Editing ARROW waveguide (section)

== Principles of Operation ==
[[File:ARROW_waveguide_example.png|thumb|487x487px|A typical system of a solid core ARROW. When coupling a light source to the core of an ARROW, the light beams that are refracted into the cladding layers destructively interfere with themselves, forming anti-resonance. This results in no transmission through the cladding layers. The confinement of light on the upper surface of the guiding core is provided by the total internal reflection with air.
]]

ARROW relies on the principle of thin-film interference. It is created by forming a Fabry-Perot cavity in the transverse direction, with cladding layers that function as [[Fabry–Pérot interferometer|Fabry-Perot etalons]].<ref>{{Cite journal|last1=Duguay|first1=M. A.|last2=Kokubun|first2=Y.|last3=Koch|first3=T. L.|last4=Pfeiffer|first4=Loren|date=1986-07-07|title=Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures|journal=Applied Physics Letters|volume=49|issue=1|pages=13–15|doi=10.1063/1.97085|issn=0003-6951|bibcode = 1986ApPhL..49...13D |hdl=10131/8010|s2cid=123001099 |url=https://ynu.repo.nii.ac.jp/?action=repository_action_common_download&item_id=4080&item_no=1&attribute_id=20&file_no=1 |hdl-access=free}}</ref> A Fabry-Perot etalon is in resonance when the light in the layer constructively interferes with itself, resulting in high transmission. Anti-resonance occurs when the light in the layer destructively interferes with itself, resulting in no transmission through the etalon.

The refractive indexes of the guiding core (n<sub>c</sub>) and the cladding layers (n<sub>j</sub>, n<sub>i</sub>) are important and are carefully chosen. In order to make anti-resonance happen, n<sub>c</sub> needs to smaller than n<sub>j</sub>. In a typical system of a solid core ARROW, as shown in the figure, the waveguide consists of a low [[refractive index]] guiding core bounded on the upper surface by air and on the lower surface by higher refractive index antiresonant reflecting cladding layers. The confinement of light on the upper surface of the guiding core is provided by the total internal reflection with air, while the confinement on the lower surface is provided by interference created by the antiresonant cladding layers.

The thickness of the antiresonant cladding layer (t<sub>j</sub>) of an ARROW also needs to be carefully chosen in order to achieve anti-resonance. It can be calculated by the following formula:

<math>t_j={\lambda \over 4n_j}(2N-1)[1-{n_c^2 \over n_j^2}+{\lambda^2 \over 4n_j^2t_c^2}]^{-1/2}, N = 1, 2, 3,...</math>
: <math>t_j</math> = thickness of the antiresonant cladding layer
: <math>t_c</math>= thickness of the guiding core layer
: <math>\lambda</math>  = wavelength
: <math>n_j</math> = refractive index of antiresonant cladding layer
: <math>n_c</math> =  refractive index of  guiding core layer
while <math>n_j > n_c > n_{air}</math>