Fabry-Perot filters

Abstract This tutorial shows how fundamental is the role plaid by interferences in many of the physical processes involved in astrophysical signal formating and consequently instmmentation. It is obvious in interferometry. Grating spectroscopy is explained within the same framework as Young experiment, and Fabry-Perot filters are explained as Michelson interferometers.Polarization interferences, used in Lyot filters, are discussed, emphasizing the analogy with echelle gratings. 

Multicavity filters. Multicavity Fabry-Perot filters are used to make very narrow transmission filters. A simple Fabry-Perot cavity (see Ch. 2) consists of a halfwave layer surrounded by two reflectors of typically 10 layers each. Figure 4 shows three transmission profiles obtained with one, two or three cavity filters. The three cavity HL) 5HH(LH) 5) " 3 filter has a 1.2 nm bandwidth. It has 60 layers. Note that the three-peak top of the transmittance. Each cavity has to be well adapted to the following one if not the resulting transmittance can be very poor. Such cavities are broadly used in telecoms in between arrays of antennas for cell phones. 

Figure 4. Transmittance of a multicavity Fabry-Perot filter.

In conclusion, it has been demonstrated that the manufacture of waveguides, Bragg reflectors, Fabry-Perot filters and anti-reflective coatings can be based on PS thin films. Such filters are applied for example in gas sensors, as described in the preceding section. 

Y. Mitsuhashi, Saturable Fabry-Perot filter for nonlinear optical image processing, Opt. Lett., 6, 111-113 (1981). 

In an interference filter, a transparent dielectric spacing material separates two partially reflective windows. This conformation forms a Fabry-Perot filter, allowing a specific set of wavelengths to pass. The outer windows are constructed of materials with higher refractive index than the center spacer, which determines the central wavelength via its thickness. The equation describing the central wavelength is... 

As mention above, Eq. 3 is similar to the equation describing the transmittance of a Fabiy-Perot, except for the cosine at the numerator. As in Fabry-Perot filters, the multiple internal reflections in OLEDs induce, at some specific wavelengths, a resonance of the light electric-field intensity (or more accurately, the irradiance) distribution inside the OLED. 

The phenomenon known as "microcavity effect" refers to the enhancement or annihilation of the emitted irradiance related to the position of the emitting material relative to this resonance peak of the irradiance. A weak microcavity effect is usually present in conventional OLEDs because internal reflections are caused by the higher refractive index of the ITO anode compared to most organic layers, and the cathode is highly reflective (Bulovic, 1998). This is usually considered a nuisance, but has been exploited in microcavity OLEDs (Jordan, 1996). With Fabry-Perot filters, the phase condition for the appearance of resonance peaks is given by the following equation ... 

An extensive mathematical treatment was performed by Hadley and Dennison [121, 122]. Only the most important formulae characterising a Fabry-Perot filter are given here... 

Fabry-Perot filters are also available commercially, with local continuously changing spectral transmittance. Such continuous filters are deposited on glass strips or on circular disks. 

Figure 16.23 (a) Quasi-static strain measured with the tunable Fabry—Perot filter (TFPF)-demodulated FBG sensor signal (b) strain wave signals measured with the Mach-Zehnder interferometer (MZI)-demodulated FBG sensor compared with that measured by the PZT sensor [47]. 

The most common and efficient type of bandpass filter is the interference filter. The basic principles of operation of such filters are illustrated by considering the simple Fabry-Perot filter. This is made by placing a spacer of dielectric medium between two partially transmitting metal films supported on a suitable substrate. These substrates are usually glass or quartz for the visible and ultraviolet whilst in the infrared they include germanium, silicon, IRTRAN II, IV and V, sapphire, indium arsenide, indium antimonide, and arsenic trisulphide. The basic principles of operation are shown in Figure 2. 

Ebermann, M., et al., 2012. Widely tunable Fabry-Perot filter based MWIR and LWIR microspectrometers. In Proc. SPIE 8374. Next-Generation Spectroscopic Technologies V,... 

Noval AM, Vaquero VS, Quijoma EP, Costa VT, Perez DG, Mendez LG, Montero I, Palma RJM, Font AC, Ruiz JPG, Silvan MM (2012) Aging of porous silieon in physiologieal conditions cell adhesion modes on scaled Id micropattems. J Biomed Mater Res A 100A(6) 1615-1622 Park JH, Gu L, von Maltzahn G, Ruoslahti E, Bhatia SN, Sailor MJ (2009) Biodegradable luminescent porous silicon nanoparticles for in vivo applications. Nat Mater 8(4) 331-336 Pavesi L, Dubos P (1997) Random porous silicon multilayers application to distributed Bragg reflectors and interferential fabry - perot filters. Semicond Sci Technol 12(5) 570... 

Zangooie S, Jansson R, Arwin H (1999) Ellipsometric characterization of anisotropic porous silicon Fabry-Perot filters and investigation of temperature effects on capillary condensation efficiency. J Appl Phys 86(2) 850-858... 

The physical construction of a Fabry Perot filter is shown in Fig. 54. The liquid crystal modulation needs to be parallel to the direction of the light in order for a refractive index change to be achieved. For this reason, the liquid crystal molecules must be tilted off the surface of the mirrors to allow the modulation to occur. The electrical field which moves the molecules must be applied from the side of the cell rather than the front... 

For light that is incident normally on a Fabry-Perot filter with a mirror separation d and index n in the cavity between the mirrors, the transmission function is given by... 

Our Br7 image reveals filamentary structure that traces the limbs of the bipolar cavities out to 80" from S106IR. The lobe interiors have a knotty appearance, hi contrast, the surface bri tness in the continuum image is more uniformly distributed. Comparison of the intensities in the on-line/ofif-line pair indicates that the continuum contributes typically 20% of the flux within the Fabry-Perot filter passband. 

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