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Abstract
Mid-infrared spectroscopy is an essential analytical method in science and industry. Unlike in the near-infrared range, grating spectrometers for the mid-infrared are rarely employed, mostly due to the limited availability and performance of suitable line array detectors. In this work, continuous-wave nonlinear-optical upconversion is used to enable mid-infrared spectroscopy. A broad spectral window between 3.7 and 4.7 μm is upconverted to 825 – 867 nm for detection on a silicon-camera-based near-infrared grating spectrometer with a high sensitivity down to sub-picowatt of input power. A theoretical model is presented that accurately describes the upconversion process and the total system behavior. Spectroscopic flame emission measurements demonstrate the applicability towards the analysis of highly dynamic processes.
© 2017 Optical Society of America
1. Introduction
Infrared spectroscopy is a key method for material characterization, recognition, and analysis. Measurements are often performed in the near-infrared (NIR), where thermoelectrically-cooled indium gallium arsenide (InGaAs) allows detection up to wavelengths of 2.5 μm. However, increasing significance falls to the mid-infrared (MIR) range with wavelengths above 3 μm, where strong, fundamental molecular lines are present [1]. Standard instrumentation for MIR spectroscopy are Fourier transform spectrometers (FTIR), complemented by tunable interband- or quantum-cascade-laser-based spectrometers. The FTIR typically covers a wide spectral range, but is limited in acquisition speed. In laser spectrometers, the spectral coverage is limited by the laser’s tuning range. Hence, these methods face challenges in complex and dynamic situations like combustion analysis, high-throughput sorting and quality control or reaction monitoring. Line-detector-based grating spectrometers offer the potential for high speed measurements combined with a wide covered spectral range, since in contrast to the above methods, the full spectra are taken simultaneously. However, line-array detectors for the MIR are rarely found, partly because the sensitivity of suitable detector materials, even cryogenically cooled, is limited by dark noise [2].
Nonlinear-optical upconversion has been demonstrated as a tool to overcome infrared detector limitations [3–5]. Here, the MIR signal is transferred to the very near-infrared, where detectors offer more beneficial properties. Upconversion has been employed for infrared spectroscopy in combination with further dispersive elements such as gratings [6–9] or making use of the wavelength-selective behavior of the nonlinear process itself [10,11].
In this work, a continuous-wave converter spectrometer system is presented for sensitive high-speed measurements of incoherent MIR signals with several thousand spectra per second. The setup utilizes intracavity upconversion in lithium niobate to transfer the MIR light to wavelengths that can be detected in a silicon-camera-based spectrometer unit. A wide span of converted wavelengths is achieved by exploiting the two branches of quasi phase matching around the inflection point combined with non-collinear conversion as was recently demonstrated in [12].
In the present work, a theoretical model is developed for the conversion process and the overall system behavior including all components which shows to be in very good agreement with experimental data. The characterization of the spectrometer is focused on spectral resolution and sensitivity. As a first application, flame emission spectroscopy is performed on the dynamic combustion process of a pyrotechnic airbag inflator module.
2. Sum frequency generation
Signal upconversion treated in this work is achieved via sum frequency generation (SFG). This aspect of the nonlinear-optical three-wave mixing describes the energy transfer from an input wave with the frequency ωi by mixing with a pump wave of frequency ωp. The frequency of the generated output wave, as illustrated in Fig. 1(a), equals the sum of the input and pump frequencies
which satisfies the conservation of energy in the process. The conversion efficiency depends on the so-called phase mismatch Δk, with
Fig. 1 a) Energy diagram of the participating waves: The generated output wave has the frequency ωo equal to the sum of the frequencies of the input wave ωi and the pump wave ωp. b) Wave vector diagram of the SFG. The derivation is limited to the plane spanned by the wave vectors ki and kp. The pump wave vector kp is always assumed to be parallel to the poling superlattice vector G.
The vectors kj with |kj| = nj ωj/c (j = i, p, o) represent the wave vectors of plane waves corresponding to the frequencies defined above. Here, c is the vacuum speed of light and nj are the refractive indices at the corresponding frequencies. The vector G, with |G| = 2π/Λ, stands for the contribution of the nonlinear medium with a quasi-phase-matching periodicity of Λ [13]. For the application described in this work, it is important to consider the case of non-collinear mixing. In the following, the description of the process is constrained to the plane that is spanned by the vectors ki and kp as depicted in Fig. 1(b). In this plane, the phase mismatch can be expressed as the scalar term
The relation shows, that the mixing angles θi and θo strongly influence the spectral behavior of the conversion.
