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Abstract
A kHz-order linewidth controllable 1550 nm single-frequency fiber laser (SFFL) is demonstrated for the first time to our best knowledge. The control of the linewidth is realized by using a low-pass filtered white Gaussian noise (WGN) signal applied on a fiber stretcher in an optical feedback loop. Utilizing WGN signals with different signal amplitudes An and different cutoff frequencies fc, the linewidths are availably controlled in a wide range from 0.8 to 353 kHz. The obtained optical signal-to-noise ratio (OSNR) is more than 72.0 dB, and the relative intensity noise (RIN) at frequency greater than 40 MHz reaches −148.5 dB/Hz which approaches the shot noise limit (−152.9 dB/Hz). This kHz-order linewidth controllable SFFL is meaningful and valuable, for optimizing the receiver sensitivity and bit error rate (BER) performance of the coherent optical communication system based on high-order quadrature amplitude modulation (QAM).
© 2017 Optical Society of America
1. Introduction
Single-frequency fiber lasers (SFFLs) have attracted increasing interest due to their promising performances of compact all-fiber configuration, high efficiency, narrow linewidth and good beam quality, all of which make them versatile in the field of Doppler wind measurement Lidar, nonlinear frequency conversion, optical communications, optical microwave source and spectroscopy [1–7]. For example, coherent optical communication as advanced technology has significant advantages of high sensitivity, large communication capacity and modulation diversification, which is becoming a main method of the communications scheme [8–10]. The linewidth of the laser source is an important characteristic especially in the high-order quadrature amplitude modulation (QAM), and its investigations are constantly reported [11–13]. However, most of these contrastive researches are just based on the theoretical simulation or using various laser sources to realize different linewidths. Therefore, how to acquire a kHz-order linewidth controllable SFFL with other desirable properties is a valuable issue, for constructively realizing the contrast and optimization experiment of the receiver sensitivity and bit error rate (BER) performance in coherent optical communication system.
In the past ten years, several techniques have been proposed to control the laser linewidth, which include two aspects: the linewidth broadening and the linewidth suppression. A method to broaden the linewidth is demonstrated utilizing a direct phase modulation [14,15]. Nevertheless, this method has made the laser frequency appear several obvious sidebands, which means the laser is not strictly working with a single-frequency status. Moreover, this non-single-frequency laser will increase BER and reduce the receiver sensitivity in coherent optical communication. On the other hand, an approach to suppress linewidth is based on the length adjusting of the laser cavity, which is driven by the error signal extracted by comparing the optical frequency with the resonance frequency of a highly stable resonator [16,17]. However, this method requires fine alignment of free space optical components, tight polarization adjustment and spatial mode matching [18]. Furthermore, ultra-stable cavities are relatively expensive, huge and fragile. Although the above methods can change the laser linewidth, a real linewidth controllable SFFL has never been reported yet.
Thanks to the development of heavily rare earth ions doped phosphate SFFL, the natural narrow linewidth of this SFFL is easily achieved [6,19], and it is much narrower than that of the current commercial lasers. Recently, we have reported the linewidth suppression mechanism of SFFL with optical feedback [20], and revealed that the variance of the optical feedback loop will obviously change the laser linewidth. In this paper, we report a novel method to control linewidth of SFFL by means of optical feedback with noise injection. By using a low-pass filtered white Gaussian noise (WGN) signal applied on a fiber stretcher in an optical feedback loop, the laser linewidth is controllable in a wide range from 0.8 to 353 kHz.
