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Abstract
We present a Kerr-lens-modelocked, three-element, diode-pumped Ti:sapphire laser producing 111-fs pulses at a repetition frequency of 1.02 GHz. Self-starting soliton-modelocked operation with an output power of 106 mW was obtained when the laser was pumped at 1.0 W with a single 527-nm laser diode. The output exhibits a relative intensity noise of 0.06% (1 Hz – 1 MHz) and locking of the repetition rate to an external reference is demonstrated with a phase error of 1.7 mrad (1 Hz–1 MHz). The simplicity of the laser makes it an attractive candidate as a module for integration into larger systems.
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1. Introduction
Diode pumping of Ti:sapphire [1,2] provides a route to the commodification of Ti:sapphire ultrafast lasers by breaking the reliance on a complex diode-pumped solid-state (DPSS) pump source. Furthermore, in the context of laser frequency combs, the ability to directly modulate the laser diode current at bandwidths commensurate with the upper state lifetime of Ti:sapphire provides direct and high-speed control of the carrier envelope offset frequency [3,4]. With appropriate management of the pump beam quality, soft-aperture Kerr-lens modelocking can be achieved in diode-pumped Ti:sapphire lasers, with examples of green [3] and blue [5] pumped lasers being reported with repetition frequencies as high as 420 MHz [3]. The extension to GHz repetition frequencies is made more challenging by the correspondingly lower pulse peak powers available, and so far no example of a diode-pumped GHz Kerr-lens-modelocked Ti:sapphire laser has been reported, to our knowledge. Here, we present an ultra-simple, three-element Kerr-lens-modelocked Ti:sapphire laser. This self-starting oscillator is pumped by a single green laser diode and provides 111-fs pulses with a repetition frequency of 1.0 GHz and an average power exceeding 100 mW.
2. Pump-beam formatting and resonator design
The laser was pumped by a single Nichia NDG7D75 laser diode, with a nominal beam divergence in the direction parallel (perpendicular) to the junction of 8.2° (42°) and emitting at 527 nm. The laser diode fast axis was collimated by an aspheric lens (f = 4.02 mm) immediately after the facet, and the slow-axis rays were subsequently expanded and collimated using a cylindrical telescope with a magnification of 6${\times} $ (Fig. 1(a)). A beam quality measurement of the fully collimated beam was made using a lens with a focal length of 80 mm and is represented in Fig. 1(b). The fast- and slow-axes M2 values were found to be 1.3 and 5.2 respectively (Fig. 1(c)). We confirmed that this choice of cylindrical telescope led to a symmetrical focal spot profile by imaging the focus after the 45-mm pump lens, obtaining a focus with dimensions of 18.5 µm ${\times} $ 20.1 µm. The spectrum of the pump diode is presented in Fig. 1(d).
Fig. 1. (a) Collimated beam profile after expanding the slow axis using a 6× cylindrical telescope. (b) Profile of the pump beam after focusing by an 80-mm-focal-length lens. (c) Divergence of individual pump beam axes and a Gaussian fit performed for each to estimate the M2 value. (d) Spectral intensity profile of the pump diode.
The laser cavity was a three-element resonator utilizing a plane-Brewster Ti:sapphire crystal and similar to the design first introduced by Ramaswamy-Paye in 1994 [6], but with the dispersion compensation provided by replacing the previously reported prismatic output coupler with a -550 fs2 coated GTI mirror. The crystal had an absorption coefficient of 4.1 cm-1 at 532 nm and a figure of merit specified as >200. The output coupling was implemented through the same crystal face used to in-couple the pump light by applying a dichroic mirror coating to the plane face which had 98% transmission at 520 nm and 99% reflectivity at 800 nm. This geometry has the advantage that the angular dispersion caused by the Brewster face is absent in this output and allows the cavity to be designed with the minimum number of intracavity elements. The out-coupled and p-polarized 800-nm light was collimated by using the same 45-mm-focal-length lens used to focus the pump light into the crystal, and a dichroic beam splitter was used to separate the output light from the incident pump light at 527 nm.
