1. Introduction
The development of lasers is an important task due to their high practical value in various areas of human activity. One of their important characteristics is the possibility to tune the optical frequency/lasing wavelength. Such lasers are called tunable. To implement this possibility, various electrically or manually controlled spectral selectors, such as tunable fiber Bragg gratings (FBGs), bulk diffraction gratings or interference filters, are used in most cases. However, these optical elements are quite expensive. One of the alternatives is to use physical effects of lasing mode competition. For example, the spatial hole burning (SHB) effect is associated with inhomogeneous gain saturation along the fiber length under the influence of a narrowband standing wave radiation formed in the laser cavity. These inhomogeneities have a period equal to half of the wavelength and are also associated with populational inhomogeneities called dynamic population gratings (DPGs). Unlike conventional static FBGs, DPGs have a relatively short lifetime (from fractions of to a dozen milliseconds) associated with finite lifetime of the upper laser level. It is known that a typical spectral width of periodic structures decreases when their length increases. In fiber lasers, DPGs are formed along the entire length of the active fiber, which can be up to units or even several tens of meters. Therefore, DPGs have high spectral selectivity down to several MHz. As a result, DPGs can play the role of fine spectral selectors allowing selection of individual longitudinal modes of the laser cavity. Note that DPG can be formed in both absorbing and amplifying media. In the former case, DPG leads to stabilization of single-frequency lasing and, in the latter case, to the initiation of a jump in the generated mode and tuning the laser frequency [
1]. A regular sequence of generated mode hops is called a self-induced wavelength/optical frequency sweeping effect (self-sweeping effect for short). The development of fiber self-sweeping lasers is described in detail in reviews [
1,
2]. In addition to these reviews and references therein, we would like to add [
3] published in 2005, one of the earliest works on self-sweeping fiber lasers which mentioned an observation of lasing line drift at a constant rate in one direction with rapid jump back. This behavior is typical for ordinary self-sweeping lasers. The authors observed the self-sweeping effect in a ring laser based on ytterbium-doped photonic crystal fiber.
The operation of a typical self-sweeping laser is described as the generation of a sequence of pulses, each of which consists of a few longitudinal modes of the cavity. In a limiting case, single-mode pulses can be generated. In this case, the laser radiation consists of the so-called “mode pulses”. The mode composition of each pulse, as well as the frequency difference between neighboring pulses, is determined by the properties of the DPG formed by the previous pulses. In the case of a large number of pulses, the process of mode hopping looks like tuning the laser wavelength. Some self-sweeping fiber lasers generating the mode pulses mentioned above have a number of advantages, such as a wide tuning range (up to 26 nm in [
4]), the capability to generate single-frequency radiation with linewidth less than 1 MHz at each pulse [
5], and discreteness of laser frequency change. However, such lasers also have some drawbacks. Although successive pulses are discrete in the frequency domain, they exhibit noticeable irregularity in the time domain (i.e., repetition rate and/or pulse duration). It may be assumed that this irregularity results from the influence of random uncontrolled processes (for example, thermal fluctuations or sound vibrations) on laser generation. As a result, this drawback complicates the use of such lasers in a number of applications [
1]. One of the solutions requires the direct measurement of intensity dynamics with high sampling rate and to use these data for further processing (see, for example, [
6]). High sampling rate and a long duration of a single sweeping scan (up to several tens of seconds) result in large data sets which require significant computing resources for mathematical processing. Moreover, implementation of this approach in a practical device also requires some individual adjustments of the measurement unit parameters based on the laser pulses characteristics (duration, duty cycle, etc.).
