1. Introduction

In the laser era, Raman spectroscopy has become a powerful tool for the study of elementary excitations in gases, liquids, and solids. Originating from inelastic scattering of light, the Raman effect directly probes vibrational modes and electronic states in matter. Due to its non-invasive nature, Raman spectroscopy is applied to the identification of explosives in security [1] and in biomedical diagnostics [2]. The applications in industry focus on structural properties of solids, for instance, for monitoring mechanical stress and crystallinity of silicon wafers [3], determining the number of monolayers in two-dimensional materials [4], and characterizing disorder in graphite [5]. Raman mapping is intensively used in mineralogical and petrological analyses in geochemistry, micropaleontology, metallogeny, where it resolves the general composition of rocks, detects and identifies mineral phases [6]. Moreover, for the first time, Raman spectroscopy will be employed in missions to Mars (Mars 2020 and ExoMars 2022) for in situ mineralogical and organic/biological analysis.

However, there are two serious disadvantages, limiting even broader use of Raman spectroscopy. These are relatively weak intensities of Raman signal due to a very small scattering cross section (typical values of $\sim 10^{-30}$ cm$^2$ sr$^{-1}$ for spontaneous Raman scattering) which occurs often alongside much stronger luminescence (typical values of cross section $\sim 10^{-19}$ cm$^2$ sr$^{-1}$) [7]. To circumvent these problems, a variety of enhanced Raman techniques [8] and luminescence suppression methods [9,10] have been developed.

In this report, we address the problem, the weak intensity of spontaneous Raman scattering and undesired strong luminescence background, by the advanced analysis of scattered light. In a conventional grating-based spectrometer, the Raman light is spatially dispersed onto a multi-pixel charge-coupled device (CCD). In contrast, our approach, the fiber-dispersive Raman spectrometer, exploits pulsed excitation and chromatic dispersion in the fiber material to disperse in time the arrivals of Raman light pulses with different wavelengths onto a single-pixel detector [11,12]. Since the detector measures arrival times, good timing resolution is of importance. One of the promising candidates for this task is the superconducting nanowire single-photon detector (SNSPD), which combines required timing resolution (small timing jitter) with single-photon sensitivity in a wide spectral range from UV to near-IR. Recent studies of timing jitter in these devices [13–16] pushed the jitter value to the fundamental limit of a few picoseconds. Due to effective gating by means of picosecond pulse excitation, relatively slow retarded (typical rise time $\sim 10^{3}$ ps) luminescence response is effectively reduced with respect to almost instantaneous (typical rise time $\sim 1$ ps) Raman response [7]. Furthermore, the single-photon sensitivity of SNSPDs circumvents the problem of low Raman intensities.

2. Fiber-dispersive Raman spectrometer: design and components

The fiber-dispersive Raman spectrometer, illustrated in Fig. 1, is comprised of the five following modules. (1) A pulse laser excites a sample that generates the scattered Raman signal. (2) A Raman probe shapes the excitation pulses, collects backscattered light, and filters the Rayleigh signal out. (3) A dispersive fiber transforms spectral information of the Raman signal into the time domain. Raman photons with different wavelengths propagate through the fiber with different velocities and arrive at the detector at different times, which we call delay times. (4) A detector module and (5) time-correlated single-photon counting (TCSPC) electronics measures and stores the time delays of detected photons. The next paragraphs contain a detailed description of each module.

 

Fig. 1. Schematics of the fiber-dispersive Raman spectrometer equipped with a single-photon detector. Arrows in the optical path depict the direction of light propagation. Values in the top-right corner are: the central excitation wavelength in free space, $\lambda _{ex}$, the standard deviation of a corresponding distribution in either wavelength, $\sigma _\lambda$, frequency, $\sigma _\nu$, or time domain, $\sigma _t$ (the latter was determined from indirect measurements). A grating spectrometer with a CCD detector was used for calibration measurements. TCSPC and CCD were connected to a computer (not shown here) for processing and displaying the data.

