We demonstrate the enhancement of ellipsometric measurements by multiple reflections of a polarized light pulse on a highly reflective target surface, using an optical cavity. The principle is demonstrated by measuring the adsorbed amount of a molecular vapor (fenchone) onto the ring-cavity mirrors. A phase shift sensitivity of about $10\u22122\xb0$ in a single laser pulse is achieved in $1\u2002\mu s$. Further improvements are discussed that should allow sensitivities of at least $10\u22124\xb0$, surpassing current commercial ellipsometers, but also surpassing their time resolution by several orders of magnitude, allowing the uses of sensitive ellipsometry to be expanded to include the study of fast surface phenomena with submicrosecond resolution.

Reflection of light provides a powerful probe for the study of surfaces. Ellipsometry has been used extensively in both fundamental and applied researches as well as practical applications in microelectronics and biosensing due to its simplicity and high sensitivity.^{1} Ellipsometers measure the so called ellipsometric ratio, $\rho $, given by^{1}

where $tan\u2009\Psi $ is the ratio of the amplitudes of the $s$ and $p$ polarization components of the reflected light, $rp/rs$, and $\Delta $ is the phase shift introduced between these components by the reflection. The ellipsometric angles $\Psi $ and $\Delta $ can be related to the refractive index profile at the interface, which itself is related to the physical properties of interest, such as the adsorbed amount or layer thickness. The time resolution of typical commercial ellipsometers is about 1 s for excellent accuracy $(10\u22123\xb0)$, but can also be in the millisecond range, however, with lower accuracy. As a result ellipsometry is mostly used for the study of steady state surfaces or of relatively slow kinetic processes. Faster instrumentation exists but with poorer accuracy.

Optical cavities have been used for the improved sensitivity and time resolution of absorption measurements, especially since the introduction of the cavity ring-down spectroscopy by O’Keefe and Deacon.^{2} More recently, various modification on the cavity ring-down technique have been used for the sensitive measurement of absorption of samples in various media and at interfaces.^{3–11} In particular, Pipino,^{12,13} Li and Zare,^{14} and Everest *et al.*^{15} used polarized light and evanescent-wave cavity ring-down spectroscopy for absorption measurements of $s$ and $p$ polarized light for various samples, for the determination of $tan\u2009\Psi $. Jacob *et al.*^{16} used the cavity ring-down technique to determine ellipsometric properties of dielectric mirrors, but did not apply their method to the ellipsometric measurement of samples.

In this paper, we demonstrate a new method for the accurate, fast, and simultaneous measurement of the ellipsometric angles $\Psi $ and $\Delta $ of highly reflecting surfaces, which allows the time resolution of ellipsometry to be improved to at least the microsecond timescale.

A polarized laser pulse is introduced into a passive optical cavity, such that the polarization has nonzero $s$ and $p$ polarization components with respect to the target reflection surface (for which reflection occurs at a nonzero incidence angle). With each reflection, a phase shift $\delta $ (characteristic of the reflection surface without a sample) is introduced between the $s$ and $p$ polarization components. When the phase shift is equal to an integer multiple of $2\pi $, the light is linearly polarized in its initial state; for all other phase shifts the light is elliptically polarized. This polarization oscillation frequency is given by

where $tr$ is the cavity round-trip time for the light pulse, $\delta $ is the $s-p$ phase shift introduced (per reflection) by the bare substrate, $\Delta $ is the change in the $s-p$ phase shift due to the presence of a sample at the target surface, and $n$ is the number of target surface reflections per round trip. Notice that to observe the polarization oscillation, the temporal pulse width of the laser (and the detection response time) should be shorter than the period of the polarization oscillation, $2\pi /\omega $. For a given $\delta $, this imposes constraints on the cavity design.

The cavity lifetime of the light pulse is described by an exponential decay and the $s$ and $p$ polarization modes have lifetimes of $\tau s$ and $\tau p$, respectively. If the cavity output is passed through a polarizer and then a detector, the time dependence of the signal intensity is described by

where $Rs$ and $Rp$ are the reflectivities of the $s$ and $p$ polarization components, $\theta i$ is the angle between the $s$ direction (perpendicular to the cavity plane) and the axis of the input polarization $(\epsilon )$, and $\theta o$ is the angle between the $s$ direction and the analysis axis $(\alpha )$ of the detection polarizer (see Fig. 1). The first two terms describe the incoherent contributions of the $s$ and $p$ polarization modes, respectively, whereas the third term describes the beating between these two modes [$\omega $ is given by Eq. (2)]. The beating term vanishes for $\theta i=0\xb0$ or 90°, or $\theta o=0\xb0$ or 90°. If the reflectivities $Rs$ and $Rp$ (and hence $\tau s$ and $\tau p$) are equal (as can be the case for total internal reflection), then maximal modulation depth occurs for $\theta i=\theta o=45\xb0$; if $Rs$ and $Rp$ (and hence $\tau s$ and $\tau p$) are unequal, the modulation depth becomes time dependent and maximizes at other values of $\theta i$ or $\theta o$.

