WO2024044577A2 - Phasemètre optique pour interférométrie - Google Patents

Phasemètre optique pour interférométrie Download PDF

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WO2024044577A2
WO2024044577A2 PCT/US2023/072632 US2023072632W WO2024044577A2 WO 2024044577 A2 WO2024044577 A2 WO 2024044577A2 US 2023072632 W US2023072632 W US 2023072632W WO 2024044577 A2 WO2024044577 A2 WO 2024044577A2
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light
sfg
lock
amplifier
frequency
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WO2024044577A3 (fr
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Sarah B. KING
Nasim S. MIRZAJANI
Clare KEENAN
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The University Of Chicago
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G01B9/02002—Interferometers characterised by controlling or generating intrinsic radiation properties using two or more frequencies
    • G01B9/02003—Interferometers characterised by controlling or generating intrinsic radiation properties using two or more frequencies using beat frequencies
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B2290/00—Aspects of interferometers not specifically covered by any group under G01B9/02
    • G01B2290/70—Using polarization in the interferometer

Definitions

  • Sum frequency generation is a second-order non-linear optical technique that is a powerful tool for probing buried interfaces by taking advantage of the symmetry properties of the complex second-order nonlinear susceptibility % (2) .
  • SFG Sum frequency generation
  • the ubiquity and importance of interfaces in chemistry makes SFG a very attractive method due to its all- optical, non-invasive nature. It has found prominence with vibrational studies in particular, for determining structure and orientation of interfacial molecules.
  • SFG spectroscopy has yet to become a widespread technique for the study of interfacial electronic structure and dynamics.
  • experiments that require repeated spectral acquisitions over varying sample properties such as time-resolved experiments, have proven uncommonly challenging.
  • An illustrative interferometric measurement system includes a light source that generates a sample beam of light and a local oscillator that oscillates a portion of the sample beam of light to form an oscillated beam of light.
  • the system includes a mirror that includes a vibrating element which causes the mirror to vibrate at a frequency, where the mirror receives the oscillated beam of light and modulates a phase of the oscillated beam of light.
  • the system includes a lock-in amplifier that is locked into the frequency of vibration of the mirror such that the lock-in amplifier receives the oscillated beam of light which has been modulated at the frequency.
  • a processor is in communication with one or more of the light source, the local oscillator, and the lock-in amplifier, and is configured to detect, based at least in part on data from the lock-in amplifier, a relative phase between the oscillated beam of light and the sample beam of light.
  • the processor is also configured to detect an interference signal and correct a pathlength difference between the oscillated beam of light and the sample beam of light based at least in part on the relative phase.
  • the processor is further configured to apply the corrected pathlength difference to the interference signal to correct for phase variation that occurs during a measurement.
  • An illustrative method for performing interferometric measurements includes generating, by a light source, a sample beam of light.
  • the method includes oscillating, by a local oscillator, a portion of the sample beam of light to form an oscillated beam of light.
  • the method includes vibrating, at a frequency, a mirror that receives the oscillated beam of light to modulate a phase of the oscillated beam of light.
  • the method includes receiving, by a lock- in amplifier that is locked into the frequency of vibration of the mirror, the oscillated beam of light which has been modulated at the frequency.
  • the method includes detecting, by a processor and based at least in part on data from the lock-in amplifier, a relative phase between the oscillated beam of light and the sample beam of light.
  • the method also includes detecting, by the processor, an interference signal.
  • the method also includes correcting, by the processor, a pathlength difference between the oscillated beam of light and the sample beam of light based at least in part on the relative phase.
  • the method further includes applying, by the processor, the corrected pathlength difference to the interference signal to correct for phase variation that occurs during a measurement.
  • Fig. 1 is a simple schematic of a Mach-Zehnder interferometer (MZI) set up for continuous phase modulation in accordance with an illustrative embodiment.
  • MZI Mach-Zehnder interferometer
  • FIG. 2 depicts modulations in the interference between two fields of a spectrometer in accordance with an illustrative embodiment.
  • FIG. 3 depicts an experimental schematic of the proposed MZI in accordance with an illustrative embodiment.
  • Fig. 4A shows a CW diode signal locked into the second harmonic of mirror vibration frequency in accordance with an illustrative embodiment.
  • Fig. 4B shows a CW diode signal locked into the third harmonic of the mirror vibration frequency in accordance with an illustrative embodiment.
  • Fig. 4C shows the SFG signal locked into the first harmonic of the mirror vibration frequency in accordance with an illustrative embodiment.
  • Fig. 5A shows the measured value of A ⁇ /> plotted against the original time delay axis in accordance with an illustrative embodiment.
  • Fig. 5B shows A ⁇ /> plotted against the reconstructed delay axis in accordance with an illustrative embodiment.
  • Fig. 5C shows the difference between the original axis plotted and the new axis, plotted against the new axis in accordance with an illustrative embodiment.
  • Fig. 5D shows the drift in path length over the full length of the scan in accordance with an illustrative embodiment.
  • Fig. 6A shows a Fourier transform of (a) the raw diode data showing the frequency of the diode at 1.89 eV in accordance with an illustrative embodiment.
  • Fig. 6B depicts frequency domain GaAs spectra showing three peaks at 2.92 eV (second harmonic of 850 nm fundamental), 3.54 eV (SFG of 850 nm and 600 nm), and 4.09 eV (second harmonic of 600 nm) in accordance with an illustrative embodiment.
