Resonant Cavity LED (RCLED)

1. Theory

• Definition: A resonant-cavity LED (RCLED) is an LED whose active layer sits inside a Fabry-Perot microcavity about one wavelength long, formed by two mirrors.
• Mirrors: Usually distributed Bragg reflectors, or a Bragg reflector with a metal mirror; the exit mirror is less reflective than the back mirror.
• Resonance condition: $2n_c{L}_{eff}\cos \theta =m\lambda$, so only certain wavelengths and angles are enhanced.
• Finesse: Set by mirror reflectivities; higher finesse gives a narrower cavity mode.
• Spontaneous emission control: The cavity redistributes spontaneous emission, enhancing it along the axis at resonance.
• Relation to VCSEL: An RCLED is a VCSEL-type cavity operated below lasing threshold.

2. Working Principle

• Emission: Carriers recombine in the active layer as in a normal LED, but the cavity favours the resonant wavelength along the axis.
• On-axis enhancement: Emission along the axis can rise by tens of times in theory, though integrated gains of about 5 are typical.
• Narrow spectrum: The cavity mode narrows the line, e.g. about 7 nm at 650 nm for a finesse near 46.
• Angular blue shift: The resonance moves to shorter wavelengths off-axis ($\lambda ={\lambda }_0\cos \theta$), so emission is directional.
• Detuning: Extraction is best when the emission peak is slightly shorter than the on-axis resonance.

3. Applications

• Plastic optical fibre links: 650 nm RCLEDs for automotive, home and industrial POF data networks, giving better fibre coupling than standard LEDs at lower cost than lasers.
• Optical sensing: Narrow-band, directional sources for encoders and gas or position sensors.

Name	Formula	Related Formulae	Variables/Constants
Resonance of the microcavity	$2n_c{L}_{eff}\cos {\theta }_{in}=m\lambda$	$L_{eff}=L_{cav}+L_{pen,1}+L_{pen,2}$ $\lambda \left(\theta \right)={\lambda }_0\cos {\theta }_{in}$ $\sin {\theta }_{ext}=n_c\sin {\theta }_{in}$	$n_c:refractiveindexofthecavitymaterial$ $\begin{array}{r}{L}_{eff}:effectivelengthofthecavity,\\ includingthepenetrationofthefield\\ intothemirrors\end{array}$ $\begin{array}{r}{\theta }_{in}:angleoftheraytotheaxisinside\\ thecavity\end{array}$ $\begin{array}{r}m:orderoftheresonance,aninteger(a\\ first-ordercavityhasanopticallength\\ ofhalfawavelength)\end{array}$ $\lambda :resonantwavelengthattheangle{\theta }_{in}$ $\begin{array}{r}{L}_{cav}:physicallengthofthecavitybetween\\ thetwomirrors\end{array}$ $\begin{array}{r}{L}_{pen,1},L_{pen,2}:penetrationdepthsofthe\\ fieldintothetwomirrors(adistributed\\ Braggreflectormadeofquarter-wavepairs\\ letsthefieldpenetrateoneorseveral\\ pairs)\end{array}$ ${\lambda }_0:resonantwavelengthontheaxis$ $\begin{array}{r}{\theta }_{ext}:angleintheair(theresonancemoves\\ toshorterwavelengthsatanangle,sothe\\ emissionatanangleisblue-shifted)\end{array}$
Finesse and linewidth of the cavity mode	$\mathcal{F}=\frac{\pi {\left(R_1{R}_2\right)}^{1/4}}{1-\sqrt{R_1{R}_2}}$	$FSR=\frac{{\lambda }^2}{2n_c{L}_{eff}}$ $\Delta {\lambda }_{cav}=\frac{FSR}{\mathcal{F}}$	$\mathcal{F}:finesseoftheFabry-Perotcavity$ $\begin{array}{r}{R}_1,R_2:powerreflectivitiesofthe\\ light-exitmirrorandofthebackmirror\end{array}$ $\begin{array}{r}FSR:freespectralrange,thespacingof\\ theresonancesinwavelength\end{array}$ $\lambda :resonantwavelength$ $\begin{array}{r}{n}_c,L_{eff}:indexandeffectivelengthofthe\\ cavity\end{array}$ $\begin{array}{r}\Delta {\lambda }_{cav}:fullwidthathalfmaximumofthe\\ cavityresonance(anarrowresonancegives\\ anarrowemissionlineofthedevice,much\\ narrowerthanthespontaneousemissionof\\ theactivelayer)\end{array}$
Enhancement of the emission on the axis	$G_e=\frac{\xi }{2}\frac{{\left(1+\sqrt{R_2}\right)}^2\left(1-R_1\right)}{{\left(1-\sqrt{R_1{R}_2}\right)}^2}$	$G_{int}\approx G_e\frac{\Delta {\lambda }_{cav}}{\Delta {\lambda }_{sp}}$ $2\xi \alpha d_a<1-R_1$	$\begin{array}{r}{G}_e:enhancementofthespectralintensity\\ attheresonancealongtheaxis,relative\\ toasourceofthesameactivelayer\\ withoutthecavity\end{array}$ $\begin{array}{r}\xi :standing-wavefactor,2fortheactive\\ layeratanantinodeofthefield,0ata\\ nodeand1whenthepositionisaveraged\end{array}$ $\begin{array}{r}{R}_1,R_2:reflectivitiesofthelight-exit\\ mirrorandofthebackmirror(theexit\\ mirrorismadelessreflectingthanthe\\ backmirror,R_1<R_2)\end{array}$ $\begin{array}{r}{G}_{int}:enhancementoftheintensity\\ integratedoverthewavelengthandthe\\ angle,muchlowerthan{G}_{e}becausethe\\ resonanceisnarrowerthanthespontaneous\\ emission(anorder-of-magnitudeestimate)\end{array}$ $\begin{array}{r}\Delta {\lambda }_{cav},\Delta {\lambda }_{sp}:widthsofthecavityresonance\\ andofthespontaneousemissionspectrum\end{array}$ $\begin{array}{r}\alpha ,d_a:absorptioncoefficientattheemission\\ wavelengthandthicknessoftheactive\\ (absorbing)layer\end{array}$ $\begin{array}{r}(thelastexpressionisadesignrule:the\\ round-tripabsorptionintheactivelayer,\\ weightedbythestanding-wavefactor,must\\ besmallerthanthetransmission1-R_{1}ofthe\\ exitmirror,otherwisethelightis\\ reabsorbedbeforeitleaves;thespacer\\ layersaretransparent,soonlytheactive\\ thicknessenters)\end{array}$

