LightMachinery manufactures the world's finest solid and air spaced etalons. One of the challenges in working with etalons is specifying the important parameters. Our Etalon Calculator is a big help but so is an understanding of the theory of the etalon.
The Fabry Perot interferometer consists of two parallel flat semi-transparent mirrors separated by a fixed distance. This arrangement is called an etalon. " (Fabry and Perot, 1897) Light that enters the etalon undergoes multiple reflections and the interference of the light emerging from the etalon during each bounce causes a modulation in the transmitted and reflected beams.
The transmission spectrum of an etalon will have a series of peaks spaced by the free spectral range. The width of each transmission peak decreases for higher finesse etalons; in fact, the finesse is defined as the ratio of the free spectral range to the full width half max. of the transmission peaks. If the absorption and scattering losses are small, the reflection spectrum of the etalon is 1 - T.
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Symbols used in the equations
n = Index of refraction of the etalon medium
λ = central wavelength of interest
R = Reflectivity of each surface of the etalon (assumed to be the same)
d = thickness of the etalon
θ = angle of the beam inside the etalon
C = Speed of Light
ƒ = Finesse
F = Coefficient of finesse
As the beam travels though the etalon the phase of the wave changes. During one bounce the phase changes by (2π/λ)2ndCOS(θ)
The Free Spectral Range can be calculated in several different types of units.
- Free Spectral Range, FSR = 1 / 2nd 1/cm
- or in Wavelength space, FSR = λ2 / 2nd nm
- or in Frequency space , FSR = C / 2nd / λ Hz
Bandwidth is the Full width at hald maximum of the peak
Bandwidth = FSR / ƒ
The Finesse, ƒ, is the ratio of the FSR to the Bandwdth, ƒ = FSR / Bandwidth
The finesse is a dimensionless quantity and the units of the Bandwidth are the same as the FSR.
The Coefficient of Finesse, F = 4R/(1-R)2 and the maximum reflectivity of the etalon is Rmax = 4R/(1+R)2
The Coeficient of Finesse and the finesse are related by the equation ƒ=PI/(2arcsin(1/F1/2))
which can be approximated to ƒ=(PI/F1/2)/2
Actual versus Theorectical Performance
Etalons are usually described in terms of FSR and finesse. In many textbooks, the finesse is calculated using only the parameter R, reflectivity. The etalon is assumed to have no loses, like scatter or imperfect surface flatness. This is like our physics class questions that started by assuming "a mass is sliding down a frictionless incline..."
So a perfect etalon with no losses or imperfections always has 100% peak transmission and this is what many people expect. In reality there are other factors that 'limit' the transmission and finesse such as suface irregularity, parallelism, coating scatter. Each one makes a contribution to limiting the finesse and then all these contributions are combined to come up with the expected finesse and transmission. In our etalon calculator one of the curves is the perfect theoretical transmission and one is the expected transmision taking into account all the defects in a real etalon, such as;
- Surface Figure - Surface figure is usually measured at the HeNe wavlength , 633. The numbers that are included in the calculator are examples of practical values. 633/20 = 30nm difficult to achieve, 633/200 = 3nm really, really difficult to achieve, depending on the aperture. We include only these numbers to prevent people from entering unrealistic quality that cannot be achieved.
- Tilt - End mirrors that are not parallel cause different changes in the phase of the beam across the etalon. This results in reduced contrast since not all the beam is emerging 'in phase' creating a bright fringe or 'out of phase' creating a dark fringe. The result is a low contrast mixing of dark and bright fringes.
Click Here to link to our online Etalon Calculator
Specifying EtalonsEtalons are generally specified by FSR, minimum Finesse and minimum transmission. All of these specifications are measurable functional specifications. The reason that reflectivity is not generally specified is that the reflectivity does not guarantee performance. Scatter, surface errors and tilt can significantly reduce finesse and transmission below the finesse that would br expected from a given reflectivity. Other parameters that are also required in order to specify an etalon are clear aperture and physical size and cross sectional shape (round or square). In summary;
- Physical size ( x y or diamter)
- Clear Aperture
- wavelength(s) or wavelength range
Air Spaced versus Solid Etalons Solid etalons are simple flat, very parallel optical components. Sometimes these etalons are used uncoated using only the 4% fresnel refection to provide the etalon effect. One of our optical calculators, Reflectance versus Angle of Incidence, an excellent way to determine the fresnel reflection for a given material and wavelength. Uncoated etalons are often used inside laser cavities since only low finesse is required filter out unwanted laser wavelengths and uncoated etalons are very damage resistant. Generally solid etalons are coated to increase the finesse of the etalon. Both sides are coated with the same coating.
Solid etalons are generally made from Fused Silica. Solid etalons are robust, simple devices however they are prone to two forms of temperture instability. Both the index of the material and the physical thickness of the etalon material change with temperture. In certain applications this temperture instability is unacceptable. Air spaced etalons reduce this problem by using air as the etalon medium, this greatly reduces the change in index with temperture. The mirror spacing is now determined by spacers that may still be made from Fused Silica or by even more stable materials such as ULE or Zerodur. Air spaced etalons are significantly more complex since there are now three components involved, two end mirrors and the spacer. The outside surfaces of the end mirrors also need to be wedged and AR coated to avoid fresnel reflections from these surfaces changing the intereference pattern generated by the etalon.
3 Piezo Tunable Etalon with Controller
Large Air Spaced Etalon
Large Solid Etalons
Thin Small Solid Etalon
There are a number of ways to tune etalons including; Tilting the entire etalon, moving the mirrors and changing the index of the medium (pressure, temperature, electrostatic). Tilt tuning is a simple tuning technique. As the etalon is tilted the FSR changes with the cosine of the anlge. The output of the etalon is smeared by tilting since each successive bounce is moved laterally along the etalon. The other tuning techniques all maintain a plane parallel structure and simple change the effective length of the etalon. This is generally done by using a piezo electric spacer in an air spaced etalon. A single hollow tube piezo can be used small etalons such as the one pictured below.
Small Piezo Tunable Etalon
Combining Etalons and Laser Line Narrowing
From time to time a single etalon just can't do the job. This generally ocurrs when attempting to create a very high finesse etalon in order to have a very narrow peak and a large FSR. This is often the case when attempting to encourage a laser emit a single wavelength (laser line narrowing). Etalons can be combined in series and the transmission function of the combined etalons is simply the product of all the etalons in the chain. The product of three etalons with different FSR's and finesse's is shown below from another LightMachinery calculator , the Etalon Combiner Calculator on the LightMachinery website.
1. G. Hernandez (1986) 'Fabry-Perot Interferomters, Cambridge Studies in Modern optics', Cambridge University Press
2. Wikipedia - Fabry–Pérot interferometer