  • Fig. 6C shows a non-uniform Fourier transform of the phase corrected data from Fig. 6A showing narrower peaks with less noise and higher intensity in accordance with an illustrative embodiment.
  • Fig. 6D shows a non-uniform Fourier transform of the phase corrected data from Fig. 6B showing narrower peaks with less noise and higher intensity in accordance with an illustrative embodiment.
  • Fig. 7 shows Bessel function values as a function of mirror modulation amplitude for various relevant wavelengths in accordance with an illustrative embodiment.
  • Fig. 8 shows the reported position of the piezo of the vibrating mirror as a function of time, determined using capacitive sensing in accordance with an illustrative embodiment.
  • Fig. 9A depicts raw spectra data obtained at different fundamental wavelengths in accordance with an illustrative embodiment.
  • Fig. 9B depicts corrected spectra data obtained at different fundamental wavelengths in accordance with an illustrative embodiment.
  • Fig. 10A depicts raw spectra data from z-cut quartz in the sample position and GaAs as the LO source in accordance with an illustrative embodiment.
  • Fig. 10B depicts corrected spectra data from z-cut quartz in the sample position and GaAs as the LO source in accordance with an illustrative embodiment.
  • FIG. 11 A shows spectra corresponding to Fig. 6D collected with a traditional frequency domain spectrometer in accordance with an illustrative embodiment.
  • Fig. 1 IB shows spectra corresponding to Fig. 10 collected with a traditional frequency domain spectrometer in accordance with an illustrative embodiment.
  • Fig. 11C shows spectra corresponding to Fig. 9 collected with a traditional frequency domain spectrometer in accordance with an illustrative embodiment.
  • Fig. 12 is a block diagram of a computing system to implement a phase correction system in accordance with an illustrative embodiment.
  • Fig. 13 depicts a system that utilizes a broadband white light probe in accordance with an illustrative embodiment.
  • Fig. 14 shows proof of principle experiment results for phase correction with the chopper and two lock in amplifier scheme of Fig. 13 in accordance with an illustrative embodiment.
  • Fig. 15 shows a comparison of the two schemes with broadband light in accordance with an illustrative embodiment.
  • Heterodyne detection sum frequency generation (HD SFG) spectrometers are used to separate and measure various spectral components of an object with great accuracy.
  • Sum frequency generation (SFG) is a second-order non-linear optical technique that has found application as a powerful tool for probing buried interfaces by taking advantage of the symmetry properties of the complex second-order nonlinear susceptibility %(2).
  • e-SFG broadband electronic SFG
  • a broadband pulse EVis(rol) is temporally and spatially overlapped with a narrowband infrared pulse ENIR(co2).
  • ENIR(co2) narrowband infrared pulse
  • the interaction of the pulses with the system susceptibility %(2) results in the SFG signal ESFG(a>l+2) radiated at the sum frequency.
  • the response of the system /(2) is encoded within the detected SFG field ESFG(col+2) and has all the spectroscopic information that is of interest to scientists.
  • Heterodyne detection is often used to detect the phase of the emitted ESFG(col+2) field, encompassing a wealth of information without which the data about y( 2) is distorted, as well as to boost the signal to noise ratio.
  • Heterodyne detection is an interference measurement where a strong, known field, called the local oscillator (LO) mixes with the SFG signal.
  • LO local oscillator
  • the interference pattern is created by changing the path length of one light wave with respect to the other, and so changing their relative phase, over the length of a scan.
  • the relative phase between the waves must be known at all times.
  • the relative phase is experimentally controlled by scanning a mechanical stage that extends or shortens the pathlength that one of the light waves travels.
  • the pathlength difference and therefore the relative phase of the two light waves is held constant, but must remain a known and constant quantity.
  • phase stability between the SFG signal and the local oscillator in such experiments is critical for obtaining an accurate signal.
  • Traditional heterodyne detection sum frequency generation (HD_SFG) spectrometers rely on passive phase stabilization techniques where phase stability between local oscillator (LO) and SFG fields is achieved by implementing collinear geometries where the LO and SFG beams are incident on the same optics and thus experience pathlength drift by the same amount.
  • Passive stabilization does not ensure stability over long periods of time and is not suitable for extended time-resolved studies.
  • Phase instability results in distorted data and low signal to noise ratio (SNR). For SFG signals which are inherently weak and difficult to detect, phase instability is detrimental.
  • Some active stabilization techniques have been used in other areas of spectroscopy (such as 2D IR spectroscopy) where phase drift is detected and a closed-loop feedback circuit is used to undo the path length difference arising from drift in the optics by readjusting the position of a mechanical stage.
  • spectroscopy such as 2D IR spectroscopy
  • phase drift is detected and a closed-loop feedback circuit is used to undo the path length difference arising from drift in the optics by readjusting the position of a mechanical stage.
  • a closed-loop feedback circuit is used to undo the path length difference arising from drift in the optics by readjusting the position of a mechanical stage.
  • the proposed system is a spectrometer that uses sum frequency generation (SFG) to unravel chemical properties of matter in buried interfaces.
