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Abstract
We investigated the frequency noise coupling mechanism of a 2 μm polarization-maintaining single frequency fiber laser (SFFL) theoretically and experimentally. The coupling of pump’s relative intensity noise (RIN) to frequency noise of a single-frequency high-gain silica fiber laser is shown experimentally to be consistent with a theoretical model where thermal expansion and thermo-optic effect mediate the coupling. The measured and theoretical frequency noise of the 2 μm SFFL with three pump sources is compared. We find using a 1550 nm single frequency laser pump source produces the lowest frequency noise, less than 100 $\rm {Hz/\sqrt {Hz}}$ at frequencies higher than 100 Hz.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Single frequency fiber lasers (SFFL) at 2 $\mu$m have attracted great attention for their potential applications. Because the 2 $\mu$m wavelength is in the "eye safe" range, the 2 $\mu$m SFFL is ideal for the usage in Light Detection and Ranging (LIDAR) systems and free space optical communication systems [1]. Furthermore, according to Mie scattering, the scattering intensity of near-infrared laser transmission in atmosphere is inversely proportional to the square of the wavelength [2], combining with many atmospheric transmission windows in the 2 $\mu$m range, the 2 $\mu$m laser can reach very long detection ranges for the LIDAR systems and has high potential in free-space optical communication. The high absorption in water and hence minimal penetration depth within human tissue, combined with the coagulation effect caused by the 2 $\mu$m laser radiation, the 2 $\mu$m laser is a promising candidate for highly precise surgical applications [1]. However, the laser frequency noise is not critical for the medical applications.
Most recently, there are proposals to use 2 $\mu$m lasers for next-generation GW detectors [3] where fused silica mirrors in the current GW detectors would be replaced by cryogenic silicon mirrors for reducing the mirror thermal noise, thermal distortions [4], and mirror surface scattering [5]. This also means cryogenic silicon can permit higher laser power (about 3 MW) which reduces high frequency quantum noise [6]. The high sensitivity of GW detectors sets a high level requirement of the frequency noise of the 2 $\mu$m SFFL in the ground-based GW detector detection band from about 1 Hz to 10 kHz.
The schemes to achieve 2 $\mu$m SFFL include distributed feedback (DFB) [7,8], distributed Bragg reflectors (DBR) [9,10], and ring cavity embedded with narrow-bandwidth filters [11,12]. In terms of performance characteristics, such as laser mode purity, laser intensity and frequency noises, and structure simplicity, a short cavity DBR SFFL - combining a pair of narrow-band fiber Bragg gratings with a short piece of rare-earth-doped fiber - shows great potential. In 2007, Geng et al. first reported a high efficiency single-frequency Tm$^{3+}$-doped fiber laser using a DBR cavity, which had a maximum output power of 50 mW [10], however this cavity suffered from high frequency noise. Subsequently, Yang et al. demonstrated significant noise reduction of the single-frequency Tm$^{3+}$-doped fiber laser. In 2015, they reported a laser with relative intensity noise (RIN) of less than -135 dB/Hz and the linewidth of less than 6 kHz [13]. In 2018, a high efficiency stable 1950 nm SFFL was demonstrated with -150 dB/Hz RIN over 8.4 MHz [14]. However, these experiments do not discuss frequency noise of the 2 $\mu$m SSFL in detail. It is known [15] that there are many sources of frequency noise in fiber lasers such as thermal noise, temperature fluctuations, acoustic noise and pump RIN. Pump RIN is often the limiting source of noise such as in Ref. [16] and Ref. [17]. These couplings mechanism have been widely demonstrated in 1 and 1.5 $\mu$m wavelength SFFL.
In this paper, we theoretically and experimentally demonstrate the frequency noise associated with pump intensity noise of a polarization-maintaining SFFL at 2 $\mu$m. By comparing the calculated and measured frequency noise of the 2 $\mu$m SFFL with three types of pump sources, we find that the RIN of the pump is responsible for the observed laser’s frequency noise. The mechanism of noise conversion follows from the conversion of pump RIN to temperature disturbances in the laser cavity [17]. Finally, by utilizing the 1550 nm single frequency laser with low RIN as the pump source, we have achieved a low frequency noise 2 $\mu$m SFFL. The measured frequency noise of the SFFL is less than 100 $\rm {Hz/\sqrt {Hz}}$ above 100 Hz.