In this work, we propose a technique to stabilize the mode-hopping period in an SLM fiber laser by influencing a cavity element periodically. The technique is aimed at mode-hopping control by using optical path oscillations in the laser cavity element. To demonstrate the method, we use an erbium-doped fiber (EDF) ring laser with continuous-wave (CW) intensity dynamics [
5]. We experimentally show for the first time that mechanical vibrations of a section of a passive fiber in such lasers can result in regular modal dynamics in both frequency and time domains. The mechanism of vibration-induced sweeping is based on small oscillations in the spectrum position of a composite reflector formed by an amplifying fiber loop mirror and a DPG, which occur because of slight modulation of the optical path length. At that, sweeping is absent without vibrations, but vibration-induced oscillations of the spectral position of the DPG-based selector initiate the mode-hopping process. In this approach, the time period of the mode hops is locked to the vibration period. In addition, experiments show that the mode dynamics in the EDF laser is sensitive to the pump wavelength. When the laser is pumped with short-wave radiation (1548 nm, which is characterized by strong absorption in the active medium), each mode hop is characterized by a successive decrease in the optical frequency by one free spectral range (FSR) of the laser cavity. In this case, linear wavelength sweeping is observed over a long time interval in an upward direction. When the laser is pumped with longer wavelength radiation (1564 nm, which is characterized by lower absorption), the direction of the frequency hop changes after every mode hop. In this case, long-term optical frequency dynamics look like optical frequency stabilization.
We believe that the results of our research are useful not only for the development of self-sweeping lasers [
1,
2] but also for the ones generating single longitudinal mode (SLM) radiation [
7]. It is well known that one of the undesirable effects in SLM lasers is mode hopping which in most cases is uncontrollable [
8]. The proposed method allows control of the mode-hopping process with external vibration. So, our research gives information about mode hopping, which can be useful for stable SLM generation.
2. Experiment
The scheme of the vibration-induced sweeping Er-doped fiber (EDF) laser based on polarization-maintaining (PM) components is shown in
Figure 1. A similar scheme was proposed in our previous work [
5]. To describe the laser operation, it is convenient to divide the laser cavity structure into linear and ring parts which are separated from each other by the central coupler with a coupling ratio of 20/80. The ring part is an amplifying fiber loop mirror (AFLM) which includes the central coupler, a reflective wavelength division multiplexer (RWDM), PM Er-doped fiber (EDF-1) and a polarizing fiber (PZF). PM EDF-1 (IXF-EDF-HD-PM, iXblue Photonics, Besançon, France), 9.6 m long with high core absorption of about 83 dB/m at 1530 nm wavelength, is used as the gain medium. To obtain lasing in the L-band telecom spectral range, a sufficiently long highly erbium-doped EDF-1 fiber is used. The PM EDF-1 is pumped with a tunable laser source based on the master oscillator power amplifier (MOPA) configuration. We use a homemade cladding-pumped erbium-doped fiber amplifier. The amplifier includes a multimode diode, a pump and signal combiner, 2 m of erbium-doped fiber, two optical isolators and a coupler (the latter was used to control the power at the output of the amplifier). It is worth noting that frequency sweeping is not related to the amplifier, because an isolator has been added to the amplifier output. The tunable master oscillator seed radiation generated by a laser diode can be tuned from 1530 to 1565 nm. Only two pump wavelengths—1548 and 1564 nm—are used in the experiments. These two characteristic wavelengths have significantly different EDF absorption, which considerably influences the EDF laser output parameters. The power of the seed radiation can be increased at maximum to about 1 W in an additional PM EDF amplifier. The pump radiation was coupled to the PM EDF-1 through a reflective port of a 1540/1610 RWDM (LightComm, Shenzhen, China). PZF (HB1550Z, Fibercore, Southampton, UK), 2.3 m long, which was used to select one of polarization states. The radiation passed through the PZF and entered the central coupler. The linear part of the cavity consists of another 1.4 m long active PM EDF, PM EDF-2, (ER35-7-PM-Coractive, Québec, QC, Canada), with reduced core absorption of about 24 dB/m at a wavelength of 1530 nm and a fiber loop mirror (FLM). The FLM reflectance of ~90% was limited by internal excess losses in the 50/50 PM fiber coupler used here. An optical isolator is used at the laser output to eliminate the influence of unwanted reflections from measuring instruments on the laser generation dynamics.
Compared to our previous laser [
5], the following changes were made: (1) the reflectance of FLM was increased from ~80 to ~90% by replacing the coupler, (2) the coupling ratio of the central coupler was decreased from 30/70 to 20/80, (3) the length of PZF was increased from 0.8 m to 2.3 m, (4) the length of PM EDF-2 was slightly decreased from 1.8 m to 1.4 m. These changes are aimed at improving the output parameters of the EDF laser (increasing the output power, as well as increasing the ratio of the SLM lasing duration and switching time between the generated modes).
