. A loop control, composed mainly by an outer diameter monitor (feedback) and a controller device that acts on the capstan’s speed, is updated at rates varying from 1 to 20 kHz [25]. Thus, considering an update rate of 5 kHz and a capstan’s normal speed of 50 m/s, then the drawing speed/tension is updated every centimeter of pulled optical fiber. Hence, any fiber section of ∼1 cm-length might experiment a constant residual stress, randomly varying each time the feedback loop is updated. These variations can be caused by the accuracy of the torque and speed of the motors, the outer diameter sensor noise, and the precision of the loop control. Assuming that the step control is ten times better than the tolerable design goal (±0.01 µm), an update fluctuation might be of the order of 100 ppm. Considering the linear relationship between stress and refractive index with a slope coefficient of ${\sim} 5 \times {10^{ - 3}}/g$, the random stresses result in a random variation of the refractive index of the order of $5 \times {10^{ - 7}}$ for every centimeter of optical fiber. Therefore, we can model the position dependent refractive index as:
In Eq. (3), ${n_i}$ is the refractive index corresponding to a fiber interval of length $\Delta $ and centered at position ${z_i}$. Each ${n_i}$ is given by ${n_i} = 1.44 + {10^{ - 6}}\delta $, where $\delta $ is a uniformly distributed random number in the interval [0,1]. For a fiber with length L, the index i belongs to the interval $[{1,L/\Delta } ]$, where $\Delta $ is assumed to be 1 centimeter.By substituting Eq. (3) in Eq. (2) for a given realization of $n(z )$, analytical integration can be easily performed where $n(z )$ is constant. The field is then calculated by numerical summing over all intervals, i.e.,
Consider now a random distributed feedback laser composed by a localized gain medium such as an SOA, with feedback coming from a Bragg grating mirror at one side and a single mode fiber at the other, modelled by its complex field reflectivity r. Having the amplitude and phase of the backscattered optical field, the CW lasing condition can be determined considering the cavity losses and gain, as well as the roundtrip phase inside the cavity. Considering the FBG reflectivity ${R_{FBG}}$, the SOA gain g and the fiber reflectivity ${R_{Fiber}}$, the threshold condition states (in dB):
where all other losses were neglected as they are indeed very small compared to the low power backscattered from the fiber. Considering the fiber pigtail length $\ell $ between the SOA and the FBG, which adds a frequency independent term to the overall phase (at least in the frequency range considered here), then the phase condition for lasing imposes: where m is an integer.Given the randomness of ${\Phi_{Fiber}}$ and ${R_{Fiber}}$, the frequency of the lasing modes will be randomly spaced within the bandwidth of the Bragg grating. We simulated these fiber parameters over 1 GHz optical bandwidth, which corresponds to the 80% flat top reflectivity of a 7.5 GHz-bandwidth FBG. To analyze the gain and phase conditions, we also considered in the simulation the frequency-independent values −1 dB, $\pi $ rad and 2 m for ${R_{FBG}}$, ${\Phi_{FBG}}$ and $\ell $, respectively. Figure 2, below, illustrates the simulation result for the cavity loss and roundtrip phase within a frequency span of 500 kHz centered at the maximum observed reflectivity (minimum loss) given by the reflectivity simulated in Fig. 1. Each reflection peak is a potential candidate for a mode, provided the phase condition is satisfied. Note that in a uniform feedback cavity such as a Fabry-Perot or a ring fiber laser, the gain is almost frequency independent through the FBG bandwidth, so that only the phase condition defines the mode frequency. In the case depicted in Fig. 2 we observe that only for the central peak both conditions are satisfied when the cavity gain equals the loss at the central frequency. If the environmental conditions were frozen, the laser threshold would be given by 2$g$ ∼ 26 dB gain needed to match Eq. (6), considering that the phase condition is also fulfilled and the phase adjusted to match Eq. (7). Hence, CW single mode operation would be obtained near threshold.
Fig. 2. Simulated phase of the electromagnetic field after a round trip in a random feedback fiber laser as a function of frequency (offset from 194.2 THz). Red dash-dot and green dash lines in the top panel represent additional gains of 3 and 6 dB provided by a single pass on the SOA. Red crosses in the bottom panel do not represent modes – they are due to the phase wrapping procedure. Blue points correspond to real solutions of the phase condition.
