Superluminescent Diode (SLD)

1. Theory

• Definition: A superluminescent diode (SLD or SLED) is an edge-emitting diode with a gain waveguide in which spontaneous emission is amplified in a single pass, giving broad, bright light without lasing.
• Between LED and laser: Much more power than an LED into a single-mode fibre, and a much broader spectrum (about 5–100 nm) than a laser.
• Amplified spontaneous emission: Output grows as $(R_{sp}/g_{net})\left[\exp (g_{net}L)-1\right]$, rising smoothly with current with no threshold.
• Feedback suppression: Lasing is avoided only if $R_1{R}_2{G}_s^2<1$, so at 30 dB gain each facet must reflect less than $10^{-3}$, and a smooth spectrum needs well below $10^{-4}$.
• Low temporal, high spatial coherence: A short coherence length (${\lambda }_0^2/\Delta \lambda$) with a single-mode beam that couples well into fibre.

2. Working Principle

• Single-pass gain: Spontaneous photons are amplified as they travel along the waveguide toward the output facet.
• Reflection control: A tilted waveguide sends reflected light out of the guided mode, and anti-reflection coatings reduce facet reflectivity further.
• Spectral ripple: Residual reflectivity produces Fabry-Perot ripple; 1 dB ripple needs an effective reflectivity below about $6\times 10^{-5}$ at 30 dB gain.
• Broad spectrum: No cavity selects a mode, so the output spans the whole gain bandwidth.
• Axial resolution: In optical coherence tomography, resolution $\Delta z\approx (2\ln 2/\pi ){\lambda }_0^2/\Delta \lambda$, so wider spectra give finer depth resolution.

3. Applications

• Optical coherence tomography: Low-coherence light sources for retinal, dermatological and cardiovascular imaging.
• Fibre-optic gyroscopes: Broadband sources that suppress coherent noise in navigation-grade gyros.
• Fibre sensing and component testing: Broadband sources for fibre Bragg grating sensors and optical spectrum characterization.