  • the spectrometer enables phase-sensitive measurements by using heterodyne detection (HD), and the design of the spectrometer ensures that instabilities in the optical setup of the spectrometer do not compromise the fidelity of the detected data.
  • FSG sum frequency generation
  • HD heterodyne detection
  • phase stability for heterodyne detected SFG (HD-SFG) data over long periods of time ensures high-quality high-fidelity data from buried interfaces for lengthy experiments such as time- resolved studies that elucidate the dynamics of molecules at interfaces.
  • the proposed spectrometer design ensures that the system is not reliant on knowledge of optical pathlength difference between the LO and SFG fields alone for the relative phase.
  • the relative phase is obtained directly through signal processing based on the underlying physics behind the design of the experimental set up.
  • the system uses continuous phase modulation of the local oscillator field to expand the interference signal in terms of its Fourier coefficients, which allows one to obtain the relative phase between the LO and the SFG field.
  • Continuous phase modulation of the LO field is achieved by reflecting the LO beam off a mirror connected to a vibrating element.
  • a lock-in amplifier is used to detect the interference signal locked into the harmonics of the mirror vibrations frequency.
  • the optical scheme can be as follows: the SFG and the LO fields make up two arms of a Mach-Zehnder interferometer.
  • the sample arm enters a delay line with a computer-controlled delay stage and the LO line is sent to a retroreflector fitted with a piezo phase shifter, vibrating the retroreflector at 800 Hz.
  • the two arms are then recombined and go through a series of dichroic mirrors to separate the UV SFG beams from the visible and near IR fundamental beams as well as the CW beam.
  • different frequencies may be used.
  • avalanche photodiode (APD) detectors can be used to detect the SFG signal and the CW reference beam.
  • the detectors are fed into a lock-in amplifier (e.g., Zurich Instruments MFLI) that is locked into the frequency of the vibrations such that only signal that is modulated by that frequency is detected.
  • the inventors have written software that processes the data from the lock-in amplifier to detect the relative phase between the LO and SFG fields, detect the interference signal, correct the pathlength difference between the LO and SFG based on their relative phase and apply the corrected pathlength difference to the interference signal.
  • a vibrating mirror is used to modulate interference. Specifically, the mirror vibrates at a known frequency (v r ) at each time delay, and the vibration induces modulations in the interferogram. The change in phase is measured at each time delay using a narrowband diode laser as a proxy.
  • sum frequency generation is a second-order non-linear optical technique that is a powerful tool for probing buried interfaces by taking advantage of the symmetry properties of the complex second-order nonlinear susceptibility x (2> .
  • e-SFG broadband electronic SFG
  • a broadband pulse Evis(un) is temporally and spatially overlapped with a narrowband near-infrared pulse ENIR(U>2).
  • ENIR(U>I +2) results in the SFG signal ESFG(U>I +2) radiated at the sum frequency in the ultraviolet region, as described by Equation (1) below:
  • Nonresonant contributions are in the real portion of /' 2
  • 2 is proportional to the square of the density of interfacial molecules and not conducive to quantitative spectrometric experiments where intensity is expected to be proportional to sample concentration or density.
  • spectra are acquired alternately with and without the presence of the pump pulse at each time delay. The unpumped (steady-state) spectrum is subtracted from the pumped spectrum to obtain AESFG. To correctly interpret time-resolved data from A
  • Phase-sensitive (PS) experiments provide a solution to these problems by detecting ESFG rather than
  • Heterodyne detection is a phase-sensitive measurement where the interference between the SFG field and a local oscillator (LO) field is measured.
  • the LO is generated separately from the SFG using the same incident fields Evis and EIR and contains the same frequencies as the SFG field.
  • the interference with LO generates both
  • the cross term is not a square modulus and can access the complex values of the electric fields.
  • heterodyne detection enables the separation of real and imaginary parts of X (2) and the measurement of the sign of the electric field. Since the LO is a much stronger signal than the SFG, mixing the two also increases the signal to noise ratio (SNR).
  • SNR signal to noise ratio
  • obtaining correct signals in heterodyne detection hinges on phase stability between the LO and SFG fields throughout the experiment. This presents a challenging technical hurdle that is particularly highlighted in the case of electronic SFG experiments that generate visible and UV light. At these wavelengths, drifts of tens of nanometers in the relative path lengths betw een the SFG and LO fields lead to dramatic phase shifts of as much as -. Small errors in the optical path length caused by, for example, ambient laboratory vibrations and thermal fluctuations compromise the stability of the interferometer, making detection of heterodyned SFG signal difficult.
  • phase-sensitive SFG methods respond to the problem of stability by employing passive phase stabilization.
  • Many vibrational and almost all electronic SFG studies use spectral interferometry of collinear LO and SFG pulses detected in frequency domain to measure phase of the SFG signal.
  • the LO and SFG light experience similar path length dnft by impinging on the same optics, facilitating passive phase stabilization.
  • passive phase stabilization is not sufficient to eliminate uncertainty in phase and amplitude between time delay measurements.
  • Phase instability is the main barrier to performing heterodyned time-resolved electronic SFG experiments.
  • the relative height of the sample and the reference must remain the same to micron accuracy for every measurement to ensure correct measurement of the phase of % (2) . This is cumbersome, particularly in the case of liquid interfaces which may undergo evaporation during the experiment.