Download Full Size | PDF

The pulse laser, a Ti:Sapphire laser (Femtosource, synergy 20), generates Fourier-transform-limited pulses at a central wavelength of $\lambda _0=797$ nm with a repetition rate of $F_{rep}=80$ MHz, a duration of $\sigma _{t0} =$ 13 fs ($\sigma$ stands onwards for standard deviation), and a spectral bandwidth of $\sigma _{\lambda 0} =$ 25.9 nm in wavelengths ($\sigma _{\nu 0} =$ 403.8 cm$^{-1}$ in wavenumbers). The laser pulses are coupled from free space into a multi-mode fiber (MMF-1 in Fig. 1) with an optical collimator. We note here that due to dispersion in the fiber, the light pulses at the fiber output become non-transform-limited. The laser can also operate in the continuous wave (CW) mode emitting radiation with a central wavelength of 780 nm and a spectral bandwidth of 3.8 nm.

The Raman probe (Ocean Optics, RPB785) (Fig. 1) is designed for 785 nm excitation wavelength. It comprises a dichroic mirror (DM), a band-pass filter (BPF), a long-pass filter (LPF), and two multi-mode fibers (MMF-1 and MMF-2). Both the excitation MMF-1 and the collection MMF-2 are step-index fibers with the same length of 1.5 m and numerical aperture of 0.22, but different core diameters of 105 $\mu$m and 200 $\mu$m, respectively. We note here that in multi-mode step-index fibers, the expected dominant source of pulse broadening in time is modal dispersion. Because the datasheets for these fibers were not provided by the manufacturer of the Raman probe, we have carried out complementary measurements using the fibers with the same core diameter and aperture and found out that they add a pulse broadening per unit fiber length of 18.5 ps/m. The excitation pulses are focused onto a sample at 7.5 mm (working distance) from the edge of the Raman probe. At the sample, spectral characteristics of exciting pulses, $\lambda _{ex} = 785$ nm and $\sigma _{\lambda ex} \approx 5$ nm (Fig. 2(a)), are determined by the bandwidth of laser pulses and the BPF, while their duration, $\sigma _t \approx 28$ ps, by the MMF-1. The DM and the LPF together filter the Rayleigh signal out from the collected backscattered light at a cut-on wavelength of 806 nm with a cut-on tolerance of $\pm 4$ nm (specified by the manufacturer). This cut-on wavelength sets the lowest limit for the spectral range, 332 cm$^{-1}$ in the Stokes shifts.

The dispersive fiber (Thorlabs, GIF50C), introduces delay time difference for Raman photons with different wavelengths. It is a multi-mode, graded-index fiber (GIF) with a 50 $\mu$m diameter germanium-doped core and a length of 45 m. In fibers of this type, chromatic dispersion dominates in pulse broadening. The effective group indices of refraction are specified by the manufacturer as $n_g = 1.482$ and 1.477 for wavelengths 850 nm and 1300 nm, respectively.

The detector module comprises a single-mode fiber (SMF) that guides the light to a single-pixel SNSPD device. The SMF (Thorlabs, SMF28) is a step-index fiber with a length of 3 m and a core diameter of 10 $\mu$m. The SNSPD chip was delivered by Superconducting Nanotechnology (Scontel). The detector with a sensitive area of about 10 $\mu$m in diameter was directly coupled to the SMF (depicted in Fig. 1) by the manufacturer. The SNSPD chip was installed at the second stage of a two-stage pulse-tube cooler (TransMIT, PTD406) with vacuum-tight optical (fiber) and electrical (coaxial) feedthroughs. At an operating temperature of 4 K, the experimental critical current of the SNSPD amounts to 40.3 $\mu$A. The SNSPD dead time is $\tau _{dead}\approx 5$ ns. This is the time the detector needs to return to the initial state after each count. Within this time, the detector is not able to detect photons. Measurements with the pulsed excitation at 797 nm ($\sigma _{t0} =$ 13 fs, $\sigma _{\lambda 0} =$ 25.9 nm) and an additional 2 m-long SMF28 fiber result in a 25.5 ps-large system jitter of the detector module (with a bias current of 37.0 $\mu$A).

