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We record vibrational spectra with two indirect schemes that depend on the real part of the index of refraction: mid-infrared refractometry and photothermal spectroscopy. In the former, a quantum cascade laser (QCL) spot is imaged to determine the angles of total internal reflection, which yields the absorption line via a beam profile analysis. In the photothermal measurements, a tunable QCL excites vibrational resonances of a molecular monolayer, which heats the surrounding medium and changes its refractive index. This is observed with a probe laser in the visible. Sub-monolayer sensitivities are demonstrated.
© 2013 Optical Society of America
1. Introduction
The development of commercial tunable quantum cascade lasers (QCLs) has opened up new possibilities in mid-infrared (MIR) vibrational spectroscopy. QCLs offer orders of magnitude more power compared to conventional thermal light sources. This has for instance allowed us to obtain vibrational circular dichroism spectra of the amino acid proline in highly absorbing aqueous solutions (OD > 3) [1]. Similarly, QCLs have been used in sensitive gas phase absorption measurements, cavity ring-down and photoacoustic spectroscopy, or liquid phase online reaction monitoring [2–4].
Typically, absorption spectroscopy is based on measuring intensity changes (imaginary part of the index) to reveal vibrational resonances, which in turn require stable light sources if weakly absorbing (e.g. dilute) species are to be detected. However, despite the higher power levels and the compact rugged design, QCLs are often plagued by intensity fluctuations, which affect the achievable sensitivity in absorption measurements. In this paper we therefore examine how vibrational spectra may be obtained that do not depend on a direct measurement of the QCL’s intensity. Rather than measuring intensity changes (imaginary part of the index), we present two schemes that are based on detecting changes of the real part of the index of refraction and thus use beam deflection as an indirect measure of MIR absorption. In both cases QCLs are used to observe vibrational spectra on a surface. First, the propagation direction of the QCL is directly monitored across a resonance, which is a form of refractometry. In the second scheme we observe changes in the real part of the index via a QCL-induced photothermal effect using a probe laser in the visible. The latter is shown to have sub-monolayer sensitivity.
The infrared spectrum of molecules is mostly characterized by distinct absorption bands. A Kramers-Kronig transformation relates the real and imaginary parts of the complex index of refraction and may thus be applied to an isolated resonance. The real part is generally observed via changes in beam direction and not via intensity measurements. Changes in the real part of the refractive index can be much larger than what is commonly observed at visible frequencies. For instance, across the ∼ 700 cm−1resonance a benzene solution’s real part of the index changes by ±0.6 refractive index units [5]. This raises the question whether the change in the real part can give rise to a deflection of the IR beam, which is then directly related to the IR absorption band. Here, we examine a more convenient experimental geometry, whereby the change in the index is observed in an imaging setup. The beam of a QCL is imaged on a infrared camera and the change in beam profile at a total internal reflection interface is used to deduce the absorption peak without measuring absolute intensities. Only relative intensity measurements within the beam profile are made and thus are immune to the QCL’s intensity fluctuations.
The second scheme makes use of the photothermal effect.QCLs have been used in photother-mal setups that measure photothermally induced surface expansions [6–8] or for molecular recognition and standoff detection. However, to the best of our knowledge QCLs have not been used in a deflection setup based on the mirage effect. The work in this paper is in part motivated by the spectacular sensitivities that have been achieved with indirect absorption measurements in liquids at visible frequencies [9], where single molecule sensitivity has been demonstrated [10–12]: A (non-resonant) probe laser was used to monitor changes in the refractive index of the solution as a function of an excitation laser that was tuned to the absorption peak of a dye molecule with a strong chromophore. Translating this scheme into the infrared, and in particular to QCL-based measurements, could exploit the high power and spectral resolution of the QCL whilst permitting a stable probe laser at visible frequencies to be used as an inexpensive and sensitive probe. Here we demonstrate QCL-based photothermal deflection measurements (mirage effect) using an IR transparent substrate with mono- and sub-monolayer sensitivity. Both schemes are now examined in turn.
