1. Introduction

Characterization of surface contaminants have recently received considerable interest due to the increasing awareness that obtaining the information about the chemical composition of surface contaminants, e.g., organic compounds, is a critical step in feeding back the production process and ensuring product quality. Spectroscopy working in the mid-infrared (MIR) region is an effective technique for identification of contaminant molecules. The way the radiation interacts with molecules provides highly specific information about molecular vibration characteristics in the “fingerprint region” [1]. Raman spectroscopy and Fourier transform infrared (FTIR) spectroscopy are the two most common techniques for probing molecular vibrations. However, the extremely small Raman Cross section (∼10⁻³⁰ cm²sr⁻¹) [2] limits the detection sensitivity of Raman spectroscopy. In contrast, IR absorption offers a cross section about eight orders of magnitude higher than that of Raman, which enables adequate sensitivity of FTIR. Unfortunately, FTIR suffers from the lack of broadband cryogenic MIR detectors. Detection of IR absorption is still performed using narrow band-gap cryogenically cooled detectors made of indium antimonide (InSb) or mercury-cadmium-telluride (MCT) [3], which are intrinsically less sensitive than the best available visible photodetectors.

Photothermal spectroscopy (PTS) [2–11] based on the pump-probe configuration has rapidly emerged as a remarkably sensitive technique that avoids the desire for broadband cryogenic MIR detectors when working in the MIR region. In this technique (we are interested in the reflection mode considering the opaque substrates for visible light), a MIR pump beam that is tuned to the absorption bands of the targeted contaminant molecules causes change of a visible beam probing the contaminant. Depending on the response of the contaminant, the change of the probe beam can be detected in different ways. The most common way is to employ a probe beam with a diffraction-limited spot to detect dR/dT, which is the reflectance change of the contaminant arising from heating by a pump beam with a large spot size [2,3,12–15]. In such a way, the photothermal imaging can be implemented by scanning the probe spot within the pump spot and the imaging resolution is only limited by the probe spot size. However, Zanuto et al. [16] pointed out that dR/dT acts only in the real part of the complex amplitude of the probe beam, which is less sensitive compared with the phase delay.

The phase delay can be induced to the probe beam by both the surface deformation resulting from the thermoelastic response of the sample and the refractive index gradient in air when the heat produced by resonance absorption of the contaminant is transferred into its surroundings [17]. In conventional phase-sensitive PTS [18–20], the phase delay caused by a narrow pump beam is imposed on the wavefront of a wide probe beam and the intensity at the center of the diffraction pattern of the probe beam is detected in a far-field plane. Recent works [7,21–28] emphasized interferometry as a sensitive alternative for phase detection in PTS. However, Flizikowski et al. [28] pointed out that the interferometer sensing merely the out-of-plane surface deformation is less sensitive than the phase-sensitive PTS, which reads a complex convolution of all the effects taking place in both the sample surface and the surrounding air.

To this end, we demonstrate a highly-sensitive PTS assisted with a dual-wavelength Mach-Zehnder interferometer (MZI), MZI-PTS in short. The MZI is dedicated to sense all the phase delays taking place at the sample surface and air and further amplify the phase delays to a large intensity difference. In what follows, we first analyze the effect of photothermal excitation on a contaminated sample through a simplified heat transfer model. The dual-wavelength MZI is then introduced in detail to demonstrate the sensing of the photothermal response. At last, we demonstrate experimentally the spectral fidelity and the sensitivity enhancement of the MZI-PTS as well as its capability in photothermal spectral imaging.

2. Method

2.1 Photothermal excitation

The photothermal excitation in the dual-wavelength MZI-PTS is shown in Fig. 1 and we take a GaAs sample with surface contaminated by a thin layer of olive oil as a theoretical illustration. An excitation beam of MIR radiation (Daylight solutions, MIRcat-2200, CW, TEM₀₀) is focused on the sample surface by a parabolic mirror (PM₃) after being expanded with a reflective beam expander (composed of PM₁ and PM₂). A mechanical chopper (SSI-instrument, OE3001) placed in the intermediate focal plane of the expander modulates the intensity of the excitation beam with a square wave. For simplicity, we assume an “air-olive oil-sample” system where air and the sample is semi-infinite and the olive oil layer is infinitely thin. While the MIR excitation beam is tuned to a wavelength that excites a molecular vibration in the olive oil, the radiation is absorbed strongly at the olive oil layer (z = 0). For instance, there is a strong absorption peak at 5.8 μm for olive oil due to C = O double bond stretching vibration [1]. The local absorbing region will then heat up, and result in temperature gradient inside both the sample and air, and accordingly lead to the thermoelastic deformation at the sample surface as well as the refractive index gradient in air [17,30–32]. Here, we denote the surface deformation of the sample surface by u_s, and the change of optical path length due to only the refractive index gradient in air by u_a.

