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Abstract
Brillouin spectrometers, used for characterizing material mechanical properties, traditionally employ etalons such as Fabry-Pérot interferometers and virtually imaged phased arrays (VIPA) that use spatial dispersion of the spectrum for measurement. Here, we introduce what we believe to be a novel approach to Brillouin spectroscopy using hot atomic vapors. Using laser induced circular dichroism of the rubidium D2 line in a ladder-type configuration, we developed a narrow-band monochromator for Brillouin analysis. Unlike etalon-based spectrometers, atomic line monochromators operate in free-space, facilitating Brillouin spectroscopy integration with microscopy instruments. We report the transmission and spectral resolution performances of the spectrometer and demonstrate Brillouin spectra measurements in liquids.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Spontaneous Brillouin light scattering arises from the interaction between the intrinsic acoustic-phonons of a material and incident photons [1]. This scattering process gives rise to a frequency shift, known as the Brillouin shift, which is linked to the material’s acoustic-phonon speed. Importantly, the acoustic-phonon speed is related to the longitudinal modulus of the material, establishing a clear relationship between the Brillouin shift and the material’s longitudinal modulus. As a result, Brillouin spectrometers have been used in materials science [2,3], applied physics [4], and more recently biomedicine [5–7] for label-free, non-contact characterizations of material properties. Brillouin spectrometers require sub-GHz resolution because the Brillouin shift is ∼3-10 GHz with a 150-400 MHz linewidth, depending on the sample. Due to these measurement constraints, very few spectrometers can resolve Brillouin spectra. Historically, multi-staged spectrometers employing high-resolution interferometers such as Fabry-Pérot etalons [8] and virtually imaged phased arrays (VIPAs) [9] are used to measure Brillouin signal.
Here, we demonstrate a novel approach to Brillouin spectroscopy using a hot atomic vapor for spectral analysis. Atomic vapors are mostly used in spectroscopy as notch filters [10,11], but they also possess absorptive properties that can be manipulated to create ultra-narrow band-pass filters, i.e. monochromators [12–17]. Atomic line monochromators are built by setting an atomic vapor between two crossed linear polarizers. The insertion of the vapor, which is prepared with an external magnetic or electromagnetic field, creates optical anisotropy, shifting the polarization of the signal and creating signal past the output polarizer. Because atomic line monochromators can reach 40-400 MHz bandwidth [15–17], they are excellent candidates for measuring Brillouin scattering. Furthermore, unlike the etalons used for Brillouin spectroscopy, atomic vapor-based spectrometers analyze light in free-space and do not introduce any constraint for optical alignment. We characterized the transmission and linewidth (i.e. spectral resolution) of our atomic line monochromator, and, as proof-of-principle, we measure spontaneous Brillouin scattering in clear liquids.
2. Principle
Our atomic line monochromator is based on the laser induced circular dichroism (LICD) effect within a rubidium-87 (87Rb) atomic vapor [15–17]. With the LICD effect, a strong pump laser prepares the vapor by reducing the absorption for a particular circular polarization on resonance. As a result, linearly polarized signal will see its polarization shifted near resonance. We have previously demonstrated an atomic line monochromator based on the LICD effect, where the signal and the pump laser are on resonance with the same 87Rb transition [18]. In this work, two different transitions will be used in a ladder-type configuration: one for optical pumping and the other for signal transmission. Figure 1 shows the pumping scheme of the new atomic line monochromator, which utilizes three 87Rb orbitals: 52S1/2, 52P3/2, and 52D3/2. Each orbital is divided into different hyperfine levels, which consists of magnetic sublevels that can be accessed depending on the frequency and polarization of the incoming light.
Fig. 1. Ladder-type pumping scheme of the atomic line monochromator. The solid (dashed) arrows indicate absorption (decay) pathways. The pump changes the electron population density (yellow) in the ground state and excited state. The σ+-polarized pump is resonant with the 52S1/2(F = 2)→52P3/2(F’=3) transition at a frequency ωpump and the π-polarized signal light is on 52P3/2(F’=3)→52D3/2(F’’=3) transition at frequencies ω0 and $\omega _0 \pm v_{\rm B}$
Initially, a right (σ+) circularly polarized pump laser, resonant with the 52S1/2(F = 2)→52P3/2(F’=3) transition at ωpump ≅ 384.2304 THz frequency and λpump ≅ 780.24 nm wavelength, propagates inside of a pure 87Rb vapor cell (Fig. 1). The σ+-polarized pump creates a + 1 change in magnetic quantum number (Δm = + 1) between the magnetic quantum numbers in the ground and excited states. The electrons spontaneously decay to the ground state following a Δm = 0, ± 1 magnetic quantum number change [19]. Thus, the σ+-polarized pump generates a cyclical effect between the ground state and the excited state magnetic sublevels until electrons occupy the 52S1/2(F = 2, mF=+2)→52P3/2(F’=3, mF’=+3) transition. When the pump is powerful enough, the transition is saturated and the electron population densities in the 52S1/2(F = 2, mF=+2) ground state and the 52P3/2(F’=3, mF’=+3) excited state are equal [20].