2. Experimental setup
The experimental setup of the linewidth controllable SFFL via the optical feedback with noise injection is shown in Fig. 1. The laser cavity is consisted by a narrow-band fiber Bragg grating (NB-FBG) and a wide-band fiber Bragg grating (WB-FBG) on each end of a 1.5 cm home-made highly Er3+/Yb3+-codoped phosphate fiber as gain fiber [6,21], respectively. The NB-FBG has a peak reflectivity of 60% and a 3 dB bandwidth of 0.06 nm, while that of the WB-FBG is > 99.95% with a 3 dB bandwidth of 0.3 nm, and the physical lengths of the FBGs are both 1.5 cm. To prevent the detrimental Fresnel reflection, the spare end of the WB-FBG is cleaved to an angle facet. The laser cavity is assembled into a copper tube and thermally stabilized through a thermoelectric cooler controller with a resolution of 0.05 °C to maintain a robust single-longitudinal-mode operation. The laser cavity is backward pumped by a 980 nm single-mode laser diode (LD) and a wavelength division multiplexer (WDM). The output laser is then launched into the port 2 of an optical circulator from the signal port of the WDM. The port 3 of the circulator and the input port of a 10/90 optical coupler are connected by an isolator, which is used to guarantee unidirectional transmission of the laser. Then the 10/90 optical coupler is employed to split 10% of the laser power to the port 1 of the circulator fusion-splicing with a fiber stretcher. The insertion loss of the fiber stretcher is 0.3 dB, the length of single-mode fiber in fiber stretcher is about 12.3 m, and the fiber stretch displacement is 0.14 μm/V [22]. This fiber loop is used to realize optical feedback and the fiber stretcher serves as a linewidth controller. A low-pass filtered WGN signal generated by an arbitrary waveform generator (AWG) is designated to the fiber stretcher to achieve laser linewidth controlling. All the experimental optical paths are well fixed on the optical table with special optical glue to reduce the unnecessary acoustic vibrations.
During the experiment, the LD is driven by a 200 mA current, and the laser output power is 12 mW at the initial state. In addition, 10% of the laser power is fed back into the laser cavity through the circulator and the power from the 90% port of the coupler is 10.5 mW. The single-longitudinal-mode operation is verified by a scanning Fabry-Perot interferometer with a resolution of 7.5 MHz and a free spectral range of 1.5 GHz in the whole experiment.
3. Results and discussion
As an introduction to the principle of the linewidth controlling by optical feedback with noise injection, let us first consider a frequency noise spectral density spectrum Sn(f) that has a constant level h below a cutoff frequency fc and drops to zero above this threshold [23]:
According to [23], the area of the spectral density spectrum Sn(f) can be separated into two sections by the β-separation line represented by β = 8In(2)f/π2. Considering the laser light field E(t) = E0exp[i(2πv0t + φ(t))], the laser autocorrelation function Γ(τ) and the laser power spectral density SE(v) are given by [24] A fairly good estimate of full wave at half maximum (FWHM) that holds for any fc is in the following form [23]:It has a relative error smaller than 4% over the entire range of the cutoff frequency fc. By introducing the WGN signals applied on the fiber stretcher, the linewidth of the fiber laser has been changed because of the altering value of h and fc.The low-pass filtered WGN signals produced by the AWG are characterized by two major parameters, which are the cutoff frequency fc and the signal amplitude An. In order to intuitively illustrate the effect caused by the individual factor, only one variant is exploited during the experiment successively. The WGN signals with a constant noise amplitude (An = 500 mVpp) and different cutoff frequencies (fc = 4, 10, 15, 20 kHz) are launched into the fiber stretcher respectively, which are shown in Fig. 2(a). Note that the An of 500 mVpp is limited by the output capability of the AWG. Because of the imperfect low-pass filter, the signal powers are not entirely equal within the passing frequency band. However, this deficiency can be solved by further optimizing the property of the low-pass filter. In addition, the peak power of the WGN signal in Fig. 2(a) gradually reduces, which results from the energy dispersion of the WGN signal with the increasing frequency band.
Fig. 2 (a) The power spectra of WGN signals with different cutoff frequencies fc = 4 kHz, 10 kHz, 15 kHz, 20 kHz with constant noise amplitude An = 500mVpp. (b) The self-heterodyne power spectra of the noise-injecting fiber laser with different cutoff frequencies fc and their Voigt fitting curves, comparing with that of the initial laser and the laser with optical feedback. The inset is the detailed self-heterodyne spectra of the initial laser and the laser with optical feedback along with Lorentz fitting curves.
