Theory
To understand how optical ring resonators work, we must first understand the optical path length difference (OPD) of a ring resonator. This is given as follows for a single-ring ring resonator:
where r is the radius of the ring resonator and is the effective index of refraction of the waveguide material. Due to the total internal reflection requirement, must be greater than the index of refraction of the surrounding fluid in which the resonator is placed (e.g. air). For resonance to take place, the following resonant condition must be satisfied:
where is the resonant wavelength and m is the mode number of the ring resonator. This equation means that in order for light to interfere construcitvely inside the ring resonator, the circumference of the ring must be an integer multiple of the wavelength of the light. As such, the mode number must be a positive integer for resonance to take place. As a result, when the incident light contains multiple wavelengths (such as white light), only the resonant wavelengths will be able to pass through the ring resonator fully.
The quality factor of an optical ring resonator can be quantitatively described using the following formula:
where is the finesse of the ring resonator, is the free spectral range, and is the full-width half-max of the transmission spectra. The quality factor is useful in determining the spectral range of the resonance condition for any given ring resonator. The quality factor is also useful for quantifying the amount of losses in the resonator as a low Q factor is usually due to large losses.
Read more about this topic: Optical Ring Resonators
Famous quotes containing the word theory:
“The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.”
—Giuseppe Mazzini (1805–1872)
“The theory seems to be that so long as a man is a failure he is one of God’s chillun, but that as soon as he has any luck he owes it to the Devil.”
—H.L. (Henry Lewis)
“There is in him, hidden deep-down, a great instinctive artist, and hence the makings of an aristocrat. In his muddled way, held back by the manacles of his race and time, and his steps made uncertain by a guiding theory which too often eludes his own comprehension, he yet manages to produce works of unquestionable beauty and authority, and to interpret life in a manner that is poignant and illuminating.”
—H.L. (Henry Lewis)