This optical pumping scheme prepares the vapor to exhibit circular dichroism for counter-propagating signal on resonance with the excited state transition 52P3/2(F’=3)→52D3/2(F’’=3) at ω0 ≅ 386.3581 THz frequency and λ0 ≅ 775.94 nm wavelength (Fig. 1). If the signal is linearly (π) polarized, and, therefore, composed of the two orthogonal circular polarization components, the circular polarization components of the signal will be absorbed differently by the atoms as governed by the selection rules for the magnetic quantum number. The left (σ_) circular polarization component will be absorbed because there are magnetic sublevels in the 52D3/2(F’’=3) hyperfine state that are free to be occupied and obey the magnetic quantum number selection rule for σ_-polarized light (i.e., Δm = -1). Instead, the σ+ component of the signal will not be absorbed because that transition is dipole forbidden. Thus, pumping at 780.24 nm has caused the vapor to be transparent for σ+-polarized light at the 52P3/2(F’=3)→52D3/2(F’’=3) resonance. We use this ladder-type pumping scheme to realize a high-resolution atomic line monochromator by inserting the optically pumped vapor in between two crossed linear polarizers. The pump-prepared vapor will rotate the polarization of the signal near resonance while off-resonance light will be unchanged and thus blocked by the linear polarizers. The transmission coefficient T of the monochromator reads:
For the case of measuring Brillouin scattered light with a Brillouin shift ±νB, because the Brillouin shift has a linear dependance on the incident laser frequency, Brillouin photons will be transmitted through the atomic line monochromator when the incident laser has been detuned ±νBaway from the 52P3/2(F’=3)→52D3/2(F’’=3) transition resonance. There will only be signal transmission through the atomic line monochromator at frequencies ω0 and ω0 ±νB. In other words, tuning the incident laser frequency around the atomic line monochromator central frequency sweeps the Brillouin signal through the bandpass window, creating a high-resolution spectrometer.
3. Experimental setup
The experimental setup is shown in Fig. 2. An epi-detection confocal microscope was built to collect Brillouin photons and combined with the atomic line monochromator for signal analysis. A tunable laser (DL pro, Toptica) acts as the incident laser and its central wavelength is near the 87Rb 52P3/2(F’=3)→52D3/2(F’’=3) transition at 775.94 nm. The incident laser was split using a 50:50 (R:T) non-polarizing beam splitter cube (BS1), with one path leading to the microscope and the other path to a Fabry-Pérot interferometer (FPI, SA30-73, Thorlabs) for laser frequency calibration. When the laser frequency was scanned, the FPI resonance peaks were used to calibrate the incident laser frequency in GHz. In the microscope path, the incident laser passes through a polarizing beam splitter cube (PBS1) and a quarter-wave plate (QW1) before being focused by a microscope objective L1 (0.11 NA, 50 mm focal length) inside of a cuvette containing the sample. At the focus, the incident laser has a diameter of 4.3 µm. The same objective collects the Brillouin signal from the focal point. Due to QW1, the polarization of the collected signal changes and is reflected by PBS1 into a microscope objective (O1) and a polarization-maintaining fiber (PMF). The PMF serves as a confocal pinhole, restricting light collection to the focal plane, and sending the light to the atomic line monochromator for analysis. Using a saturated absorption spectroscopy module (CoSy, Toptica), the pump laser frequency (TA pro, Toptica) is locked to the 87Rb 52S1/2(F = 2)→52P3/2(F’=3) transition. The pump laser diameter out of the fiber collimator is 1.35 mm. The pump is σ+-polarized using a quarter-wave plate (QW2), and a 10:90 (R:T) non-polarizing beam splitter (BS2) cube aligns the pump inside of a pure 87Rb atomic vapor cell. From the PMF, the Brillouin signal is sent through the atomic line monochromator which is mainly composed of a pure 87Rb atomic vapor cell and two crossed Glan-Taylor polarizers (GT1 and GT2; GT10-B Thorlabs). The signal is aligned to GT1 with a half-wave plate (HW1) and focused through the cell via a 4f system (L2 and L3, 200 mm focal length) to overlap with the counter-propagating pump beam inside the cell. The signal is finally transmitted through the polarizer GT2 (105:1 extinction ratio) which is crossed with GT1 and is focused onto an electron-multiplying charged-coupled device (EMCCD) camera (iXon Ultra897, Andor) using a 50 mm focal length lens (L4). A flip mirror is positioned before the final lens L4 so that it can reflect light into a photodiode detector (PDA36A2, Thorlabs). For simplicity of the data analysis, the monochromator characterization was completed with the photodiode detector instead of the EMCCD camera.
