Mach-Zehnder interferometer for measuring the pump beam–induced phase shift
This protocol is extracted from research article:
Large negative thermo-optic coefficients of a lead halide perovskite
Sci Adv, Jul 19, 2019; DOI: 10.1126/sciadv.aax0786

We measured the transient optical phase shift during pump beam irradiation of MAPbCl3 by using a Mach-Zehnder interferometer modified from the above setup (fig. S5). The MAPbCl3 single crystal was excited by 750-nm pump pulses, which were obtained from a femtosecond laser system (200 kHz; Pharos, Light Conversion) in combination with an optical parametric amplifier (OPA) (Orpheus, Light Conversion). The pulse duration was measured by the intensity autocorrelation measurement; the full width at half maximum (FWHM) of the pulse was 230 fs, assuming a Gaussian function. The spot size of the pump beam wpump (defined by the radius at which the intensity falls to 1/e of the intensity at the center) was 68.4 μm at the sample position. The light with wavelength longer than the optical bandgap of MAPbCl3 leads to two-photon absorption with a large penetration depth (see fig. S7). This induces lattice heating through relaxation of energetic carriers to the band edge and nonradiative interband recombination.

The time-resolved phase shift was measured by the pump beam–synchronized data acquisition with the modified Mach-Zehnder interferometer setup (18). To measure the phase shift, we used monochromatic light with an FWHM of ~5 nm obtained from the supercontinuum light source operated at 40 MHz and a wavelength-tunable band-pass filter (SuperChrome, Fianium). The monochromatic light was split into probe and reference beams by a PBS. The probe beam with horizontal polarization was coaxially aligned with the pump beam axis and normally incident on the (001) surface of the MAPbCl3 single crystal. The power and spot size of the probe beam at the sample position were set to 65 μW and ~36 μm, respectively. The fluence of the probe beam was ~40 nJ/cm2 and thus sufficiently weak to induce neither nonlinear absorption nor refractivity. By the second PBS, the probe and reference beams were combined, and the intensity of interference light was detected by using a photodetector (2001-FS-M, New Focus). A short-pass filter was placed after the second PBS to prevent the pump laser from entering the detector. An optical chopper operated at 4 Hz was used to modulate the pump beam, and a data acquisition module (NI USB-6251, National Instruments) was used to measure the transient response of the thermo-optic phase shift. By scanning the probe path length on the order of nanometer by the piezoelectric actuator, the optical phase was determined. The piezoelectric actuator also enables us to determine whether the measured phase shift is positive or negative. Using the above procedure, we measured the time-resolved phase shift of the probe beam in the MAPbCl3 during photoexcitation. The measurements were performed in air at room temperature.

The polarization patterns plotted in Fig. 4 were obtained after inserting a half-wave plate in front of the photodetector. By rotating it, we detected the angular dependence of the interference between probe and reference beams for different pump powers.

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