Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

Advancements in the understanding of optical materials^{1,3,4,6,7,10,13-16} have provided new insights into the creation of thin film materials for a host of optical devices, including antireflection coatings on lenses, high extinction ratio optical filters, and highly absorbing slab waveguides¹⁷. These advancements would not be possible without the use of many characterization techniques, such as ellipsometry^4,6,18, contact angle measurement, atomic force microscopy^7,11,19, and scanning/transmission electron microscopy, which assist in the iterative improvement of these technologies by providing direct measures or indirect estimates of fundamental optical material properties. Said properties, such as the refractive index, govern how the materials interact with incident photons, which directly affects their function and their use in optical applications. However, each of these techniques has limitations relating to resolution, sample preparation, cost, and complexity, and each generates only a subset of the data needed to fully characterize the material. That being said, a new set of techniques, known as evanescent field-based photoacoustics (EFPA)^{5,6,15,18,20-49} as shown in Figure 1, has the potential to estimate material properties at the nanoscale in a consolidated set of experiments. EFPA encompasses the sub-techniques of total internal reflection photoacoustic spectroscopy (TIRPAS)^{23,25,26,33-35,43-45} , photoacoustic spectroscopy/total internal reflection photoacoustic spectroscopy refractometry (PAS/TIRPAS refractometry)¹⁸, and optical tunneling photoacoustic spectroscopy (OTPAS)⁶, and has been used to estimate bulk and thin film refractive index, film thicknesses, as well as to detect absorbing materials at a prism/sample or substrate/sample interface.

In order to understand the EFPA mechanism, one must first understand the concept of photoacoustic spectroscopy (PAS), which refers to the generation of ultrasonic pressure waves by the rapid thermoelastic expansion of a chromophore, following the absorption of an ultra-short (< µsec) pulse of light (Figure 1). Theoretical and mathematical framework for the photoacoustic effect discussed in this paper can be obtained here^50-59. The resulting change in pressure can be detected by an ultrasonic microphone or transducer. The photoacoustic effect, originally discovered in 1880 with the invention of Alexander Graham Bell's photophone, was "rediscovered" in the early 1970s due to advancements in laser and microphone technology, and eventually put into practical use to fill niche applications from biomedical imaging to thin film analysis to non-destructive testing of materials.^{1,53-57,59-82} This effect can be mathematically described with one-dimensional wave equations, wherein the wave is a simple acoustic source whose pressure (p) varies in both position (x) and time (t):

with solutions for simple acoustic sources of the form⁶⁴

where p is pressure, Γ=αv_s²/C_p where α is the volume thermal expansion coefficient, v_s is the speed of sound in the medium, and C_p is the heat capacity at constant pressure, H₀ is the radiant exposure of the laser beam, c is the speed of sound in the excited medium, x is length, and t is time. The magnitude of the resulting acoustic wave relies directly upon the optical absorption coefficient of the material, µ_a, which is the inverse of the optical penetration depth, δ, which is in turn a measure of the distance the light travels until it decays to 1/e of its initial optical intensity. While Equation (1) is a general equation for a one dimensional plane wave source, typical absorbers will emit a spherical acoustic wave in three dimensions. Beyond the mathematical description, applications of the photoacoustic effect⁵⁴ span many imaging modalities such as microscopy, tomography, and even molecular imaging owing to the photoacoustic effect having high sensitivity due to the large optical absorption due to the naturally present chromophore hemoglobin. Other applications of the photoacoustic effect even include the estimation of various thin film properties^{15,16,20,21,24,26-32,36-39,41,42,56,83,84}. However, PAS does have certain limitations: (1) its extensive optical penetration depth eliminates the ability to probe near-field optical properties at surfaces (2) its efficiency of capturing the emitted acoustic energy is low due to spherical propagation of the majority of the energy away from the detector (3) samples must include chromophores in the wavelength regime under consideration.

When combined with evanescent field-based techniques, however, many of these limitations can be ameliorated. The evanescent field occurs when a beam of light undergoes total internal reflection (TIR), as described by Snell's Law, which effect also allows fiber optic waveguides to guide light large distances (km) for computation and telecommunication applications. In practical applications, the evanescent field is used in a variety of characterization and imaging technologies, including attenuated total reflectance spectroscopy (ATR). Imaging is achieved with high contrast due to the confinement of the light to within the first few hundred nanometers into the sample of interest. The evanescent field takes the form of an exponentially decaying field that extends into the external medium to an optical penetration depth that is typically on the order of the wavelength being used (usually ~500 nm or less) as shown in equations 3 and 4.

where I is the light intensity in % at a location z from the prism/sample interface, I₀ is the initial light intensity in % at the interface, z is distance in nanometers, and δ_p is the optical penetration depth as shown in equation 4. With such a small optical penetration depth, the evanescent field is able to interact with the environment very close to the interface of the two materials, and well below the optical and acoustic diffraction limits. The optical properties of materials or particles within this range may perturb the field or otherwise alter its generation, which interaction can be detected by a variety of methods^{3,5,6,10,15,17,18,21,23,25-27,29-47,84-95}.