2. MIR-refractometry
The measurement of refractive indices (refractometry) is well established in the visible [13]. Efforts have been made to transfer some of those methods to the MIR and these include refractometry with a hollow prism, an Abbe refractometer, or using interferometric methods [14–20]. An early refractive index measurement by Pfund et al. in 1935 [14] recorded the dispersion of CS2and CCl4in the solvents’ transparent (off-resonant) IR regions. Fahrenfort et al. [21] used attenuated total reflection (ATR) to measure the optical constants of benzene. They showed that the refractive index can be calculated from a measurement of the reflectivity for two angles of incidence. However, since all these methods rely on intensity measurements, they all have problems acquiring refractive index data for strongly absorbing samples (and unstable light sources). A different approach, and one that we use here, is to use transformation relations. The Kramers-Kronig transformation relates the real (n(ν)) and imaginary (k(ν)) parts of the complex refractive index ñ= n+ ikof a medium. It follows that knowledge about the real part is sufficient to obtain the imaginary part and vice versa. We will now show how it is possible to measure both parts with a refractometer setup. The idea is that by detecting the change of the angle of the total internal reflection at an interface between a glass prism and a liquid sample it should be possible to simultaneously extract n(ν) and k(ν) of the analyte.
2.1. Experimental setup
The experimental setup for the MIR-refractometer is shown in Fig. 1. A Quantum Cascade Laser (QCL, Daylight Solutions TLS-21078), tunable via an external-cavity, provides up to 200 mW in the spectral range of 1220 – 1320 cm−1. First, the output is linearly polarized by the polarizer P1, before the laser beam is expanded and collimated with two spherical mirrors (SM1 with f= 25 mm and SM2 with f2 = 200 mm) to a beam diameter of d= 30 mm. The beam is then focused onto the entrance surface of a ZnSe-prism with a parabolic mirror (PM1). After reflection at the prism/sample interface the beam exits the prism (see inset of Fig. 1). After re-collimation with a second parabolic mirror PM2 the beam is directed at a diffuser. The attenuated reflection of the laser beam’s profile is imaged by a infrared camera (640 × 480 pixels, Thermoteknix Miricle 307K-25u). Because the focus is at the entrance face of the prism, the angle of incidence at the prism/sample interface varies across the beam profile. If no sample is present (prism/air), then all angles fulfill the condition for total internal reflection (TIR) and the entire beam is reflected. However, when a sample with an index of refraction n> 1 is present, then the condition for TIR is no longer fulfilled for all angles. It follows that the intensity profile imaged by the camera will no longer be symmetric, as parts of the beam will be transmitted into the sample where they also experience absorption. We will now show that the complex refractive index of the sample can be measured by detecting and analyzing this intensity profile.
Fig. 1 Setup of the MIR-refractometer (top-down view). The linearly polarized light of a QCL is expanded, collimated and finally refocused onto the entrance side of ZnSe-prism. The inset is a detailed view of the prism (side-view).
2.2. Theoretical model
The angle of incidence (AOI) γ0of the center of the beam at the second surface of the prism (Zn-Se prism/sample interface) is a function of the AOI α0at the entrance side of the prism with refractive index npand prism angle θ1, as can be seen in Fig. 2. Accounting for the spatial extent of the beam (x) with Gaussian beam optics we assume for the beam profile a waist w0at the entrance surface of the prism. The beam’s lateral components propagate a distance z(x) to the second surface of the prism (prism/sample interface) depending on their distance xfrom the center of the beam. The radius of curvature of the wavefront is R(z(x)) = R(x) at the intersection with the prism/sample interface (Fig. 2). The angle of incidence γ(x) at this point is defined by the surface normal and R(x):
R(x) is defined as [22]: The distance z(x) is described by z(x) = z1+ x· tanγ0and z1is shown in Fig. 2. The variation of the angles of incidence over the beam cross section follow if Eq. (2)is inserted into Eq. (1):The polarization of the beam is chosen such that it is p-polarized, i.e. parallel to the plane of incidence at the prism/sample interface. The Fresnel coefficients for the reflected beam components follow [23]:
where the sample is assumed to have the complex index of refraction ñl= nl+ ikl. The intensity profile detected by the IR camera can now be calculated assuming a Gaussian profile: The real and imaginary components of the liquid’s index of refraction nland klmay now be determined by fitting Eq. (5)to the experimentally detected intensity profile. Theoretical beam profiles after reflection are shown in Fig. 3for a Gaussian beam with a focus spot size of w0= 30 μm (here α0= 25°, θ1= 45°, np= 2.4 and f= 101.6 mm).Fig. 2 Detailed views of the beam path inside the prism for a) geometrical ray optics b) a Gaussian beam profile.
Fig. 3 Calculations of the predicted intensity profile for model liquids with different values of the refractive index ñlusing Eq. (5)with w0= 30 μm, α0= 25°, θ1= 45° and np= 2.4.
