Effective-substrate theory for optical reflection from a layered substrate

Abstract

We show that reflection of a monochromatic light from a semi-infinite medium covered with a stack of layered media is equivalent to that from an effective "semi-infinite medium" characterized by two distinctive optical dielectric constants for the s-polarized and p-polarized components, respectively. Such an effective-substrate approach simplifies the analysis of ellipsometry measurements of a wide range of surface-bound processes including thin film growth and surface-bound reactions.

Label-free OIRD microarray chips with a nanostructured sensing interface: enhanced sensitivity and mechanism

“…Further theoretical analysis was performed to rationalize this observation. According to the OIRD principle, the OIRD signal of I (2 Ω ) from a certain interface is described by eqn (E1): 34,37 I (2 Ω ) = I 0 (| r p0 | 2 cos 2 α − | r s0 | 2 sin 2 α ) J 2 ( A )where I 0 is the initial light intensity of the laser; r p0 and r s0 are the p- and s-polarized reflectivity of the surface, respectively; α is the angle between the optical axis of the polarization analyzer and the p -polarized light (π/2 in this experimental setup). Ω = 50 kHz is the modulation frequency of the photoelastic modulator.…”

“…On such a chip, the OIRD detection signal originates from this newly formed layer with its thickness d reflecting the amount of captured target. The differential OIRD signal of Δ I (2 Ω ) could be calculated by subtracting the original I 0 (2 Ω ) signal before detection from the final one after detection according to eqn (E2) as follows: 34,37 Δ I (2 Ω ) = I (2 Ω ) − I 0 (2 Ω ) = I 0 [((| r 3p | 2 − | r 2p | 2 )cos 2 α − (| r 3s | 2 − | r 2s | 2 )sin 2 α )] J 2 ( A )where r 2p and r 2s are the p- and s-polarized reflectivity of the two-layer interface of the chip before detection, respectively, and r 3p and r 3s are the p- and s-polarized reflectivity of the three-layer interface after detection; both could be calculated with the layered medium theory according to the Fresnel formula, 59 and are solely related to the thickness d because other parameters remain unchanged including the effective dielectric constant and thickness of the glass and solution. The dielectric constant of the target layer could also be treated as a constant as all the biomolecules remain the same.…”

“…S9 and more details in the ESI†), resulting in improved sensitivity on the pristine FTO-based chip as observed in this work. 34,37…”

“…A home-made OIRD device was used in this study as described previously. 34 As shown in Fig. 1b, the laser light (632.8 nm, 3 mW in power) was modulated with a photoelastic modulator (PEM 100 photoelastic modulator system from Hinds Instruments) to periodically polarize between the s and p states at a frequency of 50 kHz.…”

“…[29][30][31] It is worth noting, however, that in previous work OIRD has shown astonishing sensitivity to probe sub-monolayer (0.05 monolayer) gas adsorption/desorption and 0.01 monolayer epitaxial layer growth of oxide films. [32][33][34] For protein microarray detection, we previously demonstrated the pivotal role of the chip interfacial structure on the OIRD sensitivity. [35][36][37] By introducing a functional layer with well-controlled thickness to the surface, the interfacial interference effect is activated and results in improved detection sensitivity.…”