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Abstract
Single frequency laser sources with low frequency noise are now at the heart of precision high-end science, from the most precise optical atomic clocks to gravitational-wave detection, thanks to the rapid development of laser frequency stabilization techniques based on optical or electrical feedback from an external reference cavity. Despite the tremendous progress, these laser systems are relatively high in terms of complexity and cost, essentially suitable for the laboratory environment. Nevertheless, more and more commercial applications also demand laser sources with low noise to upgrade their performance, such as fiber optic sensing and LiDAR, which require reduced complexity and good robustness to environmental perturbations. Here, we describe an ultralow noise DFB fiber laser with self-feedback mechanics that utilizes the inherent photothermal effect through the regulation of the thermal expansion coefficient of laser cavity. Over 20 dB of frequency noise reduction below several tens of kilohertz Fourier frequency is achieved, limited by the fundamental thermal noise, which is, to date, one of the best results for a free-running DFB fiber laser. The outcome of this work offers promising prospects for versatile applications due to its ultralow frequency noise, simplicity, low cost, and environmental robustness.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Single frequency lasers (SFL) with low frequency noise are indispensable to precision high-end scientific applications, including gravity-wave detection [1,2], optical clock [3,4], high-resolution spectroscopy [5], quantum sensing [6] and ultraprecise time and frequency transfer [7]. In most instances, elaborate laser frequency stabilization techniques are used to fulfil these needs through optical or electrical feedback from an external reference cavity, which benefit from high optical Q factor, such as Fabry–Perot cavities [8,9], whispering gallery mode (WGM) micro-resonators [10], absorption lines [11,12] and long-delay-line interferometers [13–15]. Although these techniques can reduce the laser frequency noise remarkably, such systems are rather complicated, expensive and very sensitive to ambient conditions. Now, a wide range of commercial applications also demand laser sources with low noise to upgrade their performance, which require reduced complexity and good robustness to environmental perturbations. For example, there is significant demand for low noise SFL in fiber optic sensing fields [16], such as distributed fiber acoustics sensing systems for reservoir monitoring and pipeline security [17,18], as well as fiber optic interferometric sensing systems for marine acoustics [19]. Low frequency noise is a key requirement for these sensing systems involving coherent detection and the noise of the laser directly determine the sensitivity and signal to noise ratio [20]. Another fast-growing application requiring low noise SFL is LiDAR, such as coherent Doppler LiDAR for wind power generation [21] and FMCW (Frequency Modulated Continuous Wave) LiDAR for autonomous driving [22], where the laser frequency noise directly impacts system performance again.
Single frequency fiber lasers have drawn intense attention for these applications due to their outstanding properties of low phase noise, narrow linewidth, and wide wavelength coverage [23]. Different configurations have been implemented to demonstrate single-longitudinal-mode operation, and most popular commercial laser are the distributed feedback (DFB) fiber lasers because of their compactness and robustness. Today’s state of the art DFB fiber lasers is capable of sub-kilohertz Lorentzian linewidth emission [24,25]. The Lorentzian linewidth (or intrinsic linewidth) of the laser is known to be originated from the spontaneous emission coupled to the lasing mode, called “Schawlow-Townes linewidth” [26], which is theoretically a pure white noise and exhibit a Lorentzian line-shape, reflects the frequency noise of a laser at high Fourier frequency. However, at low Fourier frequency, frequency noise of the fiber laser is dominated by other noise sources, including the thermal origin noise, pump induced noise and the environmental noise. For the thermal origin noise, it can be understood for the cavity length perturbation caused by the equilibrium and non-equilibrium temperature fluctuations which is proportional to the temperature T2. It has been studied in detail previously [27,28] and is believed that the frequency noise in DFB fiber laser is limited by fundamental thermal fluctuations inside the cavity especially at the low Fourier frequency. Besides the thermal noise limit, it is also known that in some DFB fiber laser with higher erbium concentration, excess frequency noise exists that is strongly dependent on the pumping arrangement [29,30]. For the pump induced noise, it comes from the refractive index fluctuation induced by the pump intensity noise. While the pumping induced noise can be reduced via using a low noise pump or using an opt-electrical feedback loop, it increases the complexity and cost of the system to some extent [31]. Finally, fiber laser still suffers the environmental noise as the fiber resonant cavity is sensitive with the vibration and acoustic noise [32]. As stated in the previous paragraph, various kinds of laser frequency stabilization techniques can be applied to suppress these noise, and tens of Hz/Hz1/2 frequency fluctuation at low Fourier frequency have been demonstrated, but these are rather expensive and complicate. Consequently, it is highly demanded to dramatically reduce frequency noise at low Fourier frequency without such complexity and expensive implementation.
