Solid-state light-phase detector

Attosecond science relies on the use of intense, waveform-controlled, few-cycle laser pulses1 to control extreme nonlinear optical processes taking place within a fraction of an optical period. A number of techniques are available for retrieving the amplitude envelope and chirp of such few-cycle laser pulses. However, their full characterization requires detection of the absolute offset between the rapidly oscillating carrier wave and the pulse envelope, the carrier–envelope phase (CEP). So far, this has only been feasible with photoelectron spectroscopy, relying on complex vacuum set-ups2–4. Here, we present a technique that enables the detection of the CEP of few-cycle laser pulses under ambient conditions. This is based on the CEP-dependence of directly measurable electric currents generated by the electric field of light in a metal– dielectric–metal nanojunction. The device holds promise for routine measurement and monitoring of the CEP in attosecond laboratories. The electric field of a laser pulse can be described as F(t) = 2 F̃(t)e−i(vLt+wCE) + c.c., where vL is the carrier frequency and the complex amplitude F̃(t) = F0f (t)e−iw(t) comprises the normalized real-field envelope, the peak amplitude F0 and the timedependent phase w(t). The CEP wCE describes the offset between the carrier wave oscillating at vL and the maximum of the realfield envelope f(t). If the pulse duration, defined as the full-width at half-maximum of f(t) (the square of the envelope) becomes comparable with the carrier period 2p/vL of the waveform, wCE affects the evolution of nonlinear electron phenomena driven by F(t), including high-order harmonic generation5,6, ionization of atoms and molecules7–9, interaction with plasmas10, as well as photoemission from metals11,12 and nanoparticles13. Attosecond control over these processes calls for control and full characterization of the applied electric field F(t). Attosecond streaking14 permits complete measurement of the vector potential of a laser pulse, from which F(t) is easily obtained as its temporal derivative. Alternatively, the combination of conventional pulse characterization techniques15–17 acquiring the normalized complex amplitude F̃(t)/F0 = f (t)e−iw(t) and a measurement of the CEP, wCE, may provide access to the full waveform. Although relative changes of the CEP can be detected by spectral characterization of mixed fields using simple and inexpensive set-ups18–21, tracking down its absolute value is currently based on nonlinear photoemission from atoms or solids with stereo above-threshold ionization (stereo-ATI)2–4 and attosecond streaking14,17, both of which require rather complex, space-consuming vacuum apparatus. Here, we report the first method to enable absolute CEP detection with a solid-state detector that is applicable in ambient conditions. Recently, we have shown that the strong electric field of an intense, linearly polarized, visible/near-infrared (vis/NIR), fewcycle laser pulse can rapidly increase the (a.c.) conductivity of a solid insulator, allowing electric currents to be induced and switched with the field of visible light22. In these experiments, we exposed amorphous silicon dioxide (bandgap Eg≈ 9 eV) to a strong, controlled electric field F(t) of a few-cycle pulse with a carrier photon energy of vL≈ 1.7 eV. The resultant transient nonlinear increase in electric polarization allowed the few-cycle field to drive a current through two unbiased gold electrodes connected to the sample. Because the effect is controlled directly by F(t), it is sensitive to the CEP22. This sensitivity can be utilized for the measurement of wCE if, and only if, the following two conditions are fulfilled: (1) the current versus wCE dependence is calibrated and (2) this calibration is robust against variations in the pulse intensity. This work addresses and fulfils these conditions by applying a series of careful experiments and numerical simulations. We used sub-4 fs ( 1.5 cycle) vis/NIR laser pulses carried at lL≈ 0.75 mm to study thewCE dependence of optical-field-induced electric currents in a metal–dielectric–metal junction and compared it with measurements simultaneously performed with a stereo-ATI phasemeter5 (Fig. 1). The junction was exposed to a strong optical field at normal incidence, with perpendicular polarization of F(t) (Fig. 1a,b). The peak electric field amplitude was set at F0≈ 1.24 V Å by focusing pulses of 4 mJ energy. This is only 1% of the total pulse energy of the utilized few-cycle laser system23. All experiments reported herein were performed in vacuum to meet the requirements of the stereoATI measurements. However, CEP detection via optical fieldinduced currents in a solid dielectric can be achieved under ambient conditions, as demonstrated in ref. 22. The stabilized CEP of the laser pulses was modulated to allow every second pulse in the train to have the same wCE (that is, wCE was altered by p for consecutive pulses). This variation of wCE is beneficial for the isolation of CEP-dependent electric currents using a lock-in amplifier for removal of CEP-independent