Wavemeter

A wavemeter reports the wavelength, frequency or wavenumber of a narrowband source, usually a laser, as a single number. It does this with an interferometer: the unknown beam and a reference of known wavelength produce fringes over the same path difference, and the ratio of fringe counts or fringe periods gives the ratio of wavelengths. Different models cover ranges from the ultraviolet to the mid-infrared, update from a few to thousands of times per second, and specify relative accuracies that range from about 10⁻⁶ to 10⁻⁸. At 1550 nm (193.4 THz), 10⁻⁶ is 193 MHz; at 632.99 nm, 10⁻⁸ is 4.7 MHz.

Designs

The scanning Michelson wavemeter, introduced in the 1970s, sends the unknown and the reference beam through the same two-arm interferometer while one arm is moved, typically by a cart on an air track or a corner cube on a flexure. Over a path change $\Delta L$, each beam produces $N = \Delta L/\lambda$ fringes, so

$$\lambda_x = \lambda_\mathrm{ref}\, \frac{N_\mathrm{ref}}{N_x} \,\frac{n(\lambda_x)}{n(\lambda_\mathrm{ref})},$$

where $n$ is the refractive index of the air in the arms. A 10 cm path change gives 158,024 fringes of a helium-neon laser at 632.816 nm (in air), so counting whole fringes alone resolves 6.3 × 10⁻⁶; phase interpolation of the final fringe improves this by one to two orders of magnitude. The traditional reference is a frequency-stabilized HeNe, whose vacuum wavelength is 632.991 nm (473.61 THz).

The Fizeau wavemeter has no moving parts. The beam illuminates one or more air-spaced or solid wedges, and a camera or linear array records the fringe pattern. The fringe period gives a coarse wavelength, and the fringe phase within a wedge of known thickness refines it; several wedges of increasing thickness, or a combination with a grating spectrometer, resolve the ambiguity of which order is being read. Fizeau instruments measure pulsed as well as continuous sources, since one exposure suffices, and the best are calibrated against an atomic line or a stabilized laser to reach the 10⁻⁷–10⁻⁸ range. Fabry-Perot designs based on an etalon of known spacing work the same way.

Air and units

Most wavemeters operate in air and correct internally to vacuum using an equation for the index of air, such as Edlén's or Ciddor's. For standard air, $n - 1$ is 2.77 × 10⁻⁴ at 633 nm and 2.73 × 10⁻⁴ at 1550 nm. Omitting the dispersion term in the formula above, when measuring 1550 nm against a HeNe, gives an error of 3.3 × 10⁻⁶, about 630 MHz. Wavelengths quoted in air and in vacuum differ by the relative amount $n - 1$, 0.175 nm for the HeNe line, so the reading must be labelled; frequency is unambiguous. Conversions between units are set out under wavelength, frequency and wavenumber. Near 1550 nm, 1 pm corresponds to 125 MHz; near 633 nm, to 748 MHz.

Where it is used

Wavemeters set and log the wavelength of tunable lasers for atomic and molecular spectroscopy, where a laser must be parked within tens of megahertz of a transition before a finer lock takes over. They detect mode hops, which appear as sudden jumps of one or more free spectral ranges of the laser cavity. Fast Fizeau instruments feed back to the laser directly, stabilizing it at the megahertz level for cold-atom and ion-trap work. In telecom test, a wavemeter checks the absolute channel frequency of DFB and tunable sources against the ITU grid more accurately than a grating optical spectrum analyzer can.

Pitfalls

A wavemeter assumes a single frequency. A laser running on two longitudinal modes produces a beat in the fringe visibility, and the instrument may report a weighted mean, an unstable value or an error. Some models include a coarse spectrometer or a visibility check to flag this, but a wavemeter does not replace a spectrum analyzer for judging mode content. Accuracy depends on calibration, which drifts with temperature and with the alignment of the input fiber; a periodic check against a known line keeps the stated accuracy meaningful. Multimode input fiber and speckle can shift the Fizeau fringe phase slightly, so manufacturers usually specify their best figures with single-mode fiber input. Resolution, the smallest change the display tracks, is often ten times finer than the absolute accuracy and should not be confused with it.

Common questions

What is the difference between a wavemeter and an optical spectrum analyzer?

A wavemeter measures the center frequency of a single-frequency source with high accuracy and does not show the spectrum. An optical spectrum analyzer displays the power spectrum with a resolution of tens of picometres and handles multimode or broadband light, with absolute wavelength accuracy from a few picometres after calibration to about 20 pm.

How accurate is a wavemeter compared with a frequency comb?

A frequency comb referenced to an atomic clock measures optical frequencies to 10⁻¹² and beyond, orders of magnitude better than any wavemeter. Wavemeters are used to identify which comb tooth a laser lies near, since a comb measurement alone is ambiguous by multiples of the repetition rate.

References: J. L. Hall and S. A. Lee, Interferometric real-time display of cw dye laser wavelength with sub-Doppler accuracy, Appl. Phys. Lett. 29, 367 (1976); B. Edlén, The refractive index of air, Metrologia 2, 71 (1966); P. E. Ciddor, Refractive index of air: new equations for the visible and near infrared, Appl. Opt. 35, 1566 (1996); E. Hecht, Optics 5th ed. (Pearson, 2017).