Quantum Cascade Laser (QCL)

1. Theory

Definition: A quantum cascade laser (QCL) is a unipolar semiconductor laser in which electrons emit photons by jumping between quantised conduction-band subbands (an intersubband transition) in a repeated stack of quantum wells, so no holes or interband recombination are involved.
Wavelength by design: The photon energy is the subband spacing, set mainly by the layer thicknesses and not by the bandgap, so one material system can cover a wide range of wavelengths, reported from about 2.6 $μ$ m to 250 $μ$ m in the mid-infrared and terahertz ranges.
Cascade: After emitting a photon in an active region the electron tunnels through an injector into the next period and can emit again, so the quantum efficiency per electron can exceed one.
Laser levels: Upper and lower subbands in coupled wells; the lower level is emptied by resonant longitudinal-optical-phonon emission (about 36 meV in GaAs) into a collector state, which gives a lower-level lifetime much shorter than the upper-level lifetime.
Transition type: Diagonal transitions lower the overlap of the two levels and favour inversion, vertical transitions raise the overlap and the gain; terahertz devices are based mainly on resonant-phonon depopulation.
Polarization: Only the field component normal to the layers couples to the transition, so the emission is TM polarised and the devices are edge emitters.
Materials: InGaAs/AlInAs on InP (the first QCL, 520 meV conduction-band offset, strain-balanced versions in the mid-infrared), GaAs/AlGaAs (first made in 1998, strongest in the terahertz range), and InAs/AlSb or InGaAs/AlAsSb for shorter wavelengths.

2. Working Principle

Biasing: Under bias the energy levels of the injector line up with the upper laser level of the next active region, so electrons are injected selectively into it.
Inversion: $Δ n_{s} = (J / e) τ_{u} (1 - τ_{l} / τ_{u l})$ ; it exists when the upper level scatters into the lower level more slowly than the lower level empties.
Gain: The modal gain $Γ g J$ is proportional to the current density, with $g$ falling as the temperature rises (in a calculated 9.3 $μ$ m device from 11.3 cm/kA at 77 K to 5.4 cm/kA at 300 K) because the transition broadens and the lifetimes shorten.
Threshold and output: $Γ g J_{t h} = α_{w} + α_{m}$ ; the optical power grows with the number of periods, for example 1.6 W continuous wave at room temperature and 2.7 W/A slope efficiency from a 40-period 4.6 $μ$ m device.
Mid-infrared performance: Room-temperature continuous-wave operation with more than 5 W and 21% wall-plug efficiency has been reported (2011).
Terahertz performance: Cooling is still needed; the reported maximum operating temperatures are 129 K continuous wave (2014) and 261 K pulsed (2022).
Spectrum control: Fabry-Perot devices are multimode at high current, while distributed-feedback and external-cavity versions are single mode and tunable.

3. Applications

Gas sensing and spectroscopy: Mid-infrared absorption spectroscopy of atmospheric gases and pollutants, security screening and medical breath analysis.
Photoacoustic sensing and free-space communication: High-power room-temperature devices in the 3-5 $μ$ m atmospheric window.
Infrared countermeasures: High-power mid-infrared sources.
Terahertz imaging and spectroscopy: Cryogenically cooled terahertz QCLs (research and development).