In this paper, we demonstrate a novel technique to reduce frequency noise of a DFB fiber laser at low Fourier frequency by utilizing the inherent photothermal effect, for the first time to the best of our knowledge, in which the nonuniform distribution of intensity inside the laser cavity introducing an intensity-wavelength response. By regulation of the thermal expansion coefficient of laser cavity, an effective self-feedback mechanics is established and the frequency noise of fiber laser can be reduced to the thermal origin noise limit in the feedback bandwidth, which up to several tens of kilohertz, agreeing well with theoretical analysis and numerical simulation. In the experiment, a noise suppression of over 20dB with the Fourier frequency below 20 kHz was achieved without any external reference or additional electronic feedback. It offers a simplicity, low cost noise reduction method, which could make contribution of applying the DFB fiber laser into the commercial applications areas such as fiber optic sensing, LiDAR and etc.
2. Principle
For DFB fiber laser, the laser resonant cavity is composed of a pi-phase shifted FBG (PS-FBG) and a nonuniform intracavity intensity distribution exists because the lasing intensity is much stronger in the phase shift location [33,34]. Similar to the photothermal effect in passive pi-phase shift FBG case studied by our group and other researchers [34–36], this nonuniform intracavity intensity distribution would induces the coupling between the resonant wavelength and intracavity laser intensity. Here, we divide the laser resonant cavity into M uniform sections and use transfer matrix theory to obtain the dependence relationship of intracavity laser intensity change $\Delta I$ on the laser wavelength shift $\Delta \lambda .$ With the parameters shown in the caption of Fig. 1, the intensity distribution inside the laser cavity at steady state is calculated, as is shown in the inset of Fig. 1 (black line). Then, $\Delta \lambda$ is introduced by changing the period of FBG and the intracavity laser intensity change $\Delta I$ is obtained using the calculated change of average intracavity laser intensity. Thus, an intensity-wavelength curve is obtained corresponding to the coefficient $\frac{{\partial I}}{{\partial \lambda }} \approx{-} 0.04\textrm{ }mW/pm,$ as is shown in the black line of Fig. 1.
Fig. 1. Intensity -wavelength trace in different conditions, corresponding to different $\frac{{\partial I}}{{\partial \lambda }}$ value (inset shows the intracavity intensity distribution in different conditions). Stimulate parameters: doping concentration $2 \times {10^{25}}\textrm{ }{m^{ - 3}};$ pump power 100 mW; original laser wavelength 1550 nm; mode field overlap factor for pump and laser field are 0.65 and 0.4; lifetime of exited state 10 ms; emission cross section area for pump and laser field are 0 and $2.6 \times {10^{ - 25}}\textrm{ }{m^2};$ absorption cross section area for pump and laser field are $2.5 \times {10^{ - 25}}\textrm{ }{m^2}$ and $1.8 \times {10^{ - 25}}\textrm{ }{m^2};$ resonant cavity length 20 mm; $\alpha$ is the thermal expansion coefficient of laser cavity.
Then, the change of intracavity intensity $\Delta I$ would influence the period of FBG through the photothermal effect, which could in turn change the laser wavelength $\delta \lambda = (\frac{{\partial \lambda }}{{\partial T}} \bullet \frac{{\partial T}}{{\partial I}}) \bullet \Delta I.$ Therefore, a feedback loop of laser wavelength is established and the feedback factor can be defined as $\frac{{\delta \lambda }}{{\Delta \lambda }} = (\frac{{\partial \lambda }}{{\partial T}} \bullet \frac{{\partial T}}{{\partial I}}) \bullet \frac{{\partial I}}{{\partial \lambda }},$ as is shown in Fig. 2. In this forum, the coefficient $\frac{{\partial \lambda }}{{\partial T}} \bullet \frac{{\partial T}}{{\partial I}}$ is mainly dependent on the thermo-optic effect of fiber, which is about 5 pm/mW for the single mode fiber of 1.5 μm [37]. Considering the coefficient $\frac{{\partial I}}{{\partial \lambda }} \approx{-} 0.04\textrm{ }mW/pm,$ the feedback factor $\frac{{\delta \lambda }}{{\Delta \lambda }}$ is about -0.2, corresponding to a rather weak feedback effect in the normal fiber laser case.
