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Abstract
Spectral imaging techniques extract spectral information using dispersive elements in combination with optical microscopes. For rapid acquisition, multiplexing spectral information along one dimension of imaged pixels has been demonstrated in hyperspectral imaging, as well as in Raman and Brillouin imaging. Full-field spectroscopy, i.e., multiplexing where imaged pixels are collected in 2D simultaneously while spectral analysis is performed sequentially, can increase spectral imaging speed, but so far has been attained at low spectral resolutions. Here, we extend 2D multiplexing to high spectral resolutions of ∼80 MHz (∼0.0001 nm) using high-throughput spectral discrimination based on atomic transitions.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The combination of optical spectroscopy and imaging is rapidly developing in many fields [1–4]. Microscopes are combined with spectrometers to create images where both spatial and spectral information are available for richer contrast. Typically, a confocal microscope is combined with a spectrometer that utilizes a diffraction grating or an etalon interferometer; the confocal microscope scans the object being imaged pixel by pixel and the spectrometer analyzes the spectral information at each pixel [4,5]. Although the combination of spatial and frequency information has found many applications, these methods tend to be slow. Specifically, applications involving scattering processes require long exposure times due to low scattering efficiency and weak signal [5]. One solution to improve the acquisition speed is to multiplex the spectral analysis, e.g., a line-scan instead of a point-scan configuration. Spectroscopy methods such as pushbroom hyperspectral microscopy [6], line-scan Raman microscopy [7], and line-scan Brillouin microscopy [8,9,10] have all been developed to demonstrate massive improvements in imaging speeds due to the simultaneous acquisition of spectral information at multiple locations. Further multiplexing to two dimensions, or full-field spectroscopy, where the frequency domain is sequentially acquired but all the pixels in the field of view are simultaneously measured at each frequency, can further improve the imaging speed because there are generally many more pixels to probe than frequencies to acquire. At low spectral resolutions, bandpass filter wheels, acousto-optic tunable filters [11], and spectral unmixing [12] have all been used for full-field spectroscopy. At higher spectral resolutions, instead, full field spectroscopy becomes increasingly harder to implement. For Raman scattering spectroscopy, a light-sheet spectrometer was recently developed by combining Fourier transform spectroscopy with light-sheet microscopy [13]. Instead, for Brillouin scattering spectroscopy, which requires sub-picometer (i.e., sub-GHz) spectral resolution, no solution for two-dimensional (2D) multiplexing currently exists.
In this work, we employ atomic vapors to create a tunable monochromator capable of narrow-band spectral resolution and 2D spectral multiplexing. The absorptive properties of the atomic vapor can be taken advantage of in order to transmit light at the very narrow hyperfine transitions of the atoms. The vapor can be prepared to transmit light at selected hyperfine transitions either by using a laser or a magnetic field that changes the absorptive and/or the dispersive properties of the vapor [14,15]. Specifically, here we characterize a monochromator based on laser induced circular dichroism (LICD) [16,17]. We also show that the transmission spectrum of the vapor can be tuned within its Doppler broadened absorption band leading to the ability to perform optical spectroscopy at sub-GHz resolution with transmission and linewidth that are competitive with state-of-the art spectrometers. Finally, as the spectral analysis capabilities of atomic-based monochromators are not limited to spatial directions, we demonstrate full-field analysis capabilities characterizing image transmission and spatial resolution through the LICD monochromator.
2. Principle
Our high-resolution monochromator is based on laser induced circular dichroism (LICD) in rubidium atomic vapors. Consider a rubidium-87 (87Rb) atomic vapor cell and the hyperfine structure of the 52S1/2→52P3/2 D2 line. Figure 1(a) shows all the allowable transitions from 87Rb 52S1/2 (Fg = 2) hyperfine ground state to the 87Rb 52P3/2 (Fe = 1, 2, 3) hyperfine excited states, as well as the so-called crossover (CO) transitions which are artifacts of the counterpropagating pump and probe beams when traveling atoms see both lasers on resonance when the frequencies are half-way between two hyperfine transitions. Figure 1(b) shows the saturated absorption (SAS) spectrum of the 87Rb (Fg = 2→Fe = 1,2,3) highlighting the hyperfine transitions and the CO peaks collected using a compact saturation spectroscopy module (CoSy, Toptica).