The quantum efficiency η of the SFG is defined as the ratio of the photon fluxes at the generated output frequency Φo and the input frequency Φi:
An expression for η can be derived from the basic coupled field equations [14]. In the case of upconverted mid-infrared thermal radiation in lithium niobate, it is valid to assume negligible depletion of the pump light at ωp. Absorption αi in the material is significant only at the mid-infrared input frequency ωi, increasing from 0.01 cm−1 at 3 μm to approximately 1 cm−1 at a wavelength of 5 μm for extraordinary polarization [15]. Then, the calculation can be done analogously to the case of downconversion in [16], and one obtains
withIn these equations, the medium is represented by its effective nonlinear coefficient deff [17], its refractive indices ni, no at the frequencies ωi, ωo, respectively [18], and the absorption coefficient αi at ωi; μ0 is the vacuum permeability and ∊0 the dielectric constant. The pump light driving the conversion enters in terms of the electric field strength Ep, and i denotes the imaginary unit. The factor L is the interaction length in the medium, which, in the collinear case, equals the length of the nonlinear-optical crystal.
3. Converter-spectrometer system
The presented system is a fiber-coupled array spectrometer for MIR signals in the range of 3 to 5 μm. The design resembles the setups proposed in [6, 12]. It comprises MIR light collection, an upconversion unit and a NIR grating spectrometer for the upconverted light. A schematic drawing is given in Fig. 2. Light from an arbitrary source is filtered through a 5-mm silicon window (SW) to remove visible and near-infrared parts and then focused to an infrared fiber waveguide by a reflective fiber coupler (RFC). The infrared fiber (IF) has a core of ZrF4 with 600 μm diameter, length of 1 m and a numerical aperture NA=0.2. Light is fed to the converter from the fiber exit through a 75-mm CaF2 lens (L1), yielding an entry numerical aperture of NA=0.09, and a longpass cavity mirror.
Fig. 2 Schematic view of the converter-spectrometer system. IS: infrared source, SW: silicon window, RFC: reflective fiber coupler, IF: ZrF4 infrared fiber, L1: CaF2 MIR lens, PPLN: periodically poled lithium niobate, PL: pump laser head, PD: photodiode, PA: piezo actuator, L2: Bk7 NIR lens system, RG: NIR ruled grating, L3: 125 mm imaging lens, CAM: Andor ZYLA 4.2 sCMOS camera, PC: personal computer for image capture and processing.
The conversion crystal is made of magnesium-doped, periodically-poled lithium niobate (PPLN). The PPLN (HC Photonics) is 20 mm long with a thickness of 2 mm and also 2 mm width of a poled channel and a poling period of 23.12 μm. A temperature-controlled mount ensures millikelvin stability of the crystal at 40°C. The input light is focused to the center of the PPLN. A passive optical cavity is formed around the crystal with a beam waist inside the crystal center of Gaussian 1/e2-intensity radius w0 = 70 μm. The cavity is pumped by a single-mode, 1.064-m fiber laser (PL) with a power of 5 W. A photodiode (PD) measures the laser power reflected from the cavity and generates the input signal for the locking electronics keeping the cavity in resonance with the help of a piezo actuator (PA). The circulating power can be estimated from the power leaking through one of the cavity mirrors with known transmittance. During measurements, power levels around 400 W were maintained within the resonator.
The upconverted light is extracted through a shortpass mirror, extended and collimated in a telescopic lens system (L2) consisting of a two lenses with focal lengths of −50 mm and 125 mm respectively. The collimated light illuminates a ruled reflective grating (RG) under an incidence angle of approximately 65 degrees against the grating normal. The grating is of quadratic shape with 25.4 mm edge length and is structured with 1800 lines per millimeter. For lowest-noise detection, a silicon sCMOS focal-plane array-camera was selected instead of a linear array sensor. The camera (CAM) has a resolution of 2048 by 2048 pixels with a pixel pitch of 6.5 μm and 16 bit well depth. Out of the 2048 lines, a minimum of 12 lines can be read out simultaneously. The maximum readout rate for this configuration is 6500 frames per second. A 125-mm lens (L3) is used to focus the diffracted spectrum on a line matching this 12-pixel height, while using nearly the full chip width in order not to limit the spectral resolution by the pixel size. The images are recorded on a personal computer (PC), where the measured spectrum Smeas is extracted by vertically binning the 12 lines.