2. Experimental setup
A schematic drawing of the 2 $\mu$m polarization-maintaining (PM) SFFL is shown in Fig. 1(a). The PM distributed Bragg reflector (DBR) structure is constructed by fusion splicing a narrow-band polarization-maintaining fiber Bragg grating (PM FBG) and a wide-band fiber Bragg grating (WB FBG) on two ends of a 1.5-cm-long highly Tm$^{3+}$-doped silica fiber (Nufern, PM-TSF-9/125). The PM FBG is written in a single mode PM fiber with a 3 dB bandwidth of 0.07 nm and a reflectivity of 84.5% at 1989.76 nm. Due to the birefringence of the PM fiber, the spectrum in reflection of the PM-FBG splits into two reflection peaks with central wavelengths corresponding to the fast (1989.19 nm) and slow (1989.76 nm) axes of the PM fiber, respectively. The WB FBG has a 3 dB bandwidth of 0.18 nm and a reflectivity of 99% at 1989.72 nm, it is fabricated on a photosensitive fiber. This pair of FBGs is chosen such that only the reflection peak corresponding to the slow axis of the PM FBG will fall into the center of the WB FBG reflectivity band. A piezoelectric transducer (PZT) is connected to the WB FBG. The gain fiber is a commercial PM Tm$^{3+}$-doped fiber, the core and cladding diameters of the fiber are 5 $\mu$m and 125 $\mu$m, respectively. The PM DBR structure is assembled into a copper tube, which is temperature controlled by thermoelectric temperature controller system. At the output port, a 2000 nm polarization-maintaining isolator (PM ISO) is used to protect the resonant cavity from end face reflection.
Fig. 1. Experimental setup of the 2 $\mu$m PM single-frequency DBR fiber laser (a). Three types of the pump: a 786 nm LD (b), a 1550 nm SFL (c) and a 1550 nm ASE (d). The symbols are: LD, laser diode; EYDF, Er/Yb-codoped fiber; DFB, distributed feedback; CLS, cladding light stripper; ISO, isolator; PM WDM, polarization-maintaining wavelength division multiplexer; PM DBR, polarization-maintaining distribute Bragg reflector; PM ISO, polarization-maintaining isolator; PZT, piezoelectric transducer.
We used three types of light sources to pump the SFFL to compare the effect of pump RIN on the SFFL frequency noise. The first pump used is a 786 nm laser diode (LD: Lumics, LU0786M250, 200 MHz) with 196 mW output power shown in the Fig. 1(b). The second pump is a 1550 nm single frequency laser (SFL) with central wavelength of 1550.15 nm and output power of 345 mW, which consists of a distributed feedback (DFB: 1550.15 nm, 20 mW, 3 MHz) single frequency laser diode and one-stage Er-doped fiber amplifier, as shown in Fig. 1(c). Figure 1(d) shows an amplified spontaneous emission (ASE) source with 352 mW output power at 1.5 $\mu$m. It consists of an ASE seed (ASE: 1549.85 nm, 25 mW, 20 nm) and an Er-doped fiber amplifier, and was used as the third pump. For all three pumps, the output power of the 2 $\mu$m SFFL was kept at 13 mW.
3. Experimental results and discussion
3.1 Relative intensity noise of different pump sources
We measured the relative intensity noise (RIN) of pump sources using an InGaAs photodetector (Thorlabs, PDA, 10CF-EC) and a vector signal analyzer (VSA, HP89410A), as shown in Fig. 2. In order to avoid saturation of the photodetector and VSA, the output power of the pumps is attenuated to about 0.5 $\rm {mW}$ (corresponding a voltage of about 5 V).
Fig. 2. Relative intensity noise (RIN) of the 786 nm LD (black), 1550 nm SFL (red), 1550 nm ASE (blue). The 1550 nm DFB is the SFL seed laser, and its RIN is represented by the green curve. The pink curve is the RIN of the 1550 nm ASE seed. The noise floor of the InGaAs photodetector is shown in cyan.
In Fig. 2, it can be seen that the 786 nm LD (black) has a much higher RIN level than 1550 nm SFL (red) and 1550 nm ASE (blue). This is because there is no mechanism to confine the central wavelength of the 786 nm LD, resulting in mode hopping and the higher RIN. The RIN curve (red) of the 1550 nm SFL shows a downward trend, which decreases from $3\times 10^{-5}\, \rm {/\sqrt {Hz}}$ at 1 Hz to $4\times 10^{-8}\, \rm {/\sqrt {Hz}}$ at 100 kHz. The SFL RIN is almost the same as the 1550 nm DFB (the seed laser of the SFL) RIN from 1 Hz to 1 kHz and 50 kHz to 100 kHz. However, from 1 kHz to 50 kHz, there is a bulge in the SFL RIN resulting in more than 10 dB excess noise over the DFB. In order to demonstrate whether this bulge is associated with amplified spontaneous emission noise (ASE) [18] in Er-doped fiber amplifier, we add a 200 GHz band-pass filter (PBF: 1550.15 nm, $\pm$ 0.25 nm) after the ISO in Fig. 1(c) to filter the ASE. Then the RIN of the 1550 nm SFL without and with the filter is measured in Fig. 3. It is clear that the RIN of SFL with filter is almost the same with the SFL without filter, indicating that the bulge is not caused by the ASE noise. Hence, the origin of the bulge in the 1550 nm SFL RIN is thought to be the result of the energy structure of the erbium ion [19]. The noise spikes in the 1550 nm SFL RIN are likely introduced by the 1550 nm DFB LD driver.
