53-dB phase noise suppression and Hz-range ... - OSA Publishing

Vol. 25, No. 16 | 7 Aug 2017 | OPTICS EXPRESS 19216

53-dB phase noise suppression and Hz-range linewidth emission in compact Brillouin/erbium fiber laser MO CHEN,* CHENYU WANG, JIANFEI WANG, HONG LUO, AND ZHOU MENG Academy of Ocean Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China *[email protected]

Abstract: We demonstrate 53-dB phase noise reduction in a compact Brillouin/erbium fiber laser (BEFL), which uses 4-m erbium-doped-fiber (EDF) providing both the Brillouin gain and linear gain. A 360-kHz-linewidth laser diode is used as the Brillouin pump (BP) and excites the Brillouin Stokes light. The linewidth of the BEFL is estimated 1.8-Hz based on the correlation between the linewidth and phase noise. Experimental result demonstrates 6-Hz linewidth by beating the emission of two compact BEFLs. This fiber laser provides a simple and effective method to reduce laser phase noise and realize ultra-narrow-linewidth light. It presents many applications in such as interferometric fiber sensing, coherent optical communications, optical clocks, and precise spectroscopy. © 2017 Optical Society of America OCIS codes: (140.3510) Lasers, fiber; (300.3700) Linewidth; (290.5900) Scattering, stimulated Brillouin.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

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#285338 Journal © 2017

https://doi.org/10.1364/OE.25.019216 Received 23 Jan 2017; revised 22 Jul 2017; accepted 26 Jul 2017; published 1 Aug 2017


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1. Introduction Ultra-narrow-linewidth lasers are of great importance to many applications, such as in precise spectroscopy, optical communications, and sensors [1–4]. Stimulated Brillouin scattering (SBS), as one of the main nonlinear effects in fibers, has attracted wide research interests for narrow-linewidth light emission [5]. A 1550-nm light injects in a silica fiber as the Brillouin pump (BP) and generates a narrow-band (typically 20 MHz) Brillouin gain spectrum with its central frequency down-shifted about 11 GHz. The frequency shift is named Brillouin frequency shift. Brillouin fiber lasers (BFLs), based on SBS in single-mode fiber (SMF), present narrow linewidth [6]. Especially, linewidth narrowing is observed that the phase noise of the BP is transferred to the Brillouin Stokes after being strongly reduced and smoothed under the combined influence of the acoustic damping and the cavity feedback [7]. In 1991, S. P. Smith et. al. experimentally demonstrated 30-Hz BFL pumped by 120-kHz BP [8]. In 1994, J Boschung et. al. indicated 3-Hz linewidth emission in a BFL [9]. In 2000, Alexis Debut et. al. theoretically analyzed the linewidth narrowing in the BFLs [7] and they experimentally validated the theory in 2001 [10]. Nevertheless, the BFL needs a critically pump-coupled resonator for maximum pump power inside the cavity. An electronic feedback circuit is required to hold the pump frequency at the center of the cavity resonance. The complex electronic controls may add noise to the laser and cause mode hopping. Brillouin/erbium fiber lasers (BEFLs) overcome the need of pump-coupled resonators by incorporating an intra-cavity erbium-doped fiber amplifier (EDFA) [11]. The EDFA compensates for the cavity losses while the laser still originates from the Brillouin gain. The Brillouin pump threshold is inversely proportional to the gain fiber length. The first BEFL adopted 100-m SMF to provide enough Brillouin gain. Such a long cavity makes the laser mode-hopping easily. The total cavity length should be less than 10-m for single-mode operation considering the 20 MHz Brillouin gain spectrum width. High-nonlinearity special fibers (20 m photonic crystal fiber) are utilized to shorten the gain fiber length, while the cavity loss is greatly increased and the pump threshold is over 100 mW [12]. Pre-pump technique is used to overcome the conflict between short SMF and sufficient Brillouin gain [13]. A low-threshold (~20 mW) BEFL was demonstrated with 5-m SMF as the Brillouin gain medium based on this technique. The above BEFLs have two sections of fibers separately as the Brillouin gain fiber and linear gain fiber. A compact BEFL is afterward proposed using a length (≤ 4m) of erbium-doped fiber (EDF) as both the Brillouin and linear gain media [14]. The linear gain eases the difficulty of exciting SBS in short gain fiber. One milliwatt BP power is sufficient to originate the operation for the BEFL. The 980 nm pump threshold is as low as about 30 mW due to the low cavity loss. Stable single-mode operation is indicated in the compact BEFL. The low phase noise of the compact BEFL was indicated in 2013 [14]. The linewidth narrowing of this kind of BEFL was investigated in 2014 and 2015 [15,16]. However, the phase noise suppression in the BEFL has not been studied. And there have been no research on the comparison between the phase noise suppression and the linewidth narrowing.


