By utilizing the poling technique, people are able to use the largest nonlinear tensor component d₃₃ (known as type-0 phase-matching) for nonlinear frequency conversion. However, the large discrepancy between the first derivative of the refractive index of fundamental and second-harmonic makes the phase-matching bandwidth become very narrow.

This kind of finite bandwidth will strongly limit the capability of frequency doubling for an ultrafast pulse as it implies the group velocity mismatch (GVM) between fundamental harmonic (FH) and second harmonic (SH) pulses, which is ~300 fs/mm in conventional type-0 phase-matching. When the GVM taking place, the SH pulse becomes broad and not compress-able as the spectral information cut by the insufficient acceptance phase-matching bandwidth.

In PPLN there is a "sweet spot" that can provide very wide band of phase-matching acceptance at 1560 nm, in which the group velocities of the FH and SH pulse are equal. By launching the FH at ordinary wave and utilizing the tensor component d₃₁, ultra broad phase-matching SH polarized at extraordinary can be perfectly phase-matched.

Fig 1(a). phase-matching configuration, (b). period tuning curve versus fundamental wavelength with type-I phase matching under different operating temperature.

This feature allow us to use a very long crystal to compensate the reduction of nonlinear coefficient (d31~2.5 pm/V vs. d33~15 pm/V), but still has a very broad phase-matching acceptance up to few tens of nm. As a result, the SHG conversion efficiency can reach more than 50%, and the entire spectrum is almost preserved.

Fig. 2 Simulated phase-matching curve of (a). type-I, (b). type-0 phase matching configuration, respectively.

In our internal experiment, we use several crystals in different length to implement ultrashort pulse SHG. The pump laser is ~100fs, 100MHz and up to 330mW average power centered at 1560nm. There is a built-in SHG port of the laser which use a 0.5mm long conventional type-0 PPLN, and all of the measurements are compared to this SHG port. When using a 5mm long PPLN in type-I phase-matching configuration, >45% conversion efficiency compatible to the SHG port are obtained. The efficiency is even improved up to 67% when we replace to the 10mm long PPLN, and >220mW optical power at 780nm was successfully obtained.

Fig. 3(a). Power scaling curves (b). efficiency curves of 5mm, 10mm PPLN in type-I (green and red) and 0.5mm PPLN in type-0 (blue) phase matching, respectively. 

In order to see the impact of the broad phase-matching spectrum, the SH spectrum is characterized by an optical spectral analyzer (OSA) and shown in following figure. One can see that both of 5 and 10 mm long crystals even showing a broader spectral width compared to the 0.5mm long conventional PPLN, proving the concept of GVM-free frequency doubling.

Fig. 4 Second harmonic spectrum measured by different phase-matching configurations.

Experimental results - compression

Later we test the approach by another laser with even shorter pulse duration down to 80fs, in which the pulse are not transform limited and expected to have some spectral phase. The results are still good with 10 and 15 mm long PPLN with the efficiency up to 40%. Then we use two chirp mirror (GDD~-550fs²) to re-compensate the SHG pulse. With 3 bounces on each mirror we are able to re-compress the SH pulse to be shorter than 50fs. Such kind of ultrafast pulse at 780 nm has wide applications such as multi-photons fluorescence microscopy, visible frequency comb generation...etc.