2.3. Measurements
Dichloromethane (DCM) exhibits an absorption peak in the tuning range of our QCL (see FTIR measurement, Fig. 5rhs.) and serves as a model solution to test the MIR-refractometer. Less than 100 μl of neat (undiluted) DCM are pipetted on the upper surface of the prism. The QCL is scanned in 1 cm−1steps over the complete tuning range and an image is recorded by the IR-camera for each step. The images are processed as schematically shown in Fig. 4. First, all the gray scale values for each CCD pixel-column are summed to obtain a 1-D beam profile. A theoretical fit of Eq. (5)to this profile reveals both, nland kl. The focus spot size w0, important for the calculation of γ(x), is determined for each wavelength using an ABCD-matrix formalism [22] together with measurements of the beam waist directly behind the laser. Also important for the evaluation is the index of refraction npof the ZnSe-prism, which is calculated via the corresponding Sellmeier equation [23]. The results from the Gaussian beam optics model are shown in Fig. 5, where they are compared to conventional FTIR-measurements. The FTIR values for the real part of the refractive index nlhave been derived from absorbance measurements using a Kramers-Kronig transformation. For the refractometer measurements neat DCM was used, whereas a 3M solution of DCM in deuterated chloroform (CDCl3) was used for the FTIR spectra. The data have been scaled by sample concentration. It is seen that the dispersion and absorption line profiles qualitatively agree for both measurements, the absolute values differ. This is in part because any distortion of the beam (partly induced by the diffuser) will affect the quality of the fit. Therefore the RMS error is calculated and shown in Fig. 5. The fit residuals are computed relative to the peak height. Overall this error is < 10%. For ν< 1260 cm−1the deviation is larger as here the camera pixel noise increases as the intensity incident on the camera becomes small. Similarly, we have analyzed the image noise on the camera and it is also shown in Fig. 5. In what follows we therefore examine another QCL-based indirect vibrational spectroscopy, which has sub-monolayer sensitivity.
Fig. 4 Image analysis and data processing. Shown are two camera images, one without (left) and one with (right) liquid sample. The gray scale values of the images are added as indicated and Eq. (5)is then fitted to the one-dimensional profiles (depicted below the camera images) to yield nand k
Fig. 5 Results of MIR refractometer measurements of dichloromethane (DCM) using Gaussian beam profiles in the fits are compared to direct FTIR absorption measurements. All data have been scaled by sample concentration. In the FTIR data nhas been determined form the corresponding kvalues using a Kramers-Kronig transformation. The RMS error and the mean image noise are plotted in the upper panels (see text for details).
3. MIR photothermal spectroscopy
Photo-thermal beam deflection techniques rely on the temperature dependence of a material’s refractive index. A temperature inhomogeneity is generated through local optical excitation and then probed by a second laser whose divergence and direction of propagation is changed. Typically, photothermal studies involve gases or condensed phases (glasses or liquids) in which an analyte of interest is selectively excited by a strong excitation laser [24]. In the MIR many substances are not transparent and most liquids have a small finite absorption cross section over the entire MIR spectral range and thus give rise to a strong unspecific thermal excitation which swamps any heat contribution from a dilute analyte. We therefore choose IR-transparent crystals as temperature sensitive substrates and this allows us to obtain sensitive spectral information of trace amounts of a solid or liquid analyte in the MIR with high spectral resolution.
3.1. Theoretical model
In the photothermal lensing or mirage effect a light beam is deflected in a medium with a thermally induced refractive index gradient. The angular change in the direction of propagation δφ⃗of a thin laser beam traveling through a medium with refractive index nand an inhomogeneous temperature field T(x⃗) along a path scan be expressed as a simple path integral for small deflections [25]:
To calculate the temperature gradient in a transparent crystal slab that has a heat (IR) absorbing layer on one of its surfaces, the corresponding heat equation has to be solved. Neglecting heat transfer due to thermal radiation and convection, the time dependent temperature field generated by an arbitrary three-dimensional heat source with a power density ∂P/∂Vis given by the following differential equation: Here the material constants density, specific heat capacity and thermal conductivity are, respectively, given by ρ, cand k. Its general solution can be given in integral form [26], but it has no analytical solution, which necessitates time consuming numerical calculations. An alternative method to determine the three dimensional temperature-field involves Fourier-transforming Eq. (7)and this has been discussed in Ref. [27], but it also requires extensive numerical calculations. We therefore simplify the discussion and only consider a gradient in one dimension, for which Eq. (7)possesses an analytical solution. When only light absorption on the surface is taken into account, the excitation power can also be introduced by a boundary condition to the homogeneous heat equation (so the right hand term of Eq. (7)vanishes). If it is further