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Abstract
We report an all-fiber single-polarization, single-frequency distributed-feedback (DFB) laser by a novel femtosecond laser line-by-line (LbL) direct-writing method. The phase-shifted fiber Bragg grating with a length of 26 mm is written in a single-mode non-polarization-maintaining (PM) Er-doped silica fiber. Single-polarization, single-frequency 1.55 µm laser oscillation is observed in the all-fiber DFB cavity configuration, with a pump threshold of 16 mW. The maximum laser output power from one port of the laser approaches 3.9 mW, and the slope efficiency of the DFB laser is 0.7% under the pump power of 640 mW. The FWHM (Full Width at Half Maximum) linewidth of the DFB fiber laser output is measured to be <1 kHz. High polarization extinction ratio of >30 dB has been observed by measuring the powers in the two orthogonal polarization directions of the DFB laser output. Single polarization mode laser oscillation has been verified. It is promising to use the femtosecond LbL writing method to achieve high-performance all-fiber single-polarization, single-frequency DFB fiber laser sources without relying on PM fiber elements.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Single polarization, single frequency (SPSF) fiber laser sources are highly demanded for many delicate high-precision optical measurements, such as resonator fiber optic gyros (R-FOG) [1] and gravitational wave detection [2]. Using such a type of high-performance laser sources can significantly suppress the phase detection errors that are caused by the power fluctuation, phase fluctuation, and polarization fluctuation in the measurements [1–4]. Typically, an all-fiber single frequency fiber laser can be achieved through either DFB or short-cavity distributed Bragg reflector (DBR) configurations [5–11]. A SPSF fiber laser can be realized by further inserting PM fiber elements, e.g., a PM gain fiber or PM FBG(s), into the fiber laser cavity [12–15]. Single polarization laser oscillation with high polarization extinction ratio (PER) can then be achieved in such an all-fiber polarization-selecting cavity.
In comparison with a short-cavity DBR fiber lasers [8–11], a DFB fiber laser are a better configuration to generate mode-hop-free single-frequency laser. In a DFB fiber laser, a phase-shifted fiber Bragg grating (PS-FBG) is built in the gain fiber [5–7]. Such a combination of PS-FBG and PM gain fiber is ideal for having frequency-stabilized all-fiber single-polarization, single-frequency laser output. However, writing PS-FBG in a PM gain fiber requires precise alignment between the exposure laser (either femtosecond laser or UV laser) beam and the polarization axes of the PM gain fiber. Such a job is not trivial and the misalignment will lead into a high number of errors in the desired polarization-dependent grating structure. Instead, Babin et al., recently reported a SPSF DFB fiber laser in a single-mode non-PM erbium-doped silica fiber (CorActive EDF-L 1500), which has a mode field diameter (MFD) of 5.9 ± 0.6 µm at 1550 nm [15]. The π-phase-shifted FBG was made by a femtosecond laser PbP technique. The birefringence of the FBG made by the femtosecond PbP method arises from the anisotropy of the induced refractive index change in the focus spot of femtosecond laser pulses in the fiber core [15–17]. The discrimination of the gains on the two orthogonal polarization directions is enhanced when the laser oscillation starts. Only one polarization mode can occur with a low pump power threshold, while another polarization mode virtually cannot start lasing. Therefore, SPSF laser oscillation can be obtained. This actually opened a door for achieving high-performance SPSF laser sources using non-PM fiber components.
The SPSF DFB fiber laser based on the PbP written PS-FBG was with the output power of only 0.7 mW at 1550 nm under the 976-nm pump power of 525 mW and a low slope efficiency of ∼0.13% [15]. The small fraction of the polarization dependent refractive index modulation in the cross-section area of the non-PM active core is believed to be the main cause for the low slope efficiency of the PbP-written SPSF DFB fiber laser. Note that the birefringence Δn in the FBGs by the femtosecond laser PbP method is typically at the order of 10−5 [15,17].
In this letter, we report an improved SPSF DFB fiber laser based on a non-PM single-mode erbium-doped optical fiber. The π-phase-shifted FBG is written in the non-PM Er-doped fiber, by a femtosecond LbL direct-writing method. SPSF laser oscillation has been experimentally observed with a narrow-linewidth (FWHM) of <1 kHz. The maximum laser output power at the wavelength of 1550 nm approaches 4 mW, under the maximum available pump power of 640 mW at 976 nm. And the slope efficiency of the DFB laser is 0.7%, approximately a factor of 5 higher than the reported DFB fiber made by the PbP writing method. Instead, another π-phase-shifted FBG is made in the non-PM Er-doped fiber, by a femtosecond PbP direct-writing method under similar laser writing conditions. However, no laser oscillation is observed in such a configuration. It therefore indicates that the LbL method is significantly advantageous over the PbP method for achieving an efficient SPSF DFB fiber laser using non-PM active fibers.