Fig. 1. Hyperfine transitions of the 87Rb D2 line. (a) Transition schematic of the D2 87Rb 52S1/2 (Fg = 2)→ 87Rb 52P3/2 (Fe = 1, 2, 3) along with the crossover (CO) peaks (dashed arrows); (b) SAS spectrum of the D2 87Rb 52S1/2 (Fg =2) hyperfine transitions.
When a right-circularly (σ+) polarized pump laser beam is on resonance with the 52S1/2 (Fg = 2)→52P3/2 (Fe = 3) transition, the atomic population cycles between the magnetic sublevels of ground and excited states, until the transition 52S1/2 (Fg = 2, mFg = + 2)→52P3/2 (Fe = 3, mFe = + 3) is populated. Figure 2(a) shows the atomic transitions and magnetic sublevels of the 87Rb 52S1/2→52P3/2 D2 line. When the pump beam is σ+ polarized, atoms will be excited and make a magnetic sublevel change Δm = + 1. The atoms that accumulate to the excited state will eventually decay from the excited state (Δm = 0, ± 1). When the σ+ polarized pump beam is powerful enough, the atomic population density in the highest magnetic sublevels of ground and excited states becomes the same, hence the transition is saturated, but only for this circular polarization state [16,17]. The pump beam has thus prepared the vapor to absorb the orthogonal circular polarization components differently, an effect known as laser induced circular dichroism (LICD). Figure 2(b) illustrates what happens when a linearly polarized probe beam counterpropagating and in resonance with the same hyperfine transition passes through the atomic vapor cell that was prepared by the σ+ polarized pump beam. The linear polarization of the probe beam can be seen as the superposition of the two orthogonal circular polarization states: the σ+ component will not be absorbed because the pump laser has saturated the transition and therefore there are no atoms available for absorption; however, according to the selection rules (Δm = -1), the left-circular polarization component (σ-) will be absorbed because lower magnetic sublevels in the excited state are free to be occupied.
Fig. 2. Relevant 87Rb transitions and LICD effect. (a) Pump laser saturation scheme. Solid arrows are absorption pathways and dashed arrows are decay pathways; (b) Probe laser absorption after pumping. The specific transitions for the right (left) circular component of the probe are depicted in red (blue).
Now, consider the atomic vapor cell sandwiched between two crossed linear polarizers. A weak probe beam, i.e., the laser beam to be spectrally analyzed, will counter-propagate with the pump beam inside of the cell. The polarization of the probe beam is prepared by the first linear polarizer before entering the atomic vapor cell, and thus it will have σ+ and σ- polarization components equal in amplitude. The probe transmission past the second polarizer will be the ratio between the output of the second polarizer and the input laser irradiance before the cell. Neglecting differential dispersion due to the Kramers-Kronig relations, the transmission T can be written as
where L is the length of the atomic vapor cell, α0 is the mean absorption coefficient of the atomic vapor, and Δα is the differential absorption coefficient of the atomic vapor [14–17]. If α+ (α-) is the absorption coefficient for right (left) circularly polarized light, then α0 and Δα are related to α+ and α- byFrom Eq. (1) we see that transmission past the second polarizer occurs only when Δα≠0, i.e., when α+≠α_. In other words, there is transmission only when the vapor exhibits circular dichroism, the imbalance between the absorption of the two circular polarizations. The imbalance is indeed induced by the pump beam, as previously explained, within a very narrow spectral region. The linewidth of the spectral region is ultimately limited by the natural linewidth of the transition, which is ∼6 MHz for Rb lines [16,17]. The linewidth is also much smaller than the Doppler-broadened linewidth, which occurs due to the multiple atoms moving at different velocities inside of the atomic vapor cell. In fact, the pump frequency can be detuned to saturate different velocity classes within the Doppler broadened band, thereby detuning the monochromator transmission to create a spectrometer with a transmission envelope limited by the Doppler width of the atomic species. The LICD phenomenon can thus be used to implement a narrow, tunable spectral window for the probe beam.