In this paper, we study the phase noise suppression in the compact BEFL in detail. Phase noise reduction in the BEFLs with 4 m and 1.5 m EDF is studied, respectively. And the case when the two BEFLs are cascaded is also investigated. The situations with different BPs, a normal distributed-feedback laser diode (DFB-LD) and a low-noise external-cavity laser diode (LD), are analyzed. The Hz-range linewidth of the compact BEFL is predicted according to the correlation between phase noise and linewidth. The prediction is validated by experiment in the end. 2. Structure and principle 2.1 BEFL structure The configuration of the compact BEFL is shown in Fig. 1. The components of this laser are all polarization-maintaining (PM), guaranteeing the single-polarization state of the laser. A 1550 nm LD provides the BP for the BEFL through an optical circulator. A length of commercialized PM EDF (Coractive), pumped by a 980 nm laser diode through a 1550 nm/980 nm wavelength-division multiplexer (WDM), acts as both the Brillouin and linear gain media in the laser. A narrow-band (~0.3 nm) tunable optical filter (TOF) is set with its passband covering the Brillouin Stokes wavelength. This narrow-band TOF suppresses the amplified spontaneous emission (ASE) outside its passband and ensures the operation wavelength of the BEFL near the Brillouin Stokes wavelength. The 3 dB optical fiber coupler extracts out the BEFL light. TOF

BP

1

3

3 EDF

2

1

2

BEFL Output

980 nm

Fig. 1. Configuration of the compact BEFL: BP, Brillouin pump; EDF, erbium-doped fiber; TOF, tunable optical filter.

2.2 BP threshold The BP injects into the EDF. Its threshold Pth to excite SBS in a length of fiber is determined by the following relation [5]: Pth ≈

21 Aeff

(1)

g B Leff

Where Aeff is the fiber effective mode area, gB is the fiber Brillouin gain coefficient, and Leff = [1-exp(-αL)/α] is the fiber effective length. When fiber length L is short, Leff≈L. Equation (1) satisfies the passive fibers. When EDF is pumped by 980 nm light, the linear gain should be taken into consideration. The following coupled nonlinear equations are used to calculate BP threshold of pumped EDF [17]: dP0 dz dP1 dz

= gP0 −

= − gP1 −

g B P0 P1 Aeff g B P1 P0 Aeff

(2)

(3)


P0 and P1 represent the power of BP and Brillouin Stokes, respectively. The linear gain coefficient g is assumed constant for simplicity. When BP is around threshold, pump depletion caused by the Brillouin Stokes can be neglected. The distribution of the BP power along the fiber is as following:

P0 ( z ) = P0 (0) exp( gz )

(4)

Putting Eq. (4) into Eqs. (2) and (3), the following relation is derived: ln[

P1 ( L ) P1 (0)

] = − ln G −

gB L Aeff ln G

P1 (0)[G − 1]

(5)

Where G = exp(gL). Equation (5) is transformed to Eq. (6) for better displaying Pth: [ln(

η GPth PN

) − ln(G )]

ln(G )

Aeff

gB 1 − G

−1

= GLPth

(6)

PN is power of one noise phonon, η is a coefficient equal to P1(0)/Pth. The effective area Aeff of EDF equals to 19 μm2 and gB equals to 5 × 10−11m/W. When EDF is not pumped by 980 nm light, BP threshold is shown as the line with rectangles in Fig. 2. The BP threshold decreases from 8 W to 0.8 W as the EDF length varies from 1 m to 10 m. When the EDF is pumped by 980 nm light, BP thresholds are shown as the lines with circles (G = 3 dB) and triangles (G = 10 dB). The parameters are η = 0.01 and PN = 0.5 nW in the calculations. Compared with the situation without 980 nm pump, BP threshold is lower with the assistance of linear gain. The larger the linear gain, the lower the BP threshold. The BP threshold is only about one hundred of milliwatts when 10-m EDF has 10-dB linear gain.

