Scanning Fabry-Perot interferometer

A scanning Fabry-Perot interferometer is a two-mirror Fabry-Perot resonator used as a tunable filter of very narrow passband. One mirror sits on a piezo actuator; a voltage ramp changes the mirror spacing by a fraction of a wavelength, the cavity's resonances sweep through the laser's spectrum, and a photodiode behind the cavity records a transmitted peak each time a resonance crosses a spectral line. On an oscilloscope triggered by the ramp, the trace is the laser's spectrum, with a resolution commonly between a few hundred kilohertz and some tens of megahertz. A confocal instrument 5.0 cm long has a free spectral range of 1.5 GHz; with a finesse of 200 it resolves 7.5 MHz, which is 0.06 pm at 1550 nm.

Free spectral range and resolution

The comb of transmission peaks repeats every free spectral range. For a plane-parallel cavity of length $L$ in air,

$$\mathrm{FSR} = \frac{c}{2L},$$

which is 99.9 GHz for $L$ = 1.5 mm. Most scanning instruments are confocal, with two spherical mirrors separated by their radius of curvature. In that geometry a ray entering off axis closes on itself only after four mirror-to-mirror passes, and all transverse modes fall onto a comb with half the plane-cavity spacing:

$$\mathrm{FSR}_\text{conf} = \frac{c}{4L}$$

so a 7.5 cm confocal cavity has an FSR of 1.0 GHz. (A beam exactly mode-matched to TEM₀₀ shows only the $c/2L$ peaks, but the $c/4L$ comb is what normal use shows.) The resolution is the width of one transmission peak, set by the finesse $\mathcal{F}$:

$$\delta\nu = \frac{\mathrm{FSR}}{\mathcal{F}}$$

For 1.5 GHz and $\mathcal{F}$ = 200 this is 7.5 MHz. Scanning one full FSR takes a mirror displacement of $\lambda/4$ in a confocal cavity, 158 nm at 633 nm, and $\lambda/2$ in a plane cavity, so a modest piezo travel covers several orders.

Use in the laboratory

The instrument shows directly what a grating optical spectrum analyzer cannot resolve. A 0.02 nm OSA bandwidth is 2.5 GHz at 1550 nm. A 30 cm helium-neon laser has longitudinal modes 500 MHz apart, and a 1.5 GHz interferometer displays up to three of them per order as separate peaks. Typical checks are:

• whether a laser runs on one mode, and the ratio of the strongest side mode to the main mode, a direct reading of the side-mode suppression ratio down to the noise floor of the detector;
• mode hops during a current or temperature sweep, which appear as a peak jumping to a new position or two peaks alternating;
• transverse modes in a laser that should run on TEM₀₀, visible as extra peaks between the longitudinal ones;
• the linewidth of a broad source, when that linewidth is well above the instrument resolution.

The frequency axis is calibrated on the trace itself: two successive transmission orders of the same line are one FSR apart, and the piezo's nonlinearity and hysteresis make this local calibration more reliable than a volts-to-hertz factor. For absolute wavelength the instrument is paired with a wavemeter, since a scanning interferometer measures frequency differences only.

Pitfalls

Aliasing. The display repeats every FSR, so a spectrum wider than one FSR folds onto itself. A 300 µm diode laser chip with modes 139 GHz apart, viewed on a 1.5 GHz instrument, shows adjacent modes offset by 0.67 FSR from each other. The FSR must exceed the full width of the spectrum, so a multimode spectrum like this one is first measured on a grating OSA, and the scanning interferometer is used to examine single modes.

Mode matching. A plane cavity, or a confocal cavity whose length is off the confocal point, transmits the input beam's higher-order transverse components at frequencies of their own, adding spurious peaks. A confocal cavity tolerates poor mode matching because all transverse modes fall on its $c/4L$ comb, which is the reason the geometry is preferred; the spacing must still be set accurately, and a plane cavity needs a properly matched beam.

Feedback. At normal incidence the input mirror reflects most of the beam straight back toward the laser, and the reflected power changes sharply as each resonance is crossed. In a semiconductor laser this feedback can itself cause the mode hops under investigation. An optical isolator or a slight tilt of the cavity axis prevents it.

Scan speed. The field in the cavity builds up over the photon lifetime, $1/(2\pi\,\delta\nu)$, 21 ns for a 7.5 MHz resonance. A ramp that sweeps across a resonance in a time comparable to this distorts and broadens the peaks.

Common questions

What is the difference between a scanning Fabry-Perot and an etalon?

Both are Fabry-Perot cavities. An etalon is usually a fixed plate used as a filter or frequency reference, tuned if at all by angle or temperature; a scanning interferometer is built for a swept spacing and serves as a spectrum analyzer for one laser.

Can it measure the linewidth of a DFB laser?

Usually not. A DFB laser with a linewidth near 1 MHz sits below a 7.5 MHz resolution, and the trace shows the instrument function. Narrow lines are measured by self-heterodyne or heterodyne methods.

References: M. Hercher, "The spherical mirror Fabry-Perot interferometer," Appl. Opt. 7, 951 (1968); A. E. Siegman, Lasers (University Science Books, 1986); M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).