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We propose a method to generate phase-locked pulses in the picosecond regime by using Stimulated Brillouin Scattering (SBS). The phase-locked comb is generated using only long length of fiber and a single frequency CW pump laser. We show that there is a phase relationship between multiple Stokes peaks in a cavity, which directly leads to pulsing without the need to add a mode-locking component. This generates highly coherent pulses in the order of ~10 ps. The repetition frequency, which is very stable is in the order of tens of GHz, is based on the SBS frequency shift and has a linear dependence with temperature (1 MHz/°C). Such a laser could therefore be used in high-speed optical clocks and optical communication system. This system allows the pulses to be generated at any wavelength by simply changing the pump wavelength.
©2012 Optical Society of America
1. Introduction
The idea of using Stimulated Brillouin Scattering (SBS) to generate pulses was initially proposed by Lugovoi and Korolev [1, 2]. SBS is a 4-wave mixing process, which may be simply described by the interaction of three principle waves, conserving energy and momentum: an optical pump, an acoustic wave and a Stokes wave [3]. SBS has the property of generating a very narrow bandwidth counter-propagating wave at a constant frequency shift determined by material properties. In a favorable configuration, SBS can be cascaded to generate multiples Stokes with a certain phase relation [4] which can enable pulsing. Phase locking of different Brillouin components to generate pulses has been demonstrated by Dianov et al. [5] in a short multi-mode fiber (MMF) Fabry-Perot cavity using an Nd:YAG crystal as the gain medium as well as by Damzen et al. [6] in a hexane gas cell, also within a Fabry-Perot cavity. In the latter case, the cavity length was adjusted so that the modes matched the SBS elements. This was done without a saturable absorber or any other non-linear component.
In the last decades, there has been increasing interest in intra-Stokes cavity mode locking [7] and relaxation oscillations [8] to generate pulses. A three-waves model using a Hopf bifurcation was proposed [9] and demonstrated [10, 11]. Soliton pulses [12] of such mode-locked lasers and phase modulation [13] were also explored recently.
In this paper, we demonstrate for the first time to our knowledge, a self pulsing SBS laser in a long ring cavity of single mode fiber (SMF) using an erbium doped fiber amplifier (EDFA) as the gain medium, which has the advantage of a low threshold and tuneable wavelength. Therefore, contrary to the limitations predicted by Dianov et al. [5], we demonstrate that a minimum of coherence can be maintained between multiple Stokes orders to allow the generation of ps pulses.
Our system gives rise to an SBS frequency comb, which has previously been widely explored for telecommunication application as multi-channel sources. The idea was first demonstrated by Hill [14] and since then many system have been proposed [15–20]. We will show here two equivalent systems to generate frequency combs of different frequency spacing and then show that each Brillouin laser does indeed generate a pulsed output of high stability.
2. Theory
In order to generate a pulse using multiple Stokes emission, either a constant or linear phase relationship must be maintained between the multi-Stokes at the output of the system. We are therefore interested here in the phase relationship between the multiple Stokes emission and the pump wavelength. SBS is generated from the coupling of a narrow bandwidth pump of wavelength λp and an acoustic wave of frequency ΩB. From the conservation of energy and of momentum, we get the following relations respectively:
Where ka, kp and ks are respectively the acoustic, optical pump and optical Stokes wave vector. Considering the acoustic wave ka acting as a travelling Bragg grating, since the refractive index is modulated by the acoustic pressure waves, and using since the wavelengths are almost identical, we can link the pump wave vector kp to the Stokes wave vector ks by Bragg grating relations [3] with the following equation:Where θ is the angle between scattered wave ks and the pump wave kp. Since in a single-mode fiber the only relevant directions are forward (θ = 0) and backward (θ = π), SBS will only occur in the backward direction owing to Eq. (2), with θ = π. Therefore, the wave vector of this Bragg grating, i.e. the acoustic wave ka, will be along the same axis.The Brillouin frequency shift corresponds to the acoustic frequency and can be explained by a Doppler shift of the pump frequency considering the propagating acoustic wave, as:
From the last relations of Eq. (1)-(3), we can see that the Stokes’ phase, i.e. its frequency ωs and wave vector ks, are linked to the pump’s phase by the acoustic frequency shift ΩB, which can be approximated to be constant for a small number of Stokes orders. Therefore, considering this approximation, we can safely assume a constant phase shift ΔφB from one Stokes wave (or seed) to another, ignoring dispersion for now. By considering now all the sources of phase shift in a long ring cavity of length L, the output phase for each Stokes j is:
Where φ0 is the output pump wavelength phase, Δφt is the phase delay due to a different cavity length ΔL from even and odd Stokes, which travel in opposite directions and may not see the same length, and Δφd is the first order dispersion delay for the length of cavity. Equation (4) is valid as long as the number of generated Stokes j orders is not too large, and the dispersion length is longer than the fiber used. The length of the fiber must be short enough so that the second order dispersion induced phase change between the Stokes waves remains << π/2. In the event of a large number of Stokes orders, we must consider the variation of ΩB, which changes from one Stokes order to another from Eq. (3) and leads to a variation of ΔφB. ΩB to the first approximation is given by:Where δΩB can be calculated from Eq. (3) as 2.8 MHz for SMF-28 silica fiber. This shift is negligible for a few Stokes orders since ΩB is ~10 GHz. However, for a large number of Stokes orders this frequency shift differential as well as the second order dispersion introduces a quadratic term in the Stokes phase φj, which degrades the pulses. The total phase shift must remain within the temporal coherence of the SBS laser, which is limited by the SBS bandwidth ΔνB and by the constancy of ΩB from one Stokes to the other. The bandwidth is linked to phonon lifetime TB and is therefore related to an internal material property:The SBS bandwidth is very small (a few MHz) and therefore has a long coherence length (~10 m of coherence length for 10 MHz bandwidth), which makes the constancy of ΩB the limiting factor. It was previously stated that such a frequency differential would be fatal to pulsing in a single-mode fiber [5], but our calculation and demonstration shows that this is not the case.
Another condition to generate pulses is to have multiple Stokes orders interacting with one another. By the Fourier transform, an increasing number of Stokes orders, and therefore a larger spectrum, leads to shorter pulses. In order to generate several Stokes waves, we must consider the threshold power for a single pass [3]:
Where gB is the Brillouin gain depending on material properties, Aeff the effective mode area and α the absorption coefficient. The threshold for 5-10 km length in SMF-28 fiber is ~4 mW. The threshold is even lower in a cavity configuration. Therefore, with a ~100 mW pump, it is easy to generate several Stokes orders and therefore generate pulses in the ps regime.3. Experimental
Two systems were explored in this paper, one combining even and odd Stokes into a single cavity, as shown in Fig. 1(a) and another separating even from odd Stokes into two cavities, where only the even Stokes orders come out at the output, as shown in Fig. 1(b). In both cases, we generate a frequency comb by cascading multiple Stokes waves. The pump generates the first order counter-propagating Stokes, spaced at 10.8 GHz for SMF-28, which in turns generates the second order Stokes in the direction of the pump, and so on. The output is measured with an Ando optical spectrum analyser (OSA) and with a FR-103XL auto-correlator.
Fig. 1 The experimental setup for pulse generation using SBS Stokes emission. (a) Single cavity system combining all Stokes and generating 10-30 ps pulses repeating at 11 GHz. (b) Two cavity system separating even and odd Stokes and generating 10-30 ps pulses repeating at 22 GHz.
The single cavity system is based on Song et al.’s design [16] with an added input coupler for the pump wavelength, which acts as a seed. This pump signal is a narrow band (few MHz) tuneable laser diode, which is amplified (50 to 400 mW) with a Pritel FA-30 erbium doped amplifier (EDFA) to be able to inject power into the system from the 95-5 coupler. Inside the cavity, another Pritel EDFA (pre-amp of LNHPFA-37) is used to amplify the injected pump wavelength and to generate multiple Stokes waves. A second 95-5 coupler is used as the output after the cavity amplifier, which is thereafter followed by a 5 to 15 km bundle of SMF-28 used as the SBS gain medium. Even and odd Stokes are combined from a Sagnac loop reflector composed of a 3 dB coupler and a 15 cm length of polarization maintaining (PM) fiber in between two polarisation controllers (PC). The PCs are set to optimize reflectivity (50% reflection was reached at 1550 nm). Because of the reflector, both even and odd Stokes waves are amplified in a single cavity system, which enable an ~11 GHz spacing frequency comb.
