We describe a method to probe the spectral fluctuations of a transition over broad ranges of frequencies and timescales with the high spectral resolution of Fourier spectroscopy, and a temporal resolution as high as the excited state lifetime, even in the limit of very low photocounting rates. The method derives from a simple relation between the fluorescence spectral dynamics of a single radiating dipole and its fluorescence intensity correlations at the outputs of a continuously scanning Michelson interferometer. These findings define an approach to investigate the fast fluorescence spectral dynamics of single molecules and other faint light sources beyond the time-resolution capabilities of standard spectroscopy experiments.
We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N time-domain measurements using a compressive-sensing reconstruction algorithm. We demonstrate the technique by resolving sparse vibrational spectra using <25% of the Nyquist rate samples in single-pulse CARS experiments. The method requires no modifications to the experimental setup and can be directly applied to any Fourier-transform spectroscopy measurement, in…
A new method, FM-FTS, combining Frequency Modulation heterodyne laser spectroscopy and Fourier Transform Spectroscopy is presented. It provides simultaneous sensitive measurement of absorption and dispersion profiles with broadband spectral coverage capabilities. Experimental demonstration is made on the overtone spectrum of C2H2 in the 1.5 $μ$m region.
Dispersive Fourier transformation is a powerful technique in which spectral information is mapped into the time domain using chromatic dispersion. It replaces a spectrometer with an electronic digitizer, and enables real-time spectroscopy. The fundamental problem in this technique is the trade-off between the detection sensitivity and spectral resolution, a limitation set by the digitizer's bandwidth. This predicament is caused by the power loss associated with optical dispersion. We overcome this limitation using Raman amplified spectrum-to-time transformation. An extraordinary loss-less -11.…
Spectra comprised of hundreds of time-components for absorption path lengths up to 130 km have been recorded around 1050 nm by combining two recent techniques, intracavity laser spectroscopy with vertical external cavity surface emitting multiple-quantum-well lasers and time-resolved Fourier transform spectroscopy. A sensitivity of 1 10^{-10} cm^{-1}.Hz^{-1/2} is achieved, for simultaneously acquired 10^4 spectral elements, three orders of magnitude better than the sensitivity obtained in previous similar experiments. Specific advantages of the method, especially for frequency and intensity me…
A combination of spatial interference patterns and spectral interferometry are used to find the global phase for non-collinear two-dimensional Fourier-transform (2DFT) spectra. Results are compared with those using the spectrally resolved transient absorption (STRA) method to find the global phase when excitation is with co-linear polarization. Additionally cross-linear polarized 2DFT spectra are correctly phased using the all-optical technique, where the SRTA is not applicable.
We propose a method to directly visualize the photonic band-structure of micron size photonic crystals using wide angle spectroscopy. By extending Fourier Imaging Spectroscopy sensitivity into the infrared range we have obtained accurate measurements of the band-structures along the high-symmetry directions (X-W-K-L-U) of polymeric three-dimensional rod-connected diamond photonic crystals. Our implementation also allows us to record single-wavelength reflectance far field patterns showing a very good agreement with simulations of the same designs. This technique is suitable for the characteriz…
We present a thorough analysis of the signal line shapes of Fourier transform-based noise-immune cavity-enhanced optical frequency comb spectroscopy (NICE-OFCS). We discuss the signal dependence on the ratio of the modulation frequency, f${_m}$, to the molecular line width, Γ. We compare a full model of the signals and a simplified absorption-like analytical model that has high accuracy for low f${_m}$/Γ ratios and is much faster to compute. We verify the theory experimentally by measuring and fitting NICE-OFCS spectra of CO${_2}$ at 1575 nm using a system based on an Er:fiber femtosecond lase…
Spatial resolution of most imaging devices is fundamentally restricted by diffraction. This limitation is manifested in the loss of high spatial frequency information contained in evanescent waves. As a result, conventional far-field optics yields no information about an object's subwavelength features. Here we propose a novel approach to recovering evanescent waves in the far field, thereby enabling subwavelength-resolved imaging and spatial spectroscopy. Our approach relies on shifting the frequency and the wave vector of near-field components via scattering on acoustic phonons. This process…
The spectral resolution of broadband Fourier-transform coherent anti-Stokes Raman spectroscopy is limited by the maximum optical path length difference that can be scanned within a short time in an interferometer. However, alternatives to the Fourier-transform exist which can bypass this limitation with certain assumptions. We apply one such approach to broadband coherent Raman spectroscopy using interferometers with short delay line (low Fourier spectral resolution) and large delay line (high Fourier spectral resolution). With this method, we demonstrate broadband coherent Raman spectroscopy …