The linewidths are measured with the loss-compensated recirculating self-heterodyne method, which involves a 48.8 km long fiber and a fiber coupled acoustic optical modulator with a frequency shift of 40 MHz [25]. The second-order heterodyne signals are demonstrated in Fig. 2(b), which show the linewidths of the initial laser, the laser with optical feedback and the noise-injecting laser with different cutoff frequencies fc. As illustrated in the inset of Fig. 2(b), the self-heterodyne signal of the initial laser shows good Lorentzian lineshape, and the initial linewidth is 2.5 kHz. By means of the linewidth suppression effect of the optical feedback [20], the linewidth of the fiber laser reduces to 0.8 kHz. While with the injection of the WGN signals, the laser linewidth is remarkably broadened and the maximum linewidth of 353 kHz is acquired. Owing to the Lorentzian lineshape superimposed with the Gaussian component, the lineshape has transformed to Voigt lineshape, which is a convolution result of a Lorentz lineshape and a Gaussian lineshape [23,26]. Because of the energy dispersion derived from the linewidth broadening, the peak radio frequency (RF) power of the self-heterodyne signal has reduced compared with that of the initial laser. It is worth noting that the broadening effect of the laser linewidth has gradually reduced along with the increasing of the cutoff frequencies fc. It indicates that the WGN signals injected into the optical feedback loop, with constant noise amplitude An, has a saturated value of the effective cutoff frequency fc [23].
Similarly, the working performances of the injecting WGN signals with different noise amplitudes An are measured as shown in Fig. 3. The WGN signals with different noise amplitudes An from 100 mVpp to 500 mVpp injected into the fiber stretcher are shown in Fig. 3(a) respectively, while the same cutoff frequency fc = 10 kHz is exploited. In the logarithmic scales, the increasing of the signal power seems like a gradual slowdown, but in reality the value has changed uniformly. The results in Fig. 3(b) manifest that the linewidths of the noise-injected laser have presented well Voigt lineshapes. However, unlike the aforementioned circumstance, the linewidths controlled by the WGN signal with enhancing amplitude An seem to monotonously increase in the experimental range. Hence it is speculated that the linewidth can be further broadened by enhancing the signal amplitude An of the WGN signal injected into the optical feedback loop.
Fig. 3 (a) The signal power spectra with different WGN signal amplitudes of An = 100, 200, 300, 400 and 500 mVpp with a constant cutoff frequency fc of 10 kHz. (b) Measured self-heterodyne spectra of the noise-injecting fiber laser and their Voigt fitting curves, comparing with the initial laser and the laser with optical feedback.
In order to more clearly investigate the variation trend of the laser linewidths during the injection of the WGN signals on the optical feedback loop, the linewidths of the noise-injecting fiber laser with different WGN signal amplitudes An and different cutoff frequencies fc are measured successively, which are shown in Fig. 4 in a colored histogram form. The WGN signal amplitudes An are controlled as a spacing of 50 mVpp from 50 to 500 mVpp along with a minimum value of 10 mVpp near the setting limit of the AWG. The cutoff frequencies fc is set as 2, 4, 6, 8, 10, 12, 15, 18, 20 kHz, respectively, where 2 kHz is the minimum cutoff frequency of the WGN signal in the AWG. In addition, the maximal setting value of 20 kHz is because that the saturation effect of the cutoff frequency fc is clearly detected. Thanks to the contribution of the injecting WGN signal on the optical feedback loop, the laser linewidth is availably controlled in a wide range from 0.8 kHz to 353 kHz. More importantly, the linear relationship between the laser linewidth and the WGN signal amplitude An is testified through nine sets of data, and the saturation effect of the cutoff frequency fc during the linewidth broadening process gradually reduces with the increasing of the WGN signal amplitude An. These results indicate that effectively enhancing the WGN signal amplitude An and properly expanding the cutoff frequency fc can further broaden the laser linewidth.
Fig. 4 Measured linewidth results of the noise-injecting fiber laser with different WGN signal amplitudes of An and different cutoff frequencies fc of the WGN signals.
To evaluate the ability of linewidth-controlling technique, linewidth controlling ratio (LCR) is one of the most important factors defined as the ratio between the linewidth of the altered laser and the minimum acquired linewidth. In Fig. 5, LCR varying with different signal amplitudes An and cutoff frequencies fc is demonstrated. One can observe in Fig. 5(a) that LCR increases linearly with the enhancement of WGN signal amplitude An while remaining the cutoff frequency fc unchanged. By contrast, in the process of expanding the cutoff frequency fc, LCR increases in a gradually slowing trend within a relatively limited tuning range, which indicates the saturation effect referring to the cutoff frequency. As pointed out by Fig. 5(b), the saturated cutoff frequency fc enhances with the increasing of signal amplitude An. In summary, it reveals that the WGN signal amplitude An plays a leading part than the cutoff frequency fc in scaling up the linewidth, and the boosting of the cutoff frequency fc can efficiently promote the stretching scope especially under the high WGN signal amplitude An.