TCSPC and readout electronics includes a control unit for the SNSPD (Scontel, CU-2SPD/P&T-005), which provides dc-bias for the SNSPD and comprises a bias-tee with a bandwidth of 0.1 - 4200 MHz and two amplifiers with a bandwidth of 0.1 - 1000 MHz and a total gain of $\sim 46$ dB. The TCSPC electronics (Becker $\&$ Hickl, SPC-150NX) measures time delays between arrivals of two voltage transients, an SNSPD response to the CFD input and a laser reference (was generated by a fast photodiode, not shown in Fig. 1) to the SYNC input, with a resolution of about $0.4$ ps (specified by the manufacturer). It also builds a histogram of these delays, which represents a Raman spectrum in the time domain.

3. Calibration measurements and system performance

Unlike a conventional Raman spectrometer, our fiber-dispersive Raman spectrometer converts the spectrum into the time domain. It is done by stretching the propagation times of light pulses due to group velocity dispersion in the 45 m-long GIF. Individual wavelength components can be resolved via the difference in their arrival time at a single-pixel SNSPD device. In order to reconstruct the spectrum in the frequency domain, one needs to perform time-wavelength calibration. As a convenient object for calibrating the instrument, we chose methanol (CH$_3$OH). Due to the high purity of commercial methanol, potential luminescent centers/inclusions occur at low concentrations and do not affect the Raman signal. Methanol is a colorless liquid. Placing it in a transparent cuvette minimizes reflection of the light exciting the Raman effect. Moreover, the Raman spectrum of methanol exhibits several strong lines at relatively small as well as at relatively large distances from each other. For calibrating the fiber-dispersive spectrometer, we used a commercial grating spectrometer equipped with a silicon-based CCD detector (OceanOptics, USB4000) by coupling it to a fiber MMF-2 as depicted in Fig. 1. The spectrometer has a 3648-pixel linear CCD array covering a 200 - 1100 nm wavelength range with a resolution of about 0.3 nm (full width at half maximum, FWHM) and maximum integration time of 10 s.

 

Fig. 2. Calibration measurements. (a) Spectrum of pulsed excitation measured with the grating spectrometer at the sample position. $\lambda _{ex}$ is the central wavelength and $\sigma _{\lambda , \nu }$ is the spectral width of the excitation. (b) Raman spectra of methanol (CH$_3$OH) in the Stokes shifted range, acquired (top) with the grating spectrometer (CCD detector) in the frequency domain and (bottom) with a fiber-dispersive spectrometer (SNSPD) in the time domain. The latter is the average of the original data points within a moving window of 25 ps (one fifth of the FWHM of a line). The three marked Raman peaks, $\lambda _0^{(1)}$, $\lambda _0^{(2)}$, and $\lambda _0^{(3)}$, are due to the C-O stretching, the CH$_3$ anti-symmetric deformation, and an overlap of the CH$_3$ symmetric and asymmetric stretching vibrational modes, respectively. (c) Wavelength-dependent delay time of light pulses propagating through the GIF to the SNSPD.