4. Upconversion modeling
For the theoretical description of the converter’s spectral transfer function, a simplified model is proposed. The model assumes a focus cone of MIR light inside the nonlinear medium with radiation density and spectral distribution independent of the angle coordinates inside the cone. The apex lies in the center of the pump-laser mode inside the PPLN, which is idealized as a distinct, cylindrical flat-top volume along the crystal with a radius equal to the cavity mode beam waist w0. The photon flux of upconverted light Φo is calculated using spherical coordinates θj, φj (j = i,o) as
This double integral over two solid angles means that the cone of incident light as well as the emerging generated cone are sampled in form of plane waves represented by their wave vectors. The contribution towards the generated flux is determined by the phase mismatch Δk corresponding to each pair of wave vectors ki, ko. In fact, only few matching pairs of wave vectors result in a small Δk and thus deliver a significant contribution. Therefore, we simplify:
where δ is the Dirac delta function andFurther, it is assumed that the angles are small enough to neglect deviations from the purely extraordinary refractive indices caused by the birefringence of the medium. Then, η becomes independent of φi, and the integral reduces to
The integration limit θlimit is the half-angle of the simulated cone. It has also to be considered that under variation of the angle θi, the effective interaction length Leff changes [19], as shown in Fig. 3. In addition, incident MIR light can be partially absorbed in the medium before entering the interaction volume. The quantum efficiency then takes the form
Fig. 3 In the case of non-collinear upconversion with a finite aperture, changes of the effective interaction length have to be considered for different angles θi.
With this, the total generated flux Φo(ωo) can be calculated by Eq. (10) using the scalar expression for Δk of Eq. 3. In order to simulate the actual signal S measured by the spectrometer, the influence of all optical components in the light path needs to be taken into account. Considered wavelength-dependent quantities in the model are the transmission 𝒯fib of the infrared fiber, the transmission 𝒯atm of atmospheric CO2, the diffraction efficiency ηG of the grating and the quantum efficiency ηCam of the camera detector:
5. Spectrometer resolution considerations
An important aspect of a spectrometer’s performance is its wavelength resolving power. Here, it is influenced by the input aperture, the resolving power of the grating and the pixel size of the camera. According to the optical layout, the pixel spacing in the detector plane of 6.5 μm is equivalent to an average wavelength bin width of 0.56 nm in the mid-infrared range, setting the ultimate limit.
The smallest wavelength difference δλ resolvable by a grating is given as [20]
where βi and βd are the angles of the incident and the diffracted light, respectively, to the grating normal. The angular behavior of the upconversion influences the resolving power through the factor W, which is the width of the illuminated part of the grating. In the presented system, the conversion unit between MIR input and NIR spectrometer features an angular dependent spectral distribution of the converted light. Due to the phase mismatch described in Eq. (3), the converter acts as a angular varying spectral filter. As a result, the collimated beam illuminating the grating contains the wavelengths around 4.2 μm in the outer part and those at the edge of the conversion band (3.7 μm and 4.7 μm) at the center. Figure 4(a) shows a calculation of the radial distribution of wavelengths in the collimated beam behind the telescope described in section 3. The numbers indicate the inner and outer half-maximum radii for each distinct wavelength. Projected on the grating, a concentric, elliptical pattern of the wavelength distribution is obtained. In order to estimate the minimum resolvable wavelength difference, δλ is calculated for each wavelength with W = Δx cos βi as shown in Fig. 4(b), where Δx = 2rmax is the outer diameter of the corresponding hollow cylinder. In cases, where the projected beam profile exceeds the grating width, this value is taken for W instead.Fig. 4 a) Spatial distribution of the converted NIR wavelengths in the collimated beam between telescope and grating. The radii rmin and rmax state the half-maximum edges for each wavelength. b) Minimum resolvable wavelength difference based on the illumination width of the grating individual to each wavelength. The flat bottom of the curve represents the case of full width grating illumination for wavelengths from 3.85 to 4.42 μm.
