LightMachinery fabricates the finest solid and air spaced etalons in the world, including Gire Tournois etalons, piezo tunable etalons, air spaced etalons, and solid etalons.
The company’s fluid jet polishing systems, enabling routine fabrication of surfaces with better than lambda/100 peak to valley. LightMachinery has the ability to fabricate and test all types of Fabry Perot etalons, ranging from 1 mm square to 100 mm in diameter.
These devices need extreme parallelism, superior quality, flat optical surfaces for achieving high performance. The polishing and metrology capabilities at LightMachinery can help to fabricate such devices with these desired qualities. A range of materials, including silicon, fused silica and even air, can be used to fabricate etalons.
Some Background on Fabry Perot Etalons
The Fabry Perot interferometer comprises two parallel flat semi-transparent mirrors that are separated by a constant distance. Light entering the etalon is reflected off multiple times, and a modulation is caused in the transmitted and reflected beams by the interference of the light from the etalon during each bounce. The phase changes by 2Ðx2ndCOS(θ)/λ during one return bounce, where θ = Angle of the beam in the etalon. Constructive and destructive interference occurs based on the angle of the beam (θ), the wavelength (λ), and the optical thickness of the etalon (nd).
An etalon’s transmission spectrum consists of a series of peaks, where constructive interference takes place, spaced by the 'free spectral range' or FSR. As observed on the online etalon designer (Figure 1), an etalon’s reflection spectrum is 1 – T if the scattering and absorption losses are small.
- FSR = 1/2nd cm-1 (wave number)
- FSR = λ2/2nd nm (wavelength)
- FSR = c/2nd Hz (frequency)
Figure 1. Online etalon calculator
The above equations do not include the mirror reflectivity, which does not influence the FSR, but influences the number of bounces and optimizes the quality of the modulation, for instance, the modulation will be better if more bounces are perfect.
The increase in mirror reflectivity makes the modulation peaks sharper with reduced width. The full width at half maximum of the peaks is referred to as the bandwidth, and the ratio between the line width and the distance between the peaks (the FSR) is termed the Finesse, F. The Bandwidth = FSR /F. And the finesse is the ratio between the FSR and the Bandwdth, F = FSR / Bandwidth.
- Bandwidth is the full width at half maximum (FWHM) of the peak
- Bandwidth = FSR / F
The finesse is a parameter with no unit and the Bandwidth has the same units of the FSR.
The Coefficient of Finesse, F is expressed as 4R/(1-R)^2, whereas the etalon’s maximum reflectivity is expressed as Rmax = 4R/(1+R)^2. The following equation relates the finesse and the Coefficient of Finesse: F=PI/(2arcsin(1/SQRT(F))). It is possible to approximate this equation to F=(PI/SQRT(F))/2 or F=PI/SQRT(4R/(1-R)^2).
Actual versus Theoretical Performance
Etalons are normally explained in terms of FSR and finesse. In many publications, the reflectivity of the mirrors (R) is only used to compute the finesse by applying the equation F=PI/SQRT(4R/(1-R)^2). No losses are assumed for the etalon, like imperfect or scatter surface flatness. The peak transmission of a perfect etalon without imperfections or losses will always be 100%.
Limits to Finesse
The finesse and transmission are limited by factors such as coating scatter, parallelism, and surface irregularity. The finesse is limited by the contributions made by each one of the factors and all these contributions come together as the expected transmission and finesse. In Figure 1, the chart describes both the perfect theoretical transmission and the anticipated transmission by considering all the imperfections in a real etalon.
The surface figure is the rms difference of the surface away from flat. The spherical error is not included in the rms surface figure and is considered separately.
The surface figure is typically measured at 633 nm (the HeNe laser wavelength) and is described as fractions of this wavelength. The numbers included in the calculator are examples of practical values such as 633/20 = 30 nm and values that are hard to achieve, 633/200 = 3 nm.
Tilt or Wedge
A change in the phase of the beam is caused across the etalon by the non-parallel end mirrors, resulting in reduced finesse, because not all of the beam is emerging 'in phase' forming a bright fringe or 'out of phase' forming a dark fringe. This leads to a low contrast mixing of bright and dark fringes (Figure 2).