 

Fig. 1. Schematic of dual-wavelength MZI-PTS. FL: focusing lens, BS: beam splitter, DM: dichroic mirror, PM: parabolic mirror, M: mirror, PD: photodetector assembled with a pinhole, QWP: quarter wave plate, HWP: half wave plate. Note the coatings of BS1 and BS2 as well as DM2 and DM3 are placed in opposite directions to balance the optical path lengths in the interferometer. The optical path compensator is placed at the reference arm because the total thickness of DM₁and DM₂ are larger than that of HWP, QWP₁ and QWP₂. Variable neutral density filters placed in the two arms are used to balance the beam intensities and is not shown in the figure to aid clarity.

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Figure 2(a) shows the simulated temperature fields in the x-z plane in the contaminated sample and air. The temperature rise at the center of the excitation beam, ΔT, reaches 5.6 K by giving an excitation wavelength of λ_e = 5.8 μm, an excitation beam radius of w_e = 15 μm, an excitation power of P_e = 10 mW and an observing time of t = 0.4 ms. The nonuniform temperature fields result in a surface deformation of the sample to be u_s = −0.85 nm and a change of optical path length in air to be u_a = −0.1 nm, as shown in Fig. 2(b). The negative sign in u_s results from the definition of the z-direction, indicating the surface expansion in the sample. The negative sign in u_a originates from the negative temperature coefficient of the refractive index of air. Figure 2(c) shows the temporal evolutions of u_s and u_a at a chopping frequency of f_c = 1250 Hz. The dc component, proportional to the average excitation power, can be filtered out with a lock-in amplifier, while the amplitude of the ac component is an indication of the absorption strength of the contaminant.

 

Fig. 2. Simulated temperature fields in the x-z plane in the sample and air for (a) contaminated surface by olive oil and (d) contamination-free surface at t = 0.4 ms. Profiles of the surface deformation of the sample and the change of optical path length in air for (b) contaminated surface and (e) contamination-free surface at 0.4 ms. Temporal evolutions of the surface deformation and the change of optical path length for (c) contaminated surface and (f) contamination-free surface at frequency of 1250 Hz. The physical properties of GaAs and air used in the simulation can be found elsewhere [29].

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In contrast, for the contamination-free sample, ΔT is only 0.085 K because the absorption coefficient of GaAs is as low as 7.66 cm⁻¹ at λ_e = 5.8 μm [33], resulting in a decrease of two orders of magnitude in both u_s and u_a, as shown in Figs. 2(d)–2(f). Therefore, the amplitude sum of the ac components of u_s and u_a will produce a signal indicative of absorption spectrum originating from molecular vibration in the contaminant.

2.2 Dual-wavelength MZI

A dual-wavelength MZI is proposed to sense u_s and u_a, as shown in Fig. 1. A probe beam (Daheng Optics, DH-HN, λ_p = 632.8 nm, 1.8 mW, TEM₀₀) and a feedback beam (CNILaser, MGL-DS-532, λ_f = 532 nm, 5 mW, TEM₀₀) with both p-polarization states (extinction ratio > 100:1) are directed in the common path by a dichroic mirror (DM₁) and then focused by a focusing lens (FL) before being split into the reference arm and the measuring arm of the MZI via a beam splitter (BS₁). The probe beam and the feedback beam are separated by DM₂ and DM₃ in the measuring arm, while most of the two beams in the MZI overlap to ensure the same sensitivity to the environmental disturbance. The probe beams in the two arms interfere after combining at BS₂, and so do the feedback beams. The interference beams at two wavelengths are then separated into four ports by DM₄ and DM₅, and recorded with four pinhole-photodetector assemblies (PD₁, PD₂, PD₃ and PD₄), respectively. For a perfectly aligned MZI, all the probe beams exit through the port 1, which is referred to as the bright port, and accordingly the port 2 is the dark port because of the destructive interference resulting from π phase shift on reflection in BS₂. The same phase shift analysis on the feedback beam paths shows the ports 3 and 4 to be the bright and dark ports, respectively.