The impact of the angle dependency of the upconversion becomes apparent in the steep increases at the edges of the spectrum, where only a small area of the grating around the imaging axis is illuminated. However, it can be seen that the wavelength resolving potential is better than 2 nm for the whole converted spectral range.
Furthermore, as in every spectrometer, the resolving ability is influenced by the entrance aperture. In the presented system the effective aperture is not the output of the mid-infrared fiber, but the pump laser mode in the crystal, on which it is imaged. The fiber itself with a core diameter of 600 μm supports such a large number of overlapping spatial modes that, in the case of thermal light sources, it can be treated as a homogeneously radiating surface. In contrast to a conventional discrete spectrometer slit, the pump laser mode constitutes a soft aperture for the upconverted NIR light. The image size of the aperture in the detector plane poses a lower limit for the minimum resolvable δλ. We assume two neighboring wavelengths being distinguishable when their aperture images are separated by more than one full width at half maximum. The intensity FWHM of the pump laser mode in the crystal is 82 μm and the resulting image size in the camera plane is 36 μm. This corresponds to a width of about 5 pixels, which at an average wavelength bin width of 0.56 nm yields a theoretical resolution limit of 2.8 nm. Thus, the resolving power of the spectrometer in its current configuration is found to be limited mainly by its aperture size. Hence the system offers a certain degree of freedom in the compromise between signal strength (conversion efficiency) and spectral resolution as in a classical spectrometer configuration by varying the pump beam focus diameter.
6. System characterization
The spectrometer was characterized with a blackbody radiator as MIR light source. The reflective fiber coupler had a numerical aperture of NA=0.006 with an effective entrance pupil of 20 mm diameter. The blackbody radiator with an aperture of 25.4 mm diameter was placed 12 cm before the fiber coupler such that it covered the full field of view of the fiber. Between the radiator and the fiber coupler, samples could be inserted for transmission measurements. Figure 5(a) shows a snapshot of the raw signal on the camera, taken at a blackbody temperature of 1000 °C. The comparison of the extracted mid-infrared spectral signal to a theoretical simulation is shown in Fig. 5(b). The simulated signal shows very good qualitative agreement with the measured data, underlining the validity of the proposed model. The growing impact of the absorption in PPLN and the spectral behavior of the other components towards longer wavelengths is illustrated by the increasing deviation of the measured and simulated data from the idealized conversion curve, where all loss mechanisms are neglected. Hereby, the PPLN absorption [15] accounts for approximately half of the losses at the long-wave edge of the spectrum. Additional losses are due to the absorption in the 1 m long ZrF4 fiber and the decreasing detection quantum efficiency of the camera. The converted signal covers a continuous range from 3.7 to almost 4.7 μm. This large span is achieved, because lithium niobate comprises two branches of phase matching, which merge at 4.2 μm in the case of pumping at 1.064 μm. The stronger wavelength dependence of the overall system efficiency compared to the results of [12] is primarily due to the smaller numerical aperture used in the present setup for non-collinear phasematching.
Fig. 5 a) Camera image and b) extracted measured signal of a blackbody radiator at 1000 °C, taken with an exposure time of 2 ms. The measurement is compared to the simulated spectroscopic signal and an idealized conversion curve, where no losses are considered.
The spectral axis of the spectrometer was calibrated with a combination of transmission measurements through a polystyrene plate and CO2 in diluted exhaled air in a gas cell, shown in Figs. 6(a) and 6(b), respectively. FTIR measurements were used as reference for the polystyrene and HITRAN simulation data [21] for CO2, respectively. In order to determine the actual resolving power of the system, the spectral instrument function in the HITRAN simulation was varied to fit the measured transmission curve. A spectral resolution of 2.3 nm was found at a wavelength of 4.4 μm. This value is close to the one derived in section 5 indicating the validity of the model assumptions proposed above.
Fig. 6 a) Transmission of 1 mm polystyrene measured by the upconversion grating spectrometer and FTIR data as reference. b) Zoom into a transmission measurement of 1.6% CO2 in air compared to a simulation with a hypothetical spectral resolution of 2.3 nm. c) Extrapolated intrinsic dark count rate over the detected NIR wavelength assuming no incident radiation at the fiber entrance. d) Signal-to-noise ratio at three exemplary wavelengths in the 1000 °C blackbody spectrum over the exposure time τ. The inserted line indicates a square root slope.
