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We report a synchronously-pumped femtosecond diamond Raman laser operating at 890 nm with a slope efficiency of 32%. Pumped using a mode-locked Ti:Sapphire laser at 796 nm with a pulse duration of 194 fs, the bandwidth of the Stokes output was broadened to enable subsequent pulse compression to 65 fs using a prism-pair. Modelling results provide an understanding of the physical mechanisms involved in the Raman conversion of femtosecond pulses, supporting an in-depth characterization of these ultrashort pulsed lasers.
© 2015 Optical Society of America
Introduction
Wavelength conversion of standard ultrafast lasers sources such as Ti:sapphire lasers can be a cost-effective route to access new wavelength ranges. Synchronously-pumped optical parametric oscillators are well-established for the conversion of femtosecond laser pulses e.g [1]. and can reach a wide range of wavelengths. We have recently demonstrated an alternative approach to the conversion of femtosecond laser pulses using a synchronously-pumped diamond Raman laser [2]; this approach can be somewhat simpler than optical parametric oscillators since Raman lasers do not require crystal phase matching.
Stimulated Raman scattering (SRS) is an inelastic scattering process where an incident pump beam passing through a Raman-active medium can generate and amplify a Stokes beam of longer wavelength than the pump leaving the material in an exited state. Raman conversion in solid-state media has been investigated in the continuous-wave (CW) [3–5], nanosecond [6] and picosecond [7–10] regimes. Single-pass SRS conversion of femtosecond pulses has been demonstrated [11, 12] in which some spectral broadening was observed. By resonating the Stokes beam and using synchronous pumping, a much lower threshold can be obtained, and efficient conversion of pulse trains from standard femtosecond oscillators can be achieved [2]. We found that self- and cross-phase modulation (SPM, XPM) caused significant spectral broadening of the wavelength-shifted femtosecond pulses, resulting in a Stokes output pulse with sub-100 fs pulse duration [2]. In this paper, we investigate in detail the characteristics of a femtosecond diamond Raman laser pumped by a Ti:sapphire laser, and compare our experiments to a numerical model that includes SPM and XPM. Compared to our earlier result [2], we now generate almost twice as much output power and a 30% shorter output pulse duration. We also observe evidence of transient back-conversion from the Stokes field to the fundamental field.
1. Experimental setup
The experimental set up for our synchronously-pumped Raman laser is shown in Fig. 1. Diamond was chosen as the Raman material because of its high gain coefficient and relatively large Raman shift (1332 cm−1) compared to most other Raman crystals, in addition to its potential for high average power operation. The diamond crystal (Type IIa, CVD-grown, 8 mm-long) had broadband AR-coatings from 796 nm - 1200 nm. The Ti:sapphire pump laser generated 194 fs pulses at 796 nm with a pulse repetition frequency of 80 MHz. The pump pulses from the laser were positively chirped, with a transform limit of approximately 130 fs. The pump beam was polarized parallel to the [111] axis of the diamond crystal: this axis has approximately 30% higher Raman gain than the [110] axis, and for this orientation, the Stokes output was polarized parallel to the pump as expected. The pump beam was focused through the input mirror M1 into the centre of the diamond crystal, reaching a focal spot radius ω0 = 25 µm.
Fig. 1 Layout of the diamond Raman laser and external pulse compressor. λ/2: half-wave plate; PBS: polarizing beam splitting cube; L1, L2: mode matching lenses; L3: focusing lens; M1: ROC = 200 mm, HR @ 890 nm, HT @ 796nm; M2: ROC = 200 mm, HR @ 890 nm; M3: plane mirror, HR @ 890 nm; M4: plane mirror, output coupler T = 6.2% @ 890 nm. External compression used two broadband 700 – 1100 nm mirrors and a dispersion-compensating prism-pair.
The Raman laser was configured as a ring cavity, consisting of two concave mirrors (M1 and M2, radius of curvature (ROC) = 200 mm) and two plane mirrors (M3 and M4). A separation of approximately 206 mm between M1 and M2 produced a TEM00 mode at the centre of the diamond with a similar beam waist (ω0 = 25 µm) to the focused pump. The cavity round-trip time was closely matched to the pump laser interpulse period by translation of mirror M4, with M2 and M3 separated by a distance of approximately 1000 mm, M3 and M4 by 1650 mm, and M4 and M1 by 897 mm. For the pump wavelength of 796 nm, we expected the Stokes spectrum to be centred around 890 nm. Mirror M1 had T = 99.5% around 796 nm; M1, M2, and M3 had R>99.9% for 800 to 920 nm; output coupler M4 had a roughly constant transmission of T = 6.2% for 870 to 920 nm.
The pump pulse and Stokes were measured using second harmonic generation (SHG) frequency-resolved optical gating (FROG). We fully characterized the laser by measuring the spectra, pulse duration and pump-to-Stokes power conversion. These experimental results are presented below with support of numerical modelling.