The cavity is represented in Fig. 2(a) and its realization is shown in the photograph of Fig. 2(b). At low power, the cavity beam radii for the sagittal and tangential directions are shown by the solid lines in Fig. 2(c). Using the theory presented by Bouma et al. [7] and Paye [8] the Kerr lens can be modelled as a Gaussian duct and used to predict the change in the intracavity radius. We extended the model of [7] to take account of the Brewster interface of the crystal and the 12° angle of the intracavity focusing mirror. The dashed lines in Figs. 2(c)–2(f) show the beam radius for an intracavity peak power of 10% of the critical power for self-focusing when the crystal-mirror distance is set to the optimal value of 24.3 mm. Optimum Kerr-lens action is predicted for a beam focused closer to the thinner edge of the Ti:sapphire crystal (the right-hand edge in Fig. 2(a)), which was consistent with experimental observations, where optimum Kerr-lens modelocking was obtained for an internal crystal path length of approximately 3.5 mm. A visible change in the mode profile of the laser could be seen when it modelocked.
Fig. 2. (a) Layout of the diode-pumped Kerr-lens-modelocked Ti:sapphire laser, and (b) photograph of the operating laser. (c) Sagittal beam radius (1/e2 intensity) throughout the whole cavity and (d) detail of the beam radius inside the Ti:sapphire crystal. (e) and (f) depict the corresponding tangential beam radius. Solid and dashed lines represent the beam profiles in cw and modelocked operation respectively. The inset of (e) shows (to scale) the beam waist profile inside the Ti:sapphire crystal, whose area reduces by $\approx $ 10% when modelocking occurs.
3. Output characterization
The dependence of the laser output power on the pump power is shown in Fig. 3(a), where the region of modelocking at higher pump powers is shaded. With a slope efficiency of 13%, the cw oscillation threshold is reached at a pump power of 199 mW and self-starting Kerr-lens modelocking is achieved at pump powers above 950 mW. Representative spectra from the system are shown in Fig. 3(b) for cw operation at 850 mW of pump power (blue) and modelocked operation at the maximum pump power of 1.1 W (red). The laser output can be seen to shift into a modelocked spectrum centered at 798 nm with a full width at half maximum (FWHM) bandwidth of 11.6 nm. The central wavelength of the modelocked spectrum is dependent on the alignment and on the optical path of the light in the crystal, shifting to a lower wavelength for shorter intra-crystal paths because of the wavelength dependence of the intracavity group-delay dispersion. The far field divergence of the modelocked output beam diameter at the maximum pump power was around 3 mrad for both axes.
Fig. 3. (a) Output power as a function of pump diode power, with a linear fit showing a slope efficiency of 13%. Self-starting Kerr-lens-modelocking occurs in the blue shaded region. (b) Modelocked and cw spectra recorded for pump powers of 1100 mW and 850 mW respectively. (c) Radio-frequency spectrum recorded at the instrument-limited resolution bandwidth of 15 kHz. (d) Oscilloscope trace of the output pulses detected on a fast photodiode with a 30-Hz chopper inserted into the intracavity beam, illustrating self-starting operation.
The radio-frequency spectrum of the laser is shown in Fig. 3(c) for a measurement span of 2.5 GHz recorded at the instrument-limited resolution bandwidth of 15 kHz. The repetition rate of the laser was 1.017 GHz, and its second harmonic can be seen at 2.033 GHz.
To emphasize the self-starting nature of modelocking, a chopper rotating at 30 Hz frequency was inserted into the laser cavity and a fast silicon photodetector was used to monitor the output. From Fig. 3(d) it can be seen how the laser self-started into a steady modelocked operation without requiring any external perturbation.
4. Time- and frequency-domain characterizations
The stability of the laser components is shown in Fig. 4 in the form of a relative intensity noise (RIN) measurement, which was recorded for frequencies from 1 Hz–1 MHz with the corresponding cumulative rms noise, integrated over observation times from 1 µs to 1 s. Figure 4(a) shows the measurement of the green pump light, and the cumulative RIN noise was measured to be around 0.035%. Figure 4(b) shows a measurement of the modelocked laser output, and the cumulative RIN was less than 0.01%, with most of the noise being contributed by the cooling system of the green pump diode. The value of RIN for the green diode is higher than the laser, with the difference being most significant in the multi-100-kHz region, where the 3-µs upper-state lifetime of Ti:sapphire suppresses intensity noise in the pump.