Name	Formula	Related Formulae	Variables/Constants
Amplified spontaneous emission in the waveguide	$P\left(L\right)=\frac{R_{sp}}{g_{net}}\left[\exp \left(g_{net}L\right)-1\right]$	$\frac{dP}{dz}=g_{net}P+R_{sp}$ $g_{net}=\Gamma g-{\alpha }_i$ $G_s=\exp \left(g_{net}L\right)$	$\begin{array}{r}P\left(L\right):opticalpowerattheoutputfacetof\\ awaveguideoflengthL,inonedirection,\\ withnofeedback\end{array}$ $\begin{array}{r}{R}_{sp}:powerofthespontaneousemission\\ coupledintotheguidedmodeperunit\\ length(itisthesourcetermanditis\\ takenasconstantalongthewaveguide)\end{array}$ $\begin{array}{r}{g}_{net}:netmodalgainperunitlength,the\\ modalgainminustheinternalloss\end{array}$ $\begin{array}{r}\Gamma :opticalconfinementfactorofthe\\ activeregion\end{array}$ $g:materialgain$ ${\alpha }_i:internalloss$ $\begin{array}{r}{G}_s:single-passpowergain(thegainofa\\ commercialdevicecanbe30dBormore)\end{array}$ $L:lengthofthegainsection$ $\begin{array}{r}(theoutputrisesgraduallywiththe\\ currentandnotwithasharpthreshold\\ becausethegainriseswiththecurrent;\\ theexpressionneglectsthesaturationof\\ thegainatahighpowerandthespectral\\ dependenceof{g}_{net})\end{array}$
Suppression of lasing by the facet reflectivity	$R_1{R}_2{G}_s^2<1$	$R_{eff}=R_0{\eta }_c\left(\theta ,w_0\right)$ $R_0={\left(\frac{n_{eff}-1}{n_{eff}+1}\right)}^2$	$\begin{array}{r}{R}_1,R_2:effectivepowerreflectivitiesof\\ thetwofacetsseenbytheguidedmode\\ (theround-tripgainmuststaybelowone\\ forthedevicenottolase)\end{array}$ $G_s:single-passpowergain$ $\begin{array}{r}{R}_{eff}:effectivereflectivityofafacet\\ afterthetiltandtheanti-reflection\\ coating\end{array}$ $\begin{array}{r}{R}_0:Fresnelreflectivityofthecleaved\\ facetatnormalincidence,about0.27for\\ n_{eff}=3.2\end{array}$ $n_{eff}:effectiveindexoftheguidedmode$ $\begin{array}{r}{\eta }_c\left(\theta ,w_0\right):fractionofthereflectedfield\\ thatcouplesbackintotheguidedmode,\\ whichfallssteeplyasthetiltangle\theta of\\ thewaveguidetothefacetnormalandthe\\ modesize{w}_{0}rise(theexpressionisthe\\ overlapofthereflectedbeamwiththe\\ mode;foraGaussianmodeof1/efield\\ radius{w}_{0}D.Marcuse,J.LightwaveTechnol.7,\\ 336(1989),givesapproximately\\ {\eta }_c=\exp \left[-{\left(2\pi n_{eff}{w}_0\theta /\lambda \right)}^2\right],whichfalls\\ verysteeply;measuredvaluesarehigher\\ becauserealmodesarenotGaussianin\\ thetails)\end{array}$ $\begin{array}{r}(areportontheeffectofthemodesize\\ givesaneffectivereflectivityof\\ 1.34\times 10^{-4}fora{7}^{\circ }tiltanda4.5\mu mmode)\end{array}$
Spectral ripple from the residual reflectivity	$\frac{P_{max}}{P_{min}}={\left(\frac{1+G_s\sqrt{R_1{R}_2}}{1-G_s\sqrt{R_1{R}_2}}\right)}^2$	$\sqrt{R_1{R}_2}=R_{eff}\left(equalfacets\right)$ $\Delta {\lambda }_{ripple}=\frac{{\lambda }^2}{2n_{g}L}$	$\begin{array}{r}{P}_{max}/P_{min}:ratioofthepeaktothevalley\\ oftheripplethattheweakFabry-Perot\\ cavityofthefacetsputsonthespectrum\\ (theAiryfunctionofacavitywithgain)\end{array}$ $G_s:single-passpowergain$ $R_1,R_2:effectivefacetreflectivities$ $\begin{array}{r}{R}_{eff}:effectivereflectivityofeachfacet\\ whenthetwoareequal\end{array}$ $\begin{array}{r}\Delta {\lambda }_{ripple}:periodoftheripplein\\ wavelength,thefreespectralrangeofthe\\ chip\end{array}$ $\lambda :wavelength$ $n_g:groupindexofthewaveguide$ $\begin{array}{r}L:lengthofthechip(theripplemustbe\\ smallcomparedwithoneforasmooth\\ spectrum,whichmeansthat{G}_s\sqrt{R_1{R}_2}mustbe\\ muchsmallerthanone)\end{array}$
Spectral width, coherence length and axial resolution	$l_c=\frac{{\lambda }_0^2}{\Delta \lambda }$	$\Delta z=\frac{2\ln 2}{\pi }\frac{{\lambda }_0^2}{\Delta \lambda }$ $\Delta z_{tissue}=\frac{\Delta z}{n_{tissue}}$	$\begin{array}{r}{l}_c:coherencelengthofthesourceinone\\ commondefinition(thedefinitionsdiffer\\ byanumericalfactorwiththeshapeof\\ thespectrum)\end{array}$ ${\lambda }_0:centrewavelength$ $\begin{array}{r}\Delta \lambda :fullwidthathalfmaximumofthe\\ emissionspectrum\end{array}$ $\begin{array}{r}\Delta z:axialresolutioninairofanoptical\\ coherencetomographysystemwithasource\\ ofaGaussianspectrum(thefullwidthof\\ thecoherencefunctionat-6dB)\end{array}$ $\begin{array}{r}{n}_{tissue}:refractiveindexofthesample,\\ whichshortenstheresolutioninthe\\ sample\end{array}$ $\Delta z_{tissue}:axialresolutioninthesample$ $\begin{array}{r}(theresolutionisbetterforawide\\ spectrumandashortwavelength,whichis\\ whythesuperluminescentdiode,witha\\ spectrummuchwiderthanthatofalaser\\ diode,isusedasthesource)\end{array}$

Important Questions

Ques: What is a superluminescent diode, and how does it differ from an LED and a laser diode?