3. Experimental setup
The schematic of the experimental setup is shown in Fig. 3. The pump laser beam (TA pro, Toptica) is a collimated Gaussian beam with a 1/e2 diameter of 1.35 mm and is used to prepare the pure 87Rb atomic vapor cell (Precision Glassblowing), which is 75 mm in length and 25 mm in diameter. The pump laser is tunable and can be locked within the D2 lines of 87Rb and 85Rb using a saturated absorption spectroscopy (SAS) module (CoSy, Toptica). The pump beam laser irradiance is controlled using a half-wave plate (λ/2) and a polarizing beam splitter (PBS) cube. A 10:90 (R:T) non-polarizing beam splitter (BS) cube is used to align the pump laser to propagate through the middle of the atomic vapor cell. The pump beam is right-circularly polarized using a quarter-wave plate (λ/4) before the BS, and its polarization is checked after being reflected by the BS. To simulate spectral analysis, we use a probe laser beam (DL pro, Toptica) that is also a collimated Gaussian beam with a 1/e2 diameter of 1.35 mm. The probe beam can also be tuned around and locked within the D2 lines of the two Rb isotopes using a second CoSy module. The probe beam is focused into the 87Rb cell by an aspherical lens (L1) with a 200 mm focal length f and aligned to counter-propagate with the pump laser inside of the atomic vapor cell. The first Glan-Taylor (GT1) polarizer (100,000:1 extinction ratio) is used to linearly polarize the probe beam before entering the vapor cell. A second aspherical lens (L2) of 200 mm focal length is used to re-collimate the laser and is part of a 4f-system with L1. A second Glan-Taylor polarizer (GT2), crossed with GT1, is placed after the BS and only transmits probe light with frequency falling in the LICD window created by the pump. The extinction of the LICD monochromator is limited by the extinction ratio of the output polarizer, which was measured to be ∼-54 dB using an optical power meter (S130C, Thorlabs). The transmitted signal is detected using a photodiode detector (PDA36A2, Thorlabs).
Fig. 3. Setup schematic: L1, L2, aspherical lenses; GT1, GT2, Glan-Taylor polarizers; BS, non-polarizing beam splitter; M, mirror; PBS, polarizing beam splitter; λ/2, half-wave plate; λ/4, quarter-wave plate; D, detector; B, beam block; f, focal length distance of lenses L1 and L2; O, object plane 4f system.
4. LICD spectrometer characterization
Figure 4 shows an exemplary transmission spectrum of the LICD monochromator (red trace). The probe irradiance is kept at 0.7 mW/cm2 before entering the 87Rb cell. The laser irradiance of the probe beam is less than the saturation laser irradiance Isat for a stationary 87Rb atom, which is 1.669 mW/cm2 [17]. The temperature of the LICD atomic vapor cell is 42°C. The frequency axis of Fig. 4 is calibrated using the CoSy module. The pump irradiance is .7 W/cm2 and the frequency is locked within the 87Rb (Fg = 2) band, and to the CO-2,3 hyperfine transition (see Fig. 1), which allowed for the highest LICD induced transmission. The three peaks correspond to the σ- transitions 52S1/2 (Fg = 2)→52P3/2 (Fe = 1, 2, 3) (see Fig. 2(b)). The transmission peak corresponding to the 52S1/2 (Fg = 2)→52P3/2 (Fe = 3) transition appears due to the saturated absorption induced by the σ+ pump. The two peaks corresponding to the 52S1/2 (Fg = 2)→52P3/2 (Fe = 1, 2) are also LICD effects. The σ_ component of the probe on resonance with the two transitions is still normally absorbed, but the σ+ is not absorbed because there are no more magnetic sublevels in the excited state to satisfy the selection rule for σ+ transitions, i.e., Δm = + 1. In particular, the highest peak corresponds to the 52S1/2 (Fg = 2)→52P3/2 (Fe = 2) transition, which exhibits the highest magnitude of its Clebsch-Gordan coefficient of the hyperfine dipole matrix ($- \sqrt {1/12} $ for the 52S1/2 (Fg =2, mFg = + 2)→52P3/2 (Fe = 2, mFe = + 1) transition versus $\sqrt {1/30} $ for the 52S1/2 (Fg = 2, mFg = + 2)→52P3/2 (Fe = 3, mFe = + 1) transition) [17]. When the pump is blocked, the probe is absorbed by the vapor and blocked by the crossed polarizer and there is no transmission, as recorded in yellow in Fig. 4. The inset of Fig. 4 plots transmission converted into decibel (dB) units. Although the polarizers have -54 dB extinction, we will not see the full extinction of the polarizers because it is below the limit of detection for the PDA36A2 photodiode, which is roughly -30 dB. Still, the inset shows that when the polarizers are crossed that the rejection is detector limited. The LICD throughput is on the order of 10-20%, consistent with previous experiments [16,17], limited by the collisional effects that the atoms experience.