Fig. 2. Simulations of BP threshold when the EDF is with 0, 3 dB and 10 dB linear gain.

When the EDF is in a resonator, the BP threshold shall further reduced under the influence of the cavity feedback. The boundary condition is P1(L) = RP1(0),where R is the power reflection ratio of the cavity. Putting the boundary condition in Eq. (6), we get the following relationship: Pth =

ln( RG ) ln G Aeff (1 − G )

gB L

(7)

Ideally, Pth is zero since RG = 1 at threshold condition. Practically, RG is a little smaller than 1 because of the spontaneous emission noise. Assuming RG = 0.9 and R = 0.5, BP threshold in 4-m EDF is predicted to be about 7 mW. Hence, the difficulty of exciting SBS in a very short EDF in a resonator is very low due to the combined influence of linear gain and cavity feedback. Experimental results have demonstrated that 1 mW BP is sufficient for this BEFL.


2.3 Phase noise suppression Phase of the BP and BEFL are represented as Φ0(τ) and Φ1(τ). The quantities of interest for the determination of phase noise spectrum are the variances σ (τ ) = [Φ (τ ) − Φ (0)] and 2

0

σ (τ ) = [ Φ (τ ) − Φ (0)] 2

1

1

1

2

. The variances σ and 2

0

σ

2 1

2

0

0

are simply connected through the relation

[7]. In phase diffusing model [18], σ (τ ) = 2πΔν τ where Δν0 represents the linewidth of the BP. The relation between the expectations of phase noise spectra of the BP and BEFL is given by σ =Kσ 2

0

2

2

2

1

0

E{PΦ ( f )} 1

E{PΦ ( f )}

=

0

0

Δν 1 Δν 0

=

1

K

2

(8)

The coefficient K = 1 + γA/Гc, where γA and Гc represent the acoustic damping rate and the cavity loss rate, respectively. The damping rate γA equals to πΔνB, where ΔνB is the full-width of half maximum (FWHM) of the Brillouin gain spectrum. The cavity loss rate Гc equals to – cln(RG)/nl, where c/n is the light velocity in the cavity length l. R is the reflection ratio of the output coupler, and G is the linear gain of the EDF. The coefficient K is largely dependent on RG. A large RG leads to strong phase noise suppression and a low BP threshold in BEFL. Assuming the BEFL of 10-m cavity with RG = 0.9, the phase noise suppression ratio K2 is about 888. Considering the practical BP threshold is less than 1 mW, K2 is predicted no less than 4 × 104. 3. Experimental results and discussions 3.1 BEFL optical spectrum A compact BEFL of 4-m EDF is constructed. Its total cavity length is about 10 m. The optical power of the 1550 nm DFB-LD and the 980 nm pump are 5 mW and 105 mW, respectively. The optical spectra of the BP and BEFL are measured by an optical spectrum analyzer (OSA, 0.02-nm resolution). The injected BP excites SBS in the EDF and generates backward Brillouin Stokes with Brillouin frequency shift. The Brillouin Stokes is amplified by both Brillouin gain and linear gain. Once the 980 nm pump is over threshold, BEFL operates and emits light. As shown in Fig. 3, the optical spectrum of the BEFL consists of the BP-induced Rayleigh scattering and wavelength-upshifted Brillouin Stokes. The wavelength of the BP is 1548.197 nm, while that of the BEFL is 1548.286 nm. The 0.089 nm discrepancy corresponds to the Brillouin frequency shift of the EDF.