At higher gains, more reflectivity peaks can satisfy the gain condition and more modes are simultaneously allowed, provided the corresponding phase condition is also satisfied. In the example depicted here, limited to 500 kHz from the 7.5 GHz bandwidth available for lasing, increasing the SOA gain by 3 dB above the threshold (red dash-dot line in Fig. 2), a total gain of 6 dB is added to the system and seven modes would eventually be lasing if the phase condition were matched. If the gain is increased by additional 3 dB (green dash line in Fig. 2), many modes will be enabled at the same time because the gain condition would be relaxed. Therefore, at low SOA gains, modes are defined mainly by the gain condition, but as the gain increases, the gain condition becomes less restrictive so that at high gain the phase condition actually defines the lasing modes. Therefore, for SOA currents high enough, unevenly spaced multimode operation should be observed.
Under laboratory conditions, tiny fluctuations in temperature, stress and/or birefringence force $|r{|^2}$ to be a time-dependent random function $|r(t ){|^2}$, so that reflectivity peaks in Fig. 1 are expected to fluctuate in time, similarly to a scintillation phenomenon. Moreover, ${\Phi_{Fiber}}$ and $\ell $ are time dependent so that CW operation of the laser is unfeasible because phase and gain conditions must be simultaneously satisfied. As the SOA gain is increased, a phase-matched scintillation peak can eventually reduce the cavity loss below twice the SOA gain, so that a laser pulse builds up as in a passive Q-switched laser randomly driven by the environmental conditions. The phase in km-long single mode fibers in laboratory environment has been already reported to vary in ms time scales [27,28] and we expect the scintillation peaks to vary in a similar way. Hence, lasing should start with Q-switched milliseconds-long pulses as the SOA gain is increased.
Because of the random nature of the cavity loss, lasing threshold needs to be defined within a statistical framework. Very low loss events can appear, generating pulses with very low probability. Assuming that the environment-induced random fluctuations of the refractive index along the fiber are described by an ergodic random process, which can be shown to be a reasonable assumption [29], then the average of the peak reflectivity density at a given frequency over time is equal to the average of the peak reflectivity density over all frequencies at a given time. Hence, we calculated the statistics of the reflectivity from five runs of our model simulations over 1 GHz bandwidth, in order to increase the statistical reliability of low probability events. Figure 3(a) displays the cumulative probability of cavity loss events smaller than a given value. We observe an increasing slope as the loss decreases below 30 dB, suggesting a lower bound near 26 dB. Hence, as the SOA gain increases, the random laser will start generating single mode pulses when the SOA single pass gain approaches 13 dB, which could be defined as a lasing threshold. Further increase in SOA gain the pulse rate increases until several modes will be lasing at the same time.
Fig. 3. (a) Simulated cumulative probability of instantaneous cavity loss. (b) Histogram of adjacent modes spacing found for simulated 8 km-long random feedback fiber laser within 1 GHz bandwidth. The average mode spacing of 26.5 kHz is close to the 25.7 kHz value from a uniform feedback fiber laser.
To evaluate randomness of the mode spacing we calculated the mode separation from the phase condition, which is usually the one used for mode calculation, considering high enough gain. The statistics of the frequency spacing between adjacent (consecutive) modes of the simulated 8 km random feedback fiber laser is presented in Fig. 3(b). The average value of mode spacing was found to be 26.5 kHz, close to the evenly spaced value of a 4 km-long Fabry Perot cavity. This is close to the value that would be obtained by direct integration of Eq. (2) with uniform fiber parameters. This figure shows that when many modes are allowed, their beat noise will cover all frequencies in a featureless white spectrum instead of the series of equally spaced tones that would be observed in a uniform fiber.