2. Results
2.1 Laser power and spectrum
We measured a pump-to-Stokes laser slope efficiency of 32% as shown in Fig. 2. The laser threshold was 0.74 W, and a power output of 820 mW was obtained for the first-Stokes at the maximum pump power. The beam quality factor M2 for the first-Stokes output was 1.35.
Fig. 2 The average Stokes output power vs. pump power, showing a maximum output of 820 mW and a 32% slope efficiency. The right-hand axis shows the residual pump power after passing through the diamond crystal. Inset: Stokes spectrum obtained at the maximum output power - the line shows the wavelength of 890 nm associated with a diamond Raman shift (1332 cm−1) of the 796 nm central pump wavelength.
The residual pump power after passing through the diamond crystal is also shown in Fig. 2. We depleted approximately 50% of the pump power at the maximum power; since only 820 mW of this power is output in the Stokes beam, and allowing for the 11% quantum-efficiency loss incurred in the Raman scattering itself, we estimate an intracavity round-trip loss of 4.5% for the Stokes beam.
The characteristics of the pump and Stokes pulses were analysed using SHG FROG. Figure 3. shows each of the measured pulses in the time domain. The pump pulse from the laser was 194 fs in duration, and positively chirped with a transform-limited duration of 130 fs. The residual pump pulse after being depleted during the transit through the diamond crystal was lengthened to 254 fs. The first-Stokes output pulse duration was measured to be 362 fs, and was strongly positively chirped. The Stokes output pulse was compressed using a dispersion-compensating prism-pair (N-SF14 glass). The optimal separation between the prisms to compensate for the dispersion of the Stokes pulse was 820 mm. After this external compression, the first-Stokes pulse had a pulse duration of 65 fs.
Fig. 3 Temporal pulse shapes from FROG measurement. Clockwise from top-left: pump pulse from Ti:sapphire laser; the residual pump pulse after passing through the diamond; the first-Stokes output pulse after compression; first-Stokes output pulse before compression.
We attribute the strong positive chirp on the Stokes pulse to group-velocity dispersion (GVD) and SPM; the normal material dispersion tends to create a positively chirped pulse with the red spectral components leading the blue, and SPM reinforces that chirp and increases the bandwidth of the Stokes field. This conclusion is supported by the distinctive shape and the broadening of the spectrum compared to the pump. The inset of Fig. 2 shows the first-Stokes spectrum, which is a similar shape to that in [2] with two sharp peaks on either side, with approximately 30 nm peak-to-peak. Note that the slight positive chirp of the pump pulse will also tend to favor a positively chirped Stokes pulse.
2.2 Numerical simulations
To explore the mechanisms for the spectral broadening and the irregular shape of the Stokes spectrum, we used a numerical rate-equation model adapted from that previously developed for picosecond synchronously-pumped Raman lasers [13]. First results from this adapted model were presented in [2] and cavity parameters were changed to suit experimental conditions here. We compare the Stokes spectra from experiment and the simulations, shown in Fig. 4. The model closely reproduces the observed width and distinct shape of the Stokes spectrum. If SPM is neglected in the model, a much narrower centrally-peaked spectrum is predicted, confirming that SPM is the key process driving the spectral behaviour of the laser. Because the Stokes field in the diamond crystal is cavity-enhanced, the peak intensity of the intracavity Stokes field is much higher than for the pump field; the model confirms that XPM of the Stokes field by the pump is not significant compared to SPM by the Stokes field itself.
Fig. 4 Comparison of first-Stokes spectra from experiment (solid line) and from simulation (dotted line). The vertical line shows the 890 nm wavelength associated with a Raman shift in diamond of the 796 nm central wavelength of the pump laser.
Continuous-wave, nanosecond and picosecond Raman lasers do not usually exhibit the effects of SPM. The resonant associated with the Raman process tends to be more than an order of magnitude larger than the non-resonant electronic responsible for self-phase modulation. However, while SPM is a near-instantaneous effect, the Raman nonlinearity is not and has a characteristic dephasing time . For ‘transient’ pulses of duration much shorter than the Raman gain coefficient is suppressed by a factor of order [14]. In this regime, for a fixed pump pulse energy, increasing the peak intensity by reducing the pulse duration does not increase the Raman gain, and the gain and laser threshold are determined by the pulse energy alone [14]. However, SPM continues to increase as the pulse duration is reduced, and so for sufficiently short pulses, we expect SPM to become significant. For diamond, we have 6.8 ps [15], and so with our <200 fs pump pulses, we are in the strongly-transient regime. As an illustration, in direct comparison with the picosecond Raman laser in [10], the present highly-transient femtosecond Raman laser has a similar Raman threshold in terms of pump pulse energy (tens of nanojoules), despite having more than an order of magnitude shorter pulse duration and so significantly higher peak intensity. While SPM was important in the present laser, it was not significant for the picosecond counterpart.
