An intrinsically phase-stable Sagnac interferometer is introduced for optimized interferometric detection in partially collinear two-dimensional (2D) spectroscopy. With a pump–pulse pair from an actively stabilized Mach–Zehnder interferometer, the Sagnac scheme is demonstrated in broadband, short-wave IR (1–2 μm), 2D electronic spectroscopy of IR-26 dye.
© 2014 Optical Society of America
Two-dimensional (2D) Fourier transform (FT) spectra show how a nonlinear signal field, as a function of radiated frequency, depends on an excitation frequency, revealing coupling between excitations . Except for a gap in the 1–2 μm short-wave IR region, 2D FT spectra are used from the terahertz  to the deep UV . Pulses in the short-wave IR  access low-energy electronic processes and next-generation photovoltaics, motivating extension to this region, where sensitivity is at a premium. 2D FT beam geometries range from fully noncollinear to fully collinear, with advantages and disadvantages for each. In all, three short pulses excite a sample, generating a nonlinear signal field that decays after the last pulse. The fully noncollinear 2D geometry produces a background-free signal field that is measured through optimized interference with a delayed local oscillator (LO) to sensitively detect both real absorptive and imaginary refractive parts of the 2D spectrum . The LO must be strong enough to raise interference with the signal above detector noise but not so strong that it swamps the signal with LO shot noise . In contrast, a limitation of partially collinear 2D spectroscopy is that the last pulse and nonlinear signal copropagate , which can make their interference more difficult to detect. Several groups have demonstrated the partially collinear pump–probe geometry [7–10], which selectively detects the real part of the 2D spectrum . The new method presented here combines the advantages of both geometries in a relatively compact and simple design: a partially collinear 2D spectrometer with a Sagnac interferometer creates a nearly background-free signal and selectively detects the absorptive 2D spectrum.
In a Sagnac interferometer, the output that returns light to the source has a symmetrical path (one beam splitter reflection with Fresnel coefficient and one transmission with Fresnel coefficient for each beam), which makes it the bright output . The more accessible, dark output of a lossless Sagnac has a phase shift  between a beam with two reflections (first- and second-surface, or and ) and one with two transmissions. The intrinsic stability and ease of alignment of a Sagnac interferometer are appealing for ultrafast phase spectroscopy and optical background suppression in pump–probe spectroscopies [12,13]. In such experiments, an external pump pulse crosses a sample inserted in the interferometer; the signal is detected via perturbation of the dark output . This Letter outlines the adaptation of such a Sagnac interferometer to a Brewster’s angle design  and its introduction for 2D spectroscopy. With a slight amplitude imbalance of the Sagnac beam splitter, destructive interference between probe and reference pulses forms an attenuated LO, which copropagates with the 2D signal field (Fig. 1).
In this experiment, pulses from a 1 kHz Ti:sapphire regenerative amplifier pump a single-pass, short-wave IR noncollinear optical parametric amplifier (NOPA) with a periodically poled stoichiometric lithium tantalate (PPSLT) crystal . The wavelength-tunable NOPA generates 1–2.5 μJ pulses that enter a grating compressor; compression with a deformable mirror uses second-harmonic generation (SHG) feedback in a genetic algorithm . After the compressor, the beam is spatially filtered with a 150 μm pinhole to remove any frequency-dependent angular deviations from the deformable mirror. Pulse durations of 30 fs are determined by zero-additional-phase spectral phase interferometry for direct electric-field reconstruction (ZAP-SPIDER)  and SHG frequency-resolved optical gating (SHG-FROG) . All spectral IR detection uses single-mode fiber coupling (ThorLabs 1060XP, ) to a 0.15 m Czerny–Turner spectrograph (Princeton Instruments SP-2150i) with a liquid nitrogen cooled pixel InGaAs array (Princeton Instruments OMAV:1024-2.2).
The 2D spectrometer consists of an actively stabilized Mach–Zehnder interferometer and a Sagnac interferometer. A broadband, inconel-coated glass window [15,19] splits the spectrometer input beam into pump and Sagnac-incident beams. All beam splitters in this apparatus exploit the air–glass interface Brewster’s angle to prevent additional surface reflections and their interference. The Brewster’s angle Mach–Zehnder interferometer with inconel beam splitters creates a pump–pulse pair (pulses and ) from the bright output with a delay, , roughly controlled by computerized translation stages. Interferometric feedback from a red He–Ne laser is used to drive a piezoelectric transducer (PZT) in one arm to lock with 0.6 nm rms stability during the 1 s collection of one interferogram. Actively stabilized steps in are taken at an integer plus a quarter cycle of the red He–Ne wavelength ; a yellow He–Ne laser is used to measure lock stability and track during a 2D scan.
The beam path entering the Sagnac interferometer is split into counterpropagating probe (, transmitted) and reference (ref., reflected) pulses in a Brewster’s angle Sagnac interferometer with a gold-coated beam splitter (Fig. 1). Thus, three pulses (, , and ) pass through two metallic beam splitters (inconel- or gold-coated, 1 mm thick glass) at oppositely signed Brewster’s angles for matched dispersion and spatial compensation before the sample. The counterpropagating reference pulse passes through the sample before the other three pulses. The off-axis collinear pump–pulse pair with delay impinges on the sample, followed by pulse at the computer-controlled delay , thus generating various nonlinear signals.
