Controlling the Carrier-Envelope Phase of Raman-Generated Periodic Waveforms

We demonstrate control of the carrier-envelope phase of ultrashort periodic waveforms that are synthesized from a Raman-generated optical frequency comb. We generated the comb by adiabatically driving a molecular vibrational coherence with a beam at a fundamental frequency plus its second harmonic. Heterodyne measurements show that full interpulse phase locking of the comb components is realized. The results set the stage for the synthesis of periodic arbitrary waveforms in the femtosecond and subfemtosecond regimes with full control.

Figure 1

Graphic representation of Eq. (1) for the commensurate case to show the relationship between (a) the frequency and (b) the phase among the comb components. (c) relates the frequency terms in (1) to the driving frequencies in the Raman case.

Figure 2

Schematic of the experimental setup. HW, half-wave plate; LN, ${\mathrm{LiNbO}}_3$ crystal; P, polarizer; PP, ${\mathrm{CaF}}_2$ prism pair; L, lens; BBO, $\beta$-barium borate; PB, Pellin-Broca prism; PD, Si photodiode. Beams from the ${\mathrm{H}}_2$ cell are shown here as different colored beams. They are in fact overlapped in space before the PB prism.

Figure 3

Heterodyne signals from sum mixing in a BBO crystal as a function of the translation of a prism in the first prism pair for the processes: (a) SHG of 2406 to 1203 nm, (b) SFG of 2406 and 1203 to 802 nm, (c) SFG of 2406 and 802 to 602 nm, and (d) SFG of 2406 and 602 to 481 nm. All scans of the prism position begin at the same “0” prism position. The signal of (a) is used to calibrate the relative prism position shown on the top to the phase difference ${\varphi }_2-2{\varphi }_1$ shown on the bottom. Each data point is the average of 30 laser shots. Each trace took about 5 minutes to complete. The squares are data points. The red solid curves are sinusoidal fits to the data. The elongated circles and the blue vertical lines highlight that there is a difference in the initial relative phases in (a)–(d).

Figure 4

Heterodyne signals at (a) 802 and (b) 602 nm used to demonstrate CEP control. The squares are data obtained by laterally translating the prism in the first prism pair. The red solid curves are sinusoidal fits to the data. Red horizontal lines represent the expected signal based on the CEP value to which it is set. The upper set of numbers adjacent to the red lines is the difference of the mean of the measured relative phase and the set value. The lower set of numbers is 1 standard deviation of the relative phase determined from the respective signal fluctuations. The panels on top of the figure show the corresponding electric field waveforms synthesized based on the measured energies of 1.9, 1.24, 0.3, 0.05, and $0.005\mathrm{mJ}/\mathrm{pulse}$, respectively, at 2406, 1203, 802, 602, and 481 nm and the CEP set for that location. Only the scan time is shown on the horizontal axis.