Fabry-Perot laser

A Fabry-Perot laser is the simplest form of edge-emitting laser: a waveguide containing the gain region, closed at each end by a cleaved semiconductor facet. The facets reflect about 0.3 of the guided light (the plane-wave Fresnel value is 0.27 for an index of 3.2 and 0.31 for 3.5), which a gain medium of a few hundred micrometers can easily overcome. Because nothing in the cavity prefers one wavelength over its neighbors, the laser oscillates on every longitudinal mode whose gain reaches threshold. A typical InP-based Fabry-Perot chip at 1310 nm, 300 µm long, shows modes 0.79 nm apart under an envelope a few nanometers wide, so several modes carry most of the power. The cavity is the Fabry-Perot resonator of classical optics with gain inside.

Mode spacing

Adjacent longitudinal modes differ by one in the number of wavelengths that fit into a round trip, so their spacing is set by the group index $n_g$ and the cavity length $L$:

$$\Delta\lambda = \frac{\lambda^2}{2 n_g L}, \qquad \Delta\nu = \frac{c}{2 n_g L}.$$

For $L = 300$ µm and $n_g = 3.6$, $\Delta\nu = 139$ GHz, which is $\Delta\lambda = 0.79$ nm at 1310 nm and 1.11 nm at 1550 nm; the round-trip time is 7.2 ps. The longitudinal mode spacing entry tabulates other lengths. A 5 nm wide envelope at 1310 nm therefore spans about six modes.

The spectrum and its behavior

The modes sit under the gain spectrum of the active region, and the strongest lies near the gain peak. As current and temperature change, the gain peak moves with the bandgap, about five times faster than the individual modes move with the refractive index, so the dominant mode jumps from one mode to the next in a series of mode hops; the wavelength temperature coefficient entry gives the two rates. The output is therefore described by a center wavelength and an RMS spectral width, a few nanometers for telecom chips, rather than by a single line.

Total power is steady, but the share in each mode fluctuates as the modes compete for the same carriers. This mode partition noise is invisible to a detector that collects all the modes. After a length of dispersive fiber the modes arrive at different times, and the fluctuating share then becomes amplitude noise in the received signal, which sets an error floor that more received power cannot remove and limits the product of bit rate and distance.

Threshold and output

The two facets act as distributed loss through the mirror loss $\alpha_m = (1/2L)\ln(1/R_1R_2)$, 40 cm⁻¹ for a 300 µm chip with $R = 0.3$ on both ends. With an internal loss of 10 cm⁻¹, threshold requires a modal gain of about 50 cm⁻¹. Uncoated chips emit equally from both facets; production devices usually put a high-reflection coating on the rear facet so that most of the power leaves through the front.

Below threshold the same cavity gives the standard gain measurement. The amplified spontaneous emission shows fringes at the mode positions, and their peak-to-valley ratio yields the net modal gain at each fringe (the Hakki-Paoli method). It needs the Fabry-Perot fringes of a cleaved chip, which is one reason test structures for new epitaxial material are cleaved Fabry-Perot bars.

Uses

The absence of a grating makes Fabry-Perot lasers the cheapest diode lasers to make. They are used where several modes do no harm: short-reach links at 1310 nm near the zero-dispersion wavelength of standard fiber, optical storage and pointer lasers, many high-power pump and industrial diodes (often stabilized in wavelength by an external fiber grating), and broad-area emitters. Where a single wavelength is needed, for dense WDM, for 1550 nm links of more than a few kilometers, or for sensing, the DFB laser replaces it, adding a grating that holds one mode with a side-mode suppression ratio of typically 35 dB or more.

Pitfalls

Spectrum analyzer resolution must be well below the mode spacing to see the individual modes and their partition; a 1 nm RBW smears a 0.79 nm comb into a smooth envelope. Feedback from fiber connectors couples readily into a cavity with uncoated facets and can lock or destabilize the modes.

Common questions

What is the difference between a Fabry-Perot laser and a DFB laser?

A Fabry-Perot laser has only facet mirrors and lases on several modes; a DFB laser has a grating along the cavity that provides wavelength-selective feedback and gives a single longitudinal mode. The DFB costs more and is needed where dispersion or wavelength channels matter.

Why does a Fabry-Perot laser have multiple modes?

The facet reflectivity is the same at every wavelength and the gain spectrum is tens of nanometers wide, much wider than the mode spacing, so several modes reach threshold with nearly equal gain.

Can a Fabry-Perot laser run single mode?

Some short cavities with narrow gain run predominantly on one mode under CW drive, but with low and unstable side-mode suppression; under modulation they return to multimode operation.

References: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012); G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993); B. W. Hakki and T. L. Paoli, "Gain spectra in GaAs double-heterostructure injection lasers," J. Appl. Phys. 46, 1299 (1975); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).