The system’s noise behavior was examined with further measurements. Here, the noise statistics at the photon counting camera sensor and the detection limit of the converter-spectrometer system in terms of noise equivalent power (NEP) are of relevance. Four major sources contribute to the noise in the measured signal: The incident MIR light itself, background light generated in the converter, efficiency noise through fluctuations in the pump intensity and camera readout noise. In the current setup, an Andor Zyla 4.2 camera is used. Its sensor features 16 bit digitisation, and a dark current of 0.04 e/pixel/s. For the measurements, as described above, the pixels from 12 sensor rows are binned. A read noise of about 8 counts per spectral bin and a sensor dark current per bin of less than 1 count per second were measured with the converter turned off. Added to this is the intrinsic background signal generated by the converter. It was determined by extrapolating a temperature series of blackbody radiator spectral analysis towards 0 K. The resulting background spectrum is shown in Fig. 6(c). An average background count rate of only 7.4 kHz over the whole spectrum is found. For typical exposure times of, e.g., 1 ms one obtains an average dark count of 7.4 per spectral bin, resulting in an average of 2.6 counts converter background noise. For the intended short exposure times of 1 ms or less it is thus smaller than the camera read noise as stated above. Therefore, the origins of the dark signal were not investigated in detail. Potential contributions to the dark spectrum come from converted thermal emission by the crystal mount, the crystal itself, and the fiber at longer wavelengths, as well as nonlinear processes in the PPLN crystal.
A series of exposures with the 1000 °C blackbody signal was taken for different exposure times τ with 1000 spectra for each τ. The signal-to noise ratio (SNR), calculated as the mean value divided by the root-mean-square (RMS) noise of all spectra was evaluated at the three exemplary wavelengths 4.05 μm, 4.15 μm and 4.58 μm, shown in Fig. 6(d). The measured SNR values closely follow a τ1/2 slope. This indicates that the SNR is limited by shot noise in the signal. The stability of the pump power is measured as better than 1% over 1 second. This means that fluctuations in the conversion efficiency could pose a limit for the SNR when this exceeds 100, but in a more advanced system, the power can be easily monitored and the signal compensated for it.
The well-known Planck spectrum of the blackbody was used to calibrate the camera signal values on the power scale. From numerical aperture and entrance aperture of the fiber coupler, the radiative spectral power density U (λ) incident on the fiber can be calculated. Comparison to the measured signal gives the calibration value in terms of power per count for each wavelength bin. In combination with a measurement of the dark noise (RMS of 1000 dark spectra as described above), the noise equivalent power per spectral bin can be calculated:
Here, Δλ (λ) is the spectral width of a wavelength bin at the corresponding wavelength λ. The signal in counts measured in the exposure time τ at a given λ is represented by S (λ, τ), and R (λ, τ) is the corresponding dark noise value. The results are shown in Fig. 7: A very low NEP per spectral bin of a few pW Hz−1/2 of MIR light at the fiber entrance is achieved, making the system a powerful tool for the spectroscopy of weak signals. While the non-collinear phasematching (necessary for broadband conversion) leads to a low total quantum efficiency in the order of 10−5, this is compensated by the low-noise detection using the sensitive sCMOS detector array of the camera.
Fig. 7 Noise equivalent power NEP at the fiber entrance per wavelength bin over the sensitive range. The bins correspond to a mean spectral width of 560 pm in the MIR. The dashed segment around 4.25 μm projects the case of a nitrogen purged setup without the CO2 absorption of natural air.
In the configuration with the used camera, spectra can be recorded with 6500 Hz acquisition rate. This rate is at least one order of magnitude faster than those of devices based on mechanical scanning like fast FTIR spectrometers [22] or MEMS-based grating spectrometers [23]. EC-QCL laser spectrometers [24] can reach measurement rates in the kilohertz range, however they are not capable of measuring in an emission scheme. Array-based direct MIR spectrometers have been reported with 390 Hz acquisition rate [25] but are still rare to find. Another key fact of a spectrometer is the signal-to-noise ratio. From a 1000 °C blackbody, the upconversion scheme demonstrated in this work can provide an SNR of 100:1 with an integration time of 1 ms and a resolution of 2.3 nm as shown in Figs. 6(b) and 6(d). Recently demonstrated MEMS spectrometers can reach comparable values only with much higher integration times (1 s) and a factor of 10 less spectral resolution [23]. Fourier-transform spectrometers usually reach SNRs of well above 100:1 [1] while providing a wide spectral span, but only at acquisition rates at the order of 100 Hz limited by the mechanical scanning.