Download Full Size | PDF

Figure 2(b) shows spectra of methanol acquired with a commercial grating spectrometer (CCD detector) in the frequency domain (10 s integration time) and with our fiber-dispersive spectrometer equipped with an SNSPD in the time domain ($\sim 450$ s integration time). In the latter case, the integration time was elongated to compensate for large optical losses of the Raman signal (about 30 dB) in fiber connections between MMF-2 and GIF and between GIF and SMF (Fig. 1). Both spectra in Fig. 2(b) were obtained under pulsed excitation (Fig. 2(a)) with a central wavelength of 785 nm and spectral width of 5 nm (77 cm$^{-1}$). Typical Raman linewidths are well below this value. The averaged excitation power at the sample was about 43 mW. The amplitudes of Raman peaks in each spectrum are defined by the sensitivity of the corresponding detector. The sensitivity of the SNSPD (optimized for telecommunication wavelengths) increases with the wavelength and reaches a maximum at 1550 nm. Contrarily, the silicon CCD detector has a drop of sensitivity at around 1000 nm. In Fig. 2(b), the time axis is reversed because in this spectral range fibers have positive group velocity dispersion, i.e. pulses with shorter wavelengths arrive with longer delays. The delay time is defined as $\tau (\lambda ) = L /v_g(\lambda )$, where $L$ is the fiber length, $v_g(\lambda ) = c / n_g(\lambda )$ is the group velocity, $c$ is the speed of light in vacuum, and $n_g(\lambda )$ is the wavelength-dependent group refractive index. We used the Sellmeier equation, which provides the wavelength-dependent refractive index $n(\lambda )$, to find $n_g(\lambda ) = n - \lambda dn/d\lambda$ and compute $\tau (\lambda )$ (the Sellmeier coefficients were taken as for the germanium-doped sample $\# 9$ in [17]). Additionally, we used a constant factor $\sim 1$ to fit $n_g(\lambda )$ to the two data points provided for the GIF by the manufacturer. Further, we picked time-wavelength positions of the three Raman peaks in Fig. 2(b) and used them as reference points to adjust (off set) the computed $\tau (\lambda )$. This gives us the calibration curve shown in Fig. 2(c). Such an adjustment accounts for the relative experimental delays, i.e. arrivals of the SNSPD response with respect to the laser reference.

The overall spectral resolution in our fiber-dispersive approach appears as the standard deviation, $\sigma _\tau$, in the stochastic delay times, $\tau (\lambda )$, of counts due to Raman photons belonging to a particular Raman spectral line. The $\sigma _\tau$, which is onwards also referred to as the pulse broadening, bears contributions from chromatic and modal dispersion in fibers carrying Raman light-pulses, from the spectral width of the exciting light-pulses and the timing jitter of the SNSPD. To determine spectral widths of the three observed Raman lines (Fig. 2(b)), we, first, converted the Raman spectrum from the time domain into the wavelength domain with the help of the calibration curve in Fig. 2(c). We then fitted the spectrum in the wavelength domain with a sum of three Gaussian functions, using their standard deviations, $\sigma _\lambda$, and amplitudes as fitting parameters. The mean values are taken from the calibration curve. We associate spectral resolution of the spectrometer at the particular wavelength with the best fit values of $\sigma _\lambda$ for the corresponding Raman line ($\sigma _\lambda =11.5$ nm for $\lambda _0^{(1)}$ and $\sigma _\lambda =10.5$ nm for $\lambda _0^{(2)}$). Mathematically, the spectral resolution and the standard deviation in the delay time are connected via the calibration curve $\tau (\lambda )$ as $\sigma _\tau = \sigma _\lambda |d\tau /d\lambda |$. The third line in Fig. 2(b), $\lambda _0^{(3)}$ at 1010 nm, is noticeably broader. In fact, it is an overlap of two closely-spaced lines due to CH$_3$ symmetric and asymmetric stretches, which are separated by about 100 cm$^{-1}$ [18]. The demonstrated spectral resolution was just sufficient to justify the usability of our approach; it can be drastically improved by eliminating the modal dispersion and narrowing the excitation spectrum.

