Picosecond time-lenses

There is an interesting analogy between the spatial problem of Fresnel diffraction and the temporal problem of first-order dispersion. This space-time analogy was recently extended to propose a time-domain analog to spatial imaging that allows for the distortionless expansion of compression of optical waveforms in time. This process is called temporal imaging. The extension includes the idea of a time-lens as a dual of a spatial lens (regular lens). The time-lens is simply a quadratic optical phase modulator in time, which is approximated by a portion of a sinusoidal phase modulator. Thus, by using phase modulators as lenses and grating pairs as dispersive elements, complete temporal imaging systems can be constructed in exact duality with spatial imaging systems. However, for practically useful time-lenses, considerable modulation is required at fairly high frequencies. The main body of the paper is the detailed design and development of a practical time-lens. This is addressed in Section II, where a resonant microwave modulator is developed based on a LiNbO₃ loaded waveguide. Multiple passes are obtained through the modulator using an off-axis path in a stable optical resonator. At 5.2-GHz operation, 44 radians of phase modulation is obtained at 1.06-μm wavelength for 13 W of microwave power. This corresponds to a time-lens with 31-ps aperture and 1.9-ps resolution. This was confirmed by demonstrating temporal focusing of 45-ps pulses to 1.9 ps. By optimizing the design of the time-lens and better thermal engineering, it may be possible to obtain subpicosecond resolution