3. Experimental setup
The experimental setup is presented in Fig. 4. Light is generated by an SOA, and the cavity is formed by a tunable fiber Bragg grating (FBG) with 7.5 GHz bandwidth and by the Rayleigh backscattered light from an 8 km-long dispersion shifted fiber (DSF). The Rayleigh incoherent backscattered power coefficient from this DSF fiber was measured with OTDR to be 3 dB greater than that of a standard SM fiber, which is in good accordance with theoretical calculation [26]. The FBG acts as both a fixed mirror and a tunable filter with 7.5 GHz 3dB-bandwidth, sharp enough to filter Brillouin scattered light out of the cavity. A polarization controller was inserted in the cavity to optimize interference effects. Optical isolators at both ends guarantee that undesired reflections are eliminated.
Fig. 4. Experimental setup of Random Feedback Fiber Laser (left) and measurement setups (right). AOFS: Acousto-Optical Frequency Shifter. DSF: Dispersion Shifted Fiber; ESA: Electrical Spectrum Analyser; FBG: Fiber Bragg Grating; OSA: Optical Spectrum Analyser (High and Low resolutions); OSC: Oscilloscope; PC: Polarization Controller; PD: Photodiode.
The characteristics of the random laser light were analyzed as follows. High resolution optical spectral analysis was performed with a 0.16 pm-resolution optical spectrum analyzer (OSA) with low (< Hz) video bandwidth (VBW), while fast optical measurements were performed with a 0.03 nm-resolution OSA with VBW of 10 kHz. Time-domain measurements were performed with a 3.5 GHz-bandwidth oscilloscope (OSC) and a 125 MHz-bandwidth amplified photodiode (PD1) - Fig. 4(b). Direct output noise spectral measurements were performed with an electrical spectrum analyzer and a 5 GHz-bandwidth photodiode (PD2) - Fig. 4(c). Self-heterodyne linewidth measurements were performed with a 107 km unbalanced Mach-Zehnder interferometer (MZI), an acousto-optic frequency shifter (AOFS) and a polarization controller (PC), in a delayed self-heterodyne scheme - Fig. 4(d).
4. Results and discussion
Analysis of the laser output optical spectrum in the 0.03 nm-resolution OSA shows that, when low currents drive the SOA, only the ASE spectrum is observed. Figure 5(a) displays how the averaged optical power at the central wavelength of the FBG varies with SOA driving current. We observe that above ∼200 mA the average output power starts increasing with the driving current, as a typical threshold in a current driven laser. The SOA gain curve is displayed in Fig. 5(b), from which we infer that the threshold behavior occurs when the SOA gain reaches 11.2 dB. Due to the higher reflectivity coefficient of the DS fiber, 3 dB should be added to the reflectivity simulations in Sec. 2, so that the model predicts that the laser should start firing pulses near a gain close to 11.5 dB, in a remarkable agreement between theoretical model and experiment.
Fig. 5. Variation of the random laser average optical power with SOA driving current for an 8 km-long dispersion shifted fiber (a). SOA end to end gain curve (b).
As expected from the simulation, near ITH, strong laser peaks are observed in both OSC and OSA, as shown in Figs. 6(a) and 6(e), respectively. Because the OSA used in these measurements was a sweeping wavelength one, its 10 kHz video bandwidth was able to detect ms-long pulses. It should also be noted that the OSA limited to 0.03 nm-resolution determines when a pulse took place rather than its real wavelength. Peak powers up to ∼30 dB above the ASE power are observed, confirming that whenever a Rayleigh scintillation peak is high enough to overcome the gain condition a Q-switched pulse is fired. These peaks are observed as ∼1 ms-long pulses (inset of Fig. 6(a)), arising at random times in a small rate. As the current is starts increasing, the pulse rate also increases, but the maximum pulse peak power remains relatively stable. One might think that the pulse peak power is limited by the single pass stimulated Brillouin scattering (SBS), but we calculated the theoretical SBS threshold power by ${P_{th}}\sim 21\; A\; /\; {g_b}\; L$, with A for the DSF equal to 50 µm2, L = 8.47 km and ${g_b}$, the Brillouin gain for silica fibers, equal to $5 \times {10^{ - 11}}$ m/W, showing a threshold power of ∼ 2.63 mW, which is much higher than the pulses peak power shown in Figs. 6(e)–(g). A similar result is obtained in [18], showing that SBS is not present in the laser cavity for low currents.