The lower wavelength of the spectral range available in the framework of the fiber-dispersive approach is determined by the excitation wavelength while the upper wavelength is defined by the maximum in the $v_g(\lambda )$. At this wavelength, which is called zero-dispersion wavelength (ZDW), $d^2n/d\lambda^2=0$. In our setup, this spectral range spans the wavelengths 785 - 1330 nm ($\sim 0-5200$ cm$^{-1}$ in the Stokes shifts). We denote by $\Delta T$ the delay time difference for two Raman photons corresponding to these two outer wavelengths. In our setup, $\Delta T \sim 1.2$ ns (Fig. 2(c)) and is mostly determined by the longest dispersive fiber GIF. We note that the $\Delta T$ should not exceed the inverse laser repetition rate $1/F_{rep}$. Otherwise, Raman photons with different wavelengths originating from two sequential exciting pulses will arrive at the detector simultaneously. Another constrain is the SNSPD dead time against the pulse repetition rate. For $\tau _{dead} > 1/F_{rep}$, only one Raman photon per $\tau _{dead} F_{rep}$ excitation pulses can be detected. In the opposite case, $\tau _{dead} < 1/F_{rep}$, the $(\tau _{dead} F_{rep})^{-1}$ Raman photons per one excitation pulse can be detected. Therefore, the smallest acquisition time of the spectrum, which is defined by the number of required photons to be detected, decreases with the decrease in the dead time. Other metrics of the SNSPD affecting the smallest acquisition time are the detection efficiency, $\alpha$, and the dark count rate, DCR. The signal-to-noise ratio is just the ratio of the rate of detected Raman photons to the rate of dark counts, $\alpha (\tau _{dead} F_{rep})^{-1}$. An increase in this ratio decreases the smallest acquisition time.

We shall note that our spectrometer possesses single-photon sensitivity. With an experimental photon counting rate of the SNSPD of $\sim 10^3$ Hz and a system detection efficiency of $\alpha < 1 \%$ in the range 800 - 950 nm, we estimate that the photon flux per detector area amounts to about $10^{5}$ photons/s. With $F_{rep} = 80$ MHz, we conclude that on average there were about $10^{-3}$ Raman photons detected per pulse.

4. Time-domain Raman spectra of two minerals

After calibrating the fiber-dispersive spectrometer, we perform measurements of two minerals, olivine and gypsum, which are characterized by relatively weak and strong Raman scattering efficiencies, respectively, and low luminescence of pure materials. These minerals have been chosen because they are important for the classification of rock-forming minerals. For example, the Raman Laser Spectrometer instrument on board the ExoMars 2024 ESA rover mission to Mars will be used to identify these minerals [19]. As seen in Fig. 3 (bottom), the Raman spectrum of olivine (Mg$_2$(SiO$_4$)) exhibits one marked Raman peak at about 840 nm (Stokes shift 840 cm$^{-1}$). This band corresponds to the characteristic doublet feature (two lines at around 820 cm$^{-1}$ and 850 cm$^{-1}$ Stokes shifts) of SiO$_4$ internal stretching vibrational modes [20]. Taking into account a relatively small scattering cross-section of olivine and large coupling losses ($\sim 30$ dB) in the optical path, detection of this line is achieved exclusively due to the single-photon sensitivity of the SNSPD. In Fig. 3 (center, top), we show two Raman spectra of gypsum (CaSO$_4\cdot$2H$_2$O): the top one is measured with a commercial grating spectrometer (CCD detector) and the bottom one with our fiber-dispersive spectrometer equipped with an SNSPD. Both spectra exhibit the Raman peak at about 853 nm (Stokes shift 1010 cm$^{-1}$), the strongest stretching vibrational mode of SiO$_4$ tetrahedra [21]. The SNSPD-based spectrum exhibits the second peak at about 1074 nm (Stokes shift 3440 cm$^{-1}$), which is not observed with the silicon-CCD detector because it appears at the edge of the CCD spectral range. This peak corresponds to the O-H stretching mode of the hydrate with a relatively large spectral line width of $\sigma _\nu =$ 390 cm$^{-1}$. In fact, this line is an overlap of two closely-spaced Raman lines reported to be at Stokes shifts of 3406 cm$^{-1}$ and 3494 cm$^{-1}$ in [22].

