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An extended cavity Ti:Sapphire oscillator exhibits stable operation for positively chirped pulses, while in the negative chirp regime multiple pulses are present in the cavity. At the border of these regimes automodulations, being an effect of the interplay between population inversion, laser medium polarization and the laser pulse field, appear. Two particular instabilities: period doubling and chaotic behavior of the pulse train envelope are observed. Complex temporal evolution of the pulse spectrum within the modulation period is investigated.
©2010 Optical Society of America
1. Introduction
Passively, Kerr-lens modelocked Ti:Sapphire oscillators have been basic tools in ultrafast phenomena laboratories for nearly twenty years. While their stability was a subject of extensive studies [1–7], still many aspects of their behaviours and dynamics are far from being understood.
Most of the research on Ti:Sapphire oscillators’ performance focus on multimode instabilities governed by the laser cavity geometry [1–5] and thus directly dependent on the round trip time. In these works, the ABCD matrix formalism is used and changes of the pulse temporal width, chirp, cavity mode radius, wavefront curvature and pulse energy are taken into account. The geometry and dispersion of the cavity combined with power-dependent losses and self phase modulation due to Kerr effect, are shown to be responsible for self-pulsations at the longitudal mode separation frequency [1–5]. Yet, none of these approaches was able to predict the existence of automodulations occurring at much lower frequencies.
Automodulations of this type (AM), which manifest them self as a slowly (compared to the pulse separation) varying envelopes of the laser output, have been observed in many other lasers [8–11], both single- and multimode ones. This phenomenon is usually described in terms of coherent nonlinear coupling mechanisms of the field and the active medium [8–11]. In particular AM, with periods in the range of 3 – 6 us, has been observed by Xing at al [6]. in a Ti:Sapphire oscillator for different positions of the cavity concave mirror, Jasapara et al. [7], have shown that the spectrum of the pulses under the envelope changes with the AM period.
In the present paper we report on the experimental evidence of nonlinear dynamics of an extended cavity Ti:Sapphire oscillator. We demonstrate and investigate automodulations of the laser pulse trains and their instabilities: period doubling and chaos.
2. Experimental setup
Figure 1(a) presents the Ti:Sapphire oscillator with the cavity extended by a Herriott cell [12]. A detailed description of this construction has been presented in [13]. A 3-pass Herriott cell reduces the laser repetition rate to 13.4 MHz. Doubled Nd:YAG laser (Coherent Verdi V-10) is used as the pump. Stable modelocking is observed for a variety of cavity configurations, similar to those presented by Lin et al. [3], – these can be attained by moving mirror CM2 in range of 1.15 mm from the inner limit of the stability region (ILSR). Maximum pulse energy of more than 220 nJ is observed for the “fish mode” (FM [3]) with CM2 positioned 0.95-1.15 mm from ILSR. AM however were observed only for vertically elongated (VE) beam profile (“vertical ellipse” mode [14]) corresponding to the CM2 mirror being closer to the Ti:Sapphire crystal (0 to 0.5 form ILSR). Intracavity dispersion may be controlled by changing the insertion of the prism P1.
Fig. 1 Experimental setup: Ti:Sapphire oscillator (CM1, CM2 – concave mirrors, f = 50 mm, C – 5 mm Ti:Sapphire crystal, P1, P2 – fused silica prisms, M1, M2 – flat mirrors,, OC – 15% output coupler) with the cavity extended by a Herriott cell (MI, ME – injection and extraction flat mirrors, M – flat mirror, GVD = −40 fs2, CM concave mirror, f = 2000 mm, GVD = −40 fs2) and pulse diagnostics system (spectrometer, m – monochromator, PD1, PD2 – fast photodiodes, RF spectrum analyzer and oscilloscope).