Fig. 3. Optical spectra of the BP and BEFL.


3.2 Phase noise suppression The phase noise is measured by a high-accuracy unbalanced Michelson fiber interferometer shown in Fig. 4. The Faraday rotating mirrors (FRMs) are used to avoid polarization fading effect and to ensure high interferometric visibility. The interferometer was shielded well from environmental noise sources, such as acoustic and vibration noise, by encapsulating it in a housing specifically designed for ambient noise isolation. A piezoelectric (PZT) fiber stretcher is incorporated into one arm of the interferometer to introduce phase modulation. The interferometric signals were received by a low-noise photoelectric detector and an analog-to-digital (A/D) convertor, and then processed by a set of software in the computer. The phase noise of the laser under test was demodulated from the interferometric signals by the phase generated carrier (PGC) technique [19]. Considering the strong phase noise suppression in BEFL and the background noise of the measuring system, we choose a rather large (185 m) optical path difference (OPD) for the interferometer to fully separate the phase noise spectra of the BP and BEFL.

Fig. 4. Experimental setup for phase noise measurement.

The phase noise spectrum of the BP is the blue curve as shown in Fig. 5. Its phase noise is −27 dB/Hz1/2 at 1 kHz frequency. Note that 0 dB/Hz1/2 equals to 1 rad/Hz1/2. The phase noise spectrum of the BEFL is the red curve in Fig. 5. The noise level of the BEFL is much lower than that of the BP. It is −80 dB/Hz1/2 at 1 kHz frequency. Totally 53 dB reduction is realized after the BP is transferred to Brillouin Stokes in the BEFL. The BEFL cavity loss rate should be 0.9932, according to Eq. (8). The BP threshold of the BEFL is calculated to be 0.45 mW, which agrees well with the practical value. It should be noted that there are two peaks at 3.2 kHz and 3.8 kHz, respectively, which are probably the noise from electrical perturbations in the laser cavity. As to why the noise value at 1 kHz is used for comparison, this is because signal frequency of some practical interferometric sensors like fiber hydrophones is usually around 1 kHz. The phase noise level at 1 kHz is significant and usually adopted for investigation. Besides, the BEFLs in the experiments are laid on the table unshiededly. They are susceptible to low-frequency (at 100-Hz range) ambient disturbances. The effect of ambient disturbances on laser performance can be neglected at 1 kHz frequency.

Fig. 5. Phase noise spectra of BP and BEFL of 4-m EDF.


The linewidth of the compact BEFL can be estimated according to Eq. (8). The linewidth of the BP is 360 kHz, measured by 25-km self-delayed heterodyne technique. It is narrowed by 53 dB after being transferred to the Brillouin Stokes. Hence, the linewidth of the compact BEFL is predicted 1.8 Hz. We used 25-km-delayed self-heterodyne technique to measure the BEFL linewidth [20]. To reduce the effect of 1/f noise, the 20-dB spectral width is used to estimate the BEFL linewidth. It is indicated with ~1 kHz linewidth. This estimated value is very coarse and far from the real value, for the instrument resolution is only 2 kHz with 100 km delay fiber. Voigt profile fitting method was then used to separate the Lorentzian component and the Guassion component in the measured spectrum. Three cases with 25-km, 50-km, and 100-km delay fiber were studied. The Lorentzian linewidth was indicated about 50 Hz with 25-km and 50-km delay fiber. The increase of the delay fiber permits the white frequency noise to fully generate the Lorentzian lineshape. Insufficient delay time leads the Lorentzian part broadened and oscillatory [21]. The spectrum was well fitted by Guassion profile when the delay fiber is 100 km, which means the Lorentzian component is very small and almost zero. Hence, we infer that the value of 50 Hz obtained with 25-km and 50-km delay fiber is partially from the Lorentzian part broadening due to the insufficient delay time. The actual Lorentzian linewdith of the BEFL is close to zero, at least less than 50 Hz. As a result, we infer the calculated 1.8-Hz linewidth here is quite reasonable and well reflect its order of magnitude.

Fig. 6. Phase noise spectra of BEFL of 1.5-m and 4-m EDF.

