All-PM Fiber Tm-Doped Laser with Two Fiber Lyot Filters Mode-Locked by CNT

: We report on the ﬁrst demonstration of the Tm-doped all-PM mode-locked ﬁber laser with CNT used as a saturable absorber and two ﬁber Lyot ﬁlters embedded into the ring resonator. Using these two ﬁlters, we were able to adjust the central wavelength of laser generation to ~1855 nm as well as to obtain the required spectral width and necessary pulse duration that are required for the proposed applications. Possible issues with the method used are discussed.


Introduction
Mode-locked fiber lasers have already become a staple of modern science and technology.Numerous advantages such as compactness, reliability, high peak power, and little-to-no alignment made them an ideal coherent light source for several applications including laser spectroscopy, high-precision metrology, LIDARs, quantum communications, medicine etc.Some applications, however, put stronger requirements for the source wavelength.For instance, strong water absorption lines near 2 µm enable efficient tissue ablation once an appropriate laser source is in disposal [1].In recent years there has been a strong interest in thulium-doped fiber lasers (TDFLs) as a promising efficient tool in lithotripsy [2,3].In addition, a lower stone ablation threshold specific to TDFL in comparison to those widely used in nephrolithotomy Ho:YAG lasers means that the TDFL can provide stone ablation at lower pulse energies.The fact that among rare-earth elementdoped fiber lasers the Tm-doped one provides the second highest output power (after Yb-doped fiber laser) makes it very promising in terms of use as a pump source in OPO shifting laser (Optical parametric oscillator) radiation in the Mid-IR spectral region and supercontinuum setups [4,5] The advantages of fiber lasers can be utilized with a Tm-doped fiber laser [6,7], which provides flexible delivery of the radiation to the tissue under treatment.Moreover, mode-locked high-peak-intensity laser sources allow high-harmonic generation for high-resolution optical microscopy to receive contrast images of cell and tissue structures and functions [8].Such non-centrosymmetric biological materials as collagen, microtubules, and muscle myosin are suitable for SHG (second harmonic generation), which is definitely a phase and wavelength-dependent process.However, Ti:Sapphire lasers have been used traditionally for these purposes but their form-factor limits use beyond the laboratory, giving compact fiber lasers a chance to become an alternative [9].Another example of a field to benefit from mode-locked fiber lasers is multiphoton microscopy (MPM).Also it is worth noting that Tm ultrafast lasers can offer average output power more than 1 kW [10], which is important for some special applications.
According to the application of choice, one should consider possible ways for efficient and stable mode-locking, wavelength selection and tuning of pulse duration.In our scheme we used single-walled carbon nanotubes (CNT), which are a well-known saturable absorber (SA) for passively mode-locked lasers and a good alternative to semiconductor saturable absorber mirrors (SESAM).Inside the cavity, CNT acts as an intensity-dependent attenuator, demonstrating an ability to turn the continuous-wave laser generation into a train of ultrashort optical pulses.Detailed descriptions of fabrication, mechanism of work and usage in mode-locked lasers can be found in a review [11].Apart from their small cost and robustness, for this particular work it is important that our CNT sample works in transmittance and has broadband operation that ensures laser mode locking at all possible wavelengths.In comparison with nonlinear techniques of mode-locking, SA based on CNT offers perfect self-starting operation.First usage of CNT for mode-locking of Tm-doped fiber laser was reported in [7].
A plethora of existing spectral filtering techniques suitable for mode-locked fiber lasers such as open-space cavities featuring diffraction grating, band pass interferometric filters, Fiber Bragg Gratings (FBG), fiber-based Lyot filters [12], etc. provide an efficient approach for optical pulse generation in a preferable spectral region.The last one is well-suited for so-called all-fiber laser configuration, which benefits from its compactness and possible increase in stability especially in all-PM design.To the best of our knowledge, all-PM Tm-doped fiber lasers utilizing Lyot filtering have not been demonstrated yet.In this paper, we use two Lyot filters in an all-PM ring cavity with CNT used as a saturable absorber in order to achieve a self-started mode-locking regime with 0.4 mW of average power at ~1855 nm, with spectral width near 1 nm, pulse duration around 14 ps, and repetition rate of 14.7 MHz giving 27 pJ of pulse energy.