  • phase-locked pulse pairs are used in many nonlinear spectroscopic techniques where phase cycling is used for selective detection of quantum pathways.
  • many techniques have been introduced including active stabilization methods using closed-loop feedback circuits, passive stabilization using diffractive optics, and acousto-optic pulse shaping.
  • phasemodulation using acousto-optic modulators (AOM) was applied to detection of 2D fluorescence and photocurrent spectroscopy. It has since become a popular method for dynamic rephasing in 2D electronic spectroscopy.
  • Phase modulation with a vibrating mirror has also been used in pseudo-heterodyning in scanning near-field optical microscopy (SNOM) to acquire background suppression and simultaneous measurement of phase and amplitude of near-field images.
  • SNOM scanning near-field optical microscopy
  • Fig. 1 is a simple schematic of a Mach-Zehnder interferometer (MZ1) set up for continuous phase modulation in accordance with an illustrative embodiment. This simplified schematic shows the time delay axis control with the stage in one arm, and real time phase modulation with a vibrating mirror in the other arm.
  • MZ1 Mach-Zehnder interferometer
  • the time delay between two interferometer arms is experimentally set by changing the optical path length difference between the LO and SFG fields, but is beset by instabilities in the optics.
  • the proposed system collects the relative phase data and corrects for all instabilities at once in post-processing.
  • a direct report of the relative phase between the LO and SFG fields allows one to reconstruct the time delay axis to account for unintended changes in the path length.
  • the proposed spectrometer design paves the way for phase stable time domain detection of heterodyne SFG spectra, eliminating the above mentioned concerns for vibrational spectra, while allowing electronic spectra to benefit from the advantages of single channel detectors with higher sensitivity, lower noise, and lower costs than frequency domain detectors. Achieving phase stability over extended periods will make time-resolved studies with long experiment run-times possible for investigating both electronic and vibrational interfacial states.
  • the SFG and LO fields each form one arm of a Mach-Zehnder interferometer (MZI).
  • MZI Mach-Zehnder interferometer
  • a time varying phase shift is applied to the LO field by reflecting the LO off a vibrating mirror, as shown in Fig. 1.
  • Equation (5) A Jacobi-Anger expansion allows for a Fourier representation of the sinusoidal frequency modulated signal as a sum of harmonic components weighted by Bessel functions of varying order. Expanding Equation (5) in this manner leads to the following expression for the phase-modulated field:
  • Jm [y] is the mth order Bessel function evaluated at y.
  • Fig. 2 depicts modulations in the interference between two fields of a spectrometer in accordance with an illustrative embodiment.
  • the upper row depicts relative phase of 0
  • the middle row depicts relative phase of pi/3
  • the bottom row depicts relative phase of pi/2.
  • the leftmost trace is a cartoon of the unmodulated interferogram, where the dots indicate the point in time delay marked by the relative phase of the two arms, A ⁇ ty and the arrows indicate how the vibrating minor modulates the interferogram intensity.
  • the middle trace in each row shows the result of the modulation at various time delays (i.e., the interference pattern in real time due to vibrations of the mirror in one arm of the interferogram) indicated by the dots.
  • the expansion of this signal into its Fourier series yields the series of peaks at harmonics m of the frequency v r , shown in the rightmost plots of Fig.
  • the intensity of the peak at the mth harmonic of the modulation frequency is denoted as Um.
  • Equation (8) shows the mathematical expression of the side-band intensities Um as detected by the lock-in amplifier.
  • Equations (8) and (9) show the dependence of Um on A ⁇ /> and its relationship to the interference of the Ei and E2 fields.
  • the detected Um signals (shown in Fig. 4, which is described in more detail below), are a periodic function of A ⁇ />, as shown in Equation 8.
  • the Um signal in Fig. 4 may be treated as an interferogram whose Fourier transform is the frequency domain spectrum of the shared frequencies in Ei and E2 fields. This implies that the Um signal detected as a function of time delay can be used to find the frequencies present in SFG and LO fields.
  • Relative phase A0 can be calculated from the ratio of intensity of two consecutive odd and even side bands as shown in Equation (10) where Jk and ]i are k (odd) and I (even) order Bessel functions:
  • Equation (11) For the case of broadband light where ESFG and ELO have finite bandwidth, a simplified expression describing the fields is a sum over the number n of colors present, shown in Equation (11): Equation (11)
  • Equation (8) This expression is substituted for the electric fields in Equation (7), with each color having a different relative phase.
  • Equation (8) becomes a sum over the number n of colors present:
  • Equation (10) for the broadband fields becomes:
  • Equation (13) is analytically intractable. Since the real source of phase instability is in path length difference, which unlike phase, is color-independent, a narrowband reference can be used for the purpose of phase detection.
  • the inventors therefore co-propagate a narrowband continuous wave (CW) laser diode with the ESFC and Eio fields, to be used for detecting the relative phase of the arms of the MZI. This is a valid approach given the generality of the signal processing procedure detailed above for any light analyzed by interferometry.
  • the frequency spectrum of the CW laser is closer to a delta function than the frequency spectra of ultrashort laser pulses are, giving a more accurate value for the phase difference between the two arms that can be converted to a path length difference.
  • visible and near infrared up-conversion pulses are generated by a commercial OPA system (e.g., Light Conversion Orpheus N-2H and N-3H) with two outputs at 600 nm (150 mW) and 850 nm (500 mW), with sub 30 fs pulse duration at 50 kHz repetition rate. Alternatively, different output values may be used. Both fields are P-polarized.