The two cavity system is very similar, but instead of using a Sagnac loop reflector after the 5 to 15 km bundle of fiber, a circulator is used to separate even order Stokes waves (in the direction of the pump), from the odd order Stokes waves (in the reverse direction of the pump). Therefore, only the pump and even Stokes (upper branch of the cavity) are emitted at the output. This system enables a 22 GHz spaced frequency comb.
4. Results
In both cavity systems, we modified the same parameters, which are the input seed power (controlled via the external EDFA), the cavity gain (controlled via the cavity EDFA) and the fiber length (5, 10 or 15 km). For both EDFAs, there is a minimum power required for the Brillouin output to be stable. If the input seed power is too low (<25 mW), the amplified spontaneous emission (ASE) of the cavity EDFA shows uncontrolled peaks, which sometimes generate an SBS frequency comb at a random wavelength, as was observed by Song et al. [16]. On the other hand, if the EDFA cavity gain is too low, the generated Brillouin frequency comb is unstable and noisy. Above these minimum levels, increasing one or the other simply increases the number of SBS peaks. The same behavior is observed for the 5 or 10 km SBS gain fiber. However, there is little change between the 10 and 15 km fiber spool, since the fiber is longer than the effective length (Eq. (8)).
An example of the measured spectra is shown in Fig. 2(a) for the single cavity system, where 9 stable peaks were observed (plus 4 more noisy peaks within −20 dBs from the first peak). The spacing between each peak is 10.87 GHz. The corresponding autocorrelation measurement is shown in Fig. 2(b), where the data is compared with the calculated values using a fast Fourier transform (FFT) for the same frequency spectrum. The background CW level is mainly due to the large intensity differences between different consecutive Stokes orders. Indeed, there is more than a 3 dB difference between the most intense Stokes wave and the consecutive one, and this decrease continues to remain around 2 to 3 dB between the subsequent SBS orders. This gives rise to a dominant carrier-wave being the most intense peak, which is slightly modulated by the subsequent peaks. Our FFT simulations have confirmed this dc background. The width of the generated pulses is of the order of 10 ps with a spacing of 92 ps, which corresponds to a comb frequency spacing of 10.87 GHz.
Fig. 2 Measurements on the single cavity system for a 10 km SMF-28 fiber. (a) Optical spectrum at the output of the system and (b) autocorrelation measurement at this same output port.
The generated frequency comb for the two-cavity system is shown in Fig. 3(a) . Six stable and 2 noisy peaks are observed within −20 dBs of the first peak. Since the odd Stokes are no longer present, the frequency spacing is doubled (21.74 GHz), which reduces by a factor of two the spacing between pulses, as shown in the autocorrelation measurement spectrum in Fig. 3(b). The data is again compared with the calculated values by the FFT for the corresponding spectrum.
Fig. 3 Measurements of the two counter-propagating cavity system for a 10 km SMF-28 fiber. (a) Optical spectrum at the output of the system at one cavity (even Stokes) and (b) autocorrelation measurement at this same output port
In both cases, cross-correlation (first pulse with the second pulse) is observed, which indicates high degree of coherence between the output pulses. The pulse width is also approximately the same for both setups since the width of spectrum is comparable, even though the frequency spacing between two Stokes waves is doubled.
By varying the cavity parameters (input seed power, EDFA cavity power and fiber length of 5, 10 or 15 km), we are able to alter the number of SBS peaks observed. By the Fourier relationship, a wider spectrum in the frequency domain will lead to shorter pulses. Therefore, we have a direct way of controlling the pulse width, as shown in Fig. 4 . A −20 dB criteria for the number of peaks was used for the width of the spectrum, since the peak intensity descends rapidly below the normally −3 dB criteria. It was also observed that even though the last peaks were very weak (−10 to −20 dB from first peak), they still influence the pulse widths. In some cases, a large difference between pulse widths is observed for spectra with same number of peaks. This can be explained by the imperfect criteria which does not take into account the shape of the spectrum, and which may be more favorable in one case compared to the other. These results are compared with calculated values by FFT of perfectly equalized peaks, which would be the ideal situation for tunability. Indeed, we can see that the FFT calculated values generally show a smaller pulse width and a more stable relationship of pulse width with number of peaks, mitigated by equalizing the output SBS wave intensities of each Stokes emission.
Fig. 4 Intensity pulse width (FWHM) for different number of generated spectral peaks in the 2 cavity system (22 GHz spacing). (a) Experimental measurement for different conditions giving a different number of peaks, which are within −20 dBs of the maximum. (b) Theoretical calculation for a number of perfectly equalized spectral peaks, which corresponds to the ideal situation.
