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:
“Many people have an oversimplified picture of bonding that could be called the “epoxy” theory of relationships...if you don’t get properly “glued” to your babies at exactly the right time, which only occurs very soon after birth, then you will have missed your chance.”
—Pamela Patrick Novotny (20th century)
“Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.”
—Willard Van Orman Quine (b. 1908)
“The theory [before the twentieth century] ... was that all the jobs in the world belonged by right to men, and that only men were by nature entitled to wages. If a woman earned money, outside domestic service, it was because some misfortune had deprived her of masculine protection.”
—Rheta Childe Dorr (1866–1948)