Fig. 6. Detected pulses emitted by random lasers at SOA driving currents of 200 mA (a), 205 mA (b), 210 mA (c) and 400 mA (d), with the corresponding optical spectra in (e), (f), (g) and (h), respectively.
Further increase in the driving current eventually lead to pulse overlapping. This is shown in Figs. 6(b) and 6(c), which present the laser output for driving currents of 205 mA and 210 mA, respectively, with correspondent optical spectra shown in Figs. 6(f) and 6(g). At these current levels, the averaged optical power increase is due to the increasing pulse rate, rather than by an increasing pulse power.
This behavior is precisely what was expected from the model description and simulations. Indeed, near threshold, very few modes have peak reflectivity high enough to reach the lasing condition in both phase and amplitude. When a scintillation peak from the fiber promotes Q-switching, pulsed laser action starts. After a while, variations in both the pigtail phase and 8 km-long fiber drive the cavity out of the phase condition and the laser power drops out. The duration of the optical pulses near threshold can be associated to a single mode with a lifetime of ∼1 ms. When the SOA gain is much further increased, many modes are satisfying the lasing conditions at the same time, giving rise to continuously overlapping pulses. This condition can be seen in Figs. 6(d) and 6(h) for 400 mA driving current.
As pulses start overlapping a strongly fluctuating output power is observed. An overlap of emitting pulses is shown in Fig. 7, where frequency modes overlap for a driving current of 210 mA. A zoom-in on the right portion of the overlapping pulses shows evidence of two strong beat notes. It is important to highlight that, in order to acquire oscilloscope data over several milliseconds, which is required for analyzing pulses overlap with typical 1 ms duration, the resolution bandwidth of the oscilloscope had to be reduced from 3.5 GHz to 10 MHz. Thus, mode beating could only be observed for very close modes, distant from each other by no more than 5 MHz, due to Nyquist limit. The electrical beating tones shown in Fig. 7, which come from the beating of optical modes, can be observed as a subcarrier frequency of 4.92 MHz modulated in amplitude by 151 kHz. These frequencies build up at the same time, around 14.5 ms, so we can infer that three optical modes are beating. It happens as follows: two modes, apart from each other by Δν = 9.84 MHz, emerge at 13.75 ms, when no beating is observed due to the low resolution bandwidth set on OSC. At 14.5 ms, a third mode arises, with optical frequency in between of the first two modes, 5.07 MHz apart from one of them, and 4.77 MHz from the other. Electric beating of these two frequencies results in the observed 4.92 MHz and 151 kHz, corresponding to the half-sum and half-difference of 5.07 MHz and 4.77 MHz, respectively.
Fig. 7. Output of random laser showing three overlapping pulses, corresponding to the overlap of three simultaneous modes. A zoom-in on the red rectangle area shows evidence of strong beat notes.
As the current is increased, multimode behavior dominates the laser output, and multimode beating, such as the one displayed in Fig. 7, should occur at all frequencies within the FBG bandwidth, as shown in Fig. 6(h), resulting in a noisy output as displayed in Fig. 6(d). The output laser spectrum was then measured with the high-resolution OSA, while the detected power spectrum was measured with a 5 GHz-bandwidth detector. Figures 8(a) and (b) display these two measurements for a driving current of 500 mA, together with a comparison between the calculated and measured electric power spectrum. The measured electric spectrum shown in Fig. 8(b) indeed exhibits the floor spectrum extending to the FBG bandwidth, confirming that the floor power in the self-heterodyne spectral measurements is due to multimode beating noise, as will be mentioned below. Further confirmation is given by the comparison between the measured output power spectrum and the expected electric spectrum obtained by the self-convolution of the measured optical spectrum in Fig. 8(b). It should be noted that the discrepancy between the calculated and measured power spectrum above 5 GHz is due to the limited bandwidth of the detector used in the experiment. The agreement between these measurements supports the statement that multimode operation occurs at high currents and multimode beating noise dominates the output spectrum. In addition, this experimental conclusion complies with the simulation result provided in Fig. 4, where a random mode spacing was achieved, thereby mode beating should continuously extend within the FBG bandwidth.