We consider the case of the two signals $I1(\theta i,\theta o=+45\xb0)$ and $I2(\theta i,\theta o=\u221245\xb0)$, which represent the output from a balanced polarimeter, as they differ in the output polarization by 90°. $I1$ and $I2$ differ only in the relative sign of the beating (third) term of Eq. (2). For this choice, notice that the sum of these two signals, $I1+I2$, is polarization independent (the beating term cancels), whereas the difference, $I1\u2212I2$, is proportional to the beating term only. These signal combinations provide a robust test to determine which oscillations are due to polarization beating and which are from other sources (such as mode beating). The ellipsometric phase angle is measured from the polarization beating frequency (a similar technique was used for measurements of circular birefringence).^{17}

Here, we demonstrate a $65\xd73.5\u2002cm2$ four-mirror ring cavity in a vacuum chamber, shown in Fig. 1. All four dielectric mirrors (with $Rs\u22480.999$ and $Rp\u22480.99$) have a 45° angle of incidence and are highly reflective for light with wavelengths of about 355 nm. A 30 ns pulse of linearly polarized 360 nm light, from an excimer-pumped dye laser, is introduced into the cavity. The output of the cavity is passed through a balanced polarimeter and signals $I1(\theta i,\theta o=+45\xb0)$ and $I2(\theta i,\theta o=\u221245\xb0)$ are detected with two photomultiplier tubes (PMTs). The angle $\theta i$ is chosen to produce a large beating signal, which in our case occurs for small angles, $\theta i\u22481\xb0$. The angles $\theta i$ and $\theta o$ are set using rotatable $\lambda /2$ plates.

The use of the cavity for ellipsometric measurements is demonstrated by introducing a molecular vapor into the cavity (fenchone vapor was chosen as it was conveniently available). Figure 2(a) shows the signal $I1$ (top, red) for an empty cavity and for a cavity filled with 1.0 mbar of fenchone gas (bottom, blue), for which fenchone molecules have adsorbed onto the surface of the mirrors. The large change in the beating frequency is clearly evident in the raw data. Figure 2(b) shows the respective different signals $I1\u2212I2$, which isolate the polarization beating, $\omega $. Fitting these oscillations with Eq. (2) (using $n=4$) yields $\delta =3.80\xb0$ and $\Delta =\u22121.04\xb0$. The standard error of the oscillation frequency, from the nonlinear least-squares fitting, was less than 0.01°. Using a simple multilayer modeling for the mirror (according to the manufacturer specifications) and adding an extra layer on top of the external mirror layer with a variable thickness $d$ and a refractive index of 1.46 for liquid fenchone, we observe that the variation of the total phase angle $\delta +\Delta $ is linear with the thickness $d$ with a slope $\Delta /d=\u22121.5\xb0/nm$, rather independent of the value of $\delta $. A layer thickness of 0.70 nm is therefore obtained. This corresponds to the approximate size of one saturated layer of fenchone adsorbed on top of the mirror surfaces, which is a reasonable result for the case of a vapor in contact with a weakly interacting solid surface.^{18}

These measurements constitute a proof of principle of the cavity enhancement of ellipsometric phase shifts. This particular setup can be used to characterize the ellipsometric properties of dielectric mirrors, such as the wavelength dependence of $\delta $ and the adsorption of gases onto the mirrors. The disadvantages of using dielectric mirrors for ellipsometric measurements are that the complex structure of the multilayer coatings introduce uncertainties into the modeling and that potential samples are limited to those that do not interfere with the light beam (such as vapors, but not liquids or solids). However, this technique can be applied more generally using evanescent-wave cavity ring down at the total internal reflective surface of prisms to study the dynamics at solid-liquid interfaces (such experiments are currently underway in our laboratory). In this case, both the modeling of the surface is much simpler and there are far fewer constraints on the types of sample that can be used. The sensitivity of this technique can be improved by at least 100 using cavities with 100 times more passes, without compromising time resolution, as they can be 100 times smaller.^{12,13} In combination with high repetition rate lasers and fast detection electronics, ellipsometric measurements can be made with submicrosecond resolution. The sensitivity of microcavities^{19} can extend, in principle, the limits of sensitivity and time resolution of cavity-enhanced ellipsometry even further.

Financial support from the EU FP7 ERC Grant “TRICEPS” (GA No. 207542) and the HGSRT grant PENED 2001 (No. ED 01479) are gratefully acknowledged.