External cavity laser (ECL)

An external cavity laser (ECL) is a semiconductor laser whose cavity is completed outside the chip. One facet of the gain chip is anti-reflection coated so that the chip cannot lase by itself; a lens collimates the light leaving that facet onto a wavelength-selective reflector, a diffraction grating in free-space designs or ring resonators on a silicon or silicon nitride chip in integrated ones, and the reflector returns a narrow band of wavelengths into the chip. Most of the round trip lies outside the gain medium, so the linewidth is far narrower than a solitary chip's: computed with the Schawlow–Townes formula, a 1 mm gain chip with 20 mm of air in its cavity has an intrinsic linewidth of about 6 kHz at 10 mW, against 3.7 MHz for a 300 µm cleaved chip. And moving the filter tunes the laser across the width of the chip's gain spectrum, tens of nanometers, which makes ECLs common sources for swept-wavelength measurements, spectroscopy and coherent optical systems.

How the external cavity narrows the line

The Schawlow–Townes linewidth grows as the square of the cold-cavity linewidth, which is set by the photon lifetime, and for a given loss per round trip the photon lifetime is proportional to the round-trip time. An external section therefore narrows the line by the square of the factor by which it lengthens the round trip:

$$\frac{\mathrm{\Delta }{\nu }_{\text{ECL}}}{\mathrm{\Delta }{\nu }_{\text{chip}}}\approx \frac{1}{F^2},F=1+\frac{n_{\text{ext}}{L}_{\text{ext}}}{n_g{L}_{\text{chip}}},$$

where $n_g{L}_{\text{chip}}$ is the optical length of the gain chip and $n_{\text{ext}}{L}_{\text{ext}}$ that of the external section. A 1 mm chip with a group index of 3.6 and 20 mm of air give $F=6.6$, a factor of 43 in linewidth. Frequency-selective feedback adds a second effect through the linewidth enhancement factor $\alpha$. When the laser runs on the long-wavelength side of the filter peak, where the feedback grows with frequency, a fluctuation that raises the frequency also lowers the cavity loss; the carrier density needed for threshold falls, and through $\alpha$ the frequency is pulled back. Kazarinov and Henry derived the general result, which also covers the extra delay that a resonant filter such as a ring adds to the round trip.

Computed with the chip parameters of the Schawlow–Townes linewidth entry (internal loss 10 cm⁻¹, group index 3.6, $n_{\text{sp}}$ = 1.6, $\alpha$ = 4) at 1550 nm and 10 mW of output:

In the ECL the chip's back facet reflects 90%, the grating and lens return 20% of the light reaching the grating into the chip, and 70% leaves as the output. The linewidth a measurement shows is wider than the intrinsic value and grows with the observation time, because changes in the length of the cavity move the frequency, as described below; How to measure laser linewidth covers the methods suited to kilohertz lasers.

Free-space designs

In the Littrow arrangement the grating is turned so that its first diffraction order returns along the incoming beam into the chip, and the zeroth order, the specular reflection, is the output. The returned wavelength obeys $\lambda =2d\sin \theta$: a 600 line/mm grating sits at 27.71° for 1550 nm, and tuning from 1520 to 1570 nm turns it by 0.97°. The output beam swings through twice that angle, 1.94°, unless a mirror fixed parallel to the grating on the same rotating arm turns it back, which leaves only a small sideways shift (Hawthorn and colleagues). The grating is selective only to a degree: the returned beam re-enters the chip only while its angle stays within the divergence of the chip's mode, which for a 3 mm collimated beam on this grating limits the feedback to a band about 0.8 nm (100 GHz) wide at 1550 nm. That band spans about 16 longitudinal modes of the example cavity, whose optical length of 23.6 mm spaces them 6.35 GHz apart, and the laser runs on the mode nearest the peak, whose feedback is about 1% stronger than its neighbors'.

In the Littman–Metcalf arrangement the beam meets the grating at grazing incidence, and the first order goes to a tuning mirror that sends it back to the grating and into the chip. The light is diffracted twice per round trip, which narrows the feedback band, and the output, the grating's zeroth order, leaves in a fixed direction while the mirror is turned to tune. The cost is output power, since the zeroth order of the second diffraction leaves the cavity unused.

Either arrangement tunes without mode hops only if the cavity length changes in proportion to the wavelength, so that the number of half-wavelengths in the cavity stays the same. Turning the grating or mirror about the right axis does this: the line where the plane of the grating surface (in the Littman–Metcalf case, also the plane of the mirror) meets the plane of the cavity's rear mirror, the chip's back facet taken at its optical distance. Liu and Littman described this geometry for the Littman–Metcalf laser, and the same rule holds in Littrow, once the phase of the grooves the beam crosses is counted with the path length. About any other axis the filter and the cavity modes move at different rates, and the laser hops to the next mode, 6.35 GHz away in the example, each time the filter peak moves by about one mode spacing.

The chip itself limits smooth tuning. Residual reflection from its coated facet forms a short cavity of its own, with modes 0.33 nm apart for a 1 mm chip, and a facet reflectance of ${10}^{-4}$ against the 20% returned from the grating still modulates the feedback by ±4.5% with that period, several times the 1% that separates neighboring modes at the grating peak. Gain chips for ECLs therefore combine the coating with a waveguide that meets the facet at an angle, as in semiconductor optical amplifiers.