  • the two pulses at 600 nm and 850 nm are made collinear using an in-coupling dichroic mirror (e.g., Thorlabs) before they enter a Mach-Zehnder type interferometer.
  • a 50/50 broadband, low GDD beamsplitter (e.g., Thorlabs) is used to split the overlapped beams into two arms.
  • a narrowband CW laser e.g., Newport LQC660-110C
  • the beam-splitter at 90 degrees to the pulsed laser light, as shown in Fig. 3, such that it travels collinearly with the pulsed light into the interferometer.
  • Fig. 3 depicts an experimental schematic of the proposed MZI in accordance with an illustrative embodiment.
  • the path of the collinear beams is shown as they enter the interferometer and are incident on the LO and sample crystals, with shaded dashes to depict the signals on each line.
  • a fundamental signal into the system is split by a beamsplitter and directed by parabolic mirrors to the sample and a local oscillator.
  • the SFG signal also shown, travelling collinearly with the SFG and LO beams throughout the MZI.
  • Each ami is focused by a parabolic mirror onto a sample or local oscillator source, in reflection geometry, and is subsequently recollimated along with the resulting SFG, where one arm of the interferometer contains the sample signal and the other functions as the local oscillator field.
  • the LO arm enters a delay line with a computer controlled delay stage (e.g., PI N565) and the sample line is sent to a retroreflector fitted with a piezo phase shifter (e.g., PI S-303), vibrating the retroreflector at 800 Hz.
  • the two arms are then recombined using a low GDD beam splitter (e.g., Thorlabs).
  • the recombined beams then go through a series of dichroic minors (e.g., Eksma) to separate the UV SFG signal from the visible and near IR fundamental fields as well as the CW laser.
  • the SFG signal is directed towards the first avalanche photodiode (e.g., Thorlabs APD 130A2).
  • the CW diode has a perpendicular polarization relative to the fundamentals and is separated from them using a Wollaston prism and is directed towards a second avalanche photodiode (e.g., Thorlabs APD 130A).
  • the photodiode outputs are passed to a lock-in amplifier (e.g., Zurich Instruments MFLI) that also serves as the signal source for the phase shifter.
  • the lock-in amplifier is simultaneously locked into multiple harmonics of the frequency of the vibrations, ft is noted that the proof-of-concept experiments that showcase the capabilities of this spectrometer use SFG spectra of a GaAs(lOO) single crystal purchased from MTI corp.
  • Fig. 4 depicts time domain data collected on the three locked-in signals received by the lock-in amplifier in accordance with an illustrative embodiment.
  • Fig. 4A shows a CW diode signal locked into the second harmonic of mirror vibration frequency in accordance with an illustrative embodiment.
  • FIG. 4B shows a CW diode signal locked into the third harmonic of the mirror vibration frequency in accordance with an illustrative embodiment. These intensities are the Um values used for detecting relative phase between the two arms of the MZI.
  • Fig. 4C shows the SFG signal locked into the first harmonic of the mirror vibration frequency in accordance with an illustrative embodiment. As discussed, the CW signals are used for determining the phase difference between the two arms of the MZI.
  • the CW diode beam is divided and co-propagated with both the LO and the SFG fields, and is subjected to the same treatments.
  • the phase modulation of the LO arm by the phase-shifter results in modulation of the interference signal.
  • the lock-in amplifier detects the intensity Um of harmonic m of the phase modulated signal in real-time for every time delay between the two arms of the MZI.
  • two channels on the lock-in amplifier were locked into the second and third harmonics of the reference frequency, Vr, which is also used as the frequency of the phaseshifter. These channels receive signal from the APD detecting the CW diode beam and are depicted in Figs. 4A and 4B.
  • a third channel is locked into the first harmonic of v r and detects the pulsed SFG signal, shown in Fig. 4C.
  • the value of the Bessel function modulates the signal intensity.
  • the Bessel function value J [y] depends on the wavelengths of light (2) present in the SFG light, the value of the integer m, and the vibration depth (AL) of the phase shifter. Judicious selection of the harmonic of the lock-in reference frequency and vibration depth of the phase shifter can increase the signal to noise ratio as well as eliminate unwanted fundamental wavelengths on the detector.
  • Fig. 5A shows the measured value of A ⁇ /> plotted against the original time delay axis in accordance with an illustrative embodiment. Given a high sampling rate and stable conditions, this plot should be a perfect saw-tooth shape, as phase changes from -n to TT for each period of the wavelength. Instabilities in phase can be seen in the form of ‘kinks’ in the plot in Fig. 5A, which are circled. The small lines in Fig. 5A show error boundaries for A ⁇ /> values. It is noted that the error is too small at some points to distinguish the upper and lower bounds in the figure. The kinks disappear from the plot when phase is plotted against a time delay axis that corresponds to the true phase difference. To achieve this, the inventors recreated the time delay axis using the measured A ⁇ /> values.
  • Fig. 5B shows A ⁇ /> plotted against the reconstructed delay axis in accordance with an illustrative embodiment. The points on the scan where phase instabilities had occurred, circled, now present a smooth trace.