A femtosecond mode-locked laser is used for the first time as a broadband infrared source for high resolution Fourier transform absorption spectroscopy. Demontration is made with a Cr^4+:YAG laser. The entire nu_1+nu_3 vibration-rotation band region of acetylene, observed after passing through a single pass 80-cm long cell, is simultaneously recorded between 1480 and 1600 nm, in 7.9 s with a signal to noise ratio equal to 1000. Two hot bands of the most abundant acetylene isotopologue and the n1+n3 band of the ^13C^12CH_2 are also present. The noise equivalent absorption coefficient at one sec…
Fourier transform spectroscopy (FTS) has been widely used in a variety of fields in research, industry, and medicine due to its high signal-to-noise ratio, simultaneous acquisition of signals in a broad spectrum, and versatility for different radiation sources. Further improvement of the spectroscopic performance will widen its scope of applications. Here, we demonstrate improved spectral resolution by overcoming the time window limitation using discrete Fourier transform spectroscopy (dFTS) with precisely periodic pulsed terahertz (THz) radiation. Since infinitesimal resolution can be achieve…
A Fourier-space based design approach for the systematic control of single and multiple photon localization states in a 1D lattice is presented. Resultant lattices are aperiodic in nature, such that lattice periodicity is not a useful optimization parameter to achieve novel field localization characteristics. Instead, direct control of field localization comes via control of the Parseval strength competition between the different Fourier components characterizing a lattice. This is achieved via an inverse optimization algorithm, tailoring the aperiodic lattice Fourier components to match that …
We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.2 microns. High power per comb mode (>10-7 W/mode) is obtained over a broad spectral span (>700 nm). The source is used for direct absorption spectroscopy with a Michelson-based Fourier transform interferometer.
In this paper, the design and the characterization of a novel interrogator based on integrated Fourier transform (FT) spectroscopy is presented. To the best of our knowledge, this is the first integrated FT spectrometer used for the interrogation of photonic sensors. It consists of a planar spatial heterodyne spectrometer, which is implemented using an array of Mach-Zehnder interferometers (MZIs) with different optical path differences. Each MZI employs a 3$\times$3 multi-mode interferometer, allowing the retrieval of the complex Fourier coefficients. We derive a system of non-linear equations…
Coherent extreme ultraviolet (XUV) radiation produced by table-top high-harmonic generation (HHG) sources provides a wealth of possibilities in research areas ranging from attosecond physics to high resolution coherent imaging. However, it remains challenging to fully exploit the coherence of such sources for interferometry and Fourier transform spectroscopy (FTS). This is due to the need for a measurement system that is stable at the level of a wavelength fraction, yet allowing a controlled scanning of time delays. Here we demonstrate XUV interferometry and FTS in the 17-55 nm wavelength rang…
Fourier transform spectroscopy with classical interferometry corresponds to the measurement of a single-photon intensity spectrum from the viewpoint of the particle nature of light. In contrast, the Fourier transform of two-photon quantum interference patterns provides the intensity spectrum of the two photons as a function of the sum or difference frequency of the constituent photons. This unique feature of quantum interferometric spectroscopy offers a different type of spectral information from the classical measurement and may prove useful for nonlinear spectroscopy with two-photon emission…
We demonstrate broadband and sensitive cavity ring-down spectroscopy using a near infrared frequency comb and a time-resolved Fourier transform spectrometer. The cavity decays are measured simultaneously and spectrally sorted, leading to purely exponential decays for each spectral element. The absorption spectra of atmospheric water and carbon dioxide are retrieved and demonstrate the high frequency resolution and absorption precision of the technique. The experimental apparatus, the measurement concept and the data treatment are described. The technique benefits from the advantages of cavity …
We demonstrate a 13-fold speed improvement in broadband cantilever-enhanced photoacoustic spectroscopy (CEPAS) by combining it with phase-controlled Fourier-transform spectroscopy (PC-FTS) instead of traditional Fourier-transform infrared spectroscopy (FTIR). PC-FTS is a modification of FTIR and capable of fundamentally faster interferogram acquisitions. The speed-improvement is beneficial for CEPAS, which is an especially sensitive version of the background-free photoacoustic spectroscopy technique. We used the PC-FTS-CEPAS technique to measure the absorption spectrum of methane in the mid-in…
Two-photon excitation spectroscopy with broad spectral span is demonstrated at Doppler-limited resolution. We describe first Fourier transform two-photon spectroscopy of an atomic sample with two mode-locked laser oscillators in a dual-comb technique. Each transition is uniquely identified by the modulation imparted by the interfering comb excitations. The temporal modulation of the spontaneous two-photon fluorescence is monitored with a single photodetector, and the spectrum is revealed by a Fourier transform.