Since MZI is known for its balanced detection nature, a stable quadrature phase bias of ±π/2 between the two arms is required for unambiguous and highly sensitive detection of u_s and u_a. However, phase biasing at different wavelengths cannot be performed by the introduction of an additional optical path difference, ΔL, via fine-tuning the mirror (M₁), because the phase bias, Δψ, is wavelength dependent on ΔL in accordance with the relation Δψ = ΔL(2π/λ). To cope with the problem, we use an achromatic phase shifter (APS) [34] consisting of a rotational HWP sandwiched between two QWPs with the fast axes fixed at 45° to introduce a wavelength independent phase bias. As shown in Fig. 1, for a horizontal polarization state input, $|H \rangle $= [1 0]^T, the output undergoing the APS placed at the reference arm can be described using the Jones matrix formalism [35]

 

Fig. 3. (a) Wavelength dependent retardances of HWP (Thorlabs, AHWP05M-600) and QWP (Thorlabs, AQWP05M-600). (b) Absolute phase bias errors induced by the APS and by fine-tuning M₁. (c) Absolute phase bias errors induced by the variation of the fast axis orientation of HWP, θ_H, in the APS at 532 nm and 633 nm, respectively.

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The achromatism of the APS can be investigated by taking the wavelength dependent retardances of the HWP and the QWP into Eq. (1). Figure 3(b) shows the phase bias error with respect to the ideal bias, −2θ_H = −90° (i.e., −π/2 or −1/4 wave), when θ_H is set to 45° in the APS. The phase bias difference between 532 nm and 633 nm is only 8×10⁻⁶ wave, indicating the superachromatism of the APS over a broadband spectral range. In contrast, the phase bias difference induced by fine-tuning M₁ is as large as 4.75×10⁻² wave.

Figure 3(c) shows the phase bias errors induced by the variation of θ_H at 532 nm and 633 nm, respectively. It is obvious that the probe beam (633 nm) and the feedback beam (532 nm) have a consistent response to the variation of θ_H owing to the superachromatism of the APS, although they have a nearly same residual error of 1.13×10⁻³ wave at θ_H = 45° as a result of the retardance errors of the HWP and the QWP, as shown in Fig. 3(a). Furthermore, the slope, dΔψ/dθ_H = 5.67×10⁻³ wave/°, gives the sensitivity of the APS to correct the phase bias.

2.3 Photothermal response

The photothermal response is obtained by sensing u = u_s+u_a with the −π/2-biased dual-wavelength MZI, which has a distinguishable feature by using a defocused probe beam as well as the pinhole-photodetector assembly. This can be explained by the mechanisms of (i) Fresnel diffraction in terms of convolution and (ii) wavefront interference as follows.

In Fig. 4(a), (u) showing a Gaussian-like distribution at the air-sample interface (z = 0) imposes a roundtrip phase delay on the wavefront of the probe beam reflected from the air-sample interface in the measurement arm, as shown in Fig. 1. Since u and the reflected wavefront are in the different coordinate frames, (x, y, z) and (x′, y′, z′), respectively, the roundtrip phase delay in the frame (x, y, z) should be projected on the frame of the reflected wavefront, (x′, y′, z′). After projection transformation, the roundtrip phase delay has a skewed-Gaussian distribution, as shown in the lower part in Fig. 4(a).

 

Fig. 4. (a) Wavefront propagation of the probe beam after interaction with u = u_s+u_a. The lower part shows the roundtrip phase delay with a skewed-Gaussian distribution imposed on the reflected wavefront. (b) Simulated diffraction pattern of the reflected wavefront after interaction with u and (c) its intensity profiles. (d) Simulated interference pattern exiting from the −π/2-biased dual-wavelength MZI and (e) its intensity profiles. (f) Simulated interference pattern exiting from the unbiased dual-wavelength MZI and (e) its intensity profiles. Here, z_d = 200 mm, w_p = 30 μm, z_p = 7.5 mm and we assume u = 100 nm. In Figs. 4(c), 4(e) and 4(g), solid lines indicate u = 100 nm and dashed lines indicate u = 0 nm.

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The reflected wavefront undergoing the roundtrip phase delay produces a diffraction pattern owing to the convolution of the system′s impulse response with the reflected wavefront [28,36,37], as shown in Fig. 4(b), and the corresponding intensity profiles are shown in Fig. 4(c). Here the probe beam waist has a radius of w_p = 30 μm and has a distance of z_p = 7.5 mm ahead of the interface. The observation plane is placed at BS₂, as shown in Fig. 1, which is around z_d = 200 mm away from the interface. We assume u = 100 nm for clear observation of the diffraction pattern. It is shown that the sidelobes lose the symmetry because of the skewed-Gaussian phase delay. The center spot intensity can be detected by the pinhole-photodetector assembly and it has a difference of 0.076 compared with that when u = 0 nm. This intensity difference produces the typical output signal of the conventional phase-sensitive PTS. It should be noted that the “defocus” probe beam here means there must be an offset between the probe beam waist and the air-sample interface. The offset can be either positive or negative but not zero, because the wavefront diffraction is extremely weak and the photothermal signal approaches zero when the offset is zero [38,39].