Important Questions

Ques: What is a resonant-cavity LED, and what does the cavity change?

A resonant-cavity light-emitting diode (RCLED) places the active layer inside a Fabry-Perot cavity of one wavelength or less, formed by a back mirror and a light-exit mirror (usually distributed Bragg reflectors, or a Bragg reflector and a metal). The cavity changes the spontaneous emission: the emission along the axis is enhanced at the resonant wavelength, the spectrum is narrower and the directionality is better than for an LED without the cavity. A lecture example with $R_1=90\%$, $R_2=97\%$ and $\xi =1.5$ gives a finesse of 46 and an on-axis enhancement of 68 (both reproduced by the formulas of the table), but a measured enhancement of about 5 for the integrated emission. Reference: E.F. Schubert, Light-Emitting Diodes, 2nd ed. (Cambridge University Press, 2006), chapters 14 and 15 (the numbers of the example are from a lecture presentation of the University of Paderborn on LEDs and RCLEDs, which was partly illegible); E.F. Schubert et al., “Resonant cavity light-emitting diode,” Appl. Phys. Lett. 60, 921 (1992).

Ques: How wide is the emission line, and how does it change with the angle?

For a cavity with $n_c{L}_{eff}=\lambda$ (second order) the free spectral range is $\lambda /2$, so at 650 nm it is 325 nm and the resonance width for the finesse of 46 is $\Delta {\lambda }_{cav}=325/46=7.0$ nm (computed), close to the 6.5 nm of the lecture example. The resonance moves to shorter wavelengths with the angle, $\lambda ={\lambda }_0\cos {\theta }_{in}$, so the emission seen at an angle is blue-shifted, and the cone of emission is limited by the width of the spontaneous emission. For $\Delta {\lambda }_{sp}=20$ nm at 650 nm, ${\theta }_{in}\approx \sqrt{2\Delta \lambda /\lambda }$ is 14${}^{\circ }$ inside the cavity, and with $n_c=3.5$ the corresponding angle in the air from $\sin {\theta }_{ext}=n_c\sin {\theta }_{in}$ is about 59${}^{\circ }$ (computed; the numbers of this example are assumed). The same lecture states that the extraction is largest when the emission wavelength is slightly shorter than the resonance of the vertical direction, the optimum detuning. Reference: the angular numbers follow from the phase condition of the first row, the condition of a Fabry-Perot etalon (E.F. Schubert, Light-Emitting Diodes, 2nd ed., chapter 14). The statement about the detuning is from the Paderborn lecture presentation (see above).

Related pages in this vault: Resonant-Cavity-Enhanced Photodetector (RCE), Vertical-Cavity Surface-Emitting Laser (VCSEL), Superluminescent Diode (SLD), Light Emitting Diode (Homojunction and Heterojunction LED), Vertical-External-Cavity Surface-Emitting Laser (VECSEL), Distributed Bragg Reflector Laser (DBR), Double-Heterostructure Fabry-Perot Laser, Nanolaser (Microdisk, Microring and Photonic Crystal), Light Emitting Diodes (InGaN, AlInGaP, UV and White).