Fig. 4. RIN measurement from 1 Hz to 1 MHz: (a) measurement of the green pump diode, (b) measurement of the modelocked laser output.
In Fig. 5 we present a time-domain analysis of the modelocked laser output. A two-photon autocorrelation of the pulses is shown (Fig. 5(a)) along with their corresponding spectrum (Fig. 5(b)), which exhibits a center wavelength of 794 nm with a -3-dB bandwidth of around 10 nm. Quadratic spectral phase was added to the measured spectrum until the calculated envelope of the interferometric autocorrelation (Fig. 5(a), red) corresponded closely with the measured autocorrelation trace. The pulse shape associated with this procedure is shown in red in Fig. 5(c), together with the transform-limited pulse shape (blue), obtained directly by Fourier-transforming the pulse spectrum. The moderate chirp on the pulses results from incomplete compensation of the group-delay dispersion introduced to the pulses by the pump lens and the other out-coupling optics. We fully expect that shorter pulses should be achievable by using an optimized intracavity GTI mirror.
Fig. 5. (a) Two-photon autocorrelation trace of the cavity pulses. (b) Corresponding modelocked spectrum. (c) Transform-limited (blue) and inferred actual (red) pulse shapes.
A piezoelectric transducer (PZT) mounted under the GTI plane mirror was used to stabilize the cavity repetition rate. A fast photodiode was used to detect the repetition-rate signal from the cavity output which was then mixed with a 1-GHz reference from a radio-frequency synthesizer to provide an error signal to the PZT that maintained the cavity length at a fixed value. Figure 6 shows the power spectral density of the error signal and the cumulative phase noise of the cavity during a one-second measurement. The noise contribution around 100 Hz can be attributed to the power supplies in the measurement systems. With total phase noise of 1.7 mrad, the timing jitter of the pulses is estimated to be 270 fs in one second.
Fig. 6. Phase-noise power spectral density of the stabilized repetition rate (blue) and cumulative rms phase error (red).
5. Conclusions
We have demonstrated a Kerr-lens modelocked three-element cavity Ti:sapphire laser with a 1-GHz repetition rate powered by a single green laser diode, which to our knowledge is the first example of a GHz-class single-diode-pumped Ti:sapphire laser to be reported. With a slope efficiency of 13%, the cw threshold of the laser is around 200 mW and the maximum modelocked output power is 116 mW at 1.1 W of pump power. The modelocking bandwidth is 10 nm and the central wavelength can be shifted from 793–798 nm depending on the length of the optical path of the intracavity beam inside the crystal. The relative intensity noise of the free-running laser is 0.06% and the cumulative phase noise of repetition-rate-locked cavity is 1.7 mrad, corresponding to a timing jitter of 270 fs in one second. The output pulses were estimated to have durations of 111 fs and peak powers of 870 W, which is sufficient for on-chip supercontinuum generation [9], which would enable stabilization of the carrier-envelope offset frequency. Shorter pulses can be expected by optimizing the dispersion compensation in the laser cavity, which was not fully optimized due to the limited choice of off-the-shelf GTI mirrors available. We expect that sub-50-fs pulses should be readily available with improved intracavity compensation of third-order dispersion.
The simplicity of the laser makes it attractive as a candidate for integration as a module into larger systems, for example multi-photon microscopes, quantum-timing systems or quantum optics experiments. Frequency down-conversion of the laser using an optical parametric oscillator (OPO) is another potential application, with its >100 mW output power being immediately compatible with the 27 mW pump threshold reported for a 1-GHz degenerate OPO [10]. Finally, the small component count of the laser makes it readily compatible with a recently reported bonding method for GHz-class Kerr-lens-modelocked lasers that eliminates all optomechanical components from the assembly and leads to a robust, low noise and turnkey femtosecond oscillator [11].
Funding
Science and Technology Facilities Council (ST/T000635/1, ST/V000403/1); Engineering and Physical Sciences Research Council (EP/P005446/1).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
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