5. Discussion
The autocorrelation measurement is in a non-collinear configuration, which avoids ASE contributions. ASE would appear as a noise spike since it is broadband, but this is not observed in our measurements. As can be observed by autocorrelation, the system indeed generates pulses, but there is however, a high CW background level in the measurements, which is also observed in the FFT simulation if we take into account the different intensities of the SBS peaks. This CW component takes away a good portion of the power of the pulses, which makes it a great nuisance. Therefore, in order to have more distinct pulses, we must equalize the intensity of the generated Stokes waves by bringing the subsequent Stokes within 3dB of the most intense wave to avoid a dominant carrier-wave, which would then make it comparable to the pulses generated by a standard mode-locked laser, in which many modes are present within the −3dB bandwidth, whereas in our case there are only a couple of modes. This would also ensure a more stable pulse and therefore a better pulse-width tunability of the system. ASE from the amplifier, the level of which is −16 dB (maximum) from the SBS peaks, can also contribute to a DC background level, although it would not be detected by the non-collinear autocorrelator and this contribution is negligible in this case (< 3% at most and ~0.5% on average), as also confirmed by our FFT calculations.
The first possible improvement would be to change the location of the cavity output. As it was shown in Ref [21], the position of different component in an SBS laser cavity influences the output spectrum. Reducing losses in the system can also improve the equalization of the spectrum, since the SBS cascading effect can be made more effective. Another possibility would be to use a frequency dependent filter customized to a specific SBS frequency comb output to equalize the SBS waves.
The time dependence of pulse intensity and repetition rate over long period (minutes) was observed to be very stable, however the signal was noisy, which may be due to the poor equalization, in other words, a high CW component. Stability of a Brillouin laser is an important factor to take into account [22], therefore losses and cavity parameters must be optimized to reduce noise to generate stable Brillouin emission.
The novelty of this system is that the pulses are not generated by cavity modes, which are spaced at 60 kHz for a 5 km cavity. We believe that these intra-cavity modes do not influence the pulsing of the SBS components because their initial phase is determined by the input pump wavelength and the subsequent phase shifts are determined by the Stokes phase shift ΔφB which is the same for all modes within the same SBS component.
6. Conclusion
We have demonstrated here the stable pulsing of a large ring-cavity single mode SBS frequency-comb laser with pulse widths down to 10 ps. This system uses the Stokes components instead of the intra-cavity modes to generate pulses. Similar to the one shown by Dianov [5] in a short multimode fiber Fabry-Perot cavity using an Nd:YAG crystal as gain medium, ours uses a long single mode fiber ring cavity with an EDFA as the gain medium, which has the advantage of low threshold and wide tunability within the Erbium band. Two systems with two different repetition frequencies, 10.87 GHz and 21.74 GHz, corresponding to the SBS natural frequency in SMF-28 have been demonstrated. The generated pulses were shown to be tuneable in the tens of ps range, where the pulse-width tunability comes from the number of generated Stokes waves. These pulses of an SBS cavity in single mode fiber were demonstrated experimentally and the results compared with simulations. Contrary to previously thought limitations due to phase matching and dispersion [5], we have demonstrated that pulsing occurs for several orders of cascaded Stokes waves. However, to generate sub-picosecond pulses, which would require over 50 Stokes waves, these problems would need to be resolved for the coherence and stability of the pulses.
The great advantage of a pulsed stimulated Brillouin scattering laser is that the repetition frequency is very stable since it depends only on material parameters and varies very slowly with temperature (1 MHz/°C) [23]. This variation in temperature can even be used to fine tune the SBS frequency with great precision. We note that it may be possible to alter the operation of such a laser using different types of fiber, such as dispersion flattened or compensating fiber modifying the threshold and/or the pulsing characteristics. Such a laser could be used as a high-speed optical clock or a modulated data source in telecommunications applications. We finally note that by selecting different Stokes orders, it would be possible to generate much higher repetition rate ps-pulses, or generate shaped pulses for applications in signal processing.
Acknowledgments
The following sources of funding are acknowledged for their support of this research: the Canadian Institute of Photonics Innovation (CIPI), RK’s Canada Research Chair on Future Photonics Systems- a program of the Government of Canada, and SL’s Natural Sciences and Engineering Research Council’s graduate scholarship, the Andre Hamer Prize.
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