Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.

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Development of the optical frequency comb has revolutionised metrology and precision spectroscopy due to its ability to provide a precise and direct link between microwave and optical frequencies 1,2 . A novel application of frequency comb technology that leverages both the ultrashort duration of each laser pulse and the exquisite phase coherence of a train of pulses is the generation of frequency combs in the extreme ultraviolet (XUV) via high harmonic generation (HHG) in a femtosecond enhancement cavity 3,4 . Until now, this method has lacked sufficient average power for applications, which has also hampered efforts to observe phase coherence of the high-repetition rate pulse train produced in the extremely nonlinear HHG process. Hence, the existence of a frequency comb in the XUV has not been confirmed. We have overcome both challenges. Here, we present generation of >200 µW per harmonic reaching 50 nm (20 µW after harmonic separation), and the observation of single-photon spectroscopy signals for both an argon transition at 82 nm and a neon transition at 63 nm. The absolute frequency of the argon transition has been determined via direct frequency comb spectroscopy. The resolved 10-MHz linewidth of the transition, limited by the transverse temperature of the argon atoms, is unprecedented in this spectral region and places a stringent upper limit on the linewidth of individual comb teeth. Due to the lack of continuous wave lasers, these frequency combs are currently the only promising avenue towards extending ultrahigh precision spectroscopy to below the 100-nm spectral region with a wide range of applications that include spectroscopy of electronic transitions in molecules 5 , experimental tests of bound state and many body quantum electrodynamics in He + and He 6,7 , development of next-generation "nuclear" clocks 8,9,10 , and searches for spatial and temporal variation of fundamental constants 11,12 using the enhanced sensitivity of highly charged ions 13,14 .Techniques developed to control a train of ultrashort pulses in the frequency domain have led to rapid advancements not only in ultrahigh precision metrology 1 , but also in generation of attosecond pulses for time-resolved studies 15 . This symbiotic relationship between time and frequency techniques continues with the development of the XUV frequency combs where HHG, a standard technique for attosecond physics, is utilized to produce phase coherent XUV radiation. In conventional HHG, a single infrared pulse generates a burst of attosecond pulses separated by half cycles of the driving laser field, resulting in the odd harmonic spectrum shown in Fig 1. In contrast, in intracavity HHG, a phase-coherent infrared pulse train is used to produce a train of such bursts that repeat at the repetition frequency of the fundamental comb. This new temporal structure is responsible for the much finer frequency comb within each harmonic order. We anticipate that high precision characterization of the HHG process enabled by the XUV frequency comb will once again pr...

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We report the extension of broadband degenerate OPO operation further into mid-infrared. A femtosecond thulium fiber laser with output centered at 2050 nm synchronously pumps a 500-μm-long crystal of orientation patterned GaAs providing broadband gain centered at 4.1 µm. We observe a pump threshold of 17 mW and output bandwidth extending from 2.6 to 6.1 µm at the -30 dB level. Average output power was 37 mW. Appropriate resonator group dispersion is a key factor for achieving degenerate operation with instantaneously broad bandwidth. The output spectrum is very sensitive to absorption and dispersion introduced by molecular species inside the OPO cavity.