Quarterwave stack

Figure 2. Transmittance spectral profile of a coating consisting of a quarterwave stack of 23 layer stack centered on 800 nm. Light gray without ripple control. Dark gray with ripple control. It can be used either as a intermediate band filter, or a shortwave dichroic beam splitter or a longwave one.

The simplest method, however, is to deposit a quarterwave stack for one wavelength on the top of another stack for a different wavelength. 

Interference mirrors are dielectric thin film coatings where low- and high-refractive index layers alternate. The optical thickness of each of the layers is equal to quarter-wavelength QJAn). They are denoted as distributed Bragg mirrors or distributed Bragg reflectors (DBR), sometimes simply as Bragg mirrors. Other names include quarter-wave mirrors (QWM), quarterwave stacks (QWS) and highly reflective (HR) layers. 

To apply the transfer matrix method to a quarterwave stack the electric field in each separate homogeneous layer of the stratified Bragg mirror structure is written as a superposition of the incident and reflected (/ plane wave, where... 

As an example of the application of transfer matrix method to the calculation of spectral reflection of quarterwave stacks. Fig. 2.37 shows the spectral reflection of a silicon-silica Bragg mirror for different numbers of layer pairs under normal incidence of light. A stop band is readily recognizable already for a small number of layer pairs. It is important that variations of the layer thickness and the materials used. 

Basically, omnidirectional mirrors are dielectric quarterwave stacks in which TIR and Bragg mirroring wavelength ranges overlap, i.e., an overlapping band gap regime exists that extends above the light cone. 

Let us now consider a stack consisting of x quarterwave layers of high index uh and of x—1 quarterwave layers of low index ni, it is denoted no HLHL. .. LHlng. Its reflectance R is... 

The absorptance per layer (Fig. 9) is smaller at 550 nm than at Aq. But its sum over the whole stack is significantly higher. Indeed the stack is optimized for Ao in order that E fades when the incoming radiation crosses the coating. It reaches nearly 0 from the 10 layer with a low index halfwave entrance layer, or slightly more with a high index quarterwave one (Fig. 11). But at A = 550 nm, E PS 20 V/m whatever the number of the layer and whatever the entrance layer, up to enter the substrate, which results in a low reflectance. 

Another type of structures for metal-dielectric mirrors are metallodielectric multilayers. In this case alternating quarterwave or subwavelength stacks of metal and dielectric are deposited. Typical for such multilayers is alow reflection in visible, but large in infrared wavelength range. Thus they basically behave as low-pass optical filters. Such stmctures were denoted in literature as heat mirrors. First heat mirrors were fabricated as early as in 1950s [252]. The simplest heat mirrors consist of three layers only, dielectric-metal-dielectric or, alternatively, dielectric-transparent conductive oxide-dielectric [253]. Full multilayer metal-dielectric reflectors with binary but also ternary layers were also considered [254]. Because of their high reflectance in infrared, but also because of their plasmonic properties [255] metal-dielectric multilayer mirrors are of interest for cavity enhancement of infrared detectors. 

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