Cascaded compression reveals a new paradigm of ultrafast cascaded nonlinearities

A new method for compressing laser pulses overcomes power constraints that hamper current compressor technology. The method suggests a paradigm shift in ultrafast cascaded nonlinearities as for the first time octave-spanning bandwidth is achieved using the largest nonlinear components of conventional frequency conversion crystals. The utility of this process was confirmed experimentally by compressing energetic (sub-mJ) near-IR femtosecond pulses to four periods in the time domain. This happened in a just 1 mm long nonlinear crystal.

Physics synopsis

B. B. Zhou, A. Chong, F. W. Wise and M. Bache, Ultrafast and octave-spanning optical nonlinearities from strongly phase-mismatched cascaded interaction, Physical Review Letters 109, 043902 (2012), [pdf]

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Frequency-resolved optical gating (FROG) measurement of the compressed 16 fs pulse.

There is always a demand of short, energetic pulses. Amplifying very short pulses to obtain more pulse energy often leaves the pulse longer than desired. Therefore pulse compression techniques are employed to subsequently compress the amplified pulses temporally. The conventional method today achieves spectral broadening occurs in one a nonlinear medium and subsequently temporal compression is done with dispersive (linear) optics like prisms or gratings. This type of compressor is very common today: a half-meter long gas filled fiber creates spectral broadening through a positive nonlinear index, and using a pair of gratings subsequently compresses the pulse temporally.


The nonlinear stage where spectral broadening occurs is always limited by the need for avoiding self-focusing. If one could reverse the sign of the nonlinearity, i.e. a negative nonlinear index of refraction thus making it self-defocusing, this would not be an obstacle. Moreover, a negative nonlinearity would allow for a soliton forming. A soliton is a nonlinear wave that exists as a balance between dispersion and nonlinearity, and with a negative nonlinearity solitons require positive dispersion to exist. Almost all materials have this type of dispersion at standard laser wavelengths. Using solitons to compress pulses is intriguing as it allows for both spectral broadening and temporal compression in the same material, and it makes the compressor extremely compact and simple.


Cascading nonlinearities is an efficient way of indirectly achieving a self-defocusing (negative) nonlinearity. Cascading occurs in frequency conversion processes where initially the frequency of light is doubled and then subsequently halved. This “cascaded nonlinearity” is most efficient under nearly phase-matched conditions, meaning the different frequencies composing the pulse propagate with almost the same phase velocity. Unfortunately under this condition the cascaded process has limited bandwidth, implying that it is inefficient for femtosecond pulse interaction. This has until now been the main obstacle for using cascading nonlinearities for ultrafast purposes.



Temporal profile of the compressed pulse, as measured with a FROG device. The 47 fs input pulse is compressed after 1 mm to 17 fs, around 4 optical periods in time domain.

In the present experiment, researchers in the Ultrafast Nonlinear Optics group at DTU Fotonik in collaboration with researchers at Cornell University realized that in order to circumvent the bandwidth problem, a very simple and straightforward solution is to make sure that the phase mismatch is large. This gives extremely large bandwidths, more than an octave. The price to pay is a large drop in nonlinear strength, and in order to compensate for this they used nonlinear crystals with huge frequency-conversion nonlinearities. The challenge was to find a crystal where the resulting cascaded negative nonlinearity was strong enough to overcome the intrinsic material positive nonlinearity. It turned out that this was possible in a standard lithium niobate crystal when pumped at longer near-IR wavelengths. By launching a sub-mJ 47 fs pulse with 1300 nm wavelength in a just 1-mm long crystal, they were able to excite a soliton that compressed the pulse to just 4 optical cycles, and which had around 80% of the energy in the main spike. The self-defocusing nature of the nonlinearity means that whole-beam or small-beam instabilities typical of self-focusing compressors was not observed. Another advantage of self-defocusing nonlinearities is that the energy in the experiment easily can be scaled up as it merely requires a crystal with a larger aperture. This experiment comprises a new paradigm of ultrafast cascading, where octave-spanning bandwidths are achieved by using large phase mismatch values, and where efficient cascading is ensured by exploiting the largest nonlinearities.


Their research indicates that if one uses conventional techniques to reduce the phase mismatch (as to increase the cascading strength) the bandwidth is strongly reduced. Thus quasi-phase matching techniques usually employed should be avoided. They also found that many other crystals have similar properties, in particular semiconductor crystals pumped at longer wavelengths (mid-IR). These crystals have never been investigated because their efficiency was thought to be too low (due to the large phase mismatch).


The researchers have yet to find a crystal that works well at 800 nm, where Ti:Sapphire amplifiers operate, but the technique should be applicable from pump pulses centered around 1 microns and up.


For more information, please contact associate professor Morten Bache, DTU Fotonik.