Complete Characterization of Phase and Amplitude of Bichromatic Extreme Ultraviolet Light

Intense, mutually coherent beams of multiharmonic extreme ultraviolet light can now be created using seeded free-electron lasers, and the phase difference between harmonics can be tuned with attosecond accuracy. However, the absolute value of the phase is generally not determined. We present a method for determining precisely the absolute phase relationship of a fundamental wavelength and its second harmonic, as well as the amplitude ratio. Only a few easily calculated theoretical parameters are required in addition to the experimental data.

Figure 1

Schematic process of interference between the partial photoelectron waves created by single- and two-photon ionizations. The (short) red arrows mark the fundamental photon, while the (long) blue one indicates the second harmonic. The horizontal lines show the lowest energy levels of helium.

Figure 2

$\beta$ parameters as a function of $\varphi$. Markers, $\beta$ parameters of dataset A as a function of phase; curves, cosine (constant) fit, odd (even) $\beta$; blue triangles, ${\beta }_1-2{\beta }_3/3$; black circles, ${\beta }_2$; green inverted triangles, ${\beta }_3$; red squares, ${\beta }_4$. Error bars show standard errors of least-squares fitting using the model described in Eq. (3). Linearly polarized light, $\lambda =86.7\mathrm{nm}$, $\lambda /2=43.4\mathrm{nm}$.