assumed, that all heat periodically generated at the surface is dissipated by conduction to the bulk, the boundary condition becomes where I0denotes the intensity of the excitation laser and αthe absorbance of the sample layer, while ωis the angular frequency with which the excitation source is modulated. For a homogenous excitation at the plane of the surface the time-dependent part of the solution of Eq. (7)yields a strongly damped 1-D temperature field [25] This is a reasonable approximation, when the beam diameter of the excitation laser is larger than the skin depth (thermal diffusion length) of the temperature modulation [25]. Strictly, this condition is not satisfied, as the excitation laser is focused, but the analysis is still useful to estimate the approximate beam deflection. Differentiating Eq. (9)and substitution into Eq. (6)gives an estimate of the expected beam deflection (see Eq. (10)). The integration in Eq. (6)is performed parallel to the surface at a distance that corresponds to half the beam diameter 2wprobeof the probe laser and over a distance 2wqcl, which corresponds to the excitation laser’s beam waist (see Fig. 6a). The absolute power of the excitation source is Pand is its intensity. The beam-deflection follows the sinusoidal surface excitation with a potential phase-lag of ϕ. It follows that the thermal diffusion length should be matched to the probe-laser’s beam waist by choosing an appropriate modulation frequency:Fig. 6 a) Schematic of the beam-deflection beneath a homogeneously illuminated absorbing surface. b) Schematic of the experimental setup consisting of the excitation beam-path (dark red) and the probe beam-path (red). The QCL is directed via a mechanical chopper and a focusing lens onto the sample. The probe laser is a fiber-coupled red diode-laser with an adjustable collimator routed with three mirrors to a position sensitive diode (PSD). Inclusion of a beam splitter allows the same setup to be used for interferometric (Sagnac) measurements. The beam path of the QCL and the probe laser are brought to coincide on the surface of a zinc-selenide-slab (shown enlarged in inset).
3.2. Measurement noise
One major disadvantage of ordinary absorption measurements is their liability to intensity noise. This limits their usefulness in measuring samples with a small absorbance α. Since the amplitude of the deflection is directly proportional to the power of the excitation laser (see Eq. (10)), the photothermal measurement is not completely immune to intensity fluctuations of the excitation laser, but the propagation of errors differs compared with a direct absorption measurement. This is seen if one compares how the intensity noise affects the relative error in both measurement schemes. For traditional transmission measurements the relative error sαof the absorbance is given by
where σI0is the error of the intensity. As α→ 0 for weakly absorbing or dilute samples, the error diverges. The practical limit is reached if α< σI0. This is in contrast to a photothermal measurement where it follows from Eq. (10), that the relative error s′αis: Because s′αis now independent of the samples’ absorbance, the fluctuations of I0no longer restrict the overall detection sensitivity, even for arbitrarily weak absorbing samples. However, as will be seen below, there are now other noise contributions that depend on the type of deflection measurement that is used. Importantly, since the photothermal signal itself is proportional to the absorption and is no longer limited by the intensity fluctuations of the incident laser (QCL), it is now possible to choose different (and thus much more sensitive) detection schemes, such as indirect deflection measurements. The sensitivity and noise now depend on the specifics of the setup (detection geometry and detectors) and this has been discussed in a number of papers [28–30]. Here we have examine two deflection geometries using a position sensitive detector (PSD) and an interferometric detection of the beam position.3.3. Experimental setup
The experimental setup is shown in Fig. 6b. We used the same MIR-QCL model (TLS-21078, 1220 – 1320 cm−1) from Daylight solutions as for the MIR refractometer in conjunction with a 658 nm probe-laser, which is a pigtailed diode laser with high pointing stability. The beam paths of the excitation and probe lasers cross at the surface of a zinc selenide crystal slab, which supports the sample. The QCL is focused onto the ZnSe-slab by an AR-coated ZnSe lens with a focus length of 30 mm, while the probe laser is focused by an adjustable fiber collimator (approx. focal length of 500 mm). The beam of the QCL is modulated by an optical chopper leading to a time-varying beam deflection of the probe beam. Depending on the beam splitter, this beam is then either routed directly or via a Sagnac interferometer onto a position sensitive diode (PSD). Weak-value amplified deflections are expected to further increase the sensitivity, which we have recently demonstrated to be useful in sensitive optical activity measurements [31]. A Sagnac interferometer has been used in conjunction with weak value amplification and is discussed in [32]. A piezo-adjustable mirror is used to compensate for the steady-state beam deflection due to the DC-heat flow into the crystal slab. The modulated detector signal is recorded with a lock-in amplifier locked to the chopper frequency. For investigation of liquid samples, the zinc selenide slab is replaced by a cuvette formed by two calcium fluoride slabs, separated by a 25 μm Teflon spacer.