 

Fig. 3. Raman spectra of olivine (bottom) and gypsum (center and top) in the Stokes shifted range acquired with the fiber-dispersive spectrometer (SNSPD) in the time domain (bottom and center) and the grating spectrometer (CCD detector) in the frequency domain (top) under 785 nm pulsed excitation. The marked Raman peak on the olivine spectrum (bottom) corresponds to the characteristic doublet of SiO$_4$ internal stretching vibrational modes. The first marked Raman peak on both gypsum spectra (center and top) corresponds to the stretching vibrational mode of SiO$_4$ tetrahedra, and the second marked Raman peak of the SNSPD-based spectrum of gypsum (center) corresponds to the O-H stretching mode of the hydrate. Both SNSPD-based spectra are the average of the original data points within a moving window of 25 ps.

Download Full Size | PDF

These results demonstrate that the fiber-dispersive spectrometer, which is at the moment clearly not optimized for such studies, already enables one to detect very characteristic vibrational modes in Mars surface minerals such as the stretching vibrations of the SO$_4$ tetrahedra, sulfate, and the hydroxyl group. These modes are envisioned to be analyzed in the framework of the ExoMars 2024 ESA rover mission to Mars [19]. For example, the SO$_4$ stretching modes differentiate sulfates from sulfides, chlorides and carbonates while the O-H stretching mode differentiates hydrated minerals from anhydrates. A further step in the analysis will use the intensity-weaker lattice modes of characteristic cations in the compounds, lying in the low-Stokes range. The spectral resolution typically required for this type of mineral identification and characterization is within 6-10 cm$^{-1}$. At this point, we would like to point out that such a resolution is feasible for the excitation lasers with appropriately long (a few ps) pulses. In the next section, we estimate the ultimate achievable resolution of the fiber-dispersive spectrometer and the required parameters of its components.

5. Discussion

For the proof-of-principle measurements with our setup, we used a broad-band femtosecond laser and multi-mode (step-index) fibers. Both components limit the spectrometer resolution to $\sim 11$ nm ($\sim 135$ cm$^{-1}$). A vast improvement is achievable by implementing a narrow-band picosecond pulse laser and eliminating modal dispersion, e.g. by replacing multi-mode step-index fibers with graded-index or even with single-mode fibers. However, it is worth noting that such an improvement would reveal another factor limiting the resolution, the timing jitter of the SNSPD. In this case, a solution is feasible by adjusting a length of a dispersive fiber and employing an SNSPD device with a smaller jitter. For instance, commercially available SNSPDs with a large sensitive area of up to 50 $\mu\textrm{m}$ in diameter combine sub-10 ps system jitter (standard deviation) with a high detection efficiency of 70% [23]. Such a large-area SNSPD can be directly coupled to a (graded-index) multi-mode fiber. This approach would eliminate high optical losses, which are inserted at the connection between GIF (50 $\mu$m core) and SMF (10 $\mu$m core).

Having as a target typical scientific requirements for a Raman instrument, namely $< 10$ cm$^{-1}$ spectral resolution and a Stokes shift range up to 4400 cm$^{-1}$ along with the commercial availability, we have evaluated the key properties of the required components. We consider a commonly used 785 nm pulse laser as an excitation source with a typical $F_{rep}=80$ MHz. For this excitation wavelength and the required Stokes shifts, the spectral range of the instrument spans from 785 nm to 1200 nm. The duration of laser pulses $\sigma _{t0}$ was a trial parameter, while their spectral bandwidth $\sigma _{\lambda 0}$ was considered to be Fourier-transform-limited, i.e. $\sigma _{\lambda 0} = \lambda _0^2 (2\pi c \sigma _{t0})^{-1}$. As a dispersive fiber, we select the commercially available GIF with a maximum length of $L = 500$ m. This length satisfies the constrain $\Delta T \leq 1/F_{rep}=12.5$ ns where $\Delta T$ corresponds to the spectral range specified above. For the SNSPD jitter, we take a commercially available $\sigma _{SPD}=10$ ps.

