In-line Spectral Interferometry in Shortwave-Infrared Laser Filaments in Air

We investigate the nonlinear propagation of intense, two-cycle, carrier-envelope phase (CEP) stable laser pulses at $1.7\mu \mathrm{m}$ center wavelength in air. We observe CEP-dependent spectral interference in the visible part of the forward-propagating white light generated on propagation. The effect is robust against large fluctuations of the input pulse energy. This robustness is enabled by rigid clamping of both the peak optical field and the phase of the propagating waveform, which has been revealed by numerical simulations. The CEP locking can enhance the yield of the CEP-dependent strong-field processes in gaseous media with long-wavelength drivers, while the observed spectral interference enables single-shot, stand-off CEP metrology in the atmosphere.

Figure 1

Measured $\theta –\lambda$ spectra for two specific values of the CEP that correspond to the most dissimilar spectra. The images are integrated over 750 laser shots. The specified CEP values are relative to an arbitrary constant number. Colors in these images correspond to actual colors, as perceived by the human eye. The insets show images of the corresponding beam patterns, were emissions at different angles are strongly overlapping. A movie composed of the $\theta –\lambda$ spectra for the gradually advancing value of the CEP is available in Ref. [27].

Figure 2

Numerical results for the $\theta –\lambda$ spectra, shown on an arbitrary linear scale, for two particular values of the input CEP that correspond to the most dissimilar spectra. The color palette is chosen to highlight the generated spectral features. A movie composed of the $\theta –\lambda$ spectra for gradually advancing values of the CEP is available in Ref. [27].

Figure 3

(a) The simulated $E$-field waveforms for the two values of the CEP that correspond to the two output $\theta –\lambda$ spectra shown in Fig. 2. (b) Corresponding output $E$-field waveforms of the on-axis emission component. Input pulse energy is 1.40 mJ. The overall CEP of the waveform is rigidly locked on passing through the filamentation zone.

Figure 4

The simulated third-harmonic content of the output temporal $E$-field waveforms. The vertical grids show the periodicity of the monochromatic wave at 525 nm wavelength, where the spectral hole is observed in the simulation. In the case of $\mathrm{CEP}=0.30\times \pi$, the output waveform at the third harmonic consists of two distinct subpulses that are predominantly out of phase with each other. In the case of $\mathrm{CEP}=0.90\times \pi$, the subpulses in the third-harmonic waveform are largely in phase and strongly overlapping.

Figure 5

The simulated complete (a) and third-harmonic (b) output fields, for the input $\mathrm{CEP}=0.30\times \pi$ and at two different energies of the input pulse, as specified in the legends. 10% energy variation causes only a very slight change of the output waveforms, both in amplitude and phase.