J. Eur. Opt. Society-Rapid Publ. 22, 5( 2026) 43
Fig. 1.( a) Angle of incidence at which the transmittance of each CSP is maximum as a function of cavity thickness.( b) Maximum transmittance at each CSP resonance peak as a function of cavity thickness, FTIR transmission at h co without Ag for comparison.( c) Modulus and( d) phase of r LMH( lighter) and r LM( darker) as functions of the incident angle. All results correspond to a setup using silver as metal( d M = 39 nm), BK7 as prism and air filling the gap between the mirrors, at k = 800 nm. propagate between the two mirrors at photonic resonance conditions. On the other hand, for h > h cr, k L,\ becomes imaginary, and only CSP resonances are allowed. In both cases, the dependence on the separation between the mirrors, d, in equation( 1) becomes straightforward, since it only appears inside the argument of either the sine or the hyperbolic sine, respectively. As a result, CSP resonances correspond to zeros of the hyperbolic sine, leading to two distinct solutions for each d at two different h, as shown in Figure 1a. It is also remarkable that one of these two curves is the continuation of the first FP resonance, forming a hybrid branch. For thick enough cavities these two plasmonic resonances become degenerated, merging at the same angular position – named the coalescence angle h co – for d > d co = max [( ln | r LMH |)/ k 00 L,\].
In this work, we emphasize the high values of transmittance in the system even for over-wavelength-thick cavities. The presented theoretical and experimental studies of maximum transmittance as a function of d reveal that it remains not only noticeable but also large for d exceeding by far the predicted penetration depth of light in the intracavity L medium. Thus, transmittance of CSP resonances in this MC can be said to resemble some kind of enhanced light tunneling. Analysis of equation( 1) reveals that r LMH is the key parameter determining this phenomenon, especially in the plasmonic regime. A brief theoretical analysis on the behavior of that reflection coefficient isalsopresented. Its modulus becomes much larger than unity near the coalescence. This may seem surprising if one thinks of Fresnel coefficients as the square root of reflectance( R). However, there is no issue with energy conservation phere because the waves involved are evanescent and jj¼ r ffiffiffiffi
R does not hold.
2 Material and methods
The experimental setup used to test our theoretical predictions is shown in Figure 2. A supercontinuum light source
( SuperK COMPACT, NKT Photonics, 450 – 2400 nm) illuminates the MC, with power adjusted by a variable neutral optical density. A cube polarizer provides a transmitted TM beam, which is a requirement for the excitation of surface plasmons. Simultaneously, part of the original beam is deflected towards a photodiode, used to monitor the beam power. The MC consists of two identical rectangular BK7 glass coupling prisms, whose largest faces are coated with thin silver films, facing each other and creating a micron-scale air gap in between. That cavity thickness is determined by iteratively comparing with subsequent theoretical configurations, varying d with the desired precision. It is modified in ~ 20 nm steps using a piezoelectric actuator( Thorlabs PIAK25), which is connected to the prisms through custom 3D-printed mounts. These are mounted on a rotation platform( URS75BCC from Newport Optics), that allows us to control the angle of incidence(± 6 mdeg accuracy). Finally, the transmitted signal is collected with a photodiode preceded by a spectral filter, enabling monochromatic mapping of T across a 2D h � d space, using incident light as a reference.
The thin silver layers on the prisms, used as MC mirrors, were deposited by physical vapor deposition( PVD), evaporating the metal through heating. The prisms were placed inside the vacuum chamber of a Baltec BAE250 Coating System by Balzers, and the pressure was reduced to ~ 10 �3 Pa. Afterwards, the silver was heated until it started to evaporate( ~ 140 ° C), and an approximately constant deposition rate was used to obtain silver films with a nominal thickness around 39 nm. Later, this value was found to be correct within an uncertainty range of ± 5 nm with a Dektak3 Surface Profilometer, as an extra check.
3
Results and discussion
The analytical model developed for transmittance of the MC was experimentally validated. Angular positions of