The same is applicable for spherical error as the phase of the light modulates over the etalon surface because of surface curvature.
The errors induced by sphere and wedge are predictable and it is possible to calculate them in specific ways. This is the reason they have been considered in LightMachinery’s calculations for expected performance.
Scatter and Material Losses
The light is leaked out of the etalon due to scatter, but the light will be absorbed by the materials during each pass. These losses are generally trivial if the appropriate materials and coatings are utilized unless having a very high finesse (more than 200).
The parameters that influence the finesse also limits it to some value. For example, the finesse of an etalon is limited to 6 when the mirror reflectivity is 60%. Similarly, all of the different imperfections limit the finesse to a certain level and these limits can be explored using LightMachinery’s etalon calculator.
Etalons are usually specified by FSR, finesse, transmission, wavelength range, and clear aperture, which are measurable functional specifications. The mirror reflectivity is typically not part of the specifications as it does not guarantee performance.
Finesse and transmission can be considerably reduced below the finesse that would be normally expected from a specific reflectivity by tilt, surface errors, and scatter.
Air Spaced versus Solid Etalons
Solid etalons (Figure 3) are simple optical components that are flat and very parallel. Sometimes, the etalon effect is provided by using these etalons in an uncoated condition using only the 4% fresnel reflection.
Uncoated etalons show high damage resistance and are typically used within laser cavities because low finesse is needed to filter out unwanted laser wavelengths. The finesse of a solid etalon can be typically increased by applying a coating over it. The same coating is used to coat both of the sides.
Fused silica, a homogenous and extremely pure material, is often used to make solid etalons. The simple yet robust solid etalons are susceptible to two forms of temperature instability. The physical thickness and the index of the etalon material modify with temperature.
This temperature instability is prohibitive in certain applications. This temperature instability can also be helpful in tuning the transmission peak position as it effectively alters the etalon thickness.
Figure 3. Solid etalons
Air Spaced Etalons
The temperature instability problem is less in air spaced etalons (Figure 4), where air is used as the etalon medium to considerably lower the change in the refractive index with respect to temperature.
Spacers made by fused silica or by high stability materials, such as Zerodur or ULE help to determine the mirror spacing. However, air spaced etalons are a more complex device due to the involvement of three components - the spacer and the two end mirrors.
It is necessary to wedge and AR coat the exterior surfaces of the end mirrors to eliminate reflections from these surfaces, resulting in unwanted etalon effects.
Figure 4. Air spaced etalons
Etalons can be tuned by many different methods: changing the index of the medium (electrostatic, temperature, pressure), moving the mirrors, and tilting the entire etalon.
The simple tuning technique is tilt tuning. There is a change in the FSR with respect to the cosine of the angle upon titling an etalon. The term "tunable etalon" (Figure 5) typically represents the piezoelectric tuning of an air spaced etalon.
Using this method, the etalon can be rapidly tuned by changing the air gap size. The transmission peak reaches one full FSR when the length of the air gap is changed by half the light wavelength. Therefore, if an etalon is utilized at 532 nm, then it can be tuned using only 266 nm of motion.
The movement of small piezo elements is easy through 10 µm. A single hollow tube piezo stack can be used to make small tunable piezo etalons, which are standard products for LightMachinery and have 4 mm clear aperture.
Three piezo elements are used to make larger piezo tunable etalons (Figure 6). Subtle tuning of the piezo elements to avoid any residual tilt error between the two mirrors and enhance the finesse is a key advantage of larger piezo tunable etalons, despite the complexity in controlling them.
Figure 5. A tunable Fabry Perot uses piezoelectric cylinders to adjust the size of the air gap and sweep the peaks of the etalon.
Figure 6. A giant 60 mm aperture piezo tunable Fizeau interferometer. End plates are matched to lambda/100 over the full aperture. This instrument uses the same method of 3 piezo stacks to allow the end mirror to be trimmed for perfect alignment and then the FSR can tuned or scanned through 9 µm of movement.
This information has been sourced, reviewed and adapted from materials provided by Bruker Nano Surfaces.
For more information on this source, please visit Bruker Nano Surfaces.