Fig. 2. Setup schematic for the atomic line monochromator. L1, L2, L3,L4 lenses; PBS1, PBS2, polarizing beam splitter; BS1, BS2, non-polarizing beam splitter; QW1, QW2, quarter-wave plate; HW1, HW2, half-wave plate; FPI, Fabry-Pérot interferometer; P, pinhole; F, bandpass filter; PD, photodiode detector; O1,O2, O3, objective lens; B, beam block; M, mirror; GT1, GT2, Glan-Taylor polarizers; FM, flip mirror; PMF, polarization maintaining fiber; FC, fiber collimator.
A feature of LICD atomic line monochromators is pump light back-reflected off the 87Rb cell window into the detector. The pump-back-reflection is on the order of several microwatts of power and obstructs the optical path of the signal, which is orders of magnitude greater than spontaneous Brillouin scattered light due to a low scattering cross-section of 10−9 [22]. To address the pump-back-reflection, two bandpass filters F (Alluxa) were placed before the detector to provide 95% transmission at 775.94 nm and ∼60 dB rejection at 780.24 nm. This is a significant improvement to the previous design of the LICD atomic line monochromator that utilized a single transition and therefore, could not use spectral filtering to block the pump background noise [18]. A spatial filter was also added after L3 and before GT2 to provide additional extinction of the pump background noise. The spatial filter was created using a 15 µm pinhole, an input lens O2 of 16.5 mm focal length, and an output lens O3 of 18 mm focal length. The spatial filter provided an additional ∼5 dB rejection of the back-reflected pump background noise while allowing ∼88% transmission of the signal.
4. Monochromator characterizations
To characterize the performances of the atomic line monochromator, the incident laser (1.35 mm diameter) is fed directly to the monochromator to simulate the Brillouin signal. The flip mirror is up so that the signal intensity can be analyzed by the photodiode detector (Fig. 2). Figure 3 shows the characteristic transmission spectrum of our atomic line monochromator (red trace). The transmission is measured as the signal intensity after GT2 divided by the intensity of the signal before the 87Rb cell. The signal power density is 0.36 mW/cm2 before entering the 87Rb cell and the pump power density is 3.35 W/cm2 before entering the 87Rb cell. The temperature of the 87Rb cell is 55.6°C. When the pump is blocked (black trace), the vapor is inert to 775.94 nm light and the laser is blocked by the polarizers, resulting in no signal transmission. When the pump is π-polarized (yellow trace), the vapor will not exhibit circular dichroism; as a result, the π-polarization of the signal is maintained and will be blocked by the second polarizer.
Fig. 3. Monochromator transmission versus laser detuning. There is transmission when the pump is on and circularly polarized. There is no transmission when the circularly polarized pump is blocked (black trace) or π-polarized (yellow trace).
The monochromator transmission band consists of one peak split into two due to the high intensity of the pump, as governed by Aulter-Townes splitting [23,24]. At this pump power density, each peak has ∼120 MHz linewidth and a peak-to-peak separation of 130 MHz as expected.
The transmission and the linewidth performances of the atomic line monochromator are characterized in Fig. 4, where the peak transmission is measured as the maximum intensity of the transmission spectrum and the linewidth is the full width at half maximum (FWHM) of the monochromator transmission band. The peak transmission and the linewidth are measures of the number of atoms that are saturated by the pump, which is highly dependent upon the pump power density and the temperature of the vapor. Figures 4(a,b) show the peak transmission and linewidth versus the pump power density when the vapor cell temperature is fixed at 55.6°C. From Fig. 4(a), as the pump becomes more powerful the LICD effect in the atomic vapor becomes more pronounced, creating more transmission. The monochromator transmission eventually plateaus beyond ∼3.3 W/cm2 because the pump has saturated the relevant transition. The linewidth increases as the pump power increases due to power broadening (Fig. 4(b)) [22]. Power broadening occurs when the pump intensity is so high that the electrons begin to oscillate more frequently between the ground and excited states, leading to a shorter transition lifetime and broader spectral peaks [19].