We compute the spectral resolution in wavelengths as $\sigma _\lambda = \sigma _\tau (|d\tau /d\lambda |)^{-1}$. The total pulse broadening $\sigma _\tau$ in our approach is defined as

 

Fig. 4. Ultimate spectral resolution of a fiber-dispersive spectrometer with indicated key parameters computed with Eqs. (1)–(3) for excitation wavelengths of (a) 785 nm and (b) 532 nm.

Download Full Size | PDF

Our evaluation based on Eqs. (1)–(3), shows that for obtaining an ultimate 3 - 10 cm$^{-1}$ spectral resolution in 0 - 4400 cm$^{-1}$ Stokes range (Fig. 4(a)) under a 785 nm excitation (corresponds to a 785 - 1200 nm spectral range with 0.2 - 1.4 nm resolution), the optimal duration of the laser pulse is $\sigma _{t0}=3$ ps and the optimal length of GIF is 500 m. Here, we completely neglected modal dispersion in GIF and the effect of short MMF fibers in the Raman probe. Figure 4(b) shows the best achievable resolution for the excitation wavelength of 532 nm and the same pulse duration $\sigma _{t0} =3$ ps, repetition rate $F_{rep}=80$ MHz, and detector jitter $\sigma _{SPD}=10$ ps. To obtain an ultimate resolution below 5 cm$^{-1}$ ($<$0.2 nm) over a Stokes range of 0 - 4400 cm$^{-1}$ (a wavelength range of 532 - 700 nm) a 230 m-long fiber GIF can be used resulting in $\Delta T = 12.5$ ns. This realization would require an optical low-pass filter at 700 nm to keep $\Delta T$ as small as 12.5 ns.

There are other detector technologies capable of single-photon counting with high timing resolution (e.g. [11,24]), which is one of the key requirements for obtaining ultimate spectral resolution in the fiber-dispersive approach. The single-photon avalanche photodiode (APD, id100, id Quantique) has a timing jitter of $\sigma _{SPD}=21$ ps and a spectral range of 350 - 900 nm, while the microchannel plate photomultiplier tube (MCP-PMT, R3809U-50, Hamamatsu) has a timing jitter of $\sigma _{SPD}=10$ ps and a spectral range of 160 - 850 nm. We evaluate their spectral resolution by following the same procedure as described above. For the excitation at the wavelength of 785 nm, a fiber-dispersive spectrometer equipped with either the ADP or the MCP-PMT would provide a 0 - 1630 cm$^{-1}$ Stokes range with $\sim 7$ cm$^{-1}$ resolution or a 0 - 980 cm$^{-1}$ Stokes range with $\sim 3$ cm$^{-1}$ resolution, respectively. Hence, both are not suitable for the fiber-dispersive approach in the near-IR range. Contrarily to 785 nm excitation, for commonly used excitation at a wavelength of 532 nm with $F_{rep}=80$ MHz, $\sigma _{t0}=3$ ps, and a fiber length of $L = 230$ m needed to keep $\Delta T=12.5$ ns for a spectral range of 532 - 700 nm (Stokes range 0 - 4400 cm$^{-1}$), a fiber-dispersive spectrometer equipped with either SNSPD, APD, or MCP-PMT would provide a resolution of either $<5$ cm$^{-1}$, 7 - 10 cm$^{-1}$, or $<5$ cm$^{-1}$, respectively. This evaluation shows that all three detectors can be alternatively employed in the fiber-dispersive spectrometer in the visible range. Along with the spectral resolution, other characteristics of the detectors such as dark count rate and dead time should be compared to meet particular requirements. Such comparison, however, remains out of the scope of this study.

