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We report self-pulsed operation of fiber Raman master oscillator power amplifiers, in which the amplifier and oscillator are pumped by one pump source successively. The pulse period is one or half of the round-trip time of the oscillator, depending on the optical length of the amplifier. A simple model is constructed to explain the observations qualitatively.
©2005 Optical Society of America
1. Introduction
Fiber Raman devices are very flexible in wavelength as gain is available at arbitrary wavelengths with right pump source, and can be widely tunable for broad Raman gain spectrum in silica fiber. Therefore, fiber Raman devices are very attractive for a variety of applications. Efficient high power fiber Raman lasers have been realized [1–3] and commercialized [4]. Here we report highly efficient pulsed operation of fiber Raman master oscillator power amplifiers (MOPA) without any active switching device.
The recent development of fiber Raman laser benefits mostly from the advancement in high power Yb doped fiber lasers, so all of them operate at near infrared wavelength regime. Frequency conversion of fiber Raman lasers to visible regime could open up potential in tunable visible fiber-based laser source, or visible lasers at wavelength not obtainable by other means [5]. In particular, frequency doubling of 1178nm fiber Raman laser or amplifier to 589nm is very interesting for the potential application in laser guide star adaptive optics [6–8]. In this context, pulsed operation of fiber Raman laser source is interesting for better frequency conversion efficiency.
In this paper, fiber Raman MOPAs, which are pumped by one laser source successively (firstly amplifier, then oscillator), are investigated. Because the oscillator and amplifier share the same pump, they are coupled to each other; the output of fiber Raman MOPAs can be self-pulsed in certain configurations. In the experiments the pulse periods are one or half of the round-trip time of the oscillator, depending on the optical length of the amplifier.
2. Experimental setup
Experimental setup is shown in Fig.1. The laser system consists of an oscillator and an amplifier, which are spliced together directly. A double clad Yb fiber laser at 1100nm is used as a pump source. Through a WDM (1100nm/1178nm), it pumps the amplifier and oscillator successively. The laser at 1178nm from the oscillator propagates leftward, gets amplified, and finally emits out through the WDM. In the experiments, several configurations with different outcoupling of the oscillator and different length of the fibers used in oscillator and amplifier are investigated. The fibers used in experiments are HI1060 single mode fiber or phosphosilicate single mode fiber.
Fig. 1. Schematic of experimental setup. FBG1 is a partially reflective fiber Bragg grating (15%, 30%, 50%), and FBG2 is a highly reflective (99%) fiber Bragg grating.
In such kind of system one may imagine following processes. When the oscillator is on, the pump laser, which reaches the oscillator, would be depleted because part of its energy is consumed by amplifying the laser. Then the pump laser reaching the oscillator could be lower than the laser threshold in certain case, so the oscillator could be off. When the oscillator is off, the pump laser would not be depleted. So the pump laser reaching the oscillator could be larger than the laser threshold again.
Mathematically, such kind of processes could lead to a fix-point or limiting-cycle solution depending on parameters, which means cw or repetitive pulsed operation, respectively. In experiments we see both type of operations indeed.
3. Results and discussion
In one of the experiments, the fiber used in the amplifier is a phosphosilicate fiber, and in the oscillator a HI1060 fiber, the reflectivity of the FBG1 is 15%. The laser system reaches threshold at a pump power of 3.7W, and remains cw until 4.4W. At 4.5W, the laser output becomes sinusoidal wave suddenly. Increasing the pump power further, the sinusoidal wave develops to pulses. Fig.2 shows typical waveforms at pump power of 4.5W, 6.7W, and 13.8W, respectively. The period of pulses is about 4.28µs, which doesn’t change with the pump power.
To understand the origin of the period, we measure the optical fiber length. Simple fiber Raman lasers with each fiber as gain medium are constructed, the beat frequencies of their cw output are measured. For the phosphosilicate fiber and HI1060 fiber used in above MOPA experiment, the beat frequencies are found to be 323.3kHz and 116.7kHz, respectively. Corresponding round trip times are 3.09µs and 8.57µs, and corresponding fiber lengths are about 320m and 890m, respectively (the refractive indexes of both fibers are considered as 1.445). One may notice the period 4.28µs is half of the round-trip time of the oscillator, 8.57µs.
Fig. 2. Waveforms of laser output at pump power of a) 13.8W, b) 6.7W, and c) 4.5W, respectively. The fiber used in the amplifier is a 320m phosphosilicate, in the oscillator an 890m HI1060 fiber, and the reflectivity of FBG1 is 15%.
Experiments with other configurations are also investigated. When FBG1 is changed to one with reflectivity 30%, the laser threshold decreases to 2.4W, the pulsing threshold increases to 12W, and the pulse period is still 4.28µs. When the reflectivity of FBG1 is 50%, the laser threshold decreases to 1.8W; the laser is cw in full pump range. In the case that the fiber used in the amplifier is a 710m phosphosilicate fiber, in the oscillator the same HI1060 fiber, and FBG1 15%, the laser threshold is 4.1W, the pulsing threshold is 5W, and the pulse period becomes 8.57µs. In the case that the fiber used in the amplifier is the 890m HI1060 fiber, in the oscillator the 320m phosphosilicate fiber, and FBG1 30%, the laser threshold is 4.9W, the pulsing threshold is 7.8W, and the pulse period becomes 3.1µs.
Figure 3 shows typical waveforms from three configurations at pump power near 11W. From these experiments we see that the periods of laser dynamics are one or half of the round trip time of the oscillator, depending on the length of the amplifier.