Fig. 5 (a) LCR versus WGN signal amplitude An under different cutoff frequencies fc of 2, 6, 10, 15, 20 kHz. (b) LCR versus WGN signal cutoff frequency fc under different WGN signal amplitudes An of 100, 200, 300, 400, 500 mVpp.
The optical spectrum of the noise-injecting fiber laser with the linewidth of 353 kHz is measured by an optical spectrum analyzer with a resolution of 0.02 nm compared with the initial fiber laser and the fiber laser with optical feedback. The three optical spectrum curves shown in Fig. 6(a) are almost coincident, indicating that the spectral feathers are not affected by the optical feedback with WGN signal injection. And the sharp unimodal is observed, which means that this linewidth controllable fiber laser has perfect optical spectrum. Eventually, the extracted optical signal-to-noise ratio (OSNR) is more than 72.0 dB.
Fig. 6 (a) Measured optical spectra of the noise-injecting fiber laser with linewidth of 353 kHz along with the initial fiber laser and the fiber laser with optical feedback. (b) Measured RIN of the fiber laser before the optical feedback, after the optical feedback, and with linewidth of 353 kHz, while the theoretical shot noise limit is also shown for comparison. The inset is measured single-longitudinal-mode character of the noise-injecting fiber laser with linewidth of 353 kHz.
To further verify the single-longitudinal-mode character of the fiber laser after WGN signal injection with the linewidth of 353 kHz, the result of a scanning Fabry-Perot interferometer with a resolution of 7.5 MHz and a free spectral range of 1.5 GHz is given in the inset of Fig. 6(b). It is concluded that the noise-injecting fiber laser operated in single-longitudinal-mode status without mode-hop and mode competition phenomena. The RIN are measured by an InGaAs photodetector (PD) with the bandwidth of 3.6 GHz and an electrical spectrum analyzer (ESA). The laser power is attenuated to 0.5 mW before being launched into the PD to ensure consistency in the entire measurements. Figure 6(b) illustrates the RIN of the SFFL before the optical feedback, and after the optical feedback with WGN injection off and on, while the theoretical shot noise limit is also shown for comparison in the frequency range from 0.5 MHz to 3.6 GHz. It is observed that after optical feedback the relaxation oscillation peak of the SFFL is reduced 25 dB from −103 dB/Hz to −128 dB/Hz. The introduction of the optical feedback has increased the external photon lifetime, and it can result in the low shift of the relaxation oscillation frequency and the suppression of RIN [20,27]. Here there arises a series of gradually weakened harmonic peaks in the RIN spectra, which are attributed to the recursion dynamics of the laser light in the optical feedback process [28]. At frequencies greater than 1 GHz, a slow increase is observed in the RIN spectra, which is caused by the noise floor of the PD. And at frequency greater than 40 MHz, the three RIN curves are almost coincident, which reach −148.5 dB/Hz and approach the shot noise limit (−152.9 dB/Hz).
4. Conclusions
In conclusion, we have demonstrated a novel technique for a SFFL to control linewidth based on optical feedback with noise injection. With different signal amplitudes An and different cutoff frequencies fc of the WGN signals, the laser linewidth is availably controlled in a wide range from 0.8 to 353 kHz. In addition, through comparing the results of LCR, it is revealed that the WGN signal amplitude An is a more primary part, and the expanding of the cutoff frequency fc can promote the controlling effect especially under the high WGN signal amplitude An. The obtained OSNR is more than 72.0 dB, and the RIN at frequency greater than 40 MHz reach −148.5 dB/Hz which approaches the shot noise limit (−152.9 dB/Hz). This kHz-order linewidth controllable SFFL has significant practical value in the comparison testing and system optimization of coherent optical communication.
Funding
National Key Research and Development Program of China (2016YFB0402204), NSFC (11674103, 61635004, 61535014, 51132004, and 51302086), the Fundamental Research Funds for Central Universities (2015ZM091 and 2017BQ002), China National Funds for Distinguished Young Scientists (61325024), Natural Science Foundation of Guangdong Province (2016A030310410), and the Science and Technology Project of Guangdong (2013B090500028, 2014B050505007, 2015B090926010, and 2016B090925004).
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