A diode-pumped, prismless Nd:glass laser oscillator, mode-locked by a semiconductor saturable absorber, was stabilized against self-Q-switching by using a phase-mismatched second harmonic crystal. Furthermore, negative-index cascaded second-order nonlinearity provided the soliton shaping mechanism with normal intracavity dispersion. Nearly Fourier-limited pulses as short as 520 fs were obtained.
©2008 Optical Society of America
Solid-state femtosecond laser sources at 1-µm wavelength are currently mostly employed as seeders for both solid-state and fiber amplifiers  or for direct applications such as terahertz pulse generation and detection  and nonlinear microscopy .
Neodymium and ytterbium diode-pumped solid-state lasers have been widely reported to operate as femtosecond sources, mode-locked by either semiconductor saturable absorbers [4-5] or Kerr-lens effect . Usually, the most preferred setup relies on the saturable absorber for the mode-locking starting, while self-phase-modulation (SPM) arising in the gain medium must be compensated by a proper amount of negative dispersion introduced by either prisms or special mirrors, allowing for stable femtosecond pulse generation.
It was shown that soliton-like femtosecond pulse generation can be also achieved in normal dispersion regime, provided that the SPM effect is sign-reversed. In Ref.  a Cr:forsterite laser was Kerr-lens mode-locked with the help of a semiconductor saturable absorber in a normal dispersion cavity, with a lithium triborate crystal (LBO) providing the necessary SPM by exploiting cascaded second-order nonlinearity.
However, owing to the much smaller emission cross-section and the longer fluorescence time, Nd and Yb lasers are especially prone to Q-switching instabilities when operating in normal dispersion regime. Recently, we proposed a novel technique [8, 9] to suppress such instability by use of a phase-mismatched second harmonic crystal acting as a two-photon passive limiter .
Here we report on a femtosecond Nd:glass laser mode-locked by a semiconductor saturable absorber with a normal-dispersion cavity, employing an LBO crystal for both negative SPM and self-Q-switching suppression. Without the LBO crystal, only Q-switching mode-locking was observed. Owing to the simplified cavity setup and lower intracavity losses, the output power was about twice that of the same laser operated with intracavity prisms for negative dispersion compensation, while the pulse duration was increased from 240 fs to 520 fs, yielding nearly the same pulse peak power.
2. Experiments and discussion
Figure 1 shows the optical layout. The laser oscillator employed a 5-mm long Nd:glass 4%-doped Brewster-cut plate. The laser glass was a Nd-doped phosphate (glass N31  from China), whose laser properties and performance are comparable to other well-known phosphate glasses .
A 1-W cw laser diode, 100×1 µm2 single emitter at 803 nm, was employed to pump the active medium (pump absorption ≈98%). The laser diode output was collimated and reshaped with a cylindrical telescope, allowing stigmatic pump spot size in the laser glass by focusing through the achromatic lens L2. The measured pump spot fairly matched the TEM00 waist radius of the symmetric, 1-m long, X-shaped cavity extending from mirror M3 to the output coupler OC (30×45 µm2 as calculated according to ABCD modeling). In cw regime, with a 2.4%-transmissivity output coupler, the absorbed pump at laser threshold was 50 mW, while as much as 227 mW were obtained at a 730-mW absorbed pump power.
Later, the resonator was modified to include a semiconductor saturable absorber mirror (SAM) with reflectivity modulation ΔR=1% (from BATOP Gmbh), along with a focusing mirror M4 (150-mm curvature) and a pair of SF10 prisms, with tip-to-tip separation of 270 mm. In this case, the mirror M3 was removed, and the output coupler was replaced by a lower transmissivity (1.4%) output coupler.
With the SAM alone, the prismless resonator operated in a chaotic regime, with random-spaced Q-switching/mode-locking spikes.
When adding the proper amount of negative dispersion, it was easy to find stable femtosecond operation, with pulses as short as 240 fs (Fig. 2), nearly Fourier-limited (time-bandwidth product ≈0.36) and with 60-mW output power. This behaviour was expected from earlier theoretical models , showing that in presence of negative dispersion the pulse energy threshold for stable femtosecond mode-locking is significantly reduced.
