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Soliton fibre laser with hybrid saturable absorber
S.Gray and A.B.Grudinin
We present an experimental study of a picosecond fiber soliton laser in which mode-locking is achieved by the combined action of MQW saturable absorber and nonlinear amplifying loop mirror (NALM). In this configuration a MQW sample acts not only as a saturable absorber but also as a passive phase modulator while the inclusion of NALM ensure fixed energy of the generated pulses. The laser stably operates at repetition rate of 250 MHz with timing jitter below 10 ps.
Passively mode-locked fibre soliton lasers are attractive sources of short optical pulses for laboratory and telecommunications applications because of their properties of simplicity, tunability and picosecond pulse generation.
There are two main types of passively mode-locked fibre lasers. The first type exploits the Kerr nonlinearity of optical fibres and usually such lasers operate in the soliton regime which results in excellent stability of individual pulses but also causes instabilities in the repetition rate which makes these lasers unsuitable for many applications. Recently, self-stabilization of the repetition rate has been observed in fibre lasers [1, 2]. This occurs because acoustic waves generated in the fibre by electrostriction cause slow perturbations of the laser cavity which modulate and retime of the pulses. Using this technique subpicosecond timing jitter has been achieved but the need for sensitive polarisation control still makes this device impractical.
Another type of passively modelocked laser is based on multi-quantum well (MQW) saturable absorbers [3-5]. This technique offers easy self starting and a stable repetition rate but often does not produce transform limited pulses. Therefore it looks rather natural to combine the desirable properties of both techniques in one configuration.
In this letter we describe experiments on a new design of fibre laser cavity which achieves these aims by combining the ease of self starting of saturable absorber modelocked lasers with the soliton shaping properties and intensity discrimination of a nonlinear amplifying loop mirror (NALM). The combined action of a semiconductor saturable absorber and a NALM form a hybrid saturable absorber which is able to suppress the spectral sidebands observed in soliton lasers and provide clean picosecond soliton pulses at the output. The presence of the semiconductor also provides a slow perturbation to the cavity which is able to provide self stabilization.
Figure 1. Experimental configuration. WDM = Wavelength division multiplexer;
PC = Polarisation controller
The configuration of the laser is shown in Fig. 1. A NALM is formed between the output ports of a 60/40 coupler and includes ~100 metres of standard telecom fibre, a polarisation controller and a 2 metre long Er/Yb codoped fibre amplifier pumped by a miniature Nd:YAG source providing 200 mW of launched pump power at 1064 nm. An InGaAs/InP MQW saturable absorber and Bragg reflector stack is butted to the input port of the NALM. The MQW consists of 82 periods of 65 Å thick InP and 78 Å thick InGaAs. The laser has two regimes of operation. In the first regime, square pulses are generated at the fundamental cavity frequency of 1.8 MHz for almost any position of the polarisation controller. The duration of the pulses can be varied from ~10 ns down to ~500 ps by varying the pump power to the amplifier while the peak power of the pulses is fixed by the power required for switching in the NALM.
The second regime of operation is reached by adjusting the polarisation controller to set the correct phase bias in the NALM for soliton pulses to be generated. When the laser entered this regime of operation it was found that passive stabilization of the soliton repetition rate occurred with the repetition rate at harmonics of the fundamental frequency. Once the correct bias in the loop has been set the laser remains stable for several hours and after being switched off will self start in the passive harmonically modelocked regime. By using polarisation maintaining fibre in the loop it may be possible to fix the phase bias in the NALM and remove any need for polarisation control.
Figure 2. (a) Pulse spectrum and (b) RF spectrum of laser output intensity (resolution 30 kHz)
Output spectra for the soliton regime of operation taken at a repetition rate of 250 MHz are shown in Fig. 2. Fig 2a shows a spectrum taken from the spare port on the WDM in the NALM. The spectral width is 1 nm indicating a pulsewidth of 2.5 ps. The spectrum also demonstrates 20 dB suppression of the spectral sidebands commonly seen in fibre soliton lasers. This is attributable to the combined intensity discrimination of both the NALM and the saturable absorber. Fig. 2b shows a spectrum taken from the spare port of the NALM. This clearly shows that the soliton part of the spectrum has been switched back into the laser by the NALM while the non-soliton radiation is rejected from the laser cavity.
A typical RF spectrum of the laser output intensity measured on a fast photodiode is shown in Fig.3. The main peak occurs at the pulse repetition rate while the smaller peaks are separated by the fundamental cavity frequency of 1.8 MHz. The spectrum demonstrates that adjacent modes of the laser are suppressed by over 40 dB and so once the laser is operating it is unlikely to switch between modes. The timing jitter of the pulses measured using RF spectra is typically less than 10 ps. The lowest measured jitter was 2.4 ps at a repetition rate of 240 MHz.
Figure 3. Illustration of the MQW refractive index changes using the simple model of equation (3) (solid lines) and the sinusoidal approximation defined by equation (4) (dotted lines) for (a) T/τ = 1 and T/τ = 2.5
The presence of the NALM in the cavity fixes the peak power of the pulses to give the correct nonlinear phase difference required for switching of the pulses. In the soliton regime of operation this also fixes the pulsewidth and quantizes the energy of the pulse which allows the pulse repetition rate to be easily tuned by adjusting the pump power to the amplifier. By varying the pump power launched into the amplifier from the mini-YAG we were able to tune the pulse repetition rate in the range ~100-400 MHz. To obtain higher repetition rates from the laser the mini-YAG was replaced by a high power YAG. In this configuration repetition rates of up to 1.5 GHz (>800th harmonic) were observed. However fluctuations of ~10% in the pump power create instabilities in the repetition rate due to extra pulses being created or disappearing from the cavity because of the quantization effect. Stable operation at such high harmonic frequencies would require stabilization of the pump power to 1 part in 103 which is obviously a disadvantage for generating very high repetition rates from this laser. Shortening the cavity length and operating at lower harmonics would reduce this requirement but this will generate shorter pulses and require higher pump powers.