2. Experiments
The PS-FBG was written in a commercial erbium doped silica fiber (Liekki Er110-4/125) by femtosecond LbL method. The gain fiber is with a geometric core diameter of ∼4 µm and a MFD of 6.5 ± 0.5 µm at 1550 nm [18]. The peak absorption of the erbium-doped core at 1530 nm is 110 dB/m. The erbium concentration is then calculated to be 5 × 10−19 ions/cm3, according to the information provided in Ref. [19]. Note that the active fiber selected here has a similar core MFD to the Er-doped fiber used in Ref. [15], while the erbium concentration of the fiber in this work is 5 times higher than that of the erbium-doped fiber in the latter.
An 800-nm Ti:sapphire laser system (Astrella, Coherent Inc.) with a pulse width of 80 fs and a repetition rate of 1-kHz was employed for the fabrication of FBGs. The details of locating the laser spot precisely at the desired position inside the core can be found in Ref. [20]. Figures 1(a) and 1(b) show the writing procedures of PbP and LbL methods. For the LbL method used in this work [as shown in Fig. 1(b)], the laser spot was first located at the core/cladding boundary and moved across the doped core with a displacement of 4 µm, which was approximately the geometric diameter of the erbium doped core. Then the laser spot moved to the x direction with a displacement of 1.072 µm, which was the designed pitch Λ forming the second-order grating at 1550 nm. The moving velocity at y and x directions were 0.03 mm/s and 0.1 mm/s, respectively. The total length of the DFB grating was 26 mm with a center π phase shift, of which length (Lp) was 1.25Λ. Note that the erbium-doped fiber has a total length of 40 mm and the unwritten lengths at the backward side and the forward side of the PS-FBG were 6 mm and 8 mm, respectively. During the FBG inscription, the pulse energy was controlled at 97 ± 1 nJ. The polarization of the femtosecond laser is perpendicular to the x axis in Fig. 1.
Fig. 1. Schematic of PS-FBGs made by (a) PbP method and (b) LbL method. Comparison of area fraction of PM-dependent induced refractive index modulation in non-PM active fiber core using (c) PbP and (d) LbL methods.
Figures 1(c) and 1(d) compare the fraction of PM-dependent laser induced refractive index modulation within the cross-sectional area of non-PM active fiber core by PbP method and LbL method. As suggested in Ref. [11], the birefringence of a PbP-written FBG is determined by the elliptical area of the laser-induced microvoids on the cross-section of the fiber core and also by the writing pulse energy. Since the scattering loss of the written FBG increases dramatically with the increase of the writing pulse energy, LbL-written FBG is obviously a straightforward approach to increase the fraction of the laser-induced microvoid area within the cross sectional area of the fiber core. For example, when that the focused laser spot size is 1 µm and the core diameter is 4 µm, the cross-sectional area of the LbL-inscribed microvoids is ∼4 times as large as the microvoid area made by the PbP method. Consequently, the laser-induced birefringence of the LbL-written FBG ought to be enhanced in comparison with the one made by the PbP method, because the former has a larger overlap between the polarization-dependent index change and the guided mode.
As the comparison, an extra DFB grating, which has the same grating structural parameters as the one made by LbL method, was made in a piece of Er110-4/125 fiber by the PbP method. And the writing pulse energy was controlled at 115 ± 1 nJ.
Figure 2 illustrates the schematic setup of optical characterization of the SPSF DFB fiber laser based on the written PS-FBG. The erbium doped DFB fiber laser was pumped by a 976-nm laser diode (LD). The pump was coupled into the Er fiber through a 980/1550 nm wavelength division multiplexer (WDM). A second 980/1550 nm WDM coupler was used after the erbium fiber to separate the laser signal and the residual pump. And the forward and backward laser output was monitored from the two 1550 nm ports of the WDM couplers. No PM fiber components were employed in the laser setup in Fig. 2. Note that the temperature of the erbium-doped fiber was maintained by a thermo-electric cooler (TEC1-12706) at 25°C.
Fig. 2. Schematic setup of SPSF DFB fiber laser. OSA: optical spectrum analyzer; LD: laser diode; WDM: 980/1550 nm wavelength division multiplexer coupler.
