Abstract
We explore background-free options to detect mid-infrared (MIR) electric transients. The MIR field and a near-infrared probe interact via sum- (SFG) and difference-frequency generation (DFG) in an electro-optic crystal. An intuitive picture based on a phasor representation and rigorous numerical calculations are used for analysis. It turns out that separating photons generated either by SFG or DFG from the local oscillator via spectral filtering leads to a signal purely proportional the MIR intensity envelope. Background-free phase information may be extracted in a spectral window containing both SFG and DFG components and blocking the local oscillator background based on its orthogonal polarization. This variant leads to signal proportional to the square of the MIR field amplitude. It is limited by the finite efficiency of polarization filtering. The Hilbert transform as a conjugate variable to the electric field in the time domain turns out to play a fundamental role for the context discussed in this paper.
Highlights
Recent progress of electro-optic sampling (EOS) in the terahertz (THz) and mid-infrared (MIR) frequency ranges has opened up direct access to the vacuum fluctuations of the electric field [1, 2], and routes towards quantum optics operating with subcycle resolution in the time domain are currently being developed [3,4,5]
Motivated by pushing the sensitivity limits for time-domain sampling of electric field amplitudes at infrared and optical frequencies, we have explored options which are not limited by the shot noise introduced due to homodyning with the subcycle readout pulses
The surprising insight is represented by the fact that interaction of the terahertz input field or its Hilbert transform result in exactly the same mixing efficiency with the subcycle probe
Summary
Recent progress of electro-optic sampling (EOS) in the terahertz (THz) and mid-infrared (MIR) frequency ranges has opened up direct access to the vacuum fluctuations of the electric field [1, 2], and routes towards quantum optics operating with subcycle resolution in the time domain are currently being developed [3,4,5]. An ellipsometric analysis of the relative optical phase of this polarization state gives direct access to either the electric field or its conjugate variable in the time domain, namely, the Hilbert transform [9] In these schemes, technical excess noise of the pulse train used for probing may be suppressed by a balanced detector, but the shot noise of the flux of coherent NIR photons remains as the limiting factor for quantum detection. The phase information vanishes which means that even in the zero crossings of the MIR transient, DFG and SFG photons are generated with the same amplitude as in the maxima of the electric field The physics of this extreme case of a wavemixing process is studied where one of the interacting fields consists of a wave packet shorter than the oscillation cycle of the other input.
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