Name	Formula	Related Formulae	Variables/Constants
Emission wavelength of an intersubband transition	$λ = \frac{h c}{E _{u} - E _{l}}$	$E_{n} \approx \frac{ℏ ^{2} π ^{2} n ^{2}}{2 m ^{*} L _{z}^{2}}$ $E_{l} - E_{d} \approx ℏ ω_{L O}$	$λ : e mi ss i o n w a v e l e n g t h, se t b y t h e s p a c in g o f tw o co n d u c t i o n - ban d s u bban d s an d n o t b y t h e ban d g a p$ $E_{u}, E_{l} : e n er g i es o f t h e u pp er an d t h e l o w er l a ser s u bban d$ $E_{n} : s u bban d e n er g y o f an i so l a t e d in f ini t e l y d ee p w e l l o f w i d t h L_{z} (o n l y a r o ug h g u i d e, b ec a u se t h e l e v e l s o f a r e a l a c t i v e r e g i o n co m e f r o m se v er a l co u pl e d w e l l s an d f ini t e ba r r i er s)$ $m^{*} : e l ec t r o n e f f ec t i v e ma ss$ $E_{d} : e n er g y o f t h e l e v e l b e l o w t h e l o w er l a ser l e v e l in t o w hi c h i t i s e m pt i e d$ $ℏ ω_{L O} : l o n g i t u d ina l - o pt i c a l - p h o n o n e n er g y, ab o u t 36 m e V in G a A s an d 30 t o 40 m e V in I n G a A s (o n e 4.6 μ m d es i g n u ses 34 m e V), so t ha t t h e l o w er l e v e l i s e m pt i e d b y f a s t r eso nan t p h o n o n e mi ss i o n$
Population inversion and gain per unit current density	$Δ n_{s} = \frac{J}{e} τ_{u} (1 - \frac{τ _{l}}{τ _{u l}})$	$g_{m o d} = Γ g J$ $g = \frac{4 π e z _{u l}^{2} τ _{u} ( 1 - τ _{l} / τ _{u l} )}{ε _{0} n _{e f f} λ 2 γ _{u l} L _{p}}$	$Δ n_{s} : s h ee t d e n s i t y o f t h e p o p u l a t i o n in v er s i o n p er p er i o d (t h e e x p r ess i o n i s t h e f i r s t - or d er t h r ee - l e v e l r es u l t)$ $J : c u r r e n t d e n s i t y$ $e : e l ec t r o n c ha r g e$ $τ_{u} : t o t a l l i f e t im e o f t h e u pp er l a ser l e v e l$ $τ_{l} : l i f e t im e o f t h e l o w er l a ser l e v e l$ $τ_{u l} : sc a tt er in g t im e f r o m t h e u pp er t o t h e l o w er l a ser l e v e l (t h e in v er s i o n n ee d s τ_{u l} > τ_{l})$ $g_{m o d} : m o d a l g ain, p r o p or t i o na l t o t h e c u r r e n t d e n s i t y$ $g : g ain coe f f i c i e n t, u s u a l l y q u o t e d in c m / k A (a c a l c u l a t e d 9.3 μ m G a A s d e v i ce g i v es 11.3 c m / k A a t 77 K an d 5.4 c m / k A a t 300 K; t h e m o d a l v a l u e Γ g o f a 4.6 μ m I n P - ba se d d e v i ce i s 4.9 c m / k A)$ $Γ : co n f in e m e n t f a c t or o f t h e m o d e in t h e a c t i v e r e g i o n$ $z_{u l} : d i p o l e ma t r i x e l e m e n t o f t h e l a ser t r an s i t i o n$ $2 γ_{u l} : f u l l w i d t h a t ha l f ma x im u m o f t h e t r an s i t i o n (an e n er g y; in o n e d e v i ce 15 m e V a t 77 K an d 25 m e V a t 300 K)$ $n_{e f f}, ε_{0}, λ : e f f ec t i v e in d e x, p er mi tt i v i t y o f f r ee s p a ce, w a v e l e n g t h in v a c uu m$ $L_{p} : l e n g t h o f o n e p er i o d o f t h e c a sc a d e$
Threshold current density	$J_{t h} = \frac{α _{w} + α _{m}}{Γ g}$	$Γ g J_{t h} = α_{w} + α_{m}$ $α_{m} = \frac{1}{L} ln \frac{1}{R}$	$J_{t h} : t h r es h o l d c u r r e n t d e n s i t y$ $α_{w} : w a v e g u i d e l oss (3.3 c m^{- 1} in a 4.6 μ m d e v i ce an d 24 c m^{- 1} in t h e 9.3 μ m d e v i ce o f t h e r e f er e n ce ab o v e)$ $α_{m} : mi r r or l oss (t h e s am e e x p r ess i o n a s in t h e F ab r y - P er o t l a ser p a g e)$ $Γ, g : co n f in e m e n t f a c t or an d g ain coe f f i c i e n t$ $L, R : c a v i t y l e n g t h an d m e an p o w er r e f l ec t an ce o f t h e f a ce t s$
Output power and wall-plug efficiency	$P = \frac{h ν}{q} η_{i} \frac{N _{p} α _{m}}{α _{w} + α _{m}} (I - I_{t h})$	$η_{w p} = \frac{P}{I V}$	$P : o pt i c a l p o w er o u t o f t h e f a ce t s$ $h ν : p h o t o n e n er g y$ $N_{p} : n u mb er o f p er i o d s (s t a g es) o f t h e c a sc a d e, t y p i c a l l y ab o u t 30, an d 40 in o n e 4.6 μ m d es i g n (t h e s l o p e e f f i c i e n cy i s p r o p or t i o na l t o N_{p} b ec a u se e a c h e l ec t r o n c an e mi t a p h o t o n in e a c h p er i o d)$ $η_{i} : inj ec t i o n e f f i c i e n cy in t o t h e u pp er l a ser l e v e l$ $α_{m}, α_{w} : mi r r or an d w a v e g u i d e l osses$ $I, I_{t h} : c u r r e n t an d t h r es h o l d c u r r e n t$ $η_{w p} : w a l l - pl ug e f f i c i e n cy, w hi c h i s t h e r a t i o o f t h e o pt i c a l p o w er t o t h e e l ec t r i c a l p o w er I V (a 4.6 μ m d e v i ce g a v e 1.6 W co n t in u o u s w a v e w i t h 8.8 % a t 300 K in 2008; a l a t er r e p or t g i v es m or e t han 5 W w i t h 21 %)$

Important Questions

Ques: Why can the emission wavelength of a quantum cascade laser be chosen by the layer thicknesses, and why does this reach wavelengths that interband diode lasers cannot?