3. Results and discussions
Figure 3 compares the transmission spectra of the π-phase-shifted FBGs written by the PbP and LbL methods. An optical spectrum analyzer (OSA, YOKOGAWA, AQ6370D) was employed for measuring the FBG transmission spectrum from the forward end of the PS-FBG DFB fiber laser (see Fig. 2). Due to the limited spectral resolution (0.01 nm) of the OSA, we were not able to obtain the accurate bandpass lineshape of the PS-FBG spectrum. A high-precision OSA with a spectral resolution better than 100 fm [15] is required to precisely resolve such fine spectral structures. It can be seen from Fig. 3 that the PS-FBG written by LbL method with a pulse energy of 97 nJ has an intensity of ∼30 dB, while the PS-FBG written by PbP method with a pulse energy of 115 nJ has an intensity of only ∼1 dB. PbP-written FBG with higher spectral intensity requires a further increase of the single pulse energy. However, the background scattering loss of the FBG was measured to be 0.5 dB and 2.0 dB for LbL-written and PbP-written method respectively. It indicates that low writing pulse energy is helpful to reduce the background loss of the directly written FBG. Second, the spectral intensity of the LbL-written FBG is higher than the PbP-written FBG, because the laser-induced microvoid area within the cross sectional area of the fiber core in the former case is larger than the latter case. It is therefore beneficial to use the LbL method rather than the PbP method for achieving a short-length FBG with adequately high spectral intensity and decently low background loss.
Fig. 3. Comparison of observed transmission spectra of PS-FBG written by PbP and LbL methods. Note that the corresponding single pulse energy for the FBG writing is noted beside each spectral trace.
According to Bragg equation
where λB is the Bragg wavelength, m is the order of the grating (m=2 here), Λ is the period of the grating (Λ=1.072 µm here), neff is the effective index of the guided mode, respectively, the laser-induced birefringence Δn of a PS-FBG is equal to ΔλB/Λ, in which ΔλB is the differential of the peak wavelength of the two orthogonal polarization directions of the FBG. Due to lack of a high precision OSA with the spectral resolution better than 100 fm [15], it is difficult to measure the peak wavelength of the ultra-narrow PS-FBG and obtain the laser-induced birefringence Δn directly. Instead, we have prepared several uniform FBGs written in SMF28 fiber by LbL and PbP methods. All FBG samples are with the reflectivity in the range of 99.0–99.9%, and the writing single pulse energy is similar to the values mentioned above. The measured birefringence Δn of the LbL-inscribed uniform FBGs is at the order of 10−4, while Δn of the PbP-inscribed uniform FBGs is at the order of 10−5. It therefore verifies the laser-induced birefringence Δn by LbL method is larger than the one by PbP method.Figure 4(a) shows the measured output power of the Er-doped DFB fiber laser versus the input pump power. It is seen that the threshold of the DFB fiber laser is 16 mW. The laser wavelength is located at 1550.45 nm, when the pump power just above the threshold. The slope of the backward laser output power versus the input pump power is 0.7%, while the slope of the forward output is 0.3%. The maximum laser output power at the wavelength of 1550 nm approaches 3.9 mW, under the maximum input pump power of 640 mW. And the slope of the backward output power from the DFB fiber laser to the input pump power is approximately 5 times as high as that of the SPSF Er-doped DFB laser made by PbP method [15].
Fig. 4. (a) Measured output power of Er-doped DFB fiber laser versus pump power. (b) Laser output spectra measured from backward (B) or forward (F) direction, with the increase of pump power.
Figure 4(b) illustrates the observed laser output spectra with the increase of the pump power. The wavelength of the backward output increases almost linearly with the increase of the input pump. This is because the thermal effect, which is attributed to the non-radiative transition of the erbium ions enhances with the absorbed pump power [12]. The slope of the laser wavelength shifting versus the pump power is measured to be 6 × 10−4 nm/mW.
By comparing the FBG transmission spectrum in Fig. 3 and the laser spectrum in Fig. 4(b), one can notice that a small discrepancy exists between the PS-FBG peak wavelength (1550.50 nm) and the laser peak wavelength (1550.45 nm). The latter was measured under a low input pump power of 35 mW, which is just above the pump threshold. Such a wavelength discrepancy between the FBG spectrum and the laser spectrum can be either attributed to the limited accuracy of the OSA, or because the real dimension of the laser-induced index change is slightly different from the laser spot size (∼1 µm). The latter could introduce phase errors in the fabricated PS-FBG and make the bandpass wavelength deviating from the central position of the DFB grating transmission peak.