For Sagnac interferometers with planar beam paths and an even number of flat mirrors, clockwise and counterclockwise rays retrace each other exactly for all rays parallel to the central ray (common path), eliminating phase distortions . Femtosecond Sagnac interferometers have employed two flat mirrors , two flat mirrors plus a telescope [13,14], and three flat mirrors plus a telescope . Inserting a telescope to increase the nonlinear signal introduces an additional inversion. Ray tracing in the horizontal plane of Fig. 1 reveals a common path because the beams undergo an even number (4) of left–right reversals within the Sagnac: one from each of the three mirrors plus one from the telescope. However, the telescope inversion makes counterpropagating images upside down relative to each other inside the Sagnac, allowing differential phase distortions, which are minimized by a 2 mm beam diameter centered on the common path horizontal plane. With one vertical inversion, all output images are upside down (similar to the horizontally reflected outputs for an odd number of mirrors ), so spatial phase imperfections in the input beam cancel.
The final component of the 2D spectrometer is the signal detection in the Sagnac dark output (Fig. 1). The gold-coated beam splitter recombines the out-of-phase probe, , and reference, , where is the field incident on the Sagnac beam splitter, to produce an attenuated LO, . The 2D signal copropagates with the LO and background terms, given by1) are of the form with wavevectors . For , and ; for , and . The only terms with a dependence are one pump–probe field with pulse or as pump, , and the sum of 2D fields, .
The Sagnac interferometer beam splitter requires careful attention to ensure a phase shift between dark outputs and while avoiding dispersion. The Brewster’s angle beam splitter (Fig. 1) has an thin film of gold deposited on a 1 mm thick BK7 substrate. The refractive index, , of amorphous gold has  to ensure a nearly phase shift (170°–171°, compared to with inconel) between dark output pulses ( versus ). Destructive interference in the dark output suppresses the in-phase component of the reference pulse and increases the phase error of the LO as the LO is attenuated. Near 1100 nm wavelength, the beam splitter absorbs 7%, reflects 37%, and transmits 56% of the incident pulse energy, yielding an LO phase error of 15° after accounting for six-fold attenuation.
2D spectra of readily available cyanine dyes were used to test the first femtosecond 2D FT spectrometer  and have been replicated in testing new approaches to 2D FT spectroscopy in the visible . Because of this work, the form of the 2D spectrum is known for cyanine dyes, making them suitable for this first demonstration of 2D FT spectroscopy in the short-wave IR. The heptamethine cyanine infrared dye IR-26 has been previously characterized with steady-state absorption and photoluminescence spectroscopy [25,26]. Here, a 30 fs pulse centered at 1100 nm is used to excite and probe dynamics at the red edge of the IR-26 spectrum in dichloroethane using degenerate, partially collinear 2D spectroscopy (flowing sample, 200 μm path length, maximum optical density (OD) at 1080 nm). IR-26 has an excited-state lifetime of 22 ps, which is two orders of magnitude less than the 1.5 ns reference delay in the Sagnac; thus, vanishes in Eq. (1). Following background subtraction of the -dependent pump–probe signals, and , in Eq. (1), an FT with respect to isolates the interference term .; division by yields .
The phase corrections of 2D spectra are simplified in the partially collinear geometry because the third pulse also acts as the LO. The only required phase correction in arises from the spectral phase difference, , between pulses and . Characterization of the Mach–Zehnder  yields a near-linear that corresponds to the lack of a sampling point in the PZT locking scheme; specifically, , where is the delay closest to zero. Phase shifting the raw 2D spectrum,2 for all-parallel pulse polarizations. In the spectrum (left panel, Fig. 2), the diagonally elongated positive peak reflects the strong correlation between excitation frequency, , and detection frequency, . Also, a slight shift above the diagonal and the off-diagonal, negative (blue) region are indicative of vibrational and solvent frequency memory . By relaxation time, nearly all correlation between and is lost: the peak is purely positive, approaches a product line shape, and is shifted above the diagonal by the Stokes shift (right panel, Fig. 2). The performance of the 2D spectrometer is verified by agreement between experimental 2D spectra and predicted spectra at large calculated with absorption line shapes, emission line shapes, and propagation-corrected pulse spectra .
The 2D spectra in Fig. 2 measure nonlinear response tensor element . Although the probe polarization is fixed, the pump pulse polarizations can be varied, for example to measure . Complementary to the Sagnac approach developed here, 2D spectra for tensor elements and have been measured using a polarizer for background suppression .
The optimization of signal detection with a Sagnac interferometer is a useful feature of this 2D spectrometer design. The thin-film gold Sagnac beam splitter increases the ratio of the third-order signal to LO by up to a factor of six compared to the pump–probe geometry. This factor can be reduced (in the case of a large signal) by a slight misalignment of the Sagnac interferometer or increased (for a small signal) by using a beam-splitter coating with more even splitting in a desired frequency range (which requires a more accurate phase shift in the dark output, obtainable with thin films of germanium). With suitable beam splitters, extension to 2D spectroscopy with a supercontinuum probe may be possible . While the final transmission through the Sagnac beam splitter attenuates the signal, the LO is effectively attenuated even more: the destructive interference in the Sagnac creates a LO with of both the intensity and laser power fluctuations of the original LO (pulse ). The ability to control and reduce the LO intensity would be especially useful in experiments on systems with weak 2D signals. The signal detection improvement, stability, and simplicity of this geometry have opened up a new wavelength region for 2D FT spectroscopy.
We thank Octavi Semonin (NREL) for coating the gold beam splitter and Giulio Cerullo for helpful discussions about the IR NOPA. This material is based upon work supported by the National Science Foundation under Grant No. CHE-1112365.
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