The blue curve in Fig. 2 represents the 1550 nm ASE RIN level. Below 1 kHz, the RIN is approximately flat, except for frequencies below 3 Hz. Between 1 kHz and 50 kHz, there is a bulge similar to 1550 nm SFL RIN spectrum. This is consistent with the bulge being associated with the energy structure of the Erbium ion in the signal amplification stages shown in Fig. 1(c) and Fig. 1(d). In the frequency range from 1 Hz to 200 Hz, the 1550 nm ASE RIN level is lower than 1550 nm SFL. The elevated SFL noise is due to the 1/f noise of the 1550 nm DFB (seed of the SFL) [20]. After 1 kHz the ASE RIN increases relative to the SFL RIN, above 10 kHz its 6 dB larger than the SFL RIN and at 100 kHz its an order of magnitude larger. This is because the 1550 nm ASE includes an ASE seed ( pink curve in Fig. 2) that has higher RIN noise than the RIN of 1550 nm DFB (the seed laser of the 1550 nm SFL).
3.2 Theoretical model of frequency noise
The coupling of pump RIN to the fiber laser frequency noise has been investigated in DFB fiber lasers [16] and DBR fiber lasers [21] respectively. The coupling mechanism is the same in both cases. A part of the pump light is absorbed by the active fiber and converted to heat. The pump RIN is therefore converted to a temperature fluctuation in the active fiber, which induces optical path length fluctuation through both thermal expansion and the thermo-optic effect (change of refractive index with temperature).
Here, we will first review the theoretical formalism of this noise coupling mechanism and then apply it to our fiber laser system with different pump sources.
As described in [21], most pump power absorbed by the active fibre is converted to output laser power, however, a fraction ($\eta$) is converted to heat. Assuming the absorption coefficient of the active fiber at the pump wavelength is $\alpha _{ap}$, $P(t)$ is the pump power at time $t$, $h(z)$ is the longitudinal distribution of pump power, and $e(r)$ is the pump light transverse mode field distribution, we may write the absorbed heat per unit time in the DBR-SFFL as [21]
The pump light transverse mode field distribution can be expressed as ,
where $w_P$ is the Gaussian radius of the pump light. Assuming that the entire pump light is coupled into the fiber core, then $w_P$ can be assumed to be equal to the radius of the fiber core.The heat equation with the heat source described in Eq. (1) may be solved in the manner described in Ref. [16] to produce an expression for the temperature fluctuation spectrum across the fiber $T(f)$ as a function of the pump power fluctuation spectrum $P(f)$.
where $N(z)=\alpha _{ap} \eta h(z),$ and $\Theta$ is the heat transfer function,Thermal fluctuations induce changes in active fiber optical path length due to thermal expansion and the thermo-optic effect. Changes in cavity optical path length result in a change in laser frequency $\Delta v(f)$ that can be described in terms of pump power fluctuations as follows,
where, $q=\alpha _L+\frac {1}{n}\frac {dn}{dT}$, $\alpha _L$ is the fiber’s linear thermal expansion coefficient, $n$ is the fiber refractive index, $dn/dT$ is the temperature coefficient of the refractive index.It was shown in [21] that the power-spectral-density of frequency fluctuations induced by a pump noise $S_p(f)$ is given by
The related parameters [22,23,24] in this article are shown by Table 1 .
Table 1. Parameters used for theoretical estimate of frequency noise.
3.3 Theoretical calculation and experimental measurement of the 2 $\mu$m PM SFFL
The frequency noise is measured using an acoustically shielded unbalanced fiber Mach-Zehnder interferometer (fMZI) [25]. The fMZI is unbalanced by adding a 10 m single mode fiber (SMF28) in one optical path of the interferometer. The fMZI is operated with quadrature biasing to maximise sensitivity to frequency noise [25,26]. The output of fMZI was focused on a photodetector (Thorlabs, PDA, 10D2) and measured by the VSA with a 100 kHz span. The quadrature biasing of fMZI is 2 volts at the photodetector output. The measured photodetector output noise spectrum was converted to the SFFL frequency noise as described in [25]. The noise floor of the fMZI is measured with one arm of fMZI blocked.
