Etalon

An etalon is a Fabry-Perot interferometer formed by two parallel partially-reflective surfaces (often integrated as a single solid glass plate with reflective coatings on each face). Light enters one face, multiply-reflects between the two surfaces, and exits the other face. Only wavelengths satisfying the round-trip phase condition are transmitted efficiently; other wavelengths are largely reflected.

Operating principle. The transmission $T(\nu)$ as a function of frequency is the Airy distribution:

$$T(\nu) \;=\; \frac{(1 - R)^2}{(1 - R)^2 + 4 R \sin^2(\phi/2)}, \quad \phi \;=\; \frac{4 \pi n d \cos\theta}{\lambda},$$

where $R$ is the mirror power reflectivity, $n$ is the etalon refractive index, $d$ is the spacing, $\theta$ is the angle inside the etalon, and $\lambda$ is the vacuum wavelength.

Transmission is maximum (= 1) when $\phi$ is an integer multiple of $2\pi$, and minimum when $\phi$ is an odd multiple of $\pi$.

Free spectral range and finesse. The frequency spacing between adjacent transmission peaks is the free spectral range:

$$\Delta\nu_\text{FSR} \;=\; \frac{c}{2 n d \cos\theta}.$$

The width of each transmission peak (FWHM) is:

$$\Delta\nu \;=\; \frac{\Delta\nu_\text{FSR}}{F}, \quad F \;=\; \frac{\pi \sqrt{R}}{1 - R},$$

where $F$ is the finesse. High-finesse etalons have narrow transmission peaks and broad transmission gaps.

Standard etalon types.

Type	Construction	Typical FSR	Typical finesse
Solid glass etalon	Single glass plate, coated faces	1 – 100 GHz	30 – 200
Air-spaced (mirrors with spacer)	Two mirrors + invar spacer	100 MHz – 30 GHz	50 – 10000
Fiber etalon	Two cleaved fiber tips facing each other	1 GHz – 1 THz	10 – 1000
Ring resonator etalon	On-chip microring	100 GHz – 1 THz	1000 – 100000
Confocal etalon	Two spherical mirrors at confocal spacing	various	100 – 10000

Applications.

1. Narrowband optical filters: pass only specific wavelengths; reject all others. Used in:

   • Wavelength-division multiplexing receivers
   • Astronomical instruments (selecting specific atomic lines)
   • Atmospheric and Raman spectroscopy
   • Solar telescopes (selecting H-alpha line)

2. Wavelength references: etalon transmission peaks at ITU grid wavelengths serve as fixed-frequency markers for locking tunable lasers. A 50 GHz FSR etalon provides a ITU 50 GHz grid reference.

3. Intracavity laser tuning: inserting an etalon into a laser cavity restricts oscillation to specific frequencies, enabling single-longitudinal-mode operation in lasers that otherwise lase multimode.

4. Frequency discriminators: the steep transmission edge of an etalon converts frequency changes into intensity changes, enabling fast frequency-error signal generation for laser stabilization.

5. Spectrum analyzers: a scanning etalon (Fabry-Perot interferometer) can resolve laser linewidth and longitudinal-mode structure with very high resolution (well below the resolution of a typical OSA).

Solid glass etalons in detail. The most common laboratory etalon: a polished glass plate with $\sim 30\%$ reflectivity coatings on both faces. Typical specifications:

Parameter	Typical value
Material	Fused silica or BK7
Thickness	0.5 – 50 mm
Surface flatness	$\lambda/100$ at 633 nm
Surface parallelism	1 – 10 arcsec
FSR	$c/(2nd) = 75/d_{[\text{mm}]} \cdot n^{-1}$ GHz for solid silica
Coating reflectivity	30% (low finesse) to 99% (high finesse)
Finesse	5 – 200
Temperature sensitivity	$\sim 1$ GHz/K (silica)

Air-spaced etalons. Higher-stability applications use Invar or ULE (ultra-low expansion) spacers separating two precision-polished mirrors. These offer:

• Adjustable spacing (via heat or piezo) for tunable filter applications
• Higher temperature stability
• Higher achievable finesse (up to $10^4$)
• Lower bulk material absorption

Standard examples: laser frequency-stabilization cavities for atomic-clock applications, ULE-spaced reference cavities used by the SI second's optical-clock implementations.

On-chip etalons (ring resonators). Silicon photonic microring resonators are 2D-confined etalons whose finesse can exceed $10^5$. Used for:

• Add-drop wavelength filters
• WDM channel multiplexing
• Microring modulators
• Optical sensors (refractive index, biosensing)
• Frequency comb generators

Etalon distortion (parallelism). Imperfect surface parallelism degrades finesse — the device acts as a continuum of slightly different etalons across its aperture. Standard fabrication tolerance is $< 1$ arcsec parallelism for high-finesse devices.

Etalon ghosts in laser systems. Stray reflections between parallel surfaces in a laser path can form an unintended etalon, creating fringes in the laser intensity vs wavelength. Common sources: input/output windows of cuvettes, parallel-faced detectors, BS surfaces. The standard fix is to slightly wedge the surfaces (1 – 5° angle) to prevent forming a finite-aperture etalon.

Distinguishing etalon from Fabry-Perot resonator. "Etalon" typically refers to a passive filter or measurement device; "Fabry-Perot" can refer to either an active laser cavity or a passive etalon. The mathematics is identical; the names reflect historical and applied-physics convention rather than physical distinction.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 11 (Fabry-Perot resonators and etalons); Hecht, Optics (5th ed., 2017), Ch. 9 for the standard treatment; Born & Wolf, Principles of Optics (7th ed., 1999), Ch. 7.