In the proposed method, the diffracted wavefront in the measurement arm will further interfere with the wavefront in the reference arm when they combine at BS₂. Figures 4(d) and 4(e) show the interference pattern exiting from the −π/2-biased dual-wavelength MZI and the corresponding intensity profiles, respectively. The asymmetrical sidelobes can be seen as well. The intensity difference of the center spots between u = 100 nm and u = 0 nm is as large as 0.298, and will double to 0.596 due to the balanced detection between PD₁ and PD₂, achieving a 7.8-folds sensitivity enhancement compared with the conventional phase-sensitive PTS in theory. In contrast, an unbiased MZI has an intensity difference of only 0.049, as shown in Figs. 4(f) and 4(g), and will double to 0.098 through differential detection, showing merely a 1.3-folds sensitivity enhancement.

From the above analysis, we point out that the proposed method not only reads the complex convolution resulting from all the phase delays taking place at the sample surface and air, but also amplifies the phase delays to a large intensity difference by interfering the convolution result (i.e., diffracted wavefront) with a reference wavefront biased by −π/2, which is the distinct advantage of the dual-wavelength MZI-PTS.

3. Results

3.1 Quadrature phase bias locking

We first evaluated the performance of quadrature phase bias locking in the dual-wavelength MZI. As shown in Fig. 1, the fast axis orientation of the HWP in the APS was set to θ_H = 0° through a precision motorized rotation stage (Thorlabs, DDR25). The compensator in the reference arm was then adjusted to cancel the optical path difference between the two arms so as to minimize the beam intensities exiting from the dark ports 2 and 4. An additional phase bias was then induced by tuning θ_H away from 0°, allowing the probe and feedback beams exiting from the bright ports to leak into the dark ports simultaneously, as shown in Figs. 5(a) and 5(b). When the fast axis of the HWP rotated by an angle of θ_H = 45.2°, the differential signal approached 0 V, i.e., 1.7 mV for the probe beam and −1.1 mV for the feedback beam due to the noise level, indicating that the phase bias of Δψ = −2θ_H = −π/2 was achieved for both beams. The rotation angle error of 0.2° results from the comprehensive effects of the retardance errors of the HWP and the QWP shown in Fig. 3(a) as well as the imperfection of the extinction ratios of laser beams. Both differential signals are linear around the quadrature points indicated with arrows, so the probe beam can be locked to the quadrature point in real time by feeding an error signal generated from the feedback beam back to the fast axis orientation of the HWP in the APS.

 

Fig. 5. Bright port, dark port and differential signals for (a) the probe beam and (b) the feedback beam. The differential signals are saturated if they exceed ±10.8 V. (c) Differential signals under free-running and feedback operations. Note the signal of the feedback beam is not shown after feedback on because it is fed back to the fast axis orientation of the HWP.

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Figure 5(c) shows the differential signals under the free-running and feedback operations, respectively. During free running, the probe and feedback beams have a consistent response to the environmental disturbance because both beams share almost the common optical path in the MZI. Once the feedback operation is active, the fast axis of the HWP tuned immediately to lock the probe beam to the quadrature point successfully.

3.2 Photothermal characterization of surface contaminants

As a proof-of-concept experiment, we printed the clean surface of a GaAs wafer with the olive oil attached to one’s fingerprint and acquired the photothermal spectrum while tuning the MIR excitation laser from 911 to 1336 cm⁻¹ with a resolution of 4 cm⁻¹. The chopping frequency of the excitation laser was set to f_c = 1250 Hz and the time constant of the lock-in amplifier (SSI-instrument, OE1022) was set to 300 ms. Although photothermal spectroscopy is free of background, which means the photothermal signal approaches zero in the absence of a targeted molecular vibration, however it still requires baseline normalization [40] by the spectral intensity of the MIR laser and the wavelength-dependent error [6,41]. Figure 6(a) shows the normalized photothermal spectrum of the olive oil contaminant obtained with the MZI-PTS. In this spectral region, several typical resonance absorption bands appear. The band at 968 cm⁻¹ presenting isolated trans double bonds is assigned to the C-H out-of-plane deformation. It is highly characteristic and is utilized by official methods for determination of total isolated trans fatty acids in fats and oils [1]. The bands at 1033, 1097, 1118, 1163 and 1238 cm⁻¹ arise from C-O stretching vibrations [42]. For the sake of comparison, we tested the absorption spectrum of the olive oil using FTIR spectrometer (Thermo Fisher, Nicolet iS50) in the spectral range from 500 to 1500 cm⁻¹ with a resolution of 1 cm⁻¹, as shown in Fig. 6(a). The typical bands in the photothermal spectrum can be found in the FTIR absorption spectrum. We deduce that the slight mismatch around the absorption bands is blamed to the compositional difference between the pure olive oil (FTIR result) and the mixture of a small amount of biological oil and fat on the finger and pure olive oil (photothermal result). To validate the deduction, we measured the photothermal spectrum of the pure olive oil applied to the wafer surface with the MZI-PTS, as shown in Fig. 6. The typical bands agree well with those in the FTIR absorption spectrum, indicating a good spectral fidelity of the MZI-PTS.