Integrated designs

An integrated ECL replaces the lens and grating with a photonic circuit: the gain chip is butt-coupled or bonded to a silicon or silicon nitride chip that carries the filter, a phase section and a reflector (heterogeneous integration). The filter is usually a pair of ring resonators of slightly different circumference, whose transmission peaks coincide only at widely spaced wavelengths, the Vernier effect. For silicon rings of 20 and 22 µm radius, taking the straight-waveguide group index of 4.18, the free spectral ranges are 4.57 and 4.16 nm and the peaks coincide every 46 nm, more than the width of the C-band; heating the larger ring enough to shift its resonances by 0.42 nm moves the coincidence, and with it the lasing wavelength, by one free spectral range of the smaller ring, 4.57 nm. Near resonance a ring also delays the light, which lengthens the effective cavity and narrows the line as a longer external section would. With long, low-loss silicon nitride feedback circuits, hybrid lasers have reached an intrinsic linewidth of 40 Hz (Fan and colleagues). Self-injection locking to a high-Q resonator is a related way of narrowing a diode laser, using light scattered back from the resonator instead of a closed external cavity.

Stability

The frequency of a cavity mode follows the cavity's optical length, $\mathrm{\Delta }\nu \mathrm{/}\nu =-\mathrm{\Delta }L\mathrm{/}L$. In the 23.6 mm example, a change of 0.12 nm in length moves the frequency by 1 MHz, and half a wavelength, 0.78 µm, moves it by a whole mode spacing. A 20 mm air path on an aluminum base expands by 0.46 µm per kelvin, so the frequency drifts by 3.8 GHz per kelvin until the laser hops; on invar the drift is 0.20 GHz per kelvin. Free-space ECLs are therefore built on temperature-controlled bases of low expansion, enclosed against air currents and sound, and tuned finely by a piezoelectric actuator that moves the grating or mirror. Vibration of nanometers becomes frequency noise of megahertz, which is why the measured linewidth depends on the observation time. The temperature and current of the chip also change the optical length, through its refractive index. Integrated ECLs have no moving parts and are far less sensitive to vibration, but drift with temperature through the refractive index of their waveguides.

Compared with a DFB laser

A DFB laser selects its wavelength with a grating along the gain region. It is small, robust and inexpensive, has a linewidth of 1 to 10 MHz and tunes through its temperature, by about 0.09 nm/K at 1550 nm (wavelength temperature coefficient), over a few nanometers. An ECL tunes over tens of nanometers with a far narrower linewidth, in exchange for a larger package, a cavity whose length has to be held to a fraction of a nanometer, and slower tuning where the filter moves mechanically. Transmitters for intensity-modulated links use DFB lasers; ECLs serve test and measurement, coherent detection, FMCW lidar, and spectroscopy and atomic physics, the use reviewed by Wieman and Hollberg, where the linewidth and the tuning range matter more. Monolithic widely tunable lasers, such as the sampled-grating DBR laser, sit between the two, and the tunable laser entry compares the architectures.

The Diffraction Grating Calculator gives the Littrow angle and the angular dispersion of the grating for any groove density, wavelength and order.

Common questions

What is an external cavity laser?

A semiconductor laser whose cavity is closed by a reflector outside the chip, usually a diffraction grating or ring resonators on a separate chip, which also selects the wavelength. The gain chip's inner facet is anti-reflection coated so that it cannot lase on its own.

Why does an external cavity laser have a narrow linewidth?

Because most of each round trip is spent in the passive external section. The photon lifetime grows in proportion to the round-trip time and the Schawlow–Townes linewidth falls as its square, so 20 mm of air added to a 1 mm chip narrows the line about 43-fold for the same loss per round trip.

What is the difference between a Littrow and a Littman–Metcalf laser?

In a Littrow laser the grating returns its first order straight to the chip, and the output beam moves as the grating turns. In a Littman–Metcalf laser the light meets the grating at grazing incidence and returns through a tuning mirror, so it is diffracted twice per round trip; the feedback band is narrower and the output direction fixed, at some cost in output power.

What is mode-hop-free tuning?

Tuning in which the laser stays on the same longitudinal mode, so that its frequency changes continuously. The cavity length has to change in proportion to the wavelength, which a grating or mirror turning about the correct pivot achieves.

References: R. F. Kazarinov and C. H. Henry, "The relation of line narrowing and chirp reduction resulting from the coupling of a semiconductor laser to a passive resonator," IEEE Journal of Quantum Electronics 23, 1401 (1987). M. G. Littman and H. J. Metcalf, "Spectrally narrow pulsed dye laser without beam expander," Applied Optics 17, 2224 (1978). K. Liu and M. G. Littman, "Novel geometry for single-mode scanning of tunable lasers," Optics Letters 6, 117 (1981). C. J. Hawthorn, K. P. Weber, and R. E. Scholten, "Littrow configuration tunable external cavity diode laser with fixed direction output beam," Review of Scientific Instruments 72, 4477 (2001). C. E. Wieman and L. Hollberg, "Using diode lasers for atomic physics," Review of Scientific Instruments 62, 1 (1991). Y. Fan et al., "Hybrid integrated InP-Si3N4 diode laser with a 40-Hz intrinsic linewidth," Optics Express 28, 21713 (2020).