Optical phase locking among multicolor femtosecond pulses has been developed by Dr. Yohei Kobayashi and Dr. Kenji Torizuka in National Institute of Advanced Industrial Science and Technology (AIST).

Ultra-short pulses are used for various applications. However, the phase of the optical field has been an uncontrolled parameter. Then the coherent superposition among independent multicolor femtosecond pulses has not been realized.

We have developed the method to measure the optical phase (carrier-envelope-offset phase) relation between different-color femtosecond pulses that were generated by different laser oscillator. The fluctuation of the cavity length difference between two laser oscillators causes the optical phase fluctuation. The cavity length fluctuates about 10nm within a short time generally. It was reduced into attometer (1 attometer: 10-18m) region when the optical-phase-difference signal among multicolor femtosecond pulses was fed back to the cavity-length. This feedback system suppressed the cavity-length fluctuation about ten orders of magnitude. By using this technique, we have generated phase-coherent multicolor femtosecond pulses. An optical parametric oscillator system generated six subharmonic femtosecond pulses in visible and infrared region with attosecond stability.

Coherent synthesis of six-subharmonic pulses with desired phase relation could generate various shape of the optical field besides sine wave such as triangle and rectangle wave. Figure 1 shows the example of the coherent superposition of three pulses with the same phases. The superimposed electric field is a sub-femtosecond pulse train. It would be useful for the investigation of ultrafast phenomena or ultrafast optical switches. The optional shape of the electric field would be useful for a quantum control of the chemical reactions. This Fourier synthesis corresponds to the generation of the ultra-wide frequency comb in a frequency domain, and it could be useful for the metrology and ultrahigh precision measurements or optical communications.

Ultrashort pulse lasers have been applied to various applications since the early days of lasers; however, the phase of the optical field has been an uncontrolled parameter. This limitation forces most applications to only use controlled intensity shapes and phase relations within a pulse. It is possible to make desired electric field shape in an electronic circuit. However, it was impossible to realize it in optical field because the optical frequency is very high to control it precisely. The coherent superposition among multicolor pulses was desired in order to realize some applications such as,

(1) Artificial control of the chemical reactions

(2) Ultrafast telecommunications

(3) Femtosecond X-ray pulse generation by Compton scattering

We have measured and controlled the optical phase relation among different-color femtosecond pulses by using feedback system. It is important to reduce the initial fluctuation of the laser system in order to control the optical phases, then we have developed compact and stable laser system. The picture of this system is shown in figure 2. The schematic of the experimental setup is shown in figure 3. The multicolor femtosecond pulses were generated by an optical parametric oscillator (OPO). The pump pulse was generated by a Ti:sapphire laser cavity, and the signal and idler pulses were generated by the OPO. The optical frequency ratio among the pump, signal and the idler was 3:2:1. The wavelengths of the pump, signal and the idler were 850nm, 1275nm, and 2550nm, respectively. The cavity length difference between a Ti:sapphire laser and the OPO was controlled in order to lock the optical phase relation among the pump, signal and the idler pulses.

If we define the optical frequency of the pump as 3ω, then the optical frequencies of the signal and the idler can be written as 2ω and ω. The wavelengths of the doubled signal (4ω₁=2ωx2) and the sum frequency between the pump and the idler (4ω₂=ω+3ω) are both 638 nm (4ω), and they are simultaneously generated from the KTP crystal by non-phase-matched processes. The sum frequency between the pump and the signal (5ω) and the second harmonic of the pump (6ω) were also generated at the same time. Thus, one OPO generates femtosecond pulses at six wavelengths (ω, 2ω, 3ω, 4ω, 5ω, 6ω). Two-4ω (638nm) lights were separated from other wavelengths by a prism or filters and led to a delay line. The polarization of the doubled signal is rotated 90deg. by a waveplate to align both polarizations, and the two lights are mixed in time and space. Combined two-4ω pulses were detected by a Si-avalanche photodiode. The beat signal between two-4ω pulses gives us information about the phase relation among pump, signal, idler, and their sum-frequency pulses. The beat frequency was compared with a reference signal by a phase comparator and an error signal generated by it changes the cavity length by using piezo-electronic transducer (PZT) and electro-optical modulator (EOM). The cavity length difference between the Ti:sapphire oscillator and the OPO varies about 10nm in free running, while it can be reduced into 1 attometer after phase locking. Thus relative cavity length fluctuation was suppressed about 10 orders of magnitude. We have confirmed the optical phase locking by observing the interferometric fringes between two-4ω pulses. Under this condition, phase relations among six pulses were all phase locked. This is the first demonstration of optical phase locking among multicolor femtosecond pulses, and this will open the way to realize optical function generator that will generate sub-femtosecond pulse train.

Figure1 Example of superposition of phase-locked multicolor pulses

Figure2 Picture of compact Ti: sapphire and OPO

Figure3 schematic of the experimental setup