A simple model is constructed to explain the observations. The classical treatment of the stimulated Raman scattering process in optical fibers yields a system of first-order coupled partial differential equations [9,10].
where P, I+, and I - stands for the power of the pump laser, the forward propagating Stokes emission, and the backward propagating Stokes emission, respectively; v is velocity of light in fiber; gr, αP, and αR are Raman gain coefficient, loss coefficient for pump light and loss coefficient for Raman signal. 2hυPB and hυRB stands for the contribution of spontaneous Raman emission, where h is Plank constant, υP and υR are the frequencies of the pump and Stokes emission, B is a Boltzmann factor [9], which is very close to 1 here. The boundary conditions are
where L and La are the fiber lengths in the oscillator and amplifier; 0, La, and La+L in bracket represent for the positions of the output end, FBG1, and FBG2, respectively; The subscript l and r stand for left and right side of the point; R 1 and R 2 are the reflectivity of the FBG1 and FBG2, respectively; P 0 is input pump power.
Since the observed dynamics are periodic, we try a general periodic solution of following form
Substitute to the boundary condition, after some algebra we find k must be π/L. So laser output is periodic with a period of 2L/v in general. However, in the experiments we have observed not only 2L/v, but also half of the round-trip time, L/v. This means all coefficients, CI+m and CI-m, with odd m equal to zero in that case. We try numerical simulation to explain this.
Fig. 3. Waveforms of laser output in three configurations with pump power near 11W (the curves are offsetted for clear presentation). From top to bottom, a) the fiber used in the amplifier is a 710m phosphosilicate fiber, in the oscillator an 890m HI1060 fiber, and the reflectivity of FBG1 is 15%; b) in the amplifier a 320m phosphosilicate fiber, in the oscillator an 890m HI1060 fiber, and FBG1 15%; c) in the amplifier an 890m HI1060 fiber, in the oscillator a 320m phosphosilicate fiber, and FBG1 30%.
In numerical simulations, the partial differential equations are discretized in space dimension, thus transformed to a set of ordinary differential equations in time dimension, which can be numerically solved readily. Fig. 4 (top) shows calculated waveforms for two configurations at pump power of 12W. In both configurations, the reflectivity of FBG1 is 15% and in the oscillator an 890m HI1060 fiber, but the fiber in the amplifier is a phosphosilicate fiber of length (I) 320m and (II) 710m, respectively, which correspond to the experimental configurations. The periods are found to be 4.25µs and 8.54µs, respectively, which are slightly less than experimental data, 4.28µs and 8.57µs. The discrepancy can be attributed to the precision of the numerical simulations. The dependence of pulse period on the optical length of the amplifier can be understood. When the optical length of the amplifier is comparable with that of the oscillator, after the previous laser pulse goes out of the amplifier, the pump laser will not be depleted and enter the oscillator again. It will excite next laser pulse after one round-trip time. When the optical length of the amplifier is much shorter than that of the oscillator, the pump laser can re-enter the oscillator not long after previous laser pulse, and so exciting multiple pulses is possible during one round-trip time of the oscillator. Fig. 4 (bottom) shows calculated waveforms for the configuration (I) at pump power of 6W, 12W, and 18W, respectively. The period doesn’t change, and the waveform evolves from sinusoidal wave to pulses as observed in experiments. The model can also qualitatively reproduce other observations, such as the increase of pulsing threshold when output coupling decrease, the laser threshold and output power as a function of pump power, etc.
Fig. 4. top) calculated waveforms for two configurations at pump power of 12W: the reflectivity of FBG1 is 15%, in oscillator an 890m HI1060 fiber, in amplifier (I) 320m and (II) 710m phosphosilicate fiber, respectively, which correspond to the experimental configurations; bottom) calculated waveforms for the configuration (I) at pump power of 1) 6W, 2) 12W, and 3) 18W, respectively.
However, the rising edge of the calculated pulses is not as sharp as in experiments. The peak power is smaller than in experiments. The duty cycle of calculated pulses is generally larger than that observed in experiments. Possibly, there are some other effects, which assist the pulsed operation, not included in our simple classical model.
Figure 5 shows the laser output power as a function of pump power for three different configurations. Maximum average power of 10.7W is obtained with pump power of 19W, which is similar to that obtained in previous study using simple oscillator [3]. So efficiency of such a MOPA scheme is as high as of an oscillator. At higher pump power, they are all saturated due to emergence of amplified spontaneous Raman scattering at 1240nm, which is a Raman Stokes emission from 1178nm. Maximum peak power of 45W is obtained at pump power of 19W when the reflectivity of FBG1 15%, length of phosphosilicate fiber in amplifier 300m, and in oscillator an 890m HI1060 fiber.
Fig. 5. the laser output power as a function of pump power for three configurations with different reflectivity of FBG1, R1, length of phosphosilicate fiber in amplifier, La, and same fiber in oscillator, which is an 890m HI1060 fiber.
The linewidth of 1178nm pulses at saturation stage is ~0.6nm, which is too broad for some important applications like frequency doubling to generate a 589nm laser guided star for adaptive optics. But it is two times narrower than that observed in simple oscillator [3], where the same FBGs are used. This is because the oscillator operates not much over threshold. In numerical simulations we find linewidth can be reduced in some scale if one designs the system to keep the oscillator near threshold. This is our next experimental goal in fact. The polarization of output is random. To generated polarized output one can use polarization-maintaining fibers.
4. Summary
In summary, we report observation of self-pulsed fiber Raman master oscillator power amplifiers pumped by one laser source successively. The pulsing behavior results from the coupling of the oscillator and amplifier for sharing the same pump source. A simple model is used to explain the observations qualitatively. Efficiency of such a MOPA scheme is as high as of an oscillator.
Acknowledgments
This work is supported by the 21st Century COE program of Ministry of Education, Science and Culture of Japan. Yan Feng’s homepage is http://yanfeng.org/work.
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