Laser pulse train is measured with two fast photodiodes (ThorLabs DET10A/M and Altechna HSP-V2), one of them being placed after a monochromator (CVI, f = 1/8m). By recording pulse trains and scanning the wavelength range with the monochromator, the spectra of individual pulses under the AM envelope were recorded with the oscilloscope (LeCroy 104Xi). Time-integrated optical spectrum is recorded with a grating spectrometer (Ocean Optics USB4000) and the pulse train RF spectrum is observed with an RF spectrum analyzer (HAMEG HM5530).
3. Laser Stability
Figure 2(a) presents a diagram of the Ti:Sapphire oscillator stability as a function of two parameters: insertion of the prism P1 and the pump power, for CM2 mirror positioned 0.23 mm from ILSR resulting in the VE laser beam profile in the far field. Three characteristic spectra for different regions of stability are also displayed. For small prism insertions (N, negative total cavity dispersion), stable modelocking with a superimposed continuous wave peak appears. Increasing the prism insertion brings the laser to the regime of multiple pulses (M). These can be observed directly in the pulse trains, as spectral interference in the laser spectrum and as side bands in the measured laser pulse autocorrelation trace. Adjacent region is an area of broad (100 – 120 nm at 10% of the maximum intensity), structured spectra (B, Fig. 2(c)). Here, the oscillator is vulnerable to any small perturbations that end the modelocking. Further on, there is the area of square-shaped spectra (P, Fig. 2(d)) characteristic for the positive cavity dispersion [15]. This is the region were the laser is most stable in the modelocked operation. Interferometric autocorrelation measurements show that the shortest pulses (40 – 60 fs, depending on the pump power) are observed for broad spectra. This is also the regime of the largest pulse energies: 80–90 nJ. Outside of this region the autocorrelation width rises to approximately 150 fs at the edges of the modelocking area and pulse energy is between 55 – 75 nJ.
Fig. 2 Measured stability map of the extended cavity Ti:Sapphire laser operating in the VE beam profile configuration (0.23 mm from inner limit of the stability region) (a): CW – continuous wave, N – gauss-like spectra with CW peak, M – multiple pulse, B – broad spectra, P – square-like spectra. Also shown are sample spectra in the three regions: (b), (c), (d).
From the stability diagram one can see that the range of parameters for which modelocking is observed in the extended cavity laser is much wider than for a standard, 100 MHz oscillator [2]. This is also the case for a wide range of CM2 mirror positions, they can be varied within about 0.5 mm range for a single beam profile with no observable effect on the overall stability.
For the VE beam profile AM can be observed between positive cavity dispersion (P) and broad spectra (B) areas.
Similar map pattern, nevertheless without the AM region, is observed for the laser aligned in the FM configuration.
4. Automodulations
Figure 3(a) shows a pulse train recorded from the laser in the AM regime. The energy of the pulses is modulated and the period of this modulation varies with the pump power between 4 – 6 μs (Fig. 3(b)). This is comparable to the life time of the lasing state (3 μs in Ti:Sapphire [16]), and is similar to this reported previously for a standard modelocked oscillator [6,7]. The modulation period decreases as the pump power is increased, this dependence being characteristic for AM [10]. The visibility of the pulse envelope, defined as (Emax-Emin)/(Emax + Emin) can be as high as 0.8.
Fig. 3 Recorded pulse train in the AM regime (a). AM period as a function of the laser pump power (b). Pulse trains in the AM period doubling regime (c). One of the pulse trains in the AM period doubling regime (c) recorded with the photodiode placed after the monohromator tuned to 758 nm (d).
Figure 4 presents the temporal evolution of the laser spectrum in the modulated pulse train. This has been composed by recording simultaneously the laser pulse train with the fast photodiode PD1 and the pulse train after the monochromator with the fast photodiode PD2. Within the AM period, the pulse spectrum evolves from a gauss-shaped for the lowest pulse energies, through a square-shaped as the pulse energy increases, and finally, at the maximum energy, becomes “M”-shaped. After that, a new, central, gauss-like feature emerges and the side bands disappear.
Fig. 4 Spectrally resolved pulse train measured in the AM regime. Pulse train profile is shown on the top and the integrated spectrum (red), compared with the averaged spectrum measured independently (black) on the right.