Eventually, AR-coated LBO crystals with lengths of 2 mm and 4 mm, cut for second harmonic generation (SHG) at 532 nm, were employed to achieve stable mode-locking without prisms (Fig. 3), with focussing M4-mirror curvatures of 100, 150, 200 mm. Tilting the crystal off-phase-matching in both directions, the spiking instability was effectively suppressed, readily achieving stable mode-locked pulse trains. While tilting the LBO in the direction providing positive SPM only yielded longer pulses (≈2-3 ps typically), with relatively narrow spectra (<1 nm) as in Ref. , reversing the phase-mismatch sign allowed stable femtosecond operation near the 3rd and 4th minima of SHG, with practically constant pulsewidth.
Comparable results were achieved with either of the LBO crystals and different focusing mirrors, yielding ≈520-fs pulses with bandwidth ≈3.1 nm. The time-bandwidth product slightly increased to ≈0.44 but remained still close to the Fourier limit. Owing to the simplified cavity setup obtained removing the prisms, the output power increased to 120 mW, therefore yielding a peak power comparable with the standard prism resonator delivering shorter pulses.
While the emission spectrum of Cr:forsterite lasers peaked at 1250 nm  minimizes both the group-velocity mismatch between fundamental and harmonic waves (GVM=Δ(1/νg)≤8 fs/mm) and the walkoff angle ρ of LBO working in xz plane (ρ≈3 mrad), at 1054 nm the GVM increases to 46 fs/mm and the walkoff angle to 6 mrad. This appears a major limitation to further pulse shortening.
Indeed, it was shown previously  that the nonlinear phase term, responsible of spectrum broadening, is proportional to the small-signal SHG efficiency η∝d 2 l 2 I/n 3 (being d the effective nonlinear coefficient, n the refractive index and I the intracavity pulse intensity). Assuming the beam size w optimized for a given crystal length l, i.e. l≈zR=πw 2/λ (Rayleigh range), the nonlinear phase modulation is proportional to η∝(d 2/n 3)lE/τ, being E the intracavity pulse energy and τ the pulsewidth.
Since relatively short crystals must be used in order to minimize the GVM, which sets the maximum length l≈τ/Δ(1/νg) for a target pulsewidth τ, the available SPM is also limited, as well as the pulse bandwidth. A figure of merit can be introduced as FOM=(d 2/n 3)/Δ(1/νg) to compare different nonlinear crystals commercially available, basically borates and periodically-poled lithium niobate (PPLN), initially neglecting the walk-off (see Tab. 1). We concentrate our attention on such crystals since they allow relatively broad-band type-I phase-matching, or quasi-phase-matching in PPLN, at 1054 nm.
This would suggest that BBO might yield SPM twice as large compared to LBO at the same pulsewidth, even with a larger GVM ≈88 fs/mm, however its ≈50-mrad walk-off severely limits the SHG efficiency  and SPM over, for example, a 4-mm crystal length with optimum spot size w=28 µm (ρl≈200 µm, with respect to ρl≈24 µm with LBO).
For comparison, at 1250 nm the FOM for LBO increases by a factor ≈6, allowing significantly higher SPM which in turns supports shorter femtosecond pulses. Incidentally, the pulsewidth observed in our experiments was longer than that of Ref.  by a comparable factor (≈9). It should also be noticed that the vibronic Cr:forsterite laser enjoys a significantly broader fluorescence bandwidth, allowing generation of sub-100-fs pulses.
A more suitable crystal seems to be the PPLN, which is not limited by walk-off due to propagation along a principal axis, provided that parasitic photorefraction is reduced properly.
We note that very short crystals, requiring angle-phase-matching, must be tilted off-phase-matching by a larger angle, thus increasing the losses at the AR-coating (usually designed for operation at normal incidence) and reducing the intracavity peak intensity available for SPM. This drawback could be circumvented by temperature tuning, a technique usually exploited with PPLN but that can be used with any crystal and that allows phase mismatching to be achieved at almost normal incidence (some minor offset is always required to avoid mode-locking perturbing etalon effects).
In conclusion, beside periodically poled materials with enhanced nonlinearity, LBO is certainly a crystal that offers many appropriate features for the application investigated in this work. The proposed technique allows a straightforward implementation of both Q-switching suppression and dispersion compensation in the femtosecond regime at ≈1-µm wavelength, without additional expensive elements such as dispersive mirrors, or prisms requiring precise alignment to minimize losses. Additional pulse shortening could be expected by increasing the pump power and brightness, since SPM is proportional to the intracavity pulse energy.
Another implication of our results is that the resonator layout might be conveniently simplified by further minimizing the number of optical components and making it more compact, also allowing for high frequency femtosecond operation in the GHz range when required.
References and links
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