However, with the analysis above, it can be known that this feedback mechanics is dependent on the coefficient of $\frac{{\partial I}}{{\partial \lambda }},$ which is affected by the intensity distribution inside the laser cavity. Therefore, the different feedback factor can be expected via controlling the intracavity intensity distribution. In the theoretical stimulation, the different intensity distribution is achieved with changing the thermal expansion coefficient $\alpha ,$ as is shown in the inset of Fig. 1, and different intensity-wavelength curve are stimulated in Fig. 1, corresponding to different value of $\frac{{\partial I}}{{\partial \lambda }}.$ It can be seen that the larger slope is achieved with reduced the thermal expansion coefficient $\alpha$ from positive to negative. With the thermal expansion coefficient $\alpha ={-} 2 \times {10^{ - 7}}/K,$ the coefficient $\frac{{\partial I}}{{\partial \lambda }}$ is about -0.19 mW/pm, which indicates the feedback factor $\frac{{\delta \lambda }}{{\Delta \lambda }} \approx{-} 1.$ Therefore, a much stronger wavelength negative feedback effect is achieved.
3. Experiment and discussion
To observe the above theory inferred frequency noise reduction effect, an experimental study is given in the following. The experimental setup can be seen in Fig. 3. The resonant cavity of DFB fiber laser with 1.55 μm wavelength is constructed by inscribing a narrowed PS-FBG on a 2 cm long highly Er/Yb co-doped fiber (about 300 dB/m absorption @976 nm). The loss difference between the two orthogonality polarization is introduced in the inscribing process to ensure the single laser mode operation. A 976 nm semiconductor laser is used to pump the fiber laser. The fiber laser spectrum is monitored using an optical spectrum analyzer (APEX) with 4 MHz resolution to ensure the single longitudinal mode during the entire experiment.
Fig. 3. The experimental setup. Pump laser: 976 nm semiconductor laser; OC: optical coupling; WDM: wavelength division multiplexing; OSA: optical spectrum analyzer.
In order to regulate the fiber thermal expansion coefficient in quantity, a special mechanical structure is designed, as is shown in Fig. 4. The assembly drawing of this structure can be seen in the upper part of Fib. 4 and the details of the structure can be seen in the lower part of Fig. 4. As is seen in Fig. 4, firstly, the left end of the laser cavity is glued on the point A of the pink part, which is made of Aluminum with the thermal expansion coefficient of 23.6×10−6/K. Secondly, the laser cavity passes through a pinhole (close to the position of point B) of the green part. Finally, the right end of the laser cavity is glued on the point B of the green part, which is made of Invar with the thermal expansion coefficient of 1.6×10−6/K. In the package process, the fiber is pre-stretched with about one Newton force to avoid the laser cavity bend. A V groove with radius 150 μm is built in the Aluminum part and the laser resonant cavity is embedded into the V groove with good thermo-contact. The Aluminum part and Invar part is connected using screws at the point C of Fig. 4. With the thermal expansion coefficient difference between the Aluminum and Invar, the length change versus temperature between the point A and point B can be controlled.
Fig. 4. A specially designed mechanical structure for regulating the fiber thermal expansion coefficient.
Specifically, with the parameter lAC (the length between point A and point C) and lBC (the length between point B and point C), the length change versus temperature between point A and point B is
Thus, the equivalent thermal expansion coefficient of the laser resonant cavity can be controlled precisely by changing the position of point A. Although this structure is similar to the fiber temperature compensation package [38], the structure here is used to precisely control the photothermal effect in our experiment, which can reduce the noise in much higher bandwidth than the temperature compensation package case. As is analyzed by the above theoretical model, with the regulation of thermal expansion coefficient, the different feedback factor and laser frequency noise reduction effect inferred by the above theoretical analysis can be expected.
To verify the noise reduction effect of the self-feedback mechanics, we measure the frequency noise of the fiber laser in different conditions. In the experiment, we set the different position of point A in the mechanical structure to regulate the equivalent thermal expansion coefficient of laser resonant cavity, as is shown in Fig. 5. With different thermal expansion coefficients, it can be seen that the distribution of intensity or temperature is changed, which is monitored by thermal imaging camera, as is shown in Fig. 5. Some identical experimental curves of laser frequency noise can be seen in Fig. 6. In Fig. 6, the frequency noise at Fourier frequency above 1 kHz is measured via a Michelson interferometer [39], while the frequency noise at Fourier frequency below 1 kHz is measured via the frequency beating with an ultra-narrow linewidth laser as the Michelson interferometer is sensitive with the environmental turbulence. Besides, to measure the original fiber laser frequency noise without the self-feedback mechanics, we measure the frequency noise by putting the fiber laser in the water to attenuate the photothermal effect, as is shown in the case 4 of Fig. 5.
Fig. 5. The different thermal expansion coefficient of laser resonant cavity via setting the different position of point A (lBC=50 mm).