In an interband diode laser the photon energy is close to the bandgap, so the wavelength is fixed by the semiconductor composition. In a quantum cascade laser the electron does not cross the gap: it moves between two confined subbands of the conduction band, and their spacing is set by the width of the wells and the height of the barriers. A single material pair such as InGaAs/AlInAs on InP can therefore cover a wide range of mid-infrared wavelengths by changing the layer thicknesses, and in GaAs/AlGaAs the same principle reaches the terahertz range, where no bandgap-based laser exists. Reference: J. Faist, F. Capasso, D.L. Sivco, C. Sirtori, A.L. Hutchinson and A.Y. Cho, “Quantum cascade laser,” Science 264, 553 (1994), the first device; R.F. Kazarinov and R.A. Suris, Sov. Phys. Semicond. 5, 707 (1971), the proposal; Wikipedia, Quantum cascade laser (accessed October 2026); Vitiello, Scalari, Williams and De Natale, Quantum cascade lasers: 20 years of challenges, Optics Express 23(4), 2015.

Ques: Why can one electron emit many photons in a quantum cascade laser, and what does this do to the output power?

The active regions are repeated as a series of periods, each with an active region and an injector, and the bias is chosen so that the electron that has emitted a photon in one active region tunnels through the injector into the upper laser level of the next period and emits again. An electron can therefore produce up to as many photons as there are periods, which makes a quantum efficiency above unity possible and gives the slope efficiency in proportion to the number of periods $N_{p}$ in $P = (h ν / q) η_{i} N_{p} α_{m} (I - I_{t h}) / (α_{w} + α_{m})$ . Increasing the number of periods from 30 to 40 in a 4.6 $μ$ m device also raised the confinement factor of the TM $_{00}$ mode from 63% to 72%, and that device gave 1.6 W continuous wave with a slope efficiency of 2.7 W/A at room temperature. Reference: Wikipedia, Quantum cascade laser (accessed October 2026); A. Lyakh et al., 1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm, Appl. Phys. Lett. 92, 111110 (2008).

Ques: Why must the lower laser level be emptied very quickly, and how do optical phonons do it?

A population inversion exists only if the electrons leave the lower level faster than they arrive from the upper level, which in the three-level result $Δ n_{s} = (J / e) τ_{u} (1 - τ_{l} / τ_{u l})$ means $τ_{l} < τ_{u l}$ . The design places the level below the lower laser level one longitudinal-optical-phonon energy lower (about 36 meV in GaAs, 30 to 40 meV in InGaAs), so that electrons scatter into it by emitting an optical phonon in a time of less than 1 ps, much faster than the scattering by acoustic phonons, which takes about 100 ps. In a 4.6 $μ$ m device the calculated lifetime of the lower level is 0.26 ps, against 1.77 ps for the upper level, so that the lower level stays nearly empty. Reference: Vitiello et al., Optics Express 23(4), 2015; A. Lyakh et al., Appl. Phys. Lett. 92, 111110 (2008); Wikipedia, Quantum cascade laser (accessed October 2026).

Ques: Why does a quantum cascade laser emit only TM-polarized light?

Confinement quantises only the motion of the electron along the growth direction, so the dipole moment of an intersubband transition lies along that direction, and only the component of the optical electric field along the growth direction can drive or be generated by the transition. This is the TM polarization of the waveguide mode formed in the plane of the layers, so the light cannot be emitted along the growth direction, and the laser is an edge emitter whose mode is a TM mode (for example TM $_{00}$ ) of a waveguide in the plane. The same rule means that the modal gain depends on how much of the TM mode overlaps the stack of periods, which is the confinement factor $Γ$ in the threshold condition. Reference: Wikipedia, Quantum cascade laser (accessed October 2026); the selection rule is the standard result of intersubband transitions in the effective-mass approximation.

Ques: Why do mid-infrared quantum cascade lasers work at room temperature, while terahertz ones still need cooling?

Heating broadens the transition and shortens the lifetimes: in a calculated 9.3 $μ$ m device the linewidth increases from 15 meV at 77 K to 25 meV at 300 K, the lifetime of the lowest injector level falls from about 3.5 ps to 0.4 ps and that of the ground active level from 1.2 ps to 0.3 ps, and the gain coefficient roughly halves, so the threshold rises with the temperature. In a mid-infrared device the photon energy (about 130 to 400 meV for 3 to 10 $μ$ m, computed) is several times the optical-phonon energy, and room-temperature continuous-wave operation has been reached with more than 5 W and 21% wall-plug efficiency. In a terahertz device the photon energy is only about 10 to 20 meV (4 THz is 16.5 meV, computed), well below the phonon energy of 36 meV, and thermal backfilling of the lower level is a main limitation cited for terahertz designs, which the resonant-phonon scheme reduces, while the upper-state lifetime falls exponentially as the electron temperature rises. The maximum operating temperatures are therefore 129 K continuous wave (2014) and 261 K pulsed (2022), and later continuous-wave values were not checked. Reference: D. Indjin, P. Harrison, R. W. Kelsall and Z. Ikonić, J. Appl. Phys. 91, 9019 (2002); Vitiello et al., Optics Express 23(4), 2015; A. Khalatpour et al., Terahertz semiconductor laser source at −12 °C, arXiv:2211.08125 (2022); arXiv:0911.0854 (Comparative analysis of resonant phonon THz quantum cascade lasers).

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