A second BEFL of 1.5-m EDF is also established. Its total cavity length is about 6 m. Its 980 nm pump power is 110 mW. The phase noise spectrum of this BEFL is shown in Fig. 6. The spectrum of the BEFL of 4-m EDF is also presented in the figure for better comparison. It is −75 dB/Hz1/2 at 1 kHz frequency, 5 dB higher than that of the BEFL with longer EDF. This can be explained by Eq. (8). The ratio of K2 decreases to 48 dB for the cavity length l is reduced to 6 m. Disregarding the calculation, intuitionally, lasers with shorter cavity are more sensitive to thermal fluctuations which shall affect the phase noise. The BEFLs with 4-m and 1.5-m EDF are cascaded. The output of the first BEFL is as the BP for the second BEFL. The noise spectrum of the cascaded BEFLs is shown in Fig. 7. The spectra of each of the BEFLs are also shown in the figure for comparison. The phase noise of the BP can be suppressed by 53 dB and 48 dB in the first and the second BEFL, respectively. Intuitionally, it shall be suppressed by 101 dB in total after the two cascaded BEFLs. The phase noise, however, nearly the same as that of the single BEFL. This interesting phenomenon can be explained as following. The ability of phase noise reduction is not infinite. The light has been narrowed to Hz-range. When this Hz-range light is injected into the second BEFL, the phase noise suppression is no longer just determined by the acoustic damping rate and the cavity loss rate. The spontaneous scattering becomes innegligible in this situation. Meanwhile, the environmental fluctuation plays an important role. In simple words,


the linewidth almost reaches the limit of this laser. A second-stage interaction is useless for a narrower linewidth which is determined by the spontaneous scattering and thermal noises. Considering the two BEFLs are barely placed on the table in the lab, it is perhaps better to do some package to isolate from the environmental perturbations for better phase noise performance.

Fig. 7. Phase noise spectra of BEFL of 4-m EDF, 1.5-m EDF and the two BEFLs cascaded.

The cascaded BEFL performs even higher phase noise level at frequencies below 1 kHz than that of the BEFL with 4 m EDF. This is due to the effect of the BEFL with 1.5 m EDF. The phase noise of the BEFL with 1.5 m EDF is higher than that of the BEFL with 4 m EDF at frequencies below 1 kHz. After the output of the BEFL with 4 m EDF is injected into the BEFL with 1.5 m EDF, the bad effect of the noiser BEFL influences the cascaded BEFL. In the present days, external-cavity laser diodes (RIO ORION module from Redfern Inc.) represent the state-of-the-art technology with low noise and narrow linewidth (~3 kHz) [22]. We use this laser as the BP to learn its phase noise reduction in the BEFL. The experimental results are shown in Fig. 8. The phase noise of the external-cavity LD is −57 dB/Hz1/2 at 1 kHz frequency. That of the BEFL is −80 dB/Hz1/2 at 1 kHz. The phase noise of the BEFL is lower than that of this LD, but it is not lower than that when an ordinary LD acts as the BP. This result is very meaningful that Hz-range-linewidth light can be realized by using an ordinary laser source in the BEFL.

Fig. 8. Phase noise spectra of low-noise external cavity LD (blue) and BEFL (red).

3.3 Direct measurement of BEFL linewidth Although the linewidth of the BEFL is predicted to 1.8 Hz in the previous section, there has no direct measurement result which can demonstrate this BEFL has Hz-range linewidth. Here, we carry out the experiment to validate the Hz-range linewidth of the compact BEFL. The


configuration of the experimental setup is shown in Fig. 9. The light of the 360-kHz-linewidth LD is split into two beams through a 3 dB coupler as the Brillouin pump for the two BEFLs, respectively. The BEFL1 is the one consisting of 4-m EDF, while BEFL2 consists of 1.5-m EDF. The output of BEFL1 is firstly amplified by an EDFA, and then its frequency is 200MHz-shifted by an acousto-optic modulator (AOM). The output of the AOM and BEFL2 beat with each other through another 3 dB coupler. The light is then detected by an optical detector and analyzed by an electrical spectrum analyzer (ESA). A variable optical attenuator (VOA) is used to protect the detector from high optical power.