  • Fig. 5C shows the difference between the original axis plotted and the new axis, plotted against the new axis in accordance w ith an illustrative embodiment. In this plot, it is apparent that the two axes are different by slight and varying amounts at each time delay, highlighting where instabilities have occurred in the optical paths.
  • Fig. 5C shows the difference between the original axis plotted and the new axis, plotted against the new axis in accordance w ith an illustrative embodiment. In this plot, it is apparent that the two axes are different by slight and varying amounts at each time delay, highlighting where instabilities have occurred in the optical paths.
  • Fig. 5C shows the difference between the original axis plotted and the new axis, plotted against the new axis in accordance w ith an illustrative embodiment. In this plot, it is apparent that the two axes are different by slight and varying amounts at each time delay, highlighting where instabilities have occurred
  • FIG. 5D shows the drift in path length over the full length of the scan in accordance with an illustrative embodiment.
  • the drift shown in Figs. 5C and 5D occurs over a range of 2 fs (equivalent to 600 nm) which is a significant amount for UV/Vis wavelengths (200 nm to 700 nm).
  • the trace shows the propagated error for calculated values of path length difference Ax demonstrating that the path length drift lies outside the error boundaries.
  • Fig. 5 thus proves the phase detection scheme works well to detect instabilities in the path lengths of the arms of the MZI.
  • Fig. 6A shows a Fourier transform of (a) the raw diode data showing the frequency of the diode at 1.89 eV in accordance with an illustrative embodiment.
  • Fig. 6B depicts frequency domain GaAs spectra showing three peaks at 2.92 eV (second harmonic of 850 nm fundamental), 3.54 eV (SFG of 850 nm and 600 nm), and 4.09 eV (second harmonic of 600 nm) in accordance with an illustrative embodiment.
  • Fig. 6C shows a Fourier transform of (a) the raw diode data showing the frequency of the diode at 1.89 eV in accordance with an illustrative embodiment.
  • Fig. 6B depicts frequency domain GaAs spectra showing three peaks at 2.92 eV (second harmonic of 850 nm fundamental), 3.54 eV (SFG of 850 nm and 600 nm), and 4.09 eV (second harmonic of 600 nm)
  • FIG. 6A shows a non-uniform Fourier transform of the phase corrected data from Fig. 6A showing narrower peaks with less noise and higher intensity in accordance with an illustrative embodiment.
  • Fig. 6D shows a non-uniform Fourier transform of the phase corrected data from Fig. 6B showing narrower peaks with less noise and higher intensity in accordance with an illustrative embodiment.
  • the mixed lock-in amplifier signal is then:
  • Equation (8) shows U m oc J m (y).
  • Bessel function evaluated at a particular AZ and A is oscillatory, with some values of AL and A yielding larger values of J m (y).
  • a value for AZ was selected that yields a relatively large J m (y) for the A values of interest.
  • a displacement amplitude of 51 nm was selected, as this value yields strong Bessel function values for the desired wavelengths.
  • Fig. 7 shows Bessel function values as a function of mirror modulation amplitude for various relevant wavelengths in accordance with an illustrative embodiment.
  • the inventors chose a mirror modulation amplitude that yields large Bessel function values for all relevant wavelengths.
  • 51 nm is near the maximum for all relevant wavelengths.
  • the inventors therefore used a 51 nm modulation amplitude for this experiment.
  • the displacement of the vibrating mirror is due to a piezo element (e.g., Physik Instrumente S-303) that is controlled by Physik Instrumente Mikromove or another source.
  • Fig. 8 shows the reported position of the piezo of the vibrating mirror as a function of time, determined using capacitive sensing in accordance with an illustrative embodiment. In Fig. 8, dashed lines denote displacement by ⁇ 51 nm.
  • Fig. 9A depicts raw spectra data obtained at different fundamental wavelengths in accordance with an illustrative embodiment.
  • Fig. 9B depicts corrected spectra data obtained at different fundamental wavelengths in accordance with an illustrative embodiment.
  • Fig. 9 shows SFG spectra obtained with GaAs as both LO source and sample when irradiated with 820 nm and 580 nm light before and after phase correction. Peaks are noisy and artificially broadened in the uncorrected spectrum as compared to the corrected spectrum.
  • Fig. 10A depicts raw spectra data from z-cut quartz in the sample position and GaAs as the LO source in accordance with an illustrative embodiment.
  • Fig. 10B depicts corrected spectra data from z-cut quartz in the sample position and GaAs as the LO source in accordance with an illustrative embodiment.
  • Fig. 10 shows SFG spectra obtained with GaAs as the LO source and z-cut quartz as the sample irradiated with 600 nm and 850 nm light before and after phase correction.
  • the OP A output is weaker at 600 nm than 580 nm, and so the SHG of 600 nm is not strong enough to be visible.
  • Spectra were collected on a traditional, frequency domain spectrometer (e.g., Ocean Insight Maya2000 Pro) in addition to the time domain spectrometer.
  • Fig. 11 A shows spectra corresponding to Fig. 6D collected with a traditional frequency domain spectrometer in accordance with an illustrative embodiment.
  • Fig. LIB shows spectra corresponding to Fig.