Long-term spectral dynamics were analyzed using a wavelength meter (WS6-200, Angstrom/HighFinesse, Novosibirsk, Russia/Tübingen, Germany), allowing us to make up to 1000 measurements per second. The process of changing the generated frequency was recorded using the heterodyning method [
9]. The output radiation of the EDF laser was mixed with the radiation of the reference single-frequency laser (TSL770, Santec, Komaki, Japan) in a fiber coupler. The intensity dynamics of generated radiation and the dynamics of heterodyne signals were measured with fast photodetectors and recorded with a digital oscilloscope (DS6104, Rigol, Suzhou, China) with 1 GHz bandwidth. The beat signal was further analyzed with fast Fourier transform in the frequency range from 100 to 500 MHz.
Taking into account previous works [
1,
5], we expected self-sweeping operation with long mode pulses. In such a laser, the linear part is used for rough frequency selection, and the ring part is used for switching to the next laser cavity longitudinal mode during the self-sweeping process. However, the results show that the described fiber laser generates stable radiation in a single longitudinal mode (SLM) regime of about 1608 nm in wavelength without any self-sweeping operation. At the same time, it was found that sweeping wavelength dynamics can be observed with the abovementioned wavelength meter when a mechanical strain is applied to the section of the laser cavity passive fiber. We used a micro-translation stage (MTS) to create a controllable strain in the section of the passive fiber. A section of PZF about 24 cm long was used as the passive fiber for certainty only (similar results presented below can be obtained with other passive fibers in the ring part of the cavity). We will call a mechanical setup for stretching the fiber the fiber optical path length modulator (FOPLM). A sketch of the FOPLM is shown in the inset to
Figure 1. It has a relatively complicated construction. For example, the fiber has an additional support between fixing points. As is shown later, the system is a mechanical cavity similar to an oscillating string. The FOPLM allowed us to observe transition between the SLM stabilization and the wavelength sweeping regimes and back to the stabilization by adjusting the strain of the passive fiber. Let us describe in more detail the influence of the strains on the laser operating regime at different pump wavelengths.
4. Discussion
Thus, our research demonstrates that, without tension of the PZF, the laser operates in the SLM regime, regardless of the pump wavelength. Tension of the PZF results in regular dynamics in both intensity and optical frequency. Moreover, the use of a short-wavelength pump with high absorption in the active fiber leads to a gradual decrease in the optical frequency by a fixed value, and the use of longer-wavelength pumping leads to periodic optical frequency hops with alternating direction after each new hop, but also by the same fixed frequency hop value (see
Figure 4b and
Figure 5b, respectively). This behavior of the optical frequency measured as long-term wavelength dynamics looks like either wavelength self-sweeping or wavelength stabilization (
Figure 2b,d, respectively).
We think that our FOPLM do not change optical fiber length from one static value to another by changing the position of the translation stage, but it behaves like an ordinary guitar string. The main result of the tension change is associated with shifting position of the vibration resonance in the FOPLM. The FOPLM is a mechanical cavity with tunable eigenfrequencies. So, tension of the fiber inside the FOPLM changes the resonant frequency but does not create oscillations in the cavity. During the experiments, it was discovered that vibrations were produced by a power supply used for an EDF amplifier in the MOPA pump laser and located on the same table with other parts of the fiber laser cavity. It has been experimentally confirmed that vibration isolation of the power supply suppresses the laser frequency dynamics. Thus, the periodicity of the optical frequency change is determined by the mechanical resonance in the power supply, and the tension of the PZF placed inside the FOPLM only shifts the position of the mechanical resonance closer to or further from the frequency of the driving force (vibration frequency of the power supply). Since we did not control the vibration frequency of the power supply (because it is determined by its design), we could only control the amplitude of the vibrations (fiber optical path length modulations) with PZF stretching (moving FOPLM resonance closer to or further from the vibration frequency). As a result the frequency of the mode hops in the experiments also turned out to be fixed (the average period of mode hops was ~12.6 ms).