The measured pump intensity noise $RIN_p$ from Fig. 2 is projected to SFFL frequency noise using Eq. (7). The calculated frequency noise and the measured frequency noise of 2 $\mu$m SFFL using the 786 nm LD, 1550 nm SFL and 1550 nm ASE pump lights are presented in Fig. 4(a) - 4(c), then they are compared in Fig. 4(d). These results generally show a reasonable pump RIN projection where the SFFL frequency noise is dominated by thermo-optic pump noise coupling for the majority of frequency band investigated. Figure 4(a) shows the measured and calculated 2 $\mu$m SFFL’s frequency noise pumped by 786 nm LD, they have a similar trend. However, the measured data is slightly higher than the calculated data, that is likely due to changes in pump noise between measurements. Likely causes are fluctuations in cavity loss and varying levels of spontaneous emission in the active fiber as described in [27,28].
Fig. 4. The calculated and measured frequency noise spectra of the 2 $\mu$m SFFL pumped by the 786 nm LD (a), 1550 nm SFL (b) and 1550 nm ASE (c). And comparison of measured frequency noise spectra (d). The frequency noise of a 2 $\mu$m SFFL in [29] is shown for comparison. The noise floor of the measurement system converted to frequency noise is shown in cyan.
In Fig. 4(b), the calculated and measured frequency noise of the SFFL pumped by 1550 nm SFL is compared. The frequency noise level is almost the same except in the frequency region from 100 Hz to 1 kHz and from 50 kHz to 100 kHz. The frequency noise shows many resonances around a few hundred Hz (about 100 Hz to 1 kHz), due to environment instability induced acoustic noise in the fMZI. After 50 kHz, the measured frequency noise appears to increase significantly. This is because the frequency noise measurement is made with the fMZI actively controlled via the PZT (in Fig. 1(a)) to maintain quadrature biasing, mechanical resonance of the PZT element at that frequency range results in the noise injection. In Fig. 4(c), we see that the measured and calculated frequency noise of the SFFL pumped by the 1550 nm ASE have a similar characteristic to the SFL pumped SFFL.
Through comparison of the SFFL frequency noise with different pump sources in Fig. 4(d), it can be seen that the 786 nm LD pump SFFL has the highest frequency noise and that the pump RIN can be determined to be the dominant contributing noise [17]. The 2 $\mu$m laser pumped by 1550 nm SFL has a frequency noise level of about $1.5\times 10^4 \rm {Hz/\sqrt {Hz}}$ to 1.4 $\rm {Hz/\sqrt {Hz}}$ from 1 Hz to 100 kHz. The frequency noise is below 100 $\rm {Hz/\sqrt {Hz}}$ for frequencies larger than 100 Hz. The 1550 nm ASE pumped 2 $\mu$m SFFL (blue curve) has similar frequency noise to the SFL pumped (red curve). However, comparing the red curve and the blue curve, a slight improvement can be seen in the ASE pumped SFFL at frequencies below 100 Hz. While above 1 kHz the SFL pump SFFL has up to 4 dB lower frequency noise than the ASE pumped SFFL. Furthermore, the two frequency noise curves both have the bulge in the frequency region from 1 kHz to 50 kHz, which is consistent with their pump RIN curves. This is another feature indicating the dominant role that pump RIN plays in SFFL frequency noise.
Through comparison of theoretical calculation and experimental measurement we can conclude that pump RIN plays a dominant role in the 2 $\mu$m SFFL frequency noise. Comparing to the previous work on the single-frequency $\rm {Tm}^{3+}$-doped fiber laser [29] our measured frequency noise is lower than theirs below 6 kHz. The linewidth of our 2 $\mu$m SFFL with 1550 nm SFL pump is measured to be $2.5 \pm 0.3$ kHz. It is clear from the frequency noise spectra of SFFL, the linewidth of 2 $\mu$m SFFL with other 2 pumps should be larger than that with 1550 nm SFL pump. Finally, considering the long-term power stability and the simplicity in system integration, the 1550 nm SFL pump is chosen to be the pump of our 2 $\mu$m SFFL. The long term frequency drift of the 2 $\mu$m SFFL with 1550 nm SFL pump was measured to be about 45 MHz per hour.
4. Conclusions
In conclusion, we have presented a theoretical and experimental analysis of pump RIN on the frequency noise of a 2 $\mu$m PM SFFL. The theoretically analyzed results indicate that the RIN of the pump source is responsible for the observed laser’s frequency noise. This is due to the pump RIN inducing temperature fluctuations. The experimental results agree reasonably well with the theoretical predictions. In addition, by utilizing the 1550 nm SFL pump, the frequency noise of the 2 $\mu$m SFLL laser is less than 100 $\rm {Hz/\sqrt {Hz}}$ at frequencies after 100 Hz. These characteristics demonstrate this topology is a promising candidate seed laser for applications in the next generation gravitational wave detection.
Funding
National Natural Science Foundation of China (61527822, 61905006, 62035002); Center of Excellence for Gravitational Wave Discovery, Australian Research Council (CE170100004).
Acknowledgments
The authors would like to thank Christian Darsow and Volker Quetschke for valuable discussions.
Disclosures
The authors declare no conflicts of interest.
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