To understand the mechanism responsible for the stabilization effect let us consider a stream of soliton pulses. When a pulse is incident on an InGaAs MQW saturable absorber the excitation of free carriers creates a refractive index change Δn, which can be as large as 0.1 . Relaxation of the carriers then drives the refractive index back towards the unsaturated value n0. Using a very simple model which neglects any effects due to saturation the time dependence of the refractive index can be described by
where τ is the free carrier lifetime.
A second pulse arriving at the saturable absorber sees a time varying refractive index which modulates the phase of the pulse and changes the carrier frequency by
where ω0 is the carrier frequency, z is the thickness of the saturable absorber andis the speed of light. Equation shows that Δω < 0 which decreases the group velocity of the second pulse and provides a repulsive force between the pulses. In a harmonically mode-locked laser this keeps the pulses apart and stops pulse bunches forming. The time dependence of Δω means that a delayed pulse is slowed down less than a premature pulse which shows that the phase modulation provided by the saturable absorber is capable of retiming the pulses and stabilizing the repetition rate.
When the laser operates in the harmonic regime we can treat the pulse stream incident on the absorber as infinitely long. The refractive index in the absorber can then be written as
where θ(t-mT) is the Heaviside function. It is easy to show from Eq.(3) that the depth of the refractive index modulation is always equal to Δn but the important parameter which determines the strength of the modulation is the value of dn/dt at time T when the next pulse arrives. It can be seen that dn/dt decreases as the ratio T/τ increases and that significant phase modulation will only occur for T/τ~1. For T/τ»1 n(t) varies very slowly and will not be effective in providing self stabilization.
To try and gain a more intuitive understanding of the self stabilization process in this laser we express this in the more conventional form of a sinusoidally varying phase modulator. This suggests defining an effective modulation depth in terms of the saturable absorber parameters Δn and T/τ to reflect the changes in modulation strength with pulse spacing. Since we are approximating equation by a sinusoidal function it is important that the first derivatives of the two functions are similar for t≈T where modulation of the pulses occurs. Considering the form of the first derivative of equation this suggests an expression of the form
where the definition of n0' ensures that n(T) = n'(T). From the definition of Δneff it can be seen that for large values of T/τ the strength of the modulation is small but increases as the ratio T/τ decreases which is in agreement with the original expression. This is demonstrated in Fig. 4 where n(t) and n'(t) are plotted for comparison for the values T/τ = 0.5 and 2.5 and n0 = 3. For T/τ = 0.5 the effective modulation depth is Δneff = 0.15 while for T/τ = 2.5 it is substantially reduced to Δneff = 0.009 and it can be seen that in both cases the two curves are quite similar at the modulation peak justifying the approximations made above. However it should be noted that Δneff approaches infinity for T/τ«1. In this case the approximations made are no longer valid but in practice this situation is usually avoided.
Using the approximate form of the refractive index perturbation we can apply soliton perturbation theory to estimate the timing jitter. Following the same procedure as  the variance of the timing jitter is given by
where G is the amplitude gain of the amplifier, Ωf is the gain bandwidth, T is the pulse separation normalized to the pulsewidth, N0 is the number of photons per unit energy and k is the wavenumber.
Equation suggests that using a saturable absorber with a shorter lifetime should allow higher repetition rates to be achieved with subpicosecond timing jitter. However as discussed above this would require a highly stabilized pump source. Note also that the use of a too fast saturable absorber at low repetition rates could not bring any good results.
To measure the lifetime of the carriers in our sample we performed a pump/probe experiment where the transmission of a weak probe pulse through the MQW was measured as a function of the time delay from an intense probe pulse. This yielded a lifetime for the absorption of the MQW of 15±3 ns. (Note that we actually require the lifetime of the refractive index changes but since both processes depend upon the density of free carriers in the semiconductor the lifetimes for absorption and refractive index will be similar.) The carrier lifetime is of the same order of magnitude as the soliton pulse spacing observed in the laser which further confirms that the MQW sample acts not only as a saturable absorber but also as a passive phase modulator.
Using typical values of T/τ = 0.25 and Δn = 0.1 gives an effective refractive index modulation depth of Δneff = 0.35. Taking the other parameters to be G2 = 5, Ωf = 10, T = 3000, N0 = 3×108 and z = 1 μm gives σ = 0.4 or 0.6 ps in physical units. This is in line with the lowest observed jitter of 2.5 ps at a repetition rate of 240 MHz.
In conclusion, we have demonstrated a new configuration of a passively modelocked fibre soliton laser using a hybrid saturable absorber formed by a semiconductor MQW and a NALM. In this configuration we have observed self stabilization of the pulse repetition rate and have shown that phase modulation by carrier induced refractive index changes in the semiconductor is the mechanism responsible for this effect. The laser is capable of generating 2.5 ps transform limited soliton pulses at repetition rates of up to 1.5 GHz. The repetition rate of the laser is tunable by adjusting the pump power although a very stable pump source would be required for high repetition rates. The combined action of the NALM and MQW saturable absorber provides up to 20 dB suppression of the spectral sidebands.
Timing jitter as low as 2.5 ps has been observed which is in good agreement with theoretical estimates. The laser is able to self start and remains stable for periods of several hours making it potentially very useful as a source of picosecond optical pulses.
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Optics Letters (1996) Vol.21(3) pp.207-209
Copyright University of Southampton 2006