The performance parameters of the laser are summarized in
. Various mode-locked states are possible depending on the diode laser pump power and the orientation of the wave plates. When pumping at 4.1 W, a stable mode-locked state with an average output power of 930 mW is obtained , corresponding to 21.9 nJ pulses emitted at 42.5 MHz rep. rate . When the output pulses are compressed to their transform limit, interferometric measurements are performed [24
], resulting in the full-width-half-maximum (FWHM) of 57 fs . Based on Fourier transform of the experimental laser spectrum and autocorrelation simulations using commercial ‘FemtoPulse Master’ software (Biophotonic Solutions Inc.), the deconvolution factor should be 1.37. This is the factor we have used to determine the experimental FWHM duration of 41.6 fs for the compressed pulses.
Fig. 3 (a) Output laser spectrum (black) and measured phase of the output pulses (red). (b) Experimental interferometric autocorrelation, AC FWHM 57 fs. (c) RF spectrum analyzer result, 1 MHz frequency span. Insert: pulse train form oscilloscope. Repetition (more ...)
The output pulse train is monitored by a fast photodiode on the oscilloscope and examined using the RF spectrum analyzer. With a 1 MHz frequency span, the RF spectrum analyzer gives a single peak at 42.48 MHz with ~70 dB signal-to-background ratio . The inset in shows the response from a fast photodiode confirming single-pulse operation. No sidebands are observed for the fundamental and higher harmonics over the 500 MHz span , which confirms stable mode-locking.
Pulse dispersion measurement and compression are accomplished using the pulse shaper. The MIIPS software scans a sinusoidal spectral phase function across the spectrum of the pulse, collects the resulting SHG spectra and derives the corresponding spectral phase distortion [19
]. Typically, seven iterations are run for the measurements presented here in order to obtain compensation within 99.7% of the theoretical transform limit, defined by the input laser spectrum. The phase function required to achieve transform limited pulses is the complementary phase obtained after double integration of the shaper-measured second-derivative.
To account for phase distortions due to optics in the pulse shaper and thereby measure the pulse phase directly at the laser output, we have independently measured the phase distortions due the pulse shaper itself by putting it in line with another pulse shaper. The measured phase at the laser output pulses is shown in . Polynomial fitting up to the third order gives ~35,000 fs2
of the second order dispersion (SOD) and ~166,000 fs3
of the third order dispersion (TOD). Note that the observed SOD is much less than the cavity dispersion of ~100,000 fs2
, calculated based on the total fiber length and the fiber group-velocity dispersion β2
= 23 fs2
/mm. This is one of the characteristic signatures of the similariton formation in the gain medium [17
After the pulse compression, the pulse shaper has been used to create two pulse replica and scan one of them in time to obtain interferometric autocorrelations [24
]. The measurements show excellent agreement with calculations using ‘FemtoPulse Master’ software [
]. Similarly, we have also compared the experimental SHG spectrum for compressed laser pulses with the calculated SHG spectrum based on the measured fundamental spectrum of the laser and a flat spectral phase . Excellent agreement between theoretical and experimental results for both linear and logarithmic scales gives us confidence in the measured parameters and that the laser pulses at the BBO crystal are transform limited.
Fig. 4 (a) Experimental and calculated SHG spectra shown in linear (solid line) and log-10 (dash line) scales. (b) Experimental THG spectrum obtained by focusing TL pulses at the surface of a glass slide. (c) Experimental and calculated interferometric autocorrelation (more ...)
Taking into account the throughput of our pulse shaper (~50% due to the reflection efficiency of the grating and mirrors), we calculate the peak power for compressed pulses to be about 250 kW. This peak power is sufficient to obtain third harmonic generation (THG) signal at the interface of air and glass [25
], see Fig. 4(b). For these measurements, the output from the pulse shaper is first focused via a 10x objective on a BBO crystal. Then the pulses are compressed at the objective focus. Once pulse compression is achieved, the BBO crystal is replaced by a 1-mm-thick glass slide. The observed THG spectrum spans ~20 nm bottom-to-bottom. The broad THG spectrum indicates that the third order dispersion is fully corrected. It is necessary to point out that, higher peak power can be obtained by improving the throughput efficiency of the pulse shaper.
We have also observed that for a fixed filter bandwidth, the spectral breathing ratio through the cavity is proportional to the pump power. When the pump power is increased over 4.1 W, the output laser spectrum continues to broaden but is no longer stable and fully coherent. Only partial pulse compression has been achieved and the resulting SHG signal is observed to be much weaker than when the output is fully coherent. When the pump power is reduced to 3.85 W, the output laser spectrum becomes narrower. Under these conditions, pulses with FWHM duration of 44.4 fs have been obtained with the average output power of 850 mW. The pulse duration increases to 57 fs with pumper power of 3.1 W.
The filter bandwidth, a key factor of the laser cavity, certainly affects the laser performance. When the collimator is moved closer to the grating and spectral filter bandwidth is increased to ~4 nm, the compressed pulses as short as 52 fs are obtained. A birefringent spectral filter of 12 nm bandwidth has also been used. With this large bandwidth filter, output spectra with steep edges and ‘cat-ears’ are obtained, which are the characteristics of dissipative soliton pulses [5
]. The output pulses are compressed to 80 fs.
According to numerical simulations, the transition from dissipative soliton to amplifier-similariton happens when the filter bandwidth is reduced below ~6 nm. The simulation results are in agreement with experimental results for several filter bandwidth conditions. Our numerical simulations also predict that, it is difficult to achieve stable mode-locking when the filter bandwidth is smaller than 3 nm.
A systematic study of the amplifier similariton laser will be needed to determine the limits on the pulse energy. Considering that the energy was not maximized in Ref [17
], the 7-fold increase in pulse energy that we find is in rough agreement with the 3-fold increase that would be expected based on the fiber core areas difference alone. The experimental results presented here can be viewed as initial experimental data in the effort to determine the maximum performance of these lasers.