Fig. 4. Characterization of the transmission and linewidth of the atomic line monochromator as a function of pump power density (a-b) and vapor cell temperature (c-d).
Figures 4(c,d) show the peak transmission and linewidth versus the 87Rb cell temperature when the pump power density is fixed at 3.35 W/cm2. From Fig. 4(c), the transmission increases as the temperature of the vapor increases because more atoms are interacting with both lasers as the temperature increases, improving the LICD effect. At temperatures exceeding 60°C, the transmission decreases. The decrease in transmission is attributed to the pump being absorbed more at the cell entrance, saturating the vapor less while traveling through the vapor due to Beer’s Law [20]. In Fig. 4(d), as the temperature increases the linewidth increases until becoming constant at ∼56°C. The linewidth eventually decreases at 70°C, most likely because the contribution of the linewidth due to the Aulter-Townes splitting decreases significantly as the vapor absorbs the laser more. Overall, the monochromator can achieve ∼13% transmission and ∼230 MHz linewidth when the pump power density was 3.35 W/cm2 and the temperature of the 87Rb cell was 55.6°C.
5. Brillouin measurements
After finding the optimal atomic line monochromator settings, the system was used to measure Brillouin spectra of liquids. Figure 5 shows Brillouin measurements of acetone and methanol using our Brillouin spectrometer, where the x-axis is the laser frequency detuning from the Rayleigh peak frequency. The laser power incident to the sample was 11.6 mW. The incident laser frequency was controlled by the diode laser cavity length, and the length of the cavity was adjusted by scanning a piezo motor. A voltage value was sent to the piezo motor using a custom LabView code, and the EMCCD camera acquires an image of the laser spot at each piezo voltage value. The acquisition time for each spectral datapoint was 200 ms with a 20 MHz step size. Each spectrum acquired consisted of 600 datapoints, leading to 2 minutes acquisition time per spectrum. The small step size was chosen to resolve the Autler-Townes splitting within the Rayleigh peak, however, the acquisition time for a single spectrum can be decreased by choosing a step size closer to the linewidth of the monochromator and taking fewer points. If we acquire a spectrum with only 40 spectral components, i.e. the number of spectral components typically resolved by a VIPA spectrometer [6], then the spectrum acquisition time for our spectrometer would be 8 seconds. The intensity of the signal at the focus was plotted as a function of the piezo voltage. The frequency axis of each scan was later calibrated from piezo voltage to GHz in post-processing using the FPI signal. Because the intensity of the signal at the Rayleigh frequency saturated the camera, the Brillouin shift was calculated as half the frequency difference between the Stokes and Anti-Stokes Brillouin peaks. The average Brillouin shift for acetone and methanol were measured to be 4.062 GHz (5.8 MHz standard deviation) and 3.868 GHz (6.8 MHz standard deviation), respectively. These measurements agree with calculated Brillouin shifts using tabulated refractive index and sound velocity values [22,25].
As expected, the two characteristic peaks of the monochromator transmission band were reflected in the Rayleigh peak because the incident laser linewidth is ∼300 kHz, orders of magnitude lower than the bandwidth of the monochromator. Instead, the linewidth of the monochromator is on the order of the natural Brillouin linewidths for acetone and methanol [22], leading to the measured linewidths of the samples being larger than their natural Brillouin linewidths. The measured linewidth for acetone and methanol were 395.31 MHz (8.75 MHz standard deviation) and 387.56 MHz (14.07 MHz standard deviation), respectively. Unlike the Rayleigh peak, the Autler-Townes splitting is not apparent in either Brillouin peaks because the natural Brillouin linewidths for acetone and methanol are larger than the 120 MHz Autler-Townes splitting. In the future, the natural Brillouin linewidth can be extracted by deconvolving the experimental data with the monochromator characteristic transmission band [26].
Although a considerable amount of the the pump-back-reflection off the 87Rb vapor cell window is blocked by the bandpass filter (Fig. 2, F), the back-reflection constitutes a significant noise source in our spectrometer. The noise behavior of our Brillouin spectrometer was characterized in Fig. 6(a,b). First, the signal-to-background ratio (SBR) of the system was measured using an acetone sample (Fig. 6(a)). Examining the SBR of the system helps us understand if the noise source is system dependent or not. The laser power incident to the acetone sample was 16.3 mW and the pump power density is kept constant at 3.35 W/cm2. The SBR was calculated as the ratio of the acetone Stokes peak’s intensity to the average intensity of the background between the Stokes and Rayleigh peaks. Multiple scans were taken with varying image exposure times ranging from 20 to 400 ms. From Fig. 6(a), the SBR of the atomic line monochromator is constant at ∼5.2 for different exposure times.