One should note that oscillations of the PZF length also led to a corresponding modulation of the fiber laser cavity length. The result of the latter modulation can be noted in
Figure 4b and
Figure 5b, where, besides kilohertz modulation associated with operation of the stabilization circuit of the heterodyne laser, additional slow modulation can be noted with a period of ~13 ms. To make these slow modulations in
Figure 4b and
Figure 5b more obvious, we reconstructed the temporal dependence of the lasing beat frequency in terms of the single cavity mode oscillations in
Figure 6a,c, respectively. Let us consider the reconstruction using
Figure 6c. The black curve shows the original beat signal presented in
Figure 5b. The blue curve is generated from the black one by adding one FSR value of the laser cavity (~10 MHz) to the beat frequencies whose values are below 235 MHz. Thus, the blue curve shows slow temporal oscillations of frequency of a single longitudinal cavity mode, confirming the modulation of the laser cavity length. Fitting of the blue curve by a sinusoidal function is shown by a red one, which demonstrates good periodicity of the mode oscillations. A similar procedure was applied to the beat frequency signal measured at shorter wavelength (1548 nm) pumping shown in
Figure 4b. Multiples of FSR values were subtracted from the beat signal to reconstruct temporal dynamics of frequency of a single longitudinal cavity mode in this case. Modulation of the cavity mode frequency is also noticeable in
Figure 6b (zoomed-in view of the red and blue curves shown in
Figure 6a), but it is partially hidden due to the presence of an additional slow frequency drift. The period of this slow modulation is equal to the mode-hopping period in
Figure 4b and is twice as large as the mode-hopping period in
Figure 5b. Thus, these results confirm our hypothesis that optical frequency hops in the laser are synchronized with modulation of the laser cavity length.
As mentioned in the Introduction, the DPGs are formed during the laser generation in the EDF of the amplifying fiber loop mirror (AFLM). The presence of a spectral reflector (in particular, DPG) inside the AFLM should lead to the appearance of some spectral structures in the reflection of the AFLM. For example, the reflection/transmission spectra of a fiber loop mirror (FLM) with inserted FBG were studied in [
10]. It was shown there that the presence of the FBG leads to the appearance of such additional structures in the reflection spectrum of the FLM. The total width of the structures is equal to the width of the FBG reflection spectrum. This spectral structure has deep modulation. The modulation period decreases with displacement (mismatch) between the geometrical center of the FBG and the FLM center. Positions of local maxima of the spectral modulation are highly sensitive (at the level of fractions of a wavelength) to changes in the value of the displacement between the centers. Similar spectral features can be expected for the reflection spectra of AFLM, in which the FBG is replaced by a DPG. However, the problem ceases to be stationary due to oscillations of the optical path. Small oscillations (of the order of fractions of a wavelength) in the position of the nodes and antinodes of the standing wave in the AFLM relative to the positions of the minima and maxima of the dynamic grating change the gain of the generated signal. In addition, the positions of the maxima of the AFLM reflection spectrum also begin to oscillate (to change spectral position). As a result, one can expect that these spectral shifts will result in the optical frequency hops.
Let us consider qualitatively the effect of such AFLM reflectance spectrum position oscillations on the laser frequency dynamics. For simplicity, let us assume that the AFLM reflectance spectrum is described by a Gaussian function and that the zero mode (lasing mode, which records DPG and produces this resonance structure) has the highest reflection as compared to neighboring ones (green line in
Figure 7a). First, let us also assume that the spectrum is centered at the optical frequency of the lasing mode. In this case, the laser will generate in the SLM regime. Let the position of the spectrum oscillate harmoniously in time. Red and blue curves (see
Figure 7a) show extreme positions of the spectrum shifted in opposite directions, and the double-sided arrow indicates the region of oscillations of the reflection maximum. If the amplitude of the reflection spectrum position oscillations is smaller than half of the cavity free spectral range (FSR), then the laser will continue lasing in the SLM regime. At larger reflection maximum shifts, another laser cavity longitudinal mode having larger reflectance will accumulate in the cavity faster and the laser will start to oscillate at this new mode. The maximum displacement of about ⅔ of FSR is shown in
Figure 7a as such an example. In this case, the laser will hop a mode with either increasing or decreasing number at the extreme positions of the AFLM spectrum (for blue and red lines in
Figure 7a, respectively). This case corresponds to experiments with long-wavelength pumping (
Figure 5), where the AFLM reflection spectrum begins to move in the opposite direction after each mode hop and a new mode hop takes place at the opposite extreme position in the backward direction again.