The feasibility of sub-Doppler broadband multi-heterodyne spectroscopy with two laser frequency combs is demonstrated with two-photon excitation spectra of the 5S-5D transitions of rubidium vapor.
A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides, additionally beyond spectral intensity distribution, reconstruction of the investigated object's phase. The noise amplification Fellgett's disadvantage is relaxed by the application of sparse wavefront noise filtering embedded in the proposed algorithm. The algorithm reliability is proved by simulation tests and results of physical experiments on transparent obj…
Nonlinear interferometers allow for mid-infrared spectroscopy with near-infrared detection using correlated photons. Previous implementations have demonstrated a spectral resolution limited by spectrally selective detection. In our work, we demonstrate mid-infrared transmission spectroscopy in a nonlinear interferometer using single-pixel near-infrared detection and Fourier-transform analysis. A sub-wavenumber spectral resolution allows for rotational-line-resolving spectroscopy of gaseous samples in a spectral bandwidth of over 700$\,$cm$^{-1}$. We use methane transmission spectra around 3.3$…
Accurate characterization of thermal emitters can be challenging due to the presence of background thermal emission from components of the experimental setup and the surrounding environment. This is especially true for an emitter operating close to room temperature. Here, we explore characterization of near-room-temperature thermal emitters using Fourier-transform infrared (FTIR) spectroscopy. We find that the thermal background arising from optical components placed between the beam splitter and the detector in an FTIR spectrometer appears as a "negative" contribution to the Fourier-transform…
Nonlinear interferometers allow spectroscopy in the mid-infrared range by detecting correlated visible light, for which non-cooled detectors with higher specific detectivity and lower dark count rates are available. We present a new approach for the registration of spectral information, which combines a nonlinear interferometer using non-degenerate spontaneous parametric down-conversion (SPDC) with a Fourier-transform spectroscopy concept. In order to increase the spectral coverage, we use broadband non-collinear SPDC in periodically poled LiNbO$_3$. Without the need for spectrally selective d…
Optical two-dimensional Fourier-transformed (2DFT) spectroscopy is used to study the coherent optical response of potassium vapor in a thin transmission cell. Rephasing and non-rephasing spectra of the D1 and D2 transitions are obtained and compared to numerical simulations. Calculations using the optical Bloch equations gives very good agreement with the experimental peak strengths and line shapes. Non-radiative Raman-like coherences are isolated using a different 2DFT projection. Density-dependent measurements show distortion of 2DFT spectra due to pulse propagation effects.