 

Fig. 6. (a) Normalized photothermal spectra of the olive oil contaminant and pure olive oil measured with MZI-PTS and phase-sensitive PTS. FTIR absorption spectrum of pure olive oil is shown for comparison. The photothermal images at (b) an absorption band of 1163 cm⁻¹ and (c) an off-resonance frequency of 1300 cm⁻¹ obtained with MZI-PTS.

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To illustrate the sensitivity enhancement, the optical setup of the MZI-PTS was modified to the conventional phase-sensitive PTS. Referring to Fig. 1, all the experimental parameters remained the same except that the reference arm of the MZI was omitted and that PD₂ was only used to receive the diffraction pattern of the probe beam. The normalized photothermal spectrum of the olive oil contaminant obtained with the phase-sensitive PTS is shown in Fig. 6(a). It is obvious that the strengths at the absorption bands decay and the spectral fidelity decreases. We define the ratio of the strengths between the resonance band and the off-resonance band as a measure of the signal contrast and accordingly we selected 1163 cm⁻¹ and 1300 cm⁻¹, respectively. The signal contrasts were estimated to be 875% and 360% for the MZI-PTS and the phase-sensitive PTS, respectively, and the sensitivity was improved by a factor of 2.4 as a consequence. Several inevitable factors may contribute to the decrease in sensitivity enhancement relative to the theoretical value (7.8), such as the degradation of the excitation beam quality, the imperfect alignment of the optical paths, the different responses of photodetectors and the finite-sized pinholes placed before the photodetectors instead of infinitesimal pinholes in the simulation as well as possible changes in the properties of the contaminant under prolonged exposure to laser radiation.

In addition, to demonstrate photothermal spectral imaging capability of the MZI-PTS, we performed point-by-point scanning on the olive oil-contaminated surface with an area of about 6×6 mm² and the scan step of 30 μm in both x and y directions. The photothermal image in Fig. 6(b) shows good contrast when the MIR laser was tuned to the absorption band at 1163 cm⁻¹, while very low contrast was observed in Fig. 6(c) at an off-resonance band of 1300 cm⁻¹. The resolution of photothermal imaging is given by the thermal diffusion length (the distance at which the initial magnitude of the thermal wave reduces by a 1/e factor), μ = α^1/2/(πf_c)^1/2, where α is the diffusivity of the sample, and was estimated to be 80 μm at the chopping frequency of 1250 Hz. A higher chopping frequency results in a short thermal diffusion length and therefore a higher resolution.

4. Summary

We demonstrated theoretically and experimentally the MZI-PTS as an effective photothermal means for in-situ characterization of the chemical composition of surface contaminants. The advantages of this method rely on two aspects. One is that we employed a balanced MZI to sense both the MIR laser-induced thermoelastic deformation and the refractive index gradient in air. We pointed out that the proposed MZI using a defocused probe beam and the pinhole-photodetector assembly achieves a 7.8-folds sensitivity enhancement compared with the conventional phase-sensitive PTS in theory because it not only reads the complex convolution originating from all the phase delays taking place at the sample surface and air in accordance with Fresnel diffraction, but also amplifies the phase delays to a large intensity difference by wavefront interference. The other is that the performance of the balanced MZI was guaranteed via employing two separate wavelengths, one for sensing and the other for phase bias feedback, to lock the working point to the quadrature point (phase bias of −π/2) in real time. The chromatism between the two wavelengths was corrected by an APS composed of a rotational HWP and two QWPs, which was proved to be superachromatic over a broadband spectral range. The comparison result of the absorption spectra of the olive oil contaminant between the MZI-PTS and the FTIR showed good spectral fidelity of the proposed method and that between the MZI-PTS and the phase-sensitive PTS demonstrated a 2.4-folds sensitivity enhancement in practice. In addition, the point-scanning manner of the MZI-PTS manifested itself to be potential in photothermal spectral imaging.