A superluminescent diode (SLD, also SLED) is an edge-emitting diode with a waveguide in which the spontaneous emission is amplified in a single pass without feedback. It gives a much higher power than an LED into a single-mode fibre, because the emission is guided and amplified, and a much wider spectrum than a laser diode, because there is no cavity that selects a mode. The output grows gradually with the current and not with a threshold. A general reference states typical bandwidths of 5 to 100 nm for modules with centre wavelengths from 400 to 1700 nm, gains of 30 dB or more in the high-power devices, and low temporal coherence with a high spatial coherence, which allows an efficient coupling into a single-mode fibre. Reference: T.P. Lee, C.A. Burrus and B.I. Miller, “A stripe-geometry double-heterostructure amplified-spontaneous-emission (superluminescent) diode,” IEEE J. Quantum Electron. 9, 820 (1973), for an early device; “Superluminescent diode,” Wikipedia, en.wikipedia.org/wiki/Superluminescent_diode, for the typical module values (a general reference, not a primary source).

Ques: Why must the facets of an SLD have such a low reflectivity?

The device must not lase, which needs $R_1{R}_2{G}_s^2<1$. For a gain of 30 dB ($G_s=1000$) the effective facet reflectivity (equal facets) must be below $10^{-3}$ just to avoid lasing, and the ripple of the spectrum is $((1+x)/(1-x){)}^2$ with $x=G_s{R}_{eff}$: it is 1.74 dB for $R_{eff}=10^{-4}$, 0.17 dB for $10^{-5}$ and 0.017 dB for $10^{-6}$, and a ripple of 1 dB needs $R_{eff}<5.8\times 10^{-5}$ (computed). The cleaved facet has $R_0\approx 0.27$, so the reflectivity is reduced by the tilt of the waveguide to the facet, which sends the reflected beam out of the mode, and by the anti-reflection coating. A report measured an effective reflectivity of $1.34\times 10^{-4}$ for a 7${}^{\circ }$ tilt and a 4.5 $\mu$m mode, and 6.25% for a 1.7 $\mu$m mode, so the mode size matters strongly; a patent on angled-facet amplifiers lists earlier residual reflectivities of $2\times 10^{-3}$, $5.8\times 10^{-4}$ and $3\times 10^{-5}$. Reference: G. De Valicourt, G.H. Duan, C. Ware, M. Lamponi and R. Brenot, “Experimental and theoretical investigation of mode size effects on tilted facet reflectivity,” IET Optoelectron. 5, 175 (2011) (the numbers are from the abstract); US Patent 4,872,180, “Method for reducing facet reflectivities of semiconductor light sources and device thereof” (the earlier values quoted there for amplifiers).

Ques: How is the width of the spectrum related to the resolution of optical coherence tomography?

The axial resolution in air of a source with a Gaussian spectrum is $\Delta z=(2\ln 2/\pi ){\lambda }_0^2/\Delta \lambda$, which is the full width at -6 dB of the coherence function. For ${\lambda }_0=1300$ nm and $\Delta \lambda =100$ nm it is 7.5 $\mu$m in air, and the coherence length defined as ${\lambda }_0^2/\Delta \lambda$ is 17 $\mu$m, which is the value given in the general reference for such a source; the two numbers differ by the definition. For ${\lambda }_0=840$ nm and $\Delta \lambda =50$ nm the resolution is 6.2 $\mu$m in air, and it is shorter by the refractive index of the sample, so about 4.6 $\mu$m for $n=1.35$ (the index is assumed). Reference: Optical coherence tomography review, arXiv:2212.04380, Eq. (6) for the resolution (“Optical coherence tomography — principles, implementation, and applications in ophthalmology”); the 17 $\mu$m value is from the Wikipedia article on the superluminescent diode.

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