The JILA Multidimensional Optical Nonlinear SpecTRometer (JILA-MONSTR) is a robust, ultra-stable platform consisting nested and folded Michelson interferometers that can be actively phase stabilized. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delay between them, while maintaining phase stability. The JILA-MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This arrangement is ideal for performing coherent optical experiments, such as …
Intracavity laser absorption spectroscopy (ICLAS) with an evacuated Cr2+: ZnSe laser is performed with a high-resolution time-resolved Fourier transform interferometer with a minimum detectable absorption coefficient equal to 4 10-9 cm-1 Hz-1/2 in the 2.5$μ$m region. This represents the extreme limit presently reached in the infrared by ICLAS with Doppler limited resolution. The broad gain band of the crystal allows a spectral coverage at most equal to 125 nm, wide enough to see entire vibration bands. Weak CO2 bands observed up to now only in the Venus atmosphere are recorded for the first ti…
Fourier transform spectroscopy (FTS) has been widely used as an analytical tool for many applications in science and engineering. In this paper, we describe the operation principle and practical implementation of an FTS prototype. First, the structure of an FTS setup based on optical interferometers is introduced, and its optical and electronic components are identified. A simple theory is presented to show the Fourier transform relationship between the measured interferogarm signal at the detector and the spectral intensity of the source. Then, simulation results based on ray-tracing method a…
This paper is devoted to the theoretical and experimental demonstration of the possibility to perform time-resolved diffusing wave spectroscopy: we successfully registered field fluctuations for selected photon path lengths that can overpass 300 transport mean free paths. Such a performance opens new possibilities for biomedical optics applications.
We demonstrate wavelength-wavelength correlations of classical broad-band amplified spontaneous emission (ASE) photons emitted by an erbium-doped fiber amplifier (EDFA) in a wavelength regime around 1530nm. We then apply these classical correlated photons in the framework of a real-world ghost spectroscopy experiment at a wavelength of 1533nm to acetylene (C2H2) reproducing the characteristic absorption features of the C-H stretch and rotational bands. This proof-of-principle experiment confirms the generalization of an ASE source concept offering an attractive light source for classical ghost…
Photon correlation spectroscopy (PCS) is based on measuring the temporal correlation of the light intensity scattered by the investigated sample. A typical setup requires a temporally coherent light source. Here, we show that a short-coherence light source can be used as well, provided that its coherence properties are suitably modified. This results in a "skewed-coherence" light beam allowing that restores the coherence requirements. This approach overcomes the usual need for beam filtering, which would reduce the total brightness of the beam.
We use two femtosecond Erbium-doped fiber lasers with slightly different repetition rates to perform a modern type of Fourier transform spectroscopy without moving parts. The measurements are done in real time, and it takes less than 50 microseconds. We work with somewhat different spectral outputs from two Erbium-doped fiber lasers and employ spectral filtering based on a 2f-2f grating setup to select the common spectral region of interest, thereby increasing the signal-to-noise ratio. The interferogram is taken with a 20 cm long gas cell, containing a mixture of acetylene and air at atmosphe…
We demonstrate lineshape measurement of an extreme-weak amplitude fluctuating light source by using the photon-counting-based second-order correlation spectroscopy combined with the heterodyne technique. The amplitude fluctuation of a finite bandwidth introduces a low-lying spectral structure in the lineshape and thus its effect can be isolated from that of the phase fluctuation. Our technique provides extreme sensitivity suited for single-atom-level applications.
Harnessing the quantum interference of photon-pair generation processes, infrared quantum absorption spectroscopy (IRQAS) can extract the infrared optical properties of a sample through visible or near-infrared photon detection without the need for an infrared optical source or detector, which has been an obstacle for higher sensitivity and spectrometer miniaturization. However, experimental demonstrations have been limited to wavelengths shorter than 5 um or in the terahertz region, and have not been realized in the so-called fingerprint region of 1500- 500 cm^-1 (6.6 to 20 um), which is comm…
We report the performance of a silicon wafer beamsplitter for use for low $Δν>0.3 cm^{-1}$ resolution Fourier transform spectroscopy at far infrared frequencies. We characterize the Si beamsplitter by comparing throughput spectra measured with it to those measured with the standard Mylar beamsplitters commonly used in that range. We find that the throughput of the silicon beamsplitter is substantially greater than that of the Mylar beamsplitters over most of the IR spectrum, and that they are comparable in some limited ranges. The 2 mm silicon beamsplitter has an etalon spacing of about 0.7 cm…