  • Fig. 11C shows spectra corresponding to Fig. 9 collected with a traditional frequency domain spectrometer in accordance with an illustrative embodiment. It is notable that the shortest wavelength peaks (SHG of 580 nm or 600 nm) are not at all or barely visible in these spectra, as the spectrometer sensitivity is lower than in the abovediscussed time domain collection scheme. Linewidths and lineshapes are in good agreement between different detection methods.
  • any of the operations described herein can be performed by a computing system that includes a processor, a memory, a user interface, a transceiver, etc.
  • the memory can be used to stored computer-readable instructions that, upon execution by the processor, cause the computing system to perform the operations described herein.
  • Fig. 12 is a block diagram of a computing system 1200 to implement a phase correction system in accordance with an illustrative embodiment.
  • the computing system 1200 can communicate directly with other computing devices (e.g., servers, processors, etc.), or through a network 1235, depending on the implementation.
  • the computing system 1200 includes a processor 1205, an operating system 1210, a memory 1215, an input/output (I/O) system 1220, a network interface 1225, and a phase correction application 1230.
  • the computing system 1200 may include fewer, additional, and/or different components.
  • the components of the computing system 1200 communicate with one another via one or more buses or any other interconnect system.
  • the computing system 1200 can be any type of computing device (e.g., tablet, laptop, desktop, etc.) that has sufficient processing power to perform the operations described herein.
  • the computing system 1200 can be incorporated as part of a spectrometer.
  • the processor 1205 can be in electrical communication with and used to control any of the system components described herein.
  • the processor can be used to execute the phase correction application 1230, process received user selections, send data and commands to the external devices, receive raw data from a spectrometer, process the data using the algorithms described herein, etc.
  • the processor 1205 can be any type of computer processor known in the art, and can include a plurality' of processors and/or a plurality of processing cores.
  • the processor 1205 can include a controller, a microcontroller, an audio processor, a graphics processing unit, a hardware accelerator, a digital signal processor, etc. Additionally, the processor 1205 may be implemented as a complex instruction set computer processor, a reduced instruction set computer processor, an x86 instruction set computer processor, etc.
  • the processor 1205 is used to run the operating system 1210, which can be any type of operating system.
  • the operating system 1210 is stored in the memory 1215, which is also used to store programs, user data, spectrometer readings and settings, network and communications data, peripheral component data, the phase correction application 1230, and other operating instructions.
  • the memory 1215 can be one or more memory systems that include various types of computer memory such as flash memory, random access memory (RAM), dynamic (RAM), static (RAM), a universal serial bus (USB) drive, an optical disk drive, a tape drive, an internal storage device, a non-volatile storage device, a hard disk drive (HDD), a volatile storage device, etc.
  • at least a portion of the memory 1215 can be in the cloud to provide cloud storage for the system.
  • any of the computing components described herein e.g., the processor 1205, etc.
  • can be implemented in the cloud such that the system can be run and controlled through cloud computing.
  • the I/O system 1220 is the framework which enables users and peripheral devices to interact with the computing system 1200.
  • the I/O system 1220 can include a display, one or more speakers, one or more microphones, a keyboard, a mouse, one or more buttons or other controls, etc. that allow the user to interact with and control the computing system 1200.
  • the I/O system 1220 also includes circuitry and a bus structure to interface with peripheral computing devices such as power sources, universal service bus (USB) devices, data acquisition cards, peripheral component interconnect express (PCIe) devices, serial advanced technology attachment (SATA) devices, high definition multimedia interface (HDMI) devices, proprietary connection devices, etc.
  • USB universal service bus
  • PCIe peripheral component interconnect express
  • SATA serial advanced technology attachment
  • HDMI high definition multimedia interface
  • the network interface 1225 includes transceiver circuitry (e.g., a transmitter and a receiver) that allows the computing device 1200 to transmit and receive data to/from other devices such as a remote data processing center, other remote computing systems, servers, websites, etc.
  • the network interface 1225 enables communication through the network 1235, which can be one or more communication networks.
  • the network 1235 can include a cable network, a fiber network, a cellular network, a wi-fi network, a landline telephone network, a micro wave network, a satellite network, etc.
  • the network interface 1225 also includes circuitry to allow device-to-device communication such as Bluetooth® communication.
  • the phase correction application 1230 can include software and algorithms in the form of computer-readable instructions which, upon execution by the processor 1205, performs any of the various operations described herein such as controlling light sources, receiving measured data, analyzing the data to determine phase shifts, applying a correction to the data based on the phase shifts, etc.
  • the phase correction application 1230 can utilize the processor 1205 and/or the memory 1215 as discussed above.
  • the phase correction application 1230 can be remote or independent from the computing system 1200, but in communication therewith.
  • the value for oU m is taken as the variance of the power of the diode as a percentage of its mean power at 0.000176. This is an upper bound on the error as it is expected that any intensity fluctuations would be cancelled out in calculating the ratio .
  • Error in AL (taken as the Bidirectional repeatability error reported by Physik Instrumente) is 1.4 nm, and error in wavelength is the FWHM of spectrum, 0.84 nm.
  • oA In the calculation for oAx, oA is taken to be zero. Calculated olAx is in nm and is converted to fs by dividing by the speed of light. The largest source of error was found to be the fluctuations in intensity of the reference diode. The calculated error is expected to be an overestimate for two reasons. First, the simultaneous and instantaneous data collection at all lock-in amplifier channels means any instabilities due source intensity fluctuations would be expected to be the same for each channel in the lock-in amplifier and therefore cancelled out in computing the U2 ratio. Second, the lock-in amplifier filters out noise that is not on the frequency of its reference signal (i.e. harmonics of the vibration frequency).