A benefit of numerical modelling is that it allows us to look at the pump and Stokes pulses in the time domain as they transit the diamond crystal, giving insight into the pulse-forming mechanism for the Stokes pulse. The simulation results shown in Fig. 5 compare the pump pulse and the Stokes pulse before and after a pass through the crystal, with the cavity length adjusted for maximum output power. (A full animation of the development of the pulses during the transit of crystal is available online.) The laser has reached steady state, and so the Stokes pulse must be unchanged after each full round trip. Note that the repetition rate of the Raman laser must then match that of the pump laser – if the natural repetition rate of the Raman laser (in the absence of gain) is detuned, the gain must reshape the pulse on each round trip to delay or advance it as required to meet this criteria.
Fig. 5 Comparison of Stokes pulse and pump pulse before (a) and after (b) the crystal. The Stokes pulse exiting the crystal also has an associated GVD on it, the final Stokes pulse is represented by the blue line. The fundamental pulse represented by the red dashed line. Plots (a) and (b) have the same intensity scale. (Media 1 shows the amplification of the Stokes pulse during a single transit through the crystal, followed by the effects of GVD, shift to account for cavity length mismatch, and loss.)
The simulations are carried out in a frame moving with the Stokes group velocity, and so the Stokes pulse is stationary in this frame, and is merely reshaped by the Raman gain, SPM and dispersion. Dispersion of course also results in a difference in group velocities of the pump and Stokes pulses. This group delay difference in diamond is 46 fs/mm; with our 194 fs pump pulses then the pump pulse will shift by its own full-width in relation to a point in the Stokes pulse after propagating 4.5 mm.
The pump pulse leads the peak of the Stokes pulse at the crystal entrance, becoming depleted as it progressively lags behind the Stokes pulse. While SPM is calculated continuously as the simulation progresses, GVD and passive losses are calculated once per round trip. The amount of GVD per round-trip is 1240 fs2 (155 fs2/mm in diamond, and with negligible GVD from the mirrors), and the loss is set to 10.7% (4.5% passive loss, and 6.2% output coupling). After Raman amplification, and the application of the GVD and loss, the Stokes pulse is returned to its original shape (in amplitude and phase) as required. Note that the wings of the Stokes pulse do not see any significant Raman gain since they do not overlap at all with the pump pulse; these wings are nevertheless in steady-state, with the passive losses compensated by power transferred from the body of the pulse into the wings by GVD.
The steep trailing edge of the Stokes pulse and oscillation in its tail is caused by local back-conversion of the Stokes power to the pump field. This occurs when the pump pulse becomes locally depleted to zero, and the persistent phonon field regenerates the pump field with a pi phase shift [16]. The phonon field is quickly depleted since phonons are destroyed in this back-conversion process, and phonons are regenerated with the usual phase for scattering power to the Stokes field, resulting the oscillation in the Stokes power in the tail of the pulse.
2.3 Behaviour with pump power and cavity detuning
We studied experimentally the Stokes spectrum as a function of pump power, and compared the measured spectra to our simulations. Since SPM should increase as the intracavity Stokes field becomes more intense, we expect the spectrum to broaden as the laser is pump harder. The experimental measurements are shown in Fig. 6(a) and compared to simulations (Fig. 6(b)). Again, we observe close agreement between experiment and simulations. We predict that by increasing the intracavity Stokes intensity further, the broadening will continue to increase; this might be achieved using a higher pump power, using a smaller cavity waist, or by compressing the Stokes pulse within the cavity (discussed below).
Fig. 6 First-Stokes spectra as a function of input pump power with results done by (a) experiment and (b) simulation.
We have measured the effect of adjusting the cavity length on output power and Stokes spectrum. The tuning range was found to be approximately 10 µm. The Stokes output power as a function of cavity length detuning dx, with dx = 0 defined as the cavity length giving maximum Stokes output power, is shown in Fig. 7. Negative detuning, corresponding to shortening the cavity, was tolerated to a much greater extent than positive detuning, as expected for such a transient Raman laser. With negative detuning, the Stokes pulse must be preferentially amplified on its trailing edge during each transit in order to effectively delay the pulse; this trailing edge amplification is naturally consistent with the build-up of phonons in the crystal as the pulses pass by [13]. Conversely, positive detuning requires preferential amplification of the leading edge of the Stokes pulse: this is more difficult to achieve, requiring the pump pulse to substantially lead the Stokes pulse at the entrance of the crystal, with a corresponding decrease in output power even for small positive detuning. Note that the model predicts the highest output power for a cavity that is 1 µm shorter than for perfect synchronization, suggesting that the experimental dx = 0 ‘maximum-power’ cavity length does not correspond to ‘exact synchronisation’ cavity length; this is not unexpected for the non-instantaneous Raman process. The simulation in Fig. 5 includes this 1 µm cavity mismatch as a shift applied to the Stokes pulse position relative to the next pump pulse.