Fig. 4. Exemplary transmission spectrum of the LICD monochromator. With no pump (yellow line), the linear probe is absorbed by the vapor and blocked by the crossed polarizer. Only in the presence of pump saturation (red line) the monochromator exhibits circular dichroism at specific hyperfine transitions. Inset, LICD transmission and “pump off” condition in units of decibels.
The transmission and the spectral resolution performances of the LICD monochromator are characterized in Fig. 5, where amplitude and linewidth (calculated as full width at half maximum, FWHM) of the highest transmission peak are evaluated. These two parameters can be controlled by the number of atoms saturated by the pump laser beam, which in turn can be tuned by the irradiance of the pump laser and the temperature of the vapor cell. Figure 5(a), (b) show the behavior of transmission and linewidth versus the pump irradiance when the LICD vapor cell temperature is fixed at 42°C. As the pump becomes more powerful and saturates the transition, the probe transmission increases until there is complete saturation at roughly 1.12 W/cm2. This power is much higher than Isat reported in [17], but it is needed to sufficiently saturate the entire length of the vapor cell at a high temperature. The linewidth of the central peak, which effectively determines the spectral resolution, increases as the pump power increases due to power broadening (Fig. 5(b)): the pump beam is so intense that it decreases the lifetime of the transition, which in turn increases the width of the peak [18]. Figure 5(c), (d) show instead the behavior of transmission and linewidth versus the vapor cell temperature when the pump irradiance is fixed at 1.12 W/cm2. At room temperature, the vapor is in equilibrium with a small portion of 87Rb atoms condensed onto the walls of the cell, thus it is necessary to heat the cell to separate the atoms from the walls of the cell and create a more active gas. As the vapor cell is heated, more atoms become available to be saturated by the pump beam and the transmission increases up until about 45°C (Fig. 5(c)). At temperatures higher than 45°C the transmission exhibits a steep decrease. Consistent with Beer’s law, the pump beam irradiance decreases and saturates less as it propagates through the absorbing vapor, leading to a decrease in probe transmission. The linewidth instead decreases with the cell temperature (Fig. 5(d)) possibly because, as more atoms interact with the lasers, the natural linewidth of the transition can be resolved.
Fig. 5. Characterization of LICD monochromator transmission and spectral resolution as a function of (a),(b) pump irradiance and (c),(d) vapor cell temperature. Insets for (a) and (b) show where the transmission FWHM are taken in the monochromator transmission spectrum.
Overall, a compromise must be found between temperature and pump power in order to achieve a good transmission level and a good spectral resolution. With a pump irradiance of 1.12 W/cm2 and a vapor cell temperature of 42°C, the monochromator transmission and linewidth are ∼17% and ∼80 MHz, respectively.