When evanescent techniques are combined with PAS, the photoacoustic waveforms produced can be used to characterize materials or particles interacting with the evanescent field, creating the evanescent-field based photoacoustics (EFPA) family of techniques, as shown in Figure 1. This family includes, but is not limited to, total internal reflection photoacoustic spectroscopy (TIRPAS), optical tunneling photoacoustic spectroscopy (OTPAS), and surface plasmon resonance photoacoustic spectroscopy (SPRPAS). The interested reader should refer to the following references for derivations of the equations used for TIRPAS^{5,6,18,23,25,26,33-35,43-47}, PAS/TIRPAS refractometry¹⁸, and OTPAS⁶. In each case, the photoacoustic effect is generated through a different excitation mechanism than simple transmittance through a prism; for instance, in TIRPAS, the light is evanescently coupled through a prism/substrate/sample interface into the chromophores (which could include the sample material itself, or guest molecules within the sample), whereas in SPRPAS, the primary mode of excitation is instead through the absorption of a surface plasmon, which is a secondary E-M wave created when the energy of the evanescent field is transferred into the electron cloud of a metal layer deposited on the prism surface. This family of techniques was originally invented in the early 1980s by Hinoue et al., and improved upon by T. Inagaki et al. with the invention of SPRPAS, but saw very little development due to technical limitations of the light sources and available detection equipment. More recently, previous investigations have shown that increased sensitivity and utility are possible with modern polyvinylidene fluoride (PVDF) ultrasonic detectors and q-switched neodymium-doped yttrium aluminum garnet (Nd:YAG) lasers. Specifically, nanosecond-pulsed Nd:YAG lasers result in a 10⁶ fold increase in the peak power, which enables EFPA techniques to become useful tools for evaluating the optical properties of a variety of materials and interfaces^{5,6,15,18,21-29,31-47,84,96}. Additionally, previous work has further shown the capability of such techniques to determine structural information about materials at an interface, which was previously never achievable with traditional photoacoustic spectroscopy (PAS) technologies due to their relatively large penetration depth^{53,55,57,59,61,62,69,73,75,80,81}.

This capability is shown in the protocols that follow under the OTPAS technique; however, on a more fundamental level the three techniques each rely on a different definitive equation, which determines the capabilities of the technology. For example, in TIRPAS, the optical penetration depth of the evanescent field, δ'_p, primarily drives the resulting acoustic signal intensity to an absorbing sample, and is described by:

where λ₁ is the wavelength of light traveling through the prism medium and is defined by the relation λ₁ = λ/n₁ wherein n₁ is the refractive index of the prism material. Additionally, θ refers to the angle of excitation, and n₂₁ refers to the ratio of the refractive indices of each medium and is defined by n₂₁ = n₂/n₁, wherein n₂ is the refractive index of the sample material. The larger the optical penetration depth, the more material is being irradiated. For the photoacoustic effect, the greater the optical penetration depth, the more material is being excited that can produce acoustic waves leading to a larger acoustic signal.

Unlike TIRPAS however, in PAS/TIRPAS refractometry the primary equation is Snell's law:

where n₁ is the refractive index of the prism, θ₁ is the angle of incidence at the prism/sample interface, n₂ is the refractive index of the sample, and θ₂ is the angle of the light that is refracted through the second medium. The sensitivity of estimating the refractive index of a material is primarily driven by the accuracy of the estimation of θ_1. In total internal reflection, which is achieved when θ₁ is beyond the critical angle which generates an evanescent field, sin θ₂ = 1 and therefore, Equation 5 reduces to n₂ = n₁sinθ₁. (Note: θ₁= θ_critical) Knowing the angle at which the numerical derivative (dP/dθ where P is the peak to peak voltage of the photoacoustic signal and θ is the angle of incidence of the light with the sample) of the photoacoustic signal has a local minima allows for the estimation of θ₁ that allows the user to solve for n₂ and thus estimate the bulk refractive index of a sample as shown in Figure 1.

Finally, in OTPAS, the following equation relates optical transmission in % to photoacoustic peak to peak voltage by:

where T is the percent optical transmission, p is the peak-to-peak voltage generated by the angular spectrum of a substrate with a film on it, p₀ is the peak-to-peak voltage generated by the angular spectrum of a substrate, β is the coupling constant based upon the refractive index of prism and the immersion oil, α is the attenuation factor, and is a factor that includes thickness and refractive index of the sample film within the evanescent field. The sensitivity of this technique to thickness and refractive index is driven by the accuracy of estimating the peak to peak acoustic signal intensities, p and p₀ at each angle of incidence in the angular spectrum. It has been shown that β can be directly calculated based upon the refractive indices of the prism and the immersion oil; consequently, it is a straightforward task to calculate the optical transmission at each angle of incidence and to then extract an estimate for the refractive index and thickness of the film through statistical curve fitting analysis. The interested reader should refer to Goldschmidt et al. for more information.^5,6

The EFPA system is a photoacoustic based system capable of estimating the thickness, thin film refractive index, bulk refractive index, and generating acoustic signals through optical absorption for detection. The system is comprised of a laser, an optical train to guide the light to the prism/sample and to the laser energy measurement side. The laser energy measurement side is used to normalize the photoacoustic signal to the incident laser energy as shown in Figure 2. The EFPA system is driven by a stepper motor driver to rotate the prism/sample for the angular spectra in PAS/TIRPAS refractometry and OTPAS. The system acquires data through a digital acquisition card and provides a user interface and automated stage control through an in house program.