Fig. 6. Atomic line monochromator noise characterizations. (a) Signal-to-background ratio of acetone Brillouin measurements as a function of camera exposure time. (b) Signal-to-noise ratio of the acetone Brillouin measurements as a function of power incident to the sample on a log-log scale.
The SBR measurement reveals a low signal strength compared to the pump-background noise, indicating inherent limitations in the detection sensitivity. To assess the device sensitivity further, we examined the signal-to-noise ratio (SNR) to estimate how far the system is from operating in the shot-noise limit where the system SNR would increase as the square root of the number of photons measured. Figure 6(b) shows the signal-to-noise ratio (SNR) versus incident laser power to an acetone sample on a log-log scale. For each scan, the peak frequency of the incident laser was set to the frequency of the acetone Stokes peak, and 300 images of 200 ms exposure time were taken. The laser power incident to the sample varied between 1 and 12 mW for each measurement. In post-processing, 50 consecutive images were selected from the original set of 300 images to ensure the stability of the signal amidst potential variations, such as fluctuations in laser intensity and laser frequency drift for the pump laser and the laser incident to the sample. The SNR was calculated as the ratio between the mean intensity of the 50 measurements and the variance in intensity of the 50 measurements. From 1 to 1.7 mW of incident laser power, the SNR is constant because the signal was at the noise floor of the pump background. At incident laser powers greater than 2 mW, the SNR increases. The dashed black line is a linear fit to the SNR data past the noise floor, where the slope of the line is 0.3975. If the system were operating in the shot-noise limited regime the slope of the fit would be 0.5. By using more incident laser power the signal would eventually increase above the noise floor enough to where measurements could be conducted in the shot-noise limit. However, due to system constraints, we could not increase the incident laser power further. Nevertheless, by performing a power law fitting with the data from Fig. 6(b), we were able to extrapolate the behavior of the system to higher incident power levels. From the extrapolated curve, we estimate that the system reaches the shot-noise limited behavior at ∼37 mW incident power.
6. Conclusions
In summary, we introduced atomic line monochromators to the Brillouin spectroscopy toolbox, which is currently limited to interferometers like the Fabry-Pérot and VIPA etalons. A promising future application for atomic line monochromators in Brillouin spectroscopy is pixel multiplexing. By combining the spectrometer with line illumination and detection, the spectrometer can be used to measure multiple Brillouin pixels in the line simultaneously, significantly reducing the average pixel acquisition time. One-dimensional pixel multiplexing has already been demonstrated using VIPA etalons in the line-scan Brillouin spectrometer [27,28]; however, the combination of spectral dispersion and optical imaging within the same system poses hard and suboptimal design constraints [29]. Since atomic line monochromators do not depend on angular dispersion for spectral analysis, the extension to pixel multiplexing becomes straightforward, as we have demonstrated previously with high-resolution full-field spectroscopy using an atomic line monochromator [18]. For future implementations of this device in Brillouin spectroscopy applications, reducing the pump back-reflection is essential to reach the superior SBR exhibited by etalon-based Brillouin spectrometers [30]. One possible solution to increase the SBR of the spectrometer is to modulate Brillouin signal using an acousto-optic modulator and separate it from the unmodulated pump background noise using a lock-in amplifier. Lock-in amplification has been used in the past for stimulated Brillouin spectroscopy to detect weak Brillouin signal [31].
Another consideration for future implementations of the device is the spectrometer extinction. The theoretical extinction of the spectrometer is the extinction of the crossed polarizers, which is 50 dB. Although this is sufficient for measurements in clear liquid samples, Brillouin measurements in biological samples necessitates >70 dB spectral extinction from Rayleigh scattered light [30]. In the future, polarizers with higher spectral extinction can be used to improve the spectral extinction at the Rayleigh peak frequency. Furthermore, a hot Rb notch filter can be inserted into the spectrometer to increase the spectral extinction by >30 dB at the Rayleigh peak frequency [27,28].
In conclusion, we have developed a new Brillouin spectrometer using an atomic line monochromator for high-resolution and highly sensitive spectral analysis. We characterized the transmission and linewidth performances of the atomic line monochromator, and we demonstrated the spectrometer proof-of-principle by measuring spontaneous Brillouin scattering in clear liquids.
Funding
National Institutes of Health (R01EY028666, R01EY030063, R21CA258008); Directorate for Biological Sciences (DBI-1942003).
Disclosures
RH, GZ, and GS have intellectual property related to Brillouin technology.
Data availability
Data for the characterization of the instrument and Brillouin scattering measurements are available from the corresponding author upon reasonable request.
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