The frequency tuning capabilities of the monochromator, and thus the ability to build a spectrometer, are shown in Fig. 6. Tuning the pump frequency within the 87Rb 52S1/2 (Fg = 2) Doppler broadened band allows us to probe and saturate different atomic velocity classes of the rubidium atoms in the vapor, thus shifting the transmission window, as shown in Fig. 6(a). The negative slope of the shift shows us that, when the pump is detuned to higher frequencies, the peak transmission shifts towards lower frequencies. The counter-detuning effect is due to the counterpropagating alignment of the lasers, which see atoms traveling at the same speed, but in different directions. Figure 6(b) shows the transmission of the highest peak of the monochromator as a function of the pump detuning from the 87Rb 52S1/2 (Fg = 2)→52P3/2 (Fe = 3) transition. A Gaussian fit (black trace in Fig. 6(b)) was used to estimate the FWHM of the envelope. The transmission envelope has a Gaussian FWHM of 509 MHz, which agrees with the Doppler width of Rb atoms [14,16]. Larger spectral ranges could be achieved with a different atomic vapor species. Potassium, for example, has a doppler-width of ∼800 MHz at 770 nm. To analyze different frequency ranges, the central frequency of the spectrum can be changed by tuning the incident beam frequency so that the spectrum falls inside the atomic vapor transmission window.
Fig. 6. Frequency scanning capabilities of the monochromator. (a) Monochromator peak frequency detuning versus pump frequency detuning. (b) Monochromator transmission versus pump detuning (Gaussian fit is shown in black).
5. Full-field spectroscopy
After characterizing transmission, resolution and tunability of the LICD monochromator, we demonstrated its capability to transmit an image, i.e., to provide simultaneous transmission of all the points in a field of view. To do so, the monochromator is designed so that the vapor cell is placed within a 4f system composed of the two 200 mm focal length lenses (L1 and L2 in Fig. 3). A USAF target (R3L1S4N, Thorlabs) was placed at the object plane O of L1, and the photodiode detector was replaced by an sCMOS camera (Andor, Zyla 4.2) at the front focal plane of the second lens.
Imaging results are shown in Fig. 7. Figure 7(a) shows a test image of the USAF target element 5 of group 2, when the vapor cell is idle, i.e., the probe beam is off resonance, the pump beam is off, and the GT polarizers are in parallel configuration. When the polarizers are crossed, there is no image transmission, as seen in Fig. 7(b). Image transmission is achieved in Fig. 7(c) when the pump and probe beams are on resonance within the 87Rb 52S1/2 (Fg = 2) absorption band. The pump beam was expanded to 1.69 mm in diameter and the irradiance was 1.12 W/cm2. The probe laser irradiance was 11.2 mW/cm2. Here, it was necessary to increase the probe power to overcome stray pump light reflected by the vapor cell window into the camera. Still, the transmission achieved in Fig. 7(c) was ∼15.6%. When the beams are off resonance, instead, no image transmission was observed, as shown in Fig. 7(d).
Fig. 7. Image transmission of a USAF target through the LICD spectrometer (a) when the vapor cell is idle and polarizers are parallel, (b) when polarizers are crossed, (c) when the LICD monochromator is fully operational with pump and probe on resonance, and (d) when the probe beam is off resonance from the pump beam. Scale bars are 500 μm.
The LICD monochromator effect on the spatial resolution of the 4f imaging system was also assessed, as shown in Fig. 8. We estimated the imaging resolution as the last resolvable USAF target group. When the cell is idle, the resolution is ultimately limited to the diameter of the first polarizer, which is 5 mm. Thus, with a 200 mm focal length lens and 780 nm illumination, the NA and the resolution of the system results to be 0.0125 and 38 μm, respectively. Importantly, when the vapor cell is active via pump saturation, the resolution is expected to be limited by the diameter of the pump beam, i.e., by the cross-sectional area of the 87Rb atoms that are saturated. We studied this effect experimentally. Figure 8(a), (b) shows the USAF chart image without activating the spectrometer, as a control condition to show that the optical system has sufficient resolution to image group 3, element 6 of the USAF target. When activating the spectrometer using a pump diameter of 1.35 mm and a pump irradiance of 1.26 W/cm2, the three white lines are hardly resolvable (Fig. 8(c), (d)), and the spatial resolution of the system was estimated to be 88.4 μm (group 3, element 4). When the pump laser was expanded to 2.54 mm while keeping the irradiance at 1.26 W/cm2, the lines become more resolvable (Fig. 8(e), (f)) and the resolution improves to 49.6 μm (group 4, element 3). Thus, the pump beam acts similarly to a pinhole in a 4f system, and the spatial resolution improves as the pinhole diameter increases. In our setup, the size of the pump beam is limited by the available power to saturate the atomic vapor transition.