The system NEP calculated above is between 0.7 and 10 pW Hz−1/2 per spectral bin. This compares well with commercial cryo-cooled detectors based on InSb or HgCdTe. It shall be mentioned here, that considerable work is currently being done on the development of HgCdTe avalanche photodiodes to achieve considerably lower NEPs. For detectors with cut-off wavelengths up to λc = 3.1 μm, NEPs of 0.03 pW Hz−1/2 have been reported [26]. Nevertheless, when comparing NEPs one has to keep in mind that the results presented here refer to the complete spectrometer including all transfer losses starting at the fiber input coupling.
7. Flame emission spectroscopy
One targeted application for the upconversion spectrometer system are measurements of high-speed gas dynamics occurring in combustion analysis. The system was employed for spectroscopic measurements on the ignition of a pyrotechnic airbag inflator module. The infrared fiber optics were directly coupled to the interior of the inflator cell as shown in Figs. 8(a) and 8(b), such that the fiber’s field of view was filled with hot gas. A sapphire window protected the fiber from direct contact with the hot exhaust gases. The camera was triggered synchronously to the ignition mechanism of the inflator. Sequences of spectra were taken at the maximum acquisition rate of 6500 frames per second with exposure times of 150 μs. The spectral resolution was reduced by a factor of 10 through data binning in order to smooth the obtained spectra. Figure 8(c) shows a subseries of spectra after the ignition at t = 0 μs.
Fig. 8 a) Optical coupling of the light guide fiber to the pyrotechnic airbag inflator. b) Detail photograph of the measurement setup: Inflator cell with attached infrared fiber. c) Time sequence of consecutively recorded emission spectra. The simulated emission range of hot CO2 is added for orientation.
The high acquisition rate allows the visualization of the thermal emission onset after ignition. The spectra show distinct gas emission in the range above 4.15 μm and comparatively low gray body emission at shorter wavelengths. A simulation of 20 % CO2 at 700 K and 10 bar is added to indicate the spectral emission range of hot CO2, which is assumed to be a dominant contribution to the spectrum. The gas dynamics become visible in the time series of spectra, especially in the growing absorption bands between 4.2 and 4.3 μm imposed on the broader emission, indicating accumulation of cooler CO2 in the optical path. The observation of thermal emission beyond 4.5 μm indicates the presence of other gaseous combustion products. Their identification as well as detailed spectroscopic analysis will be subject to further investigation. Spectroscopic data like the one presented here has the potential to contribute towards improved kinetic models of highly dynamic combustion processes.
8. Conclusion
In this work, a spectrometer system for fast recording of spectra in the mid-infrared range with wavelengths up to 4.7 μm has been presented. The spectrometer transfers light from the MIR to shorter wavelengths by nonlinear-optical upconversion and records the spectra on a silicon camera. A spectral range of approximately 1 μm, centered around 4.2 μm, has been accessed this way. This range is well suited for the monitoring of combustion product gases, but can in principle be shifted by using different pump laser wavelengths.
A theoretical model of the conversion, including MIR absorption in PPLN and influences of further system components, was developed in order to predict the converted spectra with good accuracy. This model will support further development of the system towards specific tasks. Characterization of the spectrometer shows a wavelength resolution high enough to resolve single rotational lines of CO2. Sources of noise contribution that limit the sensitivity have been investigated and weighted against each other. The system in total operates at low noise levels leading to a noise equivalent power of few pW Hz−1/2 and less over the full spectrum. While the employed camera was chosen for a good overall trade-off between resolution, noise and acquisition speed, any near-infrared array detector can be used, e.g. for higher frame rates.
The current results indicate the large potential of the approach for fast, grating-based spectrometers in the wavelength range beyond the current limit set by InGaAs detectors. Especially process-analytical industrial applications could benefit from such mid-infrared spectrometers.
Funding
Fraunhofer Internal Programs (MAVO 826 529)
Acknowledgments
The authors thank I. Breunig and T. Beckmann for helpful discussions.
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