  • the proposed instrument can be expanded to include the use of a broadband white light probe light.
  • the inventors have added a scheme to separate the overlapping peaks resulting from second harmonic generation (SHG) and SFG of the broadband white light.
  • Fig. 13 depicts a system that utilizes a broadband white light probe in accordance with an illustrative embodiment. As shown, in this embodiment, new components have been added to the system. The new' components include a broadband white light source, a chopper (or modulator) positioned in each of the broadband white light path and the narrowband upconverter light path, and a second lock-in amplifier unit.
  • the second lock-in amplifier is incorporated into the system, in sync with the first lock-in amplifier.
  • a first chopper modulates the intensity of the white light probe with frequency vi
  • a second chopper modulates the intensity of the upconverter line with frequency V2.
  • the intensity of the SFG light is modulated with frequency vi + V2. Locking into this frequency, the second lock-in amplifier is used only to amplify the SFG peaks, removing the SHG peaks from the spectrum.
  • the first lock-in amplifier can be used for phase detection as before.
  • Fig. 14 shows proof of principle experiment results for phase correction with the chopper and tw o lock in amplifier scheme of Fig. 13 in accordance with an illustrative embodiment.
  • the experiments w ere conducted using narrowband light at 820nm and 670nm.
  • the top panel of Fig. 14 shows spectra from set up with one lock-in amplifier and no choppers for comparison.
  • the bottom panel is the spectrum of two lock-in amplifier scheme and two choppers. As shown, there is only a single SFG peak present, with all other peaks eliminated.
  • Fig. 15 shows a comparison of the two schemes with broadband light in accordance with an illustrative embodiment. In the bottom panel of Fig. 15, the weaker broadband SFG light around 4 eV is more clearly present.
  • the inventors have developed a new design for phase-sensitive detection of electronic sum frequency generation spectra.
  • the system is able to measure the relative phase between the local oscillator and the SFG signal. This enables the system to account for any phase drifts arising from instabilities in the optical set-up, resulting in much higher SNR, correct lineshapes, and spectral accuracy in SFG spectra.
  • Phase stability in the spectra facilitates heterodyning to achieve simultaneous detection of phase and amplitude.
  • Heterodyne detection decouples real and imaginary parts of the detected SFG electric field, which will afford accurate spectra, eliminate non-resonant contributions, and elucidate the orientation of molecules at the interface.
  • Slow phase drifts that distort phase-sensitive data over long scans are corrected through directly measuring the relative phase difference between LO and SFG signals and translating it into a new, more accurate time delay axis.
  • Time-domain detection allows for more accurate SFG spectra with high frequency resolution while taking advantage of more sensitive and cost-effective single channel detectors.
  • Collinear geometry of the two fundamentals Evis and ENIR leads to a smaller room for error in the phase of reference with respect to the sample, such that normalizing the sample spectrum by the reference spectrum will yield accurate phase and amplitude for % (2) .
  • This spectrometer design will revolutionize the study of buried interfaces by paving the way for time-resolved phase-sensitive experiments without risking compromising the data due to phase drifts over time. As discussed, some iterations of this spectrometer are able to take advantage of a broadband white light source along with a NIR E2 pulse to probe multiple resonances at once, providing a wealth of data with each scan.
  • the methods described herein and the relevant signal processing can be more broadly applied to any interferometric measurements that require high phase stability, breaking ground for more innovative spectroscopic techniques in the visible and ultraviolet regions.

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  • General Physics & Mathematics (AREA)
  • Investigating Or Analysing Materials By Optical Means (AREA)
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Abstract

Un système de mesure interférométrique comprend une source de lumière qui génère un faisceau d'échantillon de lumière et un oscillateur local qui fait osciller une partie du faisceau d'échantillon de lumière pour former un faisceau de lumière oscillant. Le système comprend un miroir qui comprend un élément vibrant qui amène le miroir à vibrer à une fréquence, le miroir recevant le faisceau de lumière oscillant et modulant une phase du faisceau de lumière oscillant. Le système comprend un amplificateur de verrouillage qui est verrouillé dans la fréquence de vibration du miroir de telle sorte que l'amplificateur de verrouillage reçoit le faisceau de lumière oscillant qui a été modulé à la fréquence. Un processeur est en communication avec une ou plusieurs de la source de lumière, de l'oscillateur local et de l'amplificateur de verrouillage, et est conçu pour détecter, sur la base, au moins en partie, de données provenant de l'amplificateur de verrouillage, une phase relative entre le faisceau de lumière oscillant et le faisceau d'échantillon de lumière. Le processeur est également conçu pour détecter un signal d'interférence et corriger une différence de longueur de trajet entre le faisceau de lumière oscillant et le faisceau d'échantillon de lumière sur la base, au moins en partie, de la phase relative. Le processeur est en outre conçu pour appliquer la différence de longueur de trajet corrigée au signal d'interférence pour corriger une variation de phase qui se produit pendant une mesure.
PCT/US2023/072632 2022-08-22 2023-08-22 Phasemètre optique pour interférométrie WO2024044577A2 (fr)

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