Role of Intrapulse Coherence in Carrier-Envelope Phase Stabilization

The concept of coherence is of fundamental importance for describing the physical characteristics of light and for evaluating the suitability for experimental application. In the case of pulsed laser sources, the pulse-to-pulse coherence is usually considered for a judgment of the compressibility of the pulse train. This type of coherence is often lost during propagation through a highly nonlinear medium, and pulses prove incompressible despite multioctave spectral coverage. Notwithstanding the apparent loss of interpulse coherence, however, supercontinua enable applications in precision frequency metrology that rely on coherence between different spectral components within a laser pulse. To judge the suitability of a light source for the latter application, we define an alternative criterion, which we term intrapulse coherence. This definition plays a limiting role in the carrier-envelope phase measurement and stabilization of ultrashort pulses. It is shown by numerical simulation and further corroborated by experimental data that filamentation-based supercontinuum generation may lead to a loss of intrapulse coherence despite near-perfect compressibility of the pulse train. This loss of coherence may severely limit active and passive carrier-envelope phase stabilization schemes and applications in optical high-field physics.

Figure 1

Numerical simulations of the intrapulse coherence of supercontinuum pulses according to Eq. (3). Simulations are based on an ensemble of 1000 input pulses with 10 fs duration and 1% energy standard deviation. (a)–(c) Mean value (thick blue line) and standard deviation (thin orange line) of the FOM. The first maximum of the FOM has been marked by a dashed red line. (d)–(g) Standard deviation of $\mathrm{\Delta }\phi$; cf. Eq. (4). (a), (d) Symmetric spectral broadening due to self-phase modulation. (b), (e) Asymmetric spectral broadening due to plasma generation driven by a multiphoton process of the order of 6. (c), (f) Full simulation of nonlinear propagation in sapphire according to Ref. [24].

Figure 2

Measured supercontinuum spectra for the use of a 2 mm thick sapphire plate, a torating 2 mm thick ${\mathrm{CaF}}_2$ plate, an 8 bar xenon cell (Rayleigh range about 2–3 cm), and an sequence of two quartz plates and seven fused silica plates of 50 and $100\mu \mathrm{m}$ thickness, respectively. The spectral region around the 800 nm pump wavelength has been suppressed by suitable spectral filtering to allow the high-resolution characterization of the spectral wings relevant for $f$-to-$2f$ interferometry. The strongest spectral asymmetry appears for xenon, which suggests prevalent plasma-based spectral broadening. The rather symmetric spectra for sapphire indicate a dominance of self-phase modulation.

Figure 3

Fringe contrast measurements of the $f$-to-$2f$ interferometer spectra. The modulation sideband and background were extracted by Fourier filtering from raw data sets. Signals are normalized to the standard deviation of the signal amplitude seen at each pixel of a line scan camera. The central wavelength varies from 437 (Xe) to 510 nm (${\mathrm{CaF}}_2$, ${\mathrm{Al}}_2{\mathrm{O}}_3$), as different phase-matching conditions and nonlinear crystals had to be employed for the best FOM.