As is shown in Fig. 6, we have achieved different frequency noise reduction effect with different self-feedback factor by regulating the equivalent thermal expansion coefficient. It can be seen that the measured frequency noise is rather sensitive with different equivalent thermal expansion coefficient and a better noise reduction is achieved with changing the equivalent thermal expansion coefficient ${\alpha _0}$ from positive to negative. This result shows good agreement with the theoretical prediction and the best noise reduction effect has been achieved with the thermal expansion coefficient of -1.98×10−6/K, as is shown in case 1 trace of Fig. 6. While, with the thermal expansion coefficient of -2.6×10−6/K, the frequency noise degrades again, because over-feedback exists with larger feedback factor, as is shown in case 3 trace of Fig. 6. Comparing the trace of case 4 and case 1 in Fig. 6, the frequency noise of the fiber laser is reduced by about 20 dB below several tens of kilohertz Fourier frequency. Also, it can be seen from Fig. 6 that the bandwidth of this noise reduction method induced by the photothermal effect is about 20 kHz, which shows good agreement with several tens of microsecond photothermal effect relaxation time in our previous study result [34].
To see the performance limit of this self-feedback mechanics, the residual noise of fiber laser in case 1 is analyzed. As is studied by S. Foster, the thermal noise determines the noise floor of the DFB fiber laser and it can be calculated by using the formula (9) in [27], in which we define the heat source strength $Q = 8 \times {10^{ - 8}}\textrm{ }{J^2}/{\rm{m}^3}.$ The result is shown in the green line of Fig. 7(a). It can be seen that the theoretical calculated trace and experimental measured frequency noise trace of case 1 match well at low Fourier frequency. So, it can be concluded that in the feedback bandwidth of the self-feedback mechanics, the laser frequency noise induced by pump noise and environmental noise has been reduced completely and has reached the thermal noise limit. Furthermore, to evaluate the noise reduction effect, the frequency noise of the high performance commercial single frequency fiber laser-NKT Koheras X15 under the frequency locked mode has been measured using the same method, as is shown in the blue line of Fig. 7(a). It can be seen that in the feedback bandwidth, the frequency noise of case 1 is half orders of magnitude better than the one of NKT Koheras X15, which is to-date one of the best results for a free-running DFB fiber laser. Moreover, to see the robustness of the ultralow noise fiber laser to the environmental perturbations, the laser frequency noise and center wavelength are measured in different ambient temperature, as is shown in Fig. 7(b). With different ambient temperature, the ultralow frequency noise almost remains equal (the slight difference can be attributed to the different thermal noise level at different ambient temperature). It means that the self-feedback mechanics can be demonstrated at different stable point and the frequency noise of fiber laser can be reduced to the thermal noise limit in a wide temperature range. Also, it can be seen from the figure that the center wavelength of laser is changed with different ambient temperature and it is obvious that the wavelength can be stable via a laser ambient temperature control. This laser frequency noise reduction technique can contribute to upgrade the performance of commercial applications such as fiber optic sensing and LiDAR, which require low noise laser source with reduced complexity and good robustness to environmental perturbations [20–22].
Fig. 7. (a) The different level of laser frequency noise in different conditions. (b) The laser frequency noise and center wavelength versus different ambient temperature.
Finally, to evaluate the influence of this self-feedback mechanics on the intensity noise of fiber laser, the relate intensity noise (RIN) of the fiber laser with and without the self-feedback mechanics has been measured, as is shown in Fig. 8. It can be seen that the measurement result is almost identical, which means the intensity noise of fiber laser dose not degrade with the self-feedback mechanics.
4. Conclusion
In conclusion, an ultralow noise DFB fiber laser with self-feedback mechanics is demonstrated, by utilizing the inherent photothermal effect through regulation of the thermal expansion coefficient of laser cavity. A systematic theoretical model is proposed and experimental study shows that a frequency noise self-feedback mechanism is established via the photothermal effect. By utilizing the inherent photothermal effect through regulation of the thermal expansion coefficient of laser cavity, the pump induced noise and environmental noise is reduced completely and over 20 dB frequency noise reduction is achieved. The frequency noise of fiber laser has reached to the thermal noise limit at low Fourier frequency successfully and this report would make contribution of applying the free-running DFB fiber laser into the commercial applications areas such as fiber optic sensing, LiDAR and etc.
Funding
National Natural Science Foundation of China (61535014, 61775225, 61805260, 61875210); Shanghai Sailing Program (18YF1426100); Natural Science Foundation of Shanghai (18ZR1444300); Strategic Priority Research Program of Chinese Academy of Science (XDB43000000); Civil Aerospace “13th Five-Year” Preliminary Research Project (30501020107HT02).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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