Experimental Scheme and Methods
Figure 1 shows the experimental setup of the all-PM Tm-doped mode-lock fiber laser.CNTs serve as a passive saturable absorber with a typical response time of ~0.7 ps and modulation depth of ~10% sufficient for reliable self-starting mode-lock.CNTs were synthesized by the aerosol CVD method [13] that provides polymer-free thin (~60 nm) film without the need for post-processing with liquid chemistry, with the lowest electronic transition tuned to a laser generation wavelength for higher modulation depth [14].The absence of polymer matrix serves for better thermal stability of CNT [15], allowing a stable long-lasting mode locked generation [16,17].The films are placed in a module formed with two FC/APC connectors by the dry-transfer method, where the film simply sticks to the fiber ferule from the filter under soft pressing.FC/APC connectors are preferable to suppress back reflection, which is important because the sample is located after an amplifier in the laser scheme.A homemade multielement first cladding GTWave [18] fiber-based Er-Yb laser at ~1570 nm with a maximum output power of 300 mW is used as a pump source for ~0.6 m Tm-doped PM fiber (iXblue, abs.@1.5750 dB/m) through the WDM 1570/1850 nm.The second wavelength-division multiplexing coupler removes unabsorbed pump radiation from the cavity.The laser pulses are extracted from the cavity through the fiber-optic coupler with a 90/10 ratio.The net-cavity β 2 is estimated to be ~−0.396ps 2 at 1855 nm, implying the possibility of classic soliton formation.Two sections of commercial single mode PM fiber with L1 ~0.18 m and L2 ~2 m, spliced at 45° to the fiber in the rest scheme and separated with two fast-axis-blocked fiber isolators (that additionally provide unidirectional pulses propagation), form two Lyot filters with locked ~42 nm and ~3.7 nm peak wavelength spacing, respectively.The lengths of the fibers in the Lyot filters were adjusted to achieve the required laser line width and peak wavelength.Both filters were placed on a solid metal plate inside a styrofoam-made chamber for passive thermal stabilization.The main idea is to use a superposition of both transmission functions and Tm fiber gain bandwidth, as a result, to enable generation only within a small spectral gap in the vicinity of 1850 nm.Here B is a birefringence of PM fiber, which represents the refractive index difference between the slow axis and fast axis: B = nslow-nfast.While a 'narrow'-bandwidth Lyot filter (NBF) with 3.7 nm period enables the generation wavelength to be precisely set and the pulse duration adjusted, a 'wide'-bandwidth filter (WBF) with 42 nm helps to suppress neighboring transmission maxima of NBF.The idea to use fiber Lyot filters for spectral filtering in fiber lasers is not novel, and was described and discussed in several works, for example [19,20] where the approach was applied to Yb-doped ultrashort pulse lasers.The main advantages of this method are simplicity, all-fiber design, and simple tunability by fiber length or temperature.In comparison with some other approaches (diffractive gratings, FBGs) Lyot filters offer the possibility for much simpler tuning within a broader range of bandwidth.