Let us consider now a slightly different case, when the AFLM reflection spectrum is initially shifted from optical frequency of lasing mode. As an example, the green line in
Figure 7b corresponding to the reflection spectrum recorded by lasing mode is shifted by ⅓ FSR. The laser will operate in the SLM generation regime without AFLM reflection spectrum oscillations. Let us add some small oscillations of the AFLM reflection spectrum position. In this case the conditions for a mode hopping will be achieved only for the direction corresponding to the initial shift of the AFLM reflection spectrum (blue line in
Figure 7b). When the spectrum shifts in the opposite direction (red line in
Figure 7b), the reflectance for the zero mode will remain larger than for the others. This case corresponds to the short-wavelength pumping (
Figure 4). Taking this qualitative picture of the vibration-induced mode hopping into account, one can conclude that the larger the initial frequency shift, the smaller the oscillation of the reflection spectrum position required for the hop to the neighboring mode.
Note that in conventional self-sweeping lasers it is assumed that the value of the shift is large enough and there is no need for oscillation of an optical frequency selector position for the mode hopping to occur. In this case, the repetition rate of the mode hops is determined by the recording speed of the DPGs. One should also note the following: (1) the qualitative picture of the mode hops presented above (
Figure 7) implies that the DPG recording (re-recording) time should be long enough, as compared with the AFLM optical path length modulation period. (2) The possibility of controlling the moment of the mode hops in conventional self-sweeping lasers by changing the AFLM length requires additional research.
Let us return to the temporal characteristics of the laser again. It is important to compare a ratio between the lifetime of the DPG (τ ≈ 10 ms in erbium) and the period of the optical path oscillations T (i.e., the period of the AFLM reflection spectrum oscillations). On the one hand, the period T should not be too long compared to the lifetime τ, so that the position of the DPG in the amplifying fiber does not have time to be re-recorded, when the position of nodes and antinodes in a generated standing wave slowly changes by the FOPLM. On the other hand, the period T should not be too short, because the DPG requires time for formation after each new mode hop. For example, the problem of suppression of DPG formation in ruby lasers was discussed in the 1970s [
11,
12]. The authors proposed to quickly change the optical path lengths on both sides of the ruby laser active medium in antiphase, so that the DPG would not have time to be recorded. In our case, the period of the optical path modulation (mode hops) in the laser (T ≈ 13.2 ms) is comparable to the upper laser level lifetime in erbium τ ≈ 10 ms (i.e., T ≈ τ). Therefore, it was possible both to record highly selective DPGs and to shift the positions of the nodes and antinodes of a standing wave in the AFLM relative to the maxima and minima of the DPG when changing the optical path length in the AFLM. Thus, such a time ratio allowed us to experimentally demonstrate the transition from optical frequency stabilization to vibration-induced sweeping when we applied FOPLM to the AFLM in the erbium-doped fiber ring laser.
Another important result demonstrated experimentally in our work is the dependence of the vibration-induced sweeping process on the pump wavelength. This fact was observed previously in self-sweeping lasers. For example, self-sweeping with fixed normal sweeping direction [
4] or with variable sweeping direction (as well as with wavelength stopping) depending on pump power [
13] is observed for thulium-doped fiber lasers pumped at wavelengths of 1540 or 1570 nm, respectively. The authors associated the self-sweeping direction change with the presence of unpumped regions in the long gain fiber with strong pump absorption resulting in nonuniform distribution of the population inversion along the gain fiber length. The length of the amplifying part of the gain fiber increases with the pump and the self-sweeping direction becomes the same as for pumping at a lower absorption wavelength of 1540 nm. One should also note that self-sweeping in the reverse direction was also observed in ytterbium-doped fiber lasers [
14,
15].