Next, we would like to discuss other advantages of the fiber-dispersive Raman spectroscopy with an SNSPD, which are effective gating by means of picosecond pulse excitation and the single-photon sensitivity in the near-IR range. It is well known that the major challenge in Raman spectroscopy is to get rid of undesired luminescence. There are several ways to reduce luminescence. The most common way is to employ a near-IR laser excitation in the range from 785 to 1064 nm [10]. Another way is to use the short-pulse excitation instead of CW. Being excited with pulses shorter than the rise time of luminescence (typically on the nanosecond level), the luminescence signal does not reach its steady-state intensity within the duration of the excitation pulse [25]. Contrarily, Raman signal with the rise time less than one picosecond, does reach the steady-state value within the duration of the excitation pulse. Therefore, unless the duration of the excitation pulse is smaller than the Raman rise time or longer than the luminescence rise time, the relative luminescence intensity with respect to the Raman intensity decreases. To illustrate this effect, we measured Raman spectra of a silicon crystal with a CW ($\lambda _{ex}=782$ nm, $\sigma _\lambda =2.6$ nm) and pulsed excitation ($\lambda _{ex}=785$ nm, $\sigma _\lambda =5$ nm). In both cases, the grating spectrometer with the CCD detector was used. As clearly seen in Fig. 5, for CW excitation, a broad photoluminescence peak is much stronger than the Raman signal at 520 cm$^{-1}$ (zone-centered optical phonon of silicon). Under pulsed excitation, the photoluminescence signal is considerably reduced and remains smaller than the Raman signal. Independently on gating, the almost instantaneous Raman scattering will be further separated from the remaining luminescence in the time domain.

The broad spectral single-photon sensitivity of the SNSPD is very attractive for measuring Raman light known for its weak intensity due to a very small scattering cross-section. For instance, the Raman line of gypsum at approximately $1074$ nm (3440 cm$^{-1}$) has been resolved exclusively due to the broad spectral sensitivity of the SNSPD device. Resolving this line with a conventional spectrometer would require decreasing the excitation wavelength or using an indium gallium arsenide (InGaAs)-based CCD detector.

 

Fig. 5. Raman spectra of a silicon crystal obtained with a grating spectrometer (CCD detector) under 782 nm CW excitation (top) and 785 nm pulsed excitation (bottom). The bottom curve is the average of the original spectrum within a moving window of 9 nm. On both spectra, the Raman peak (marked with the arrow) corresponds to the zone-center optical phonon.

Download Full Size | PDF

6. Conclusion

We have demonstrated a prototype of the fiber-dispersive Raman spectrometer with single-photon sensitivity. We have found two factors limiting the spectrometer resolution: (i) methodological, i.e. chromatic dispersion in the fiber material and (ii) instrumental, undesired spectral and time broadenings added by components of the instrument. In the present implementation serving as proof-of-principle, the main limitation is the broad-band excitation along with modal dispersion in multi-mode (step-index) fibers of the Raman probe, i.e. the instrumental factors. This limitation can be relaxed via implementing a narrow-band laser with picosecond light pulses and eliminating modal dispersion. For each particular task, the spectrometer design should be, as a rule, specifically adapted and advantages are balanced against other constraints. We have evaluated key properties for spectrometer components in order to meet the requirements on resolution and spectral range for mineralogical analysis. In the Stokes range up to 4400 cm$^{-1}$, the fiber-dispersive approach can provide a resolution of 3 - 10 cm$^{-1}$ for the excitation wavelength 785 nm and an ultimate resolution below 5 cm$^{-1}$ for the excitation wavelength 532 nm. We have determined the main advantages of the fiber-dispersive approach for Raman spectroscopy. These are single-photon sensitivity, considerable reduction of luminescence, and the capability to perform time-resolved Raman spectroscopy. With the emergence of first short-pulse lasers approaching readiness levels for space applications (e.g. [26]), these features make fiber-based Raman spectrometers an attractive alternative to conventional Raman instruments.