Development of Neutral-Density Infrared Filters Using Metallic Thin Films
- PDF / 379,283 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 49 Downloads / 196 Views
substrate, respectively. Interference in the substrate caused oscillations in the spectra. A numerical method was used to reduce the spectral resolution by truncating the interferogram before performing the Fourier transform, which eliminated the oscillations. Previous comparison of FTIR measurements with laser measurements at 10.6 gim using filters with thin substrates (150 nm) indicated that the uncertainty in optical density is ±1% [1]. A commercial apparatus was modified for reflectance measurements to achieve improved measurement accuracy. The angle of incidence was fixed at approximately 20 degrees. For random polarization, the optical properties at 20 degrees are almost identical to those at normal incidence. A reference mirror was made by depositing a 150 nm-thick gold film on a silicon substrate. The reported reflectance of gold film ranges from 0.985 to 0.995 [3]. Therefore, no mirror correction was made. The uncertainty in the reflectance is estimated to be ±0.02 for reflectance greater than 0.50. The reflectance of a bare silicon substrate measured using this method agrees within 0.01 of the calculated value. ANALYSIS The reflectance and transmittance of film-substrate composites are functions of the refractive indices and thicknesses of both the film and substrate. Since the interference in the substrate is eliminated by numerically reducing the spectral resolution, the radiation in the film can be treated as completely coherent and that in the substrate as completely incoherent. [4] For the film-substrate composite, the reflectance for incidence from the film side, RF, the reflectance for incidence from the substrate side, Rs, and the transmittance, T (which is the same for incidence from either side) are related to the film thickness, dF, the substrate thickness, ds, the complex refractive index of the film, FF = nF + iicF, and the complex refractive index of the substrate, ns = ns + ixs [5-7]: RF = Ra +psr2T2 I(1 -ps§Rb), RS = PS + Rb(ps)
2
/(1 psRb),
(1)
(2)
and 2 T= rsTa(1-Ps)(1-ps'rsRb).
(3)
Here, Ps = [(ns _2+22 1) + s] / [(ns +2 1)2 + K9 ] is the reflectivity of the air-substrate interface and rs = exp(-4rtsds I A) is the transmittance along the path inside the substrate (where A is the wavelength in vacuum). In the above equations, Ra and Ta are the reflectance and transmittance for radiation propagating from the air to the film as if the substrate were semi-infinite, and Rb is the reflectance for radiation propagating from the substrate to the film, i.e., 2 ( - 2 -12, Ra = Fa + Fb exp(i2SF) Rb= r, + Fa exp(i 2 8F) and Ta=-ns i +atb exp(i8 F) 2
a l+rFarbepi9
aexp(i
2 8SF)n l+Fa~bexp(i Ta=
8F)
For near-normal
incidence, the complex Fresnel reflection coefficients are and rb=(HF-fls)1(flF+flS), where 1fo=no=1 is the refractive index of the air, the complex Fresnel transmission coefficients are F'a = 2nT 0 / (nO + nF) and Fa=(i-0-F)/(TO+iTF)
tb = 2 iTF / (nF +nTs), and the complex phase change is 9F = 2 anFdF/IA. Notice that the refractive index, reflectance, and transmittance are f
Data Loading...