Fig. 8. (a) Random laser optical spectrum measured in a high resolution (0.16 pm) OSA; (b) Measured and calculated electrical power spectrum. Both measured curves were obtained when driving the SOA with 500 mA.
The linewidth of the random laser was measured with the delayed self-heterodyne technique by using an MZI unbalanced by 535 µs and an AOFS, which shifts the optical frequency in one arm of the MZI by 86.83 MHz - Fig. 4(d). As typical durations of light pulses are around 1 ms (see inset of Fig. 6(a)), the MZI delay is short enough to insure a minimum ∼50% overlap of a single pulse whilst still long enough to guarantee the Wiener-Khintchin condition for ∼ kHz linewidth measurements [26]. Figure 9(a) displays the linewidth measurement results for seven different currents driving the SOA, which were obtained from averaged spectra at the ESA. As the random laser only presents single mode operation near the threshold, then, to measure the linewidth of an individual lasing mode, the SOA driving current must be set to ITH. However, the pulse rate is extremely low at ITH, and the mode spectrum falls below the noise floor of the spectrum analyzer. Linewidth measurements could be observed for driving currents greater than 278 mA, when self-mode beating arose centered at the AOFS shifting frequency. At such current, the 3 dB-linewidth was found to be 4 kHz, and it increases with SOA gain up to 7 kHz. Thus, we can infer that the mode linewidth is at most 4 kHz, which agrees with the calculated width of reflectivity peaks (<10 kHz) obtained from Fig. 3. In addition, such narrow linewidth corresponds to a coherence length greater than 20 km, which is in accordance with the theoretical model that assumed a coherence length greater than twice the optical fiber length.
Fig. 9. (a) Random laser linewidth for different SOA driving currents; (b) Intensity of the mode mean power and multimode beat noise floor.
At currents higher than 278 mA several modes are beating to form the measured spectra. While the self-beat of each mode gives rise to the mode peak at 86.83 MHz, multimode beat will generate the floor level observed in Fig. 9(a). The intensity of the self-beat note slightly increases for driving currents up to 338 mA, where saturation is observed. On the other hand, the floor level keeps increasing further on, as shown in Fig. 9(b). In agreement with the behavior pictured in Figs. 5(a) and 6, we see that the initial increase in the average power is due to the increase in the frequency of laser pulses, which maintain their peak power relatively constant. The increase in the floor power, also observed in [18], is due to the increase in the multimode population in the laser output. As demonstrated in Fig. 8, the floor level extends to the FBG bandwidth, but the measurements of Fig. 9 were limited by the 125 MHz-bandwidth detector used in this high resolution measurement.
An important feature of the spectral measurements in Fig. 9 is that the measured power of the self-beating signal saturates with the SOA current, whereas the multimode floor keeps increasing, indicating that more coexisting modes are present in the laser output. Since there are more modes in the output, the self-beating note should increase correspondingly, unless the mode power decreases accordingly. This experiment supports the conclusion that at high currents mode power diminishes and is limited by mode competition, whereas near threshold it is relatively constant.
5. Conclusions
Mode characteristics of random feedback lasers with localized gain were presented. A model was developed to explain mode structure and dynamics. Simulation results indicate that the nonuniform longitudinal mode spacing is due to residual stress in the optical fiber from the manufacturing process, which cause random variations in the refractive index. Small fluctuations of the fiber environmental conditions give rise to a scintillation effect in the Rayleigh backscattered light, therefore modulating the effective fiber reflectivity. This model description can be extended to any random feedback laser based on coherent distributed backscattering in optical fibers. The model also predicts that the scintillation effect induces randomly driven passive Q-switched pulses near threshold. The statistical prediction of the model for the threshold current remarkably agrees with the experimental results. Experimental results confirms that single longitudinal mode operation is only possible close to the threshold current, whereas multimode operation dominates when the SOA current is increased. Mode beating in multimode regime was observed to continuously cover the full laser emission band. Mode linewidth is ≤ 4 kHz and it increases up to 7 kHz at higher driving currents. Spectral analysis indicates that multimode operation dominates the laser output at high currents, when mode output power is limited by mode competition.
Funding
Conselho Nacional de Desenvolvimento Científico e Tecnológico.
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