Fig. 9. Experimental setup to measure the Hz-range linewidth of the BEFL.

The bandwidth resolution of the ESA is set to 1 Hz. The spectrum of the beat signal is shown in Fig. 10. The 3-dB linewidth of the BEFL is indicated to be 6 Hz, which is at the same order of magnitude as the predicted value of ‘1.8 Hz’. The Hz-range linewidth of this BEFL is validated by both theory and experiment.

Fig. 10. Beat note of two BEFLs with 4 m EDF and 1.5 m EDF.

3.4 Discussions Firstly, it is worth discussing the difference between the Brillouin gain spectra of the EDF and the passive fibers in the BEFL cavity, and its possible effect on the laser emission. In our proposed BEFL, there are totally 4 kinds of fibers in the cavity, including the EDF, the tail fiber of the circulator, the tail fiber of the TOF, and the tail fiber of the coupler. The circulator, the TOF, and the coupler are purchased from different companies. We do not have the fibers they used, and their detailed Brillouin frequency shifts are unknown. Generally, different fibers have different Brillouin gain spectra. Stimulated Brillouin scattering is initiated from the spontaneous scattering noises along the whole length of the fibers in the BEFL cavity, according to the distributed fluctuating model [23]. But when the final singlefrequency resonation is established, only the fiber whose Brillouin gain spectrum covers the lasing light provides the Brillouin amplification. We measured the Brillouin frequency shift of the EDF, which was about 11.06 GHz. We also measured the beat frequency of the BEFL output and the 11-GHz-down-shifted signal of the BP, finding it is 50MHz. Hence, the Stokes frequency is about 11.05 GHz down shifted from the BP, which matches the Brillouin frequency shift of the EDF well. As a result, we deduce the EDF provides the Brillouin gain.


Secondly, the phase noise suppression in this low-threshold compact BEFL is of great importance in high-coherence fields. For example, the phase noise or the linewidth of the light source affects the sensitivity of interferometric fiber sensors. Many methods have been proposed to realize low-noise light source, such as erbium-doped fiber laser (EDFL) based on saturable absorber and external cavity LD. These lasers present ~3 kHz linewidth, and are widely used in present fiber sensors. The compact BEFL simply and effectively generates Hzrange-linewidth light by using an ordinary commercialized DFB-LD. It presents great potential in interferometric fiber sensors. And the BEFL can also find important applications in many other fields which have even higher requirement on laser linewidth, such as gravitational wave detection, optical atomic clocks, and quantum computation [24,25]. 4. Conclusions In summary, the phase noise suppression in compact BEFL is studied. The phase noise of the BP is much reduced after being transferred to the Brillouin Stokes due to the combined influence of the acoustic damping and cavity loss rate. The linear gain in the EDF eases the difficulty of exciting SBS in short gain fiber and improves the phase noise suppression ability by enhancing the resonator finesse. A compact BEFL of 4-m EDF is constructed. The phase noise of this BEFL is 53-dB lower than that of the BP (a DFB-LD with 360-kHz linewidth). The phase noise suppression ratio is related to the cavity length. The phase noise of the BEFL of 1.5-m EDF is 48 dB lower than that of the same BP. Reducing the phase noise of the BP does not further decreasing the BEFL phase noise because it has reached the fundamental limit due to the spontaneous scattering and thermal noise. The linewidth of the BEFL is predicted 1.8 Hz according to the correlation between laser linewidth and phase noise. Direct measurement indicated that it presents 6-Hz linewidth by beating the output of two BEFLs. Hz-range ultra-narrow-linewidth light can be achieved by using an ordinary LD through the compact BEFL. It presents many applications in interferometric fiber sensors, optical atomic clocks, quantum computation, and so on. Funding Major Applied Basic Research Project in the Research Program of National University of Defense Technology (ZDYYJCYJ20140701); National Natural Science Foundation of China (61605244, 61505258); and Scientific Research Project of NUDT (JC15-11-02).