Fourier-transform spectroscopy (FTS) has been widely used as a standard analytical technique over the past half-century. FTS is a simple and robust autocorrelation-based technique that is compatible with both temporally coherent and incoherent light sources, which functions as an active or passive spectrometer. However, this technique has been mostly used for static measurements due to the low scan rate imposed by technological restrictions. This has impeded its application to continuous rapid measurements, which would be of significant interest for a variety of fields, especially when monitor…
Active Fourier Spectroscopy: From fixed sampling protocols to adaptive measurement
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；University of Oxford（牛津大学）；Max Planck Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Center for Molecular Fingerprinting (CMF)（分子指纹中心）
Intensity, wavevector, phase, and polarization are the most important parameters of any light beam. Understanding the wavevector distribution has emerged as a very important problem in recent days, especially at nanoscale. It provides unique information about the light-matter interaction. Back focal plane or Fourier plane imaging and spectroscopy techniques help to measure wavevector distribution not only from single molecules and single nanostructures but also from metasurfaces and metamaterials. This review provides a birds-eye view on the technique of back focal imaging and spectroscopy, di…
In quantum mechanics, photons are bosons -- there is no restriction on the number of them that occupy the same quantum state, so many of them can bunch together, and this is well known as photon bunching effect. However, photon bunching and multiphoton interference of bunched photons have never been directly observed from a broadband thermal chaotic light source. Nevertheless, it has been known that the interference intensity of a number N of bunched photons oscillates with a wavelength of N times shorter than the wavelength of the constituent single photons, which should be observable in Four…
Optical spectrum analysis is the cornerstone of spectroscopic sensing, optical network performance monitoring, and hyperspectral imaging. While conventional high-performance spectrometers used to perform such analysis are often large benchtop instruments, on-chip spectrometers have recently emerged as a promising alternative with apparent Size, Weight, and Power (SWaP) advantages. Existing on-chip spectrometer designs, however, are limited in spectral channel count and signal-to-noise ratio (SNR). Here we demonstrate a transformative on-chip digital Fourier transform (dFT) spectrometer that ca…
The spectral dynamics of a mid-infrared multimode Cr^2+:ZnSe laser located in a vacuum sealed chamber containing acetylene at low pressure is analyzed by a stepping-mode high-resolution time-resolved Fourier transform interferometer. Doppler-limited absorption spectra of C_2H_2 in natural isotopic abundance are recorded around 4000 cm^-1 with kilometric absorption path lengths and sensitivities better than 3 10^-8 cm-1. Two cold bands are newly identified and assigned to the n_1+n_4^1 and n_3+n_5^1 transitions of ^12C^13CH_2. The n_1+n_5^1 band of ^12C_2HD and fourteen ^12C_2H_2 bands are obse…
Broadband precision spectroscopy is indispensable for providing high fidelity molecular parameters for spectroscopic databases. We have recently shown that mechanical Fourier transform spectrometers based on optical frequency combs can measure broadband high-resolution molecular spectra undistorted by the instrumental line shape (ILS) and with a highly precise frequency scale provided by the comb. The accurate measurement of the power of the comb modes interacting with the molecular sample was achieved by acquiring single-burst interferograms with nominal resolution precisely matched to the co…
Fourier transform infrared (FTIR) spectrometers have been the dominant technology in the field of mid-infrared (MIR)spectroscopy for decades. Supercontinuum laser sources operating in the MIR spectral region now offer the potential to enrich the field of FTIR spectroscopy due to their distinctive properties, such as high-brightness, broadband spectral coverage and enhanced stability. In our contribution, we introduce this advanced light source as a replacement for conventional thermal emitters. Furthermore, an approach to efficient coupling of pulsed MIR supercontinuum sources to FTIR spectrom…
Extracting as much information as possible about an object when probing with a limited number of photons is an important goal with applications from biology and security to metrology. Imaging with a few photons is a challenging task as the detector noise and stray light are then predominant, which precludes the use of conventional imaging methods. Quantum correlations between photon pairs has been exploited in a so called 'heralded imaging scheme' to eliminate this problem. However these implementations have so-far been limited to intensity imaging and the crucial phase information is lost in …
Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using near-field infrared spectroscopic techniques to characterize materials nondestructively and with nanoscale spatial resolution. However, sub-optimal understanding of a technique's implementation can complicate data interpretation and even act as a barrier to enter the field. Here we outline the key detection and processing steps involved in producing scattering-type near-field nanoscale Fourier transform infrared spectra (nano-FTIR). The largely self-contained work (i) explains how normalized comp…