Fig. 7 Plot of first-Stokes output power as a function of cavity detuning, with maximum output of 820 mW at dx = 0 µm (by definition).
Spectra were also collected at maximum pump power for different cavity lengths, shown in Fig. 8(a). At maximum Stokes output power (defined at cavity length detuning of dx = 0 µm) the Stokes spectra was broadest. This is expected, since higher intracavity intensity increases the SPM. As the cavity is made shorter (negative dx) the peak at the blue end of the spectra diminishes with the red peak shifting towards the center wavelength of 890 nm.
Fig. 8 Plots of first-Stokes spectra as a function of cavity detuning, with results done by (a) experiment and (b) simulation.
The simulation results Fig. 8(b) for the changing cavity length also agree well with the experiment. We see the collapse of the blue-end peak on the Stokes spectra and the shifting of the right-end peak towards the Raman center at 890 nm as the cavity is made gradually shorter.
2.4 Comparison to prior results
We now contrast the results of our previous paper [2] with the results presented here. Table 1 presents a summary of the differences between the present laser and that in [2]. The present laser used a plane-cut AR-coated diamond crystal with the pump polarized along the [111] axis, compared to a Brewster-cut diamond crystal with the pump polarized along the [110] axis in [2]. The Brewster crystal causes a beam expansion in the tangential place as the pump beam refracts into the diamond, by a factor of the refractive index (n = 2.4 for diamond); the absence of this expansion in the present laser increases the pump intensity in the diamond. The [111] axis also has ~30% higher Raman gain than [110]. These factors explain the much lower threshold (by a factor of 2.2) in the present laser despite using the same output coupling mirror. With the two lasers operating with similar slope efficiency, the maximum output power was significantly increased in the present laser; we thus attribute the increased bandwidth and associated reduction in the compressed Stokes pulse duration from 95 fs to 65 fs to increased SPM associated with the near-doubling of the intracavity Stokes power. The present laser could operate over a significant range of cavity length detuning, enabling us to explore how this variable affected the laser behavior; the cavity tuning range for this laser was 10 μm compared to less than 2 μm in previous femtosecond work [2]. We attribute this increased tolerance to detuning to the fact that the present laser operated much further above threshold, and so more significant pulse reshaping, required when the cavity length is detuned [13], was possible. Note that our earlier 6 ps synchronous Raman laser [10] had a cavity tuning range of 445 μm. Consider that as the pulse duration of the pump and Stokes pulse gets shorter, we expect the tolerance to cavity mismatch to decrease; in the present laser the 362 fs intracavity Stokes pulse is almost 20-times shorter.
Table 1. Comparison of diamond crystals and experiment results.
3. Conclusion
We have presented an in-depth characterisation of a synchronously-pumped femtosecond Raman laser, generating 65 fs pulses centred at 890 nm from pump pulses of 194 fs centred at 796 nm. We explored the importance of both SRS and SPM in shaping the pulse spectrum, which ultimately provide an effective means for pulse shortening of our first-Stokes output.
We highlight the future possibility of using prisms pairs in the cavity or using chirped mirrors to make the overall chromatic dispersion anomalous. Coupled with SPM, this opens the way for soliton-like pulse forming mechanisms, which may lead to a broader spectrum and shorter pulse durations from this type of laser. A similar laser design has been studied in fibres [17-19] ; the solid-state counterpart could avoid stability issues caused in these lasers by the very long cavities required.
While the present laser generated output centred at 890 nm, well within the capabilities of a tunable Ti:sapphire oscillator, we highlight that the laser is relatively insensitive to the pump wavelength. This Raman approach can extend the wavelength coverage of any available ultrafast laser source, by pumping with that laser source tuned towards the long-wavelength end of its range. The Raman laser can also be continuously tuned by tuning the pump laser, with no adjustments to the Raman laser necessary since there are no phase-matching considerations. We also hope in future to cascade the Raman laser to generate second-Stokes output, thus accessing even longer wavelengths. As an example of what may be possible using such a cascaded Raman laser, with a Ti:sapphire pump laser that can tune between 840 and 950 nm, one can reach all wavelengths from 840 nm to 1270 nm.
Acknowledgments
This work was funded by an Australian Research Council Linkage Project LP110200545, in association with M Squared Lasers Ltd. Michelle Murtagh is equally supported by an iMQRES scholarship at Macquarie University and Tranche 2 studentship at University of Strathclyde. Richard P. Mildren acknowledges the support of an Australian Research Council Future Fellowship (FT0990622). This work was carried out in part at the OptoFab node of the Australian National Fabrication Facility (ANFF).
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