Average pulse duration in the AM regime is 180 – 200 fs, which is consistent with the results of Jasapara et. al [7].
Stability of the AM, contrary to the modelocking stability of the laser itself, is very sensitive to a number of parameters. The width of the AM region in the prism insertion parameter changes as the CM2 mirror position is varied. Nevertheless, the AM would always appear on the border between the broad spectra (B) and positive dispersion (P) regions of the stability map. Entering the AM region always results in a change of the laser optical spectrum – one of the slopes of the square-like spectrum (Fig. 2(d)) becomes tilted.
As the laser is tuned towards the borders of the stable AM region, instabilities appear. Among them, period doubling behaviors with different visibility of the modulation can be observed. Figure 3c presents a measured pulse train with period doubling clearly visible, and one of its spectral components (Fig. 3(d)). Measured temporal evolution of the laser spectrum in the period doubling regime is displayed in Fig. 6 . The spectrum temporal evolution is similar to that of the stable AM – initially Gauss-like spectrum becomes square and “M” shaped as the pulse energy increases.
In Fig. 5(c) a pulse train recorded with the chaotic-like behavior of the AM is presented along with one of its spectral components in Fig. 5(d). It is worth noting that the chaotic behavior is present in the pulse train envelope. This is revealed in the pulse train Fourier Transform: Fig. 7 presents the photodiode signal RF spectrum measured with a spectrum analyzer. The pictures span 1 MHz centered at the oscillator’s repetition frequency (13.4 MHz). Figure 7(a) shows the RF spectrum of the AM pulse train: apart from the repetition frequency, components with sum and difference of the repetition frequency and the AM frequency (below 200 kHz) are visible. RF spectrum in the period doubling regime is presented in Fig. 7(b). New peaks, corresponding to half of the AM frequency, emerge between previously present peaks. Figure 7(c) depicts the RF spectrum of the chaotic AM signal. The low frequency (close to the AM frequency) components appear – the signature of the chaotic behavior.
Fig. 5 Recorded pulse trains of the AM in the chaotic regime (a) and one of its spectral components (centered at 758 nm) (b). Different, “stable-looking” pulse train in the chaotic regime (c) and one of its spectral components at 758 nm (d).
Fig. 7 Measured RF spectra of the pulse train in the automodulation regime (a), automodulations with period doubling (b), and chaotic behavior of the automodulations (c). Display spans 1 MHz centered at 13.4 MHz.
Interestingly, chaotic behavior can closely resemble stable modelocked operation (Fig. 5(c)). Yet, while spectrally resolved, deep modulations of the pulse energy are visible (Fig. 5(d)).
5. Conclusions
We have presented a detailed study of the stability of a passively modelocked, extended cavity Ti:Sapphire oscillator. The laser works most stably in the positive cavity dispersion regime. We demonstrate a well-defined range of parameters where automodulations of the laser pulse trains occur. Two instabilities of automodulations were observed: period doubling and chaos.
Contrary to the previously reported chaos-like transients in Ti:Sapphire modelocked oscillators, related to the high RF frequencies, close to the repetition frequency [1–5] these cannot be explained by cavity-geometry-related effects. The behaviors we observe appear at low frequencies and are AM-related – like automodulations themselves, they are governed by the nonlinear laser dynamics involving changes of the population inversion, laser medium polarization and the laser pulse field [8–11]. Jasapara et.al [7]. proposed theoretical model explaining regular AM, although occurring in different range of dispersion than in our paper, anyway they do not consider the dynamics of AM laser output. To our knowledge these dynamical effects have not been reported or predicted before. We believe that the knowledge of these processes can be used for the verification of the advanced models describing Ti:Sapphire lasers dynamics.
6. Acknowledgement
T. K. acknowledges support of the Foundation of Polish Science MPD Program co-financed by the EU European Regional Development Fund. P.W. gratefully acknowledges generous support of the Foundation for Polish Science founded by a grant from Iceland, Liechtenstein and Norway through the EEA Financial Mechanism.
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