In addition, no laser oscillation was observed in the PbP-written DFB fiber sample, even under the maximum available pump power of 640 mW, probably due to the high background loss and the weak spectral intensity of the PS-FBG made by the PbP method.
Figure 5 shows the single frequency characteristics measured by the scanning F-P etalon. The backward laser output was launched into a Scanning Fabry–Perot interferometer (SFPI) (Thorlabs SA200-12B) and an oscilloscope (Keysight Infiniivision DSO-X 3034A). The SFPI has a free spectral range (FSR) of 1.5 GHz, a finesse of 200, and a resolution of 7.5 MHz. As shown in Fig. 5, the sawtooth wave represents the voltage cycle of the SFPI and the red peaks represent the number of longitudinal modes over a ramping voltage cycle. It is seen that within the FSR of 1.5 GHz, only one longitudinal mode exists, confirming that the DFB fiber is truly single frequency laser. Note that the time interval between the two peaks in Fig. 5 is 6.46 × 10−3 s and therefore the corresponding frequency span is 232.2 MHz for each millisecond.
Delayed self-heterodyne interferometer was employed for determining the linewidth of the Er-doped DFB fiber laser. First, the backward output of the fiber laser under the maximum pump power of 640 mW was divided into two branches. One branch was connected to an acousto-optic modulator (AOM, Gooch & Housego) with a carrier frequency of 80 MHz. Another branch was connected to the SMF28 fiber delay and a polarization controller (PC). The two branches were then combined through a 50:50 fiber coupler. The beat signal spectrum was measured by an Agilent N9320B RF spectrum analyzer (as shown in Fig. 6). The length of the used fiber delay was 50.4 km, equivalent to a limiting frequency resolution of ∼1.3 kHz [7]. The Lorentzian fitting gives a 20dB-bandwidth of ∼4 kHz, suggesting that the FWHM linewidth of the Er-doped DFB fiber laser is ∼200 Hz. In addition, the existence of the ripples besides the main beat note reveals strong effects of long coherence length of the DFB fiber laser and indicates that the true linewidth of the DFB fiber laser ought to be substantially less than the resolution of the measurement setup. Hence, it suggests that the linewidth of this DFB fiber laser by LbL method is sub-kilohertz, which is one order of magnitude less than that of the Er-doped DFB fiber by PbP method [15].
Fig. 6. Measured delayed self-heterodyne RF beat signal with its Lorentzian fit at maximum output power. The inset is the beat note within 500 MHz bandwidth.
Figure 5 and the inset of Fig. 6 both show that only single beat signal exists within the frequency range up to 1.5 GHz, which is corresponding to a birefringence Δn of 1.1 × 10−5 [according to Eq. (1)]. Such a birefringence is equivalent to a differential of wavelength of 0.012 nm, slightly above the spectral resolution of the OSA (0.01 nm) employed in this work.
Second, since the laser-induced birefringence Δn of the LbL-written phase-shifted FBG is estimated to be at the order of 10−4, if an orthogonal polarization mode exists in the laser output, the wavelength gap between the principal linear polarization mode and orthogonal polarization mode is calculated to be 0.1 nm or more, far above the OSA’s spectral resolution. However, no second lasing peak is observed in Fig. 4, within the whole available pump power range.
In the measurement of the linear polarization extinction ratio (PER) of the backward laser output, the combination of a PC and in-line fiber polarizer was used for obtaining the maximum power Pprincipal and the minimum power Porthogonal. The linear polarization extinction ratio was then calculated, according to $PER(dB) = 10{\log _{10}}(\frac{{{P_{principal}}}}{{{P_{orthogonal}}}})$. Within the whole pump power range, the PER was measured to be >30 dB.
Based on the above measurement results including Figs. 4–6 and the PER measurement, it therefore verifies that this narrow-linewidth single-frequency DFB fiber laser is with single polarization mode.
Figure 7 shows the measured relative intensity noise (RIN) of the backward output of the SPSF DFB fiber laser under the maximum pump power of 640 mW. It is seen that the RIN beyond 1 MHz is shot-noise limited and below −110 dB/Hz. Note that the peak at ∼920 kHz is caused by the relaxation oscillations of the fiber laser. The peak position of such relaxation oscillations is related to the lifetime of the upper level of Er3+ ions in the 1.55-µm 4I13/2-4I15/2 lasing transition and also the lifetime of the photons in the DFB cavity [21].
Fig. 7. Relative intensity noise (RIN) spectrum of the backward output of SPSF DFB fiber laser under maximum input pump power.
