The use of photonic crystal fibers pumped by femtosecond pulses has enabled the generation of broad optical supercontinua with nano-joule input energies. This striking discovery has applications ranging from spectroscopy and metrology to telecommunication and medicine. Amongst the physical principles underlying supercontinuum generation are soliton fission, a variety of four-wave mixing processes, Raman induced soliton self-frequency shift, and dispersive wave generation mediated by solitons. Although all of the above effects contribute to supercontinuum generation none of them can explain the generation of blue and violet light from infrared femtosecond pump pulses, which has been seen already in the first observations of the supercontinuum in photonic crystal fibers. In this work we argue that the most profound role in the shaping of the short-wavelength edge of the continuum is played by the effect of radiation trapping in a gravity-like potential created by accelerating solitons. The underlying physics of this effect has a straightforward analogy with the inertial forces acting on an observer moving with a constant acceleration.
The use of photonic crystal fibers pumped by femtosecond pulses has enabled the generation of broad optical supercontinua with nano-joule input energies [1,2]. This striking discovery has applications ranging from spectroscopy and metrology [3] to telecommunication [4] and medicine [5]. Amongst the physical principles underlying supercontinuum generation are soliton fission [6], a variety of four-wave mixing processes [7,8,9,10], Raman induced soliton self-frequency shift [11,12], and dispersive wave generation mediated by solitons [6,12,13].
Although all of the above effects contribute to supercontinuum generation none of them can explain the generation of blue and violet light from infrared femtosecond pump pulses, which has been seen already in the first observations of the supercontinuum in photonic crystal fibers [1]. In this work we argue that the most profound role in the shaping of the short-wavelength edge of the continuum is played by the effect of radiation trapping in a gravity-like potential created by accelerating solitons. The underlying physics of this effect has a straightforward analogy with the inertial forces acting on an observer moving with a constant acceleration.
A common method of producing broad optical spectra from a spectrally narrow femtosecond pump relies upon the fact that fibers with a silica core (having few micron diameters) and surrounded by a photonic crystal cladding with various geometries, can be designed to have a zero group velocity dispersion (GVD or simply dispersion) wavelength λ 0 in a proximity of 800nm [1,2,6,8], which matches the wavelength of a mode-locked Ti-Sapphire laser.
Close to λ 0 the dispersion is small and so the input pulse can sustain a high peak power over a considerable length, which together with the small size of the fiber core, enhances variety of nonlinear effects, thus initiating a dramatic spectral broadening known as supercontinuum generation [1,2,6,7,8,9,10,13]. The measurements of supercontinuum spectra generated with a femtosecond pump have been successfully reproduced in numerical modeling using the generalized nonlinear Schrödinger equation (see Eq. ( 2) in [2]). A typical example of the spectral evolution calculated using this model and leading to the supercontinuum generation by a 200fs pulse is shown in Figs. 1(a,b). The dispersion of the modeled fiber is shown in Fig. 1(c). Having λ 0 close to 800nm shifts the range of the anomalous GVD towards much shorter wavelengths than in telecom fibers and extends the range in which optical solitons can exist.
The first stage (0 < z < 0.1m) of the spectral broadening in Fig. 1(a) is due to the formation of symmetric spectral sidebands through the well known effect of self-phase modulation, which is mediated by instantaneous Kerr nonlinearity [14,15]. The slope of the group velocity dispersion and its sign change do not play a significant role during this stage. At the second stage of the spectral evolution (0.1m< z < 0.2m) the asymmetry between the shortand long-wavelength edges of the spectrum becomes pronounced. The long-wavelength edge is shaped by the process of soliton formation (soliton fission) [6]. With further propagation the solitons are further shifted towards longer wavelengths by intrapulse Raman scattering [11,12,15,16]. If dispersion is anomalous then the longer wavelengths correspond to smaller group velocities, and so the solitons continuously slow down with propagation. The spectrum at the short-wavelength edge is created by resonant radiation from the solitons [6,13] and by the four-wave mixing of solitons with dispersive waves [7,8]. The dispersive waves generated by both of these mechanisms initially have group velocities smaller than the ones of the solitons and lag behind the latter [8]. However, the solitons are continuously decelerated and therefore the dispersive waves catch up with and start to interact with the solitons. This interaction leads to emission of new frequencies at even shorter wavelengths [8].
Importantly, the wave packets emitted through the above process experience normal group velocity dispersion, see Figs. 1(a,c). Normal dispersion can not be compensated for by the focusing nonlinearity of the silica and hence these packets, however strong or weak, are expected to spread out in time. Therefore the efficiency of their interaction with the soliton (which is proportional to the amplitude of the wave packet [7]) should be noticeably reduced after distances comparable to the dispersion length (∼ 10cm) and the associated spectral broadening should cease to continue. However, experimental and numerical observations demonstrate continuous frequency shifting of the short-wavelength edge of the continuum without significant energy loss, see Fig. 1(a). Also, simultaneous spectral and time-domain analysis of the experimental and numerical data by means of the cross-correlated frequency resolved optical gating (XFROG) gives a full impression of the format
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