The optimum experimental conditions are determined by a stepwise empirical optimization of the modulation frequency and the beam waist. Best results where obtained for wqcl= 36 μm and wprobe= 70 μm and a modulation frequency of ω/2π= 180 Hz. For a power P= 200 mW, a skin depth μ= 134 μm, and the material constants for zinc selenide, we can estimate an angular deflection of Δφ= α× 5.4×10−3rad (Eq. (10)). Assuming a typical limit of detection of ≈ 20 nanoradian for a position sensitive detector (quadrant photodiode) this suggests a lower limit of detection of α= 3.7 × 10−6. The actual deflection is likely to be smaller.
3.4. Photothermal spectra
We first record photothermal spectra using the direct detection with a PSD (SPOT-9DMI, UDT Sensors Inc.). The deflection due to a thin fluid layer (d= 25 μm) of deuterated chloroform (CDCl3) is measured using, respectively, 10 mW and 0.3 mW. The latter corresponds to a 30-fold smaller absorbance, and as expected the signals diminish linearly (see Fig. 7). Traditional transmission based measurements would suggest a reduced SNR by 1/30. However, in the deflection measurement in this setup, we find that the SNR only reduces by a factor of just 5.
A detector setup using an interferometer should be even more sensitive, and this is indeed what we find here. To determine the sensitivity of such a setup, weakly absorbing samples were prepared by depositing the self-assembling silane Trichloroperfluorooctylsilane (TPS) on the surface of the substrate. The TPS formed monomolecular layers, as was verified with atomic-force-microscopy. The interferometer and the superior power level of the cw-QCL source (here 200 mW) allow us to detect the weak absorbance of this molecular monolayer with high resolution (where we estimate that the absorption is not yet saturated). Figure 8shows the comparison between the photothermal absorbance spectrum and that from a commercial FTIR. The latter required 200 averages. The main spectral feature exhibits a magnitude of about 5 × 10−4in the FTIR spectrum with a SNR of about 7, while the photothermal spectrum shows a SNR of about 50. The preparation of a considerably less absorbing sample is difficult and therefore the detection limit of the interferometric setup is estimated by reducing the laser power. At 10 mW the SNR does not significantly change. If a linear dependence on the laser power holds, then it follows that at full laser power (200 mW) samples with an absorption of about 2.5 × 10−5should still be detectable with the same SNR. A SNR = 1 corresponds to an absorption as small as 5 × 10−7, which corresponds to one part in a thousand of a molecular monolayer, or about 20 picogram of the analyte within the focus of the IR-laser (where we have assumed an area of 20 Å2per molecule [34]). This is significantly more sensitive than what can be observed in a conventional, intensity-based, absorption measurement.
Fig. 7 Photo-thermal absorption-spectra of a 25 μm thick film of deuterated chloroform (direct PSD detection). The FTIR spectrum was obtained from a 100 μm thick film.
Fig. 8 Comparison of two photo-thermally gained absorption-spectra (upper diagram, interferometric detection) with the corresponding absorbance FTIR spectrum (lower diagram) of a molecular monolayer of Trichloroperfluorooctylsilane (TPS) and the ATR-FTIR-spectrum of the undiluted liquid silane (data taken from [33]). The drastic rise of the FTIR-monolayer-signal can be attributed to a strong thin-film-interference, which the photo-thermal technique is insensitive to.
4. Conclusions and outlook
Vibrational spectroscopy in the MIR is demonstrated with quantum cascade lasers without the need to directly measure absolute intensities. A MIR refractometer is introduced that relies on detecting changes in the real part of the index of refraction (angles of reflection) to deduce the absorption via a beam profile analysis. In the present setup it requires an expensive imaging setup, but its sensitivity and ease of implementation would benefit from position sensitive detectors in the MIR, which are not yet commercially available. The second scheme is based on the photothermal effect. Here a QCL laser excites an analyte, and the deflection of a stable diode laser in the visible is used to detect the thermally induced refractive index gradients. The method is relatively straightforward to implement and is shown to be several orders of magnitude more sensitive than ordinary absorption schemes. Its SNR does not depend directly on the power of the MIR laser making it tolerant to intensity fluctuations. The details will depend on the specifics of the deflection setup. We have therefore tested two schemes: one based on a position sensitive detector (PSD), and the other based on an interferometric deflection setup. The latter is demonstrated to have sub-monolayer sensitivity.
Acknowledgments
This work was in part supported by the FhGinternal program Attract (grant 692247).
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