Figure 8 shows the power stability of the backward laser output for 3 hours under maximum input pump power of 640 mW. The rms deviation is calculated to be 0.1%, showing high power stability of this SPSF DFB fiber laser source.
Fig. 8. Power stability of backward output of SPSF DFB fiber laser for 3 hours under maximum input pump power of 640 mW.
Under the maximum pump power of 640 mW, the PER of >30 dB has been confirmed within a 2-hour continuous observation, indicating the excellent stability of the polarization state of the SPSF fiber laser.
Figure 9 shows the frequency drifting of the longitudinal mode of the backward laser output within 1 hour under maximum input pump power of 640 mW. The trace was manually recorded every 4–5 minutes, using the setup of the Scanning Fabry–Perot interferometer and the oscilloscope. It is seen that the single frequency signal fluctuates within the time range of 0.76 ms, corresponding to 1-hour frequency stability of ±88 MHz. Such a moderate frequency stability also verifies the stability of the polarization state of the SPSF fiber based on the DFB grating made by the LbL method. Note that commercial single-frequency fiber laser modules, such as Rock OEM module of NP Photonics [22], typically have 1-hour frequency stability of 20 MHz. The temperature of the thermoelectric cooler was monitored by a thermistor detector and recorded by the software on the laptop. It is seen that during the frequency stability measurement, the temperature is maintained at 25 ± 0.01°C. Because for a silica based linear fiber laser cavity, the laser frequency shift at 1.55 µm is 1.65 GHz for a 1°C shift in temperature [23], the temperature fluctuation of ±0.01°C is corresponding to the frequency fluctuation of ±16.5 MHz. Therefore, we attribute the major cause of the frequency instability of the SPSF laser in this work to the lack of anti-vibration isolation. It has been noticed that the frequency fluctuation of the DFB fiber laser setup occurs due to the random vibration from the environment. Further improvement on the mechanical insolation on the DFB fiber laser is currently ongoing.
Fig. 9. Frequency stability of backward output of SPSF DFB fiber laser for 1 hours under maximum input pump power of 640 mW.
Additionally, the pump threshold of the DFB fiber laser can be estimated by the following formula [15]:
where gs(Ppump) is the pump-power (Ppump) dependent signal-gain per unit length in the fiber due to the population inversion of erbium ions, κ (=πΔn/λ, in which Δn is the laser-induced refractive index change, and λ is the working wavelength) is the coupling coefficient of PS-FBG, L is the FBG length, α* is the coefficient of the unsaturated losses (∼50 dB/km for erbium doped silica fiber [15]), and αPSFBG is the scattering loss of the femtosecond inscribed PS-FBG, respectively. The scattering loss of the femtosecond LbL-written phase-shifted FBG, αPSFBG, was measured to be 12% (∼0.5 dB), while the αPSFBG, of the PbP-written PS-FBG was 5% (∼0.2 dB) [15]. Note that the PS-FBG strength, κL, can be obtained from the reflectivity R of the PS-FBG by R = tanh(κL)2 [24]. Therefore, the reason why the threshold of the SPSF DFB fiber laser made by LbL method in this work is nearly twice of that of the SPSF DFB fiber laser made by PbP method [15] should be mainly due to the higher scattering loss of the LbL written PS-FBG. However, the excellent performances of the LbL-written SPSF DFB fiber laser, such as the high slope efficiency, sub-kHz linewidth, and high PER (see the comparison between Er3+-doped SPSF DFB fibers made by PbP and LbL methods in Table 1), indicate that the LbL method is promising for realizing high-performance SPSF DFB fiber lasers using non-PM active fibers.
Table 1. Comparison of Er3+-doped SPSF DFB fibers made by PbP and LbL methods.
4. Conclusion
In summary, we have presented a PS-FBG with enhanced birefringence, using a femtosecond laser line-by-line direct-writing method. All-fiber SPSF DFB laser is observed with an improved slope efficiency of 0.7%, narrow-linewidth of sub-kHz, ultra-high laser power stability, high PER of >30 dB, high power stability of 0.1 rms deviation, and reasonable frequency stability of ±88 MHz. All in all, the all-fiber 1.55µm SPSF DFB fiber laser by the femtosecond laser LbL-writing method can be a promising source in high-precision 1.55-µm R-FOG system or a high-performance seed for power amplifiers, without relying on a PM active fiber.
Funding
Graduate Research and Innovation Projects of Jiangsu Province (2020XKT787); Priority Academic Program Development of Jiangsu Higher Education Institutions.
Disclosures
The authors declare no conflicts of interest.
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