Results
Optical spectra were measured using optical spectrum analyzer Agilent 86140.One can see the resulting spectrum (FWHM ~0.5 nm) in Figure 2, as well as both Lyot filters' transmission functions with relevant approximation.
The average pulse power measured by power meter Ophir Nova II does not exceed 0.4 mW at the ring-laser output, which is not enough to achieve sufficient accuracy in pulse duration measurement.For that reason, we used a homemade fiber amplifier based on highly concentrated Tm-doped fiber (TDFA) fabricated by ICHPS RAS to increase the average power to >2 mW.The short length of active Tm-doped fiber in the amplifier allowed pulse characteristics to be kept almost unchanged.Two of commercial single mode PM fiber with L 1 ~0.18 m and L 2 ~2 m, spliced at 45 • to the fiber in the rest scheme and separated with two fast-axis-blocked fiber isolators (that additionally provide unidirectional pulses propagation), form two Lyot filters with locked ~42 nm and ~3.7 nm peak wavelength spacing, respectively.The lengths of the fibers in the Lyot filters were adjusted to achieve the required laser line width and peak wavelength.Both filters were placed on a solid metal plate inside a styrofoam-made chamber for passive thermal stabilization.The main idea is to use a superposition of both transmission functions T 1,2 = cos 2 (π • B • L 1,2 /λ) and Tm fiber gain bandwidth, as a result, to enable generation only within a small spectral gap in the vicinity of 1850 nm.Here B is a birefringence of PM fiber, which represents the refractive index difference between the slow axis and fast axis: B = n slow − n fast .While a 'narrow'-bandwidth Lyot filter (NBF) with 3.7 nm period enables the generation wavelength to be precisely set and the pulse duration adjusted, a 'wide'-bandwidth filter (WBF) with 42 nm helps to suppress neighboring transmission maxima of NBF.The idea to use fiber Lyot filters for spectral filtering in fiber lasers is not novel, and was described and discussed in several works, for example [19,20] where the approach was applied to Yb-doped ultrashort pulse lasers.The main advantages of this method are simplicity, all-fiber design, and simple tunability by fiber length or temperature.In comparison with some other approaches (diffractive gratings, FBGs) Lyot filters offer the possibility for much simpler tuning within a broader range of bandwidth.

Results
Optical spectra were measured using optical spectrum analyzer Agilent 86140.One can see the resulting spectrum (FWHM ~0.5 nm) in Figure 2, as well as both Lyot filters' transmission functions with relevant approximation.
The average pulse power measured by power meter Ophir Nova II does not exceed 0.4 mW at the ring-laser output, which is not enough to achieve sufficient accuracy in pulse duration measurement.For that reason, we used a homemade fiber amplifier based on highly concentrated Tm-doped fiber (TDFA) fabricated by ICHPS RAS to increase the average power to >2 mW.The short length of active Tm-doped fiber in the amplifier allowed pulse characteristics to be kept almost unchanged.Although the spectral filtering method used resulted in an efficient wavelength selection, we observed a clear trend of the central generation wavelength to shift to a shorter wavelength over time (Figure 4a).The shift itself is related to filters section temperature variation, which changes the length and birefringence value of both Lyot filters The measured by Femtochrome FR-103HS autocorrelation (AC) trace (Figure 3a) resulted in ~13.6 ps (sech 2 fitting) pulse duration.Thus, calculated TBP (Time Bandwidth Product) [21] is ~0.59, which means that pulses have noticeable uncompensated chirp since sech2-shaped bandwidth-limited pulses have the TBP about 0.315.The repetition rate of the pulse train is measured with RF spectrum analyzer (Keysight N9320B) around 14.7 MHz, and the radiofrequency spectrum is shown