Fig. 8. Image transmission of the USAF target at different pump diameters and irradiances. Test image and correspondent laser irradiance profile (a),(b) when the monochromator is not operating, (c),(d) when the monochromator is operating with 1.35 mm pump diameter, and (e),(f) 2.54 mm pump diameter. (g) Spatial resolution of our system versus the irradiance of the pump beam. The red crosses indicate experimental values taken with 0.42 W/cm2, 1.26 W/cm2, and 7.55 W/cm2 pump irradiances when the laser 1/e2 diameter is 1.35 mm. The black dashed line is the fit of the data using the Rayleigh criterion and Eq. (4), as explained in the text.
Next, we established an operational definition of the effective diameter of the pump beam for the sake of imaging resolution. For this phenomenon, the critical physical property is the preparation of the 87Rb atoms, thus the effective pump beam diameter is determined by having enough pump irradiance to saturate the atoms in a certain cross-sectional area. To confirm this idea experimentally, we kept the pump 1/e2 diameter at 1.35 mm and changed the pump irradiance while recording the spatial resolution. Indeed, we observed that changing the irradiance of the pump beam is equivalent to changing the diameter of a limiting pinhole in our 4f imaging system, as seen in Fig. 8(g). A pump irradiance of 0.42 W/cm2 yields a resolution of 111.36 μm, 1.26 W/cm2 yields a resolution of 88.5 μm, and 7.55 W/cm2 yields a resolution of 78.7 μm. To estimate the effective cross-sectional area of the pump beam that sufficiently saturates the vapor, we used the definition of a Gaussian irradiance profile to calculate the effective diameter deff of a Gaussian laser beam
where ω is the 1/e2 diameter, Ieff is the irradiance of the Gaussian beam at deff, and I0 is the peak irradiance at the center of the laser beam. By assuming that ω = 1.35 mm and using Ieff as a free parameter, we used the Rayleigh criterion to fit the three estimated resolutions as a function of the pump peak irradiance shown in Fig. 8(g). Using the fit, we found that the cross-sectional area that predicts the experimental resolution was at Ieff=13.59 mW/cm2, which is in good agreement with the experimental data (R2 = 0.92). The back-calculated laser diameters at the 13.59 mW/cm2 threshold were 1.76 mm for the 0.42 W/cm2 pump irradiance, 2.02 mm for 1.26 W/cm2, and 2.41 mm for 7.55 W/cm2. The effective diameter of the limiting aperture of the imaging system are thus ∼1.3-1.8 fold greater than the 1/e2 diameter of the pump beam.6. Conclusions
In conclusion, we have demonstrated a high-resolution spectrometer capable of 2D spectral multiplexing. The spectrometer is composed by a tunable monochromator based on atomic vapors selective saturated absorption. The monochromator transmission spectrum can be tuned across the Doppler broadened bands, and the transmission envelope of the monochromator is limited to the Doppler width of the atomic vapor species. For the purpose of practical spectroscopy, the three transmission peaks will act as the point-spread-function (PSF) of the spectrometer, where the PSF will be deconvolved in postprocess to extract the spectral information. For future applications, the performances of the LICD monochromator are competitive with Fabry-Perot and VIPA etalon-based spectrometers [19,20], thus paving the way for Brillouin or Rayleigh-wing spectroscopy in full-field configuration.
Funding
Directorate for Biological Sciences (1942003); Fischell Institute for biomedical devices (Young Investigator Fellowship).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data for the characterization of the instrument are available from the corresponding author upon request.
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