in Figure 3b.It is seen that RF spectra are free from any sidebands.Calculated pulse energy before the amplifier was 27 pJ.The measured by Femtochrome FR-103HS autocorrelation (AC) trace (Figure 3a) resulted in ~13.6 ps (sech 2 fitting) pulse duration.Thus, calculated TBP (Time Bandwidth Product) [21] is ~0.59, which means that pulses have noticeable uncompensated chirp since sech2-shaped bandwidth-limited pulses have the TBP about 0.315.The repetition rate of the pulse train is measured with RF spectrum analyzer (Keysight N9320B) around 14.7 MHz, and the radiofrequency spectrum is shown in Figure 3b.It is seen that RF spectra are free from any sidebands.Calculated pulse energy before the amplifier was 27 pJ.Although the spectral filtering method used resulted in an efficient wavelength selection, we observed a clear trend of the central generation wavelength to shift to a shorter wavelength over time (Figure 4a).The shift itself is related to filters section temperature variation, which changes the length and birefringence value of both Lyot filters Although the spectral filtering method used resulted in an efficient wavelength selection, we observed a clear trend of the central generation wavelength to shift to a shorter wavelength over time (Figure 4a).The shift itself is related to filters section temperature variation, which changes the length and birefringence value of both Lyot filters and thus their transmission maxima position.It is also evident that the peak level of the output laser line spectrum changes as the transmission maximum of NBF 'scans' WBF until a certain stationary temperature is reached.Figure 4b shows that the spectral width at −3 dB level varies as well from 1.2 to 0.5 nm, depending on the relative peak position of NBF and WBF.
Overall, spectral filtering stability could be improved by implementing active cooling or replacing the Lyot filters with Fabry-Pérot interferometric filters or other types of filter.When we removed the NBF filter from the cavity, the spectral width of the laser pulse became much larger (>10 nm), and pulse duration became much shorter (~1 ps).If both filters were removed from the cavity the position of the laser line shifted to 1870-1880 nm, the spectral width became much broader and Kelly sidebands appeared in the spectrum, indicating that the laser generated classical solitons.In this regime we were able to measure autocorrelation trace directly from laser output without an amplification stage.Typical pulse duration was measured to be ~1.5 ps, which is similar to results obtained in work [7] where no spectral filtering was used in Tm-doped fiber laser with CNT used as SA.
and thus their transmission maxima position.It is also evident that the peak level of the output laser line spectrum changes as the transmission maximum of NBF 'scans' WBF until a certain stationary temperature is reached.Figure 4b shows that the spectral width at -3 dB level varies as well from 1.2 to 0.5 nm, depending on the relative peak position of NBF and WBF.Overall, spectral filtering stability could be improved by implementing active cooling or replacing the Lyot filters with Fabry-Pérot interferometric filters or other types of filter.When we removed the NBF filter from the cavity, the spectral width of the laser pulse became much larger (>10 nm), and pulse duration became much shorter (~1 ps).If both filters were removed from the cavity the position of the laser line shifted to 1870-1880 nm, the spectral width became much broader and Kelly sidebands appeared in the spectrum, indicating that the laser generated classical solitons.In this regime we were able to measure autocorrelation trace directly from laser output without an amplification stage.Typical pulse duration was measured to be ~1.5 ps, which is similar to results obtained in work [7] where no spectral filtering was used in Tm-doped fiber laser with CNT used as SA.

Discussion
It is seen from the previous section that very simple and cost-effective double Lyot filters allow us to achieve the required pulse characteristics of mode-locked lasers including peak wavelength and pulse duration.They also have good potential for pulse parameters tunability by various options, particularly variation in PM fibers length in the Lyot filters and variation in Lyot filters temperature.Nevertheless, the results on laser stability presented in Figure 4 show that to achieve stable lasing wavelength one needs to apply special efforts.In this section we discuss some possible reasons for instability of laser behavior.
According to the formula for filter transmission-T (see Section 2) temperature may affect two parameters: PM fiber length-L and birefringence of PM fiber-B.Thus, it is necessary to estimate various reasons, including variations in L and B with temperature.A typical coefficient of thermal expansion for fused silica is CTE = 5.5 × 10 −7 [22], and thus length variation can be expressed as L CTE L t = Δ ⋅ ⋅Δ , where Δt is a temperature vari- ation.Temperature dependence of birefringence can be obtained using equation

Discussion
It is seen from the previous section that very simple and cost-effective double Lyot filters allow us to achieve the required pulse characteristics of mode-locked lasers including peak wavelength and pulse duration.They also have good potential for pulse parameters tunability by various options, particularly variation in PM fibers length in the Lyot filters and variation in Lyot filters temperature.Nevertheless, the results on laser stability presented in Figure 4 show that to achieve stable lasing wavelength one needs to apply special efforts.In this section we discuss some possible reasons for instability of laser behavior.
According to the formula for filter transmission-T (see Section 2) temperature may affect two parameters: PM fiber length-L and birefringence of PM fiber-B.Thus, it is necessary to estimate various reasons, including variations in L and B with temperature.A typical coefficient of thermal expansion for fused silica is CTE = 5.5 × 10 −7 [22], and thus length variation can be expressed as ∆L = CTE • L • ∆t, where ∆t is a temperature variation.Temperature dependence of birefringence can be obtained using equation ∆B = γ • ∆t, where γ = −5.6 • 10 −7 is a typical coefficient of birefringence variation with temperature for PANDA fiber [23].
Both coefficients are nearly equal and have different signs, but due to the great difference between the values of L = 2 m and B ~4.4 × 10 −4 in our case the influence of γ is more than three orders of magnitude greater then CTE.In fact, it means that in our case it is not necessary to consider the influence of CTE and only variation in birefringence with temperature is important.Finally, using the equation for filter transmission T one can see that the variation in peak wavelength shift ∆λ~0.9nm observed in Figure 4 can be explained by temperature variation in PM fiber in the Lyot filters for a value of about ∆t~0.26 • C; this is a reasonable level of temperature variation for systems without active stabilization.We measured long term stability of the temperature in the styrofoam-made chamber with quite poor accuracy ±0.1 • C, which provides enough range required to explain the observed wavelength shift.The blue shift of the peak wavelength indicates that fiber temperature in the filters rises with time.Simple calculations show that WBF and NBF experience similar peak wavelength variations with the temperature despite different lengths of PM fiber.Finally, we can conclude that the presented mechanism of peak wavelength variation can be considered as a main factor that fully describes the observed variation of laser line position.
Figure 4b shows that dependence of pulses spectral width is not monotonous with time unlike peak wavelength, and thus correlation between bandwidth and peak wavelength is not obvious.In our opinion the observed variation in pulses spectral width from 0.5 to 1.3 nm cannot be explained by change in spectral bandwidth of Lyot filters, since for reasonable temperature variation the filters bandwidth is nearly unchanged.In fact, the underpinning mechanism for such behavior of pulse bandwidth and duration is unclear and requires further investigation.We believe that one of important conditions for this future investigation is a precise active thermal stabilization of the Lyot filters with accuracy better than 0.01 • C, which was unavailable in our previous experiments.
Thus, this work demonstrates that the Lyot filter is an efficient spectral filtering technique for all-PM fiber lasers, regardless of an active dopant.Moreover, the methods examined are applicable for both CW and pulsed regimes.This two-Lyot filters approach allowed us to vary output parameters of such lasers without relying on dedicated (and usually, expensive) spectral filtering optical components.With proper thermal stabilization applied, one could maintain the pulse regime at any selected central wavelength.Thermal sensitivity of the Lyot filter could also be used as a mechanism for wavelength tuning.

Conclusions
As a result, we achieved a self-starting mode-locking in all-PM Tm-doped fiber lasers, with CNT as a saturable absorber and two Lyot filters inside the cavity that allowed us to tune generation central wavelength to 1855 nm.NBF enables us to set central generation wavelength precisely and to adjust the pulse duration varying the filter bandwidth, while WBF effectively suppresses neighboring transmission maxima of the NBF.The investigated spectral filtering approach can be used to obtain the required output parameters of optical pulses in all-PM fiber lasers with simple components especially for in lab usage.For practical applications, the fiber Lyot filters used must be precisely thermally stabilized to achieve high stability of laser pulse characteristics.This approach also allows one to tune central wavelengths of the laser line by variation in temperature, which can be useful for several applications.

Figure 2 .Figure 3
Figure 2. Optical spectrum (solid) and combined transmission function (TF) of two Lyot filters (dashed).Inset: experimentally obtained TF and its approximation.The measured by Femtochrome FR-103HS autocorrelation (AC) trace (Figure3a) resulted in ~13.6 ps (sech 2 fitting) pulse duration.Thus, calculated TBP (Time Bandwidth Product)[21] is ~0.59, which means that pulses have noticeable uncompensated chirp since sech2-shaped bandwidth-limited pulses have the TBP about 0.315.The repetition rate of the pulse train is measured with RF spectrum analyzer (Keysight N9320B) around 14.7 MHz, and the radiofrequency spectrum is shown in Figure3b.It is seen that RF spectra are free from any sidebands.Calculated pulse energy before the amplifier was 27 pJ.

Figure 4 .
Figure 4. Variation in output spectra vs. time (a).Central wavelength of the lasing spectrum (triangles) and corresponding spectral width (circles) variation with time (b).
coefficient of birefringence variation with temperature for PANDA fiber[23].Both coefficients are nearly equal and have different signs, but due to the great difference between the values of L = 2 m and B ~4.4 × 10 −4 in our case the influence of γ is

Figure 4 .
Figure 4. Variation in output spectra vs. time (a).Central wavelength of the lasing spectrum (triangles) and corresponding spectral width (circles) variation with time (b).