Theory of Metal-Cavity Surface-Emitting Microlasers and Comparison With Experiment

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 17, NO. 6, NOVEMBER/DECEMBER 2011 1681

Theory of Metal-Cavity Surface-EmittingMicrolasers and Comparison With Experiment

Shu-Wei Chang, Member, IEEE, Chien-Yao Lu, Student Member, IEEE, Shun Lien Chuang, Fellow, IEEE,Tim D. Germann, Udo W. Pohl, and Dieter Bimberg, Fellow, IEEE

Abstract—We present a theoretical model of the recently demon-strated metal-cavity surface-emitting microlaser, which lases atroom temperature with continuous-wave operation. A transfer-matrix method with the effective index of the guided mode as theinput and an emission model that incorporates the modal charac-teristics explain the experimental results, such as the asymmetricallineshape well. We also discuss the design rules and approachesto improve the performance of the nanoscale laser. With the com-bination of the metal coating and distributed Bragg reflector, ofwhich the multilayer thicknesses are redesigned according to themodal dispersion of a small metallic waveguide, the laser size canbe potentially reduced to the subwavelength regime. In addition,our rigorous rate-equation model explains the output power versusinjection current with excellent agreement.

Index Terms—Metal cavity, semiconductor microlaser.

I. INTRODUCTION

THERE is growing interest along with breakthroughs insemiconductor plasmonic nanolasers. The main motiva-

tion for the development of such semiconductor lasers withmetal-cavity structures is to reduce the laser size toward thenanoscale, which is a challenging task for conventional dielec-tric cavities. We note that the pioneering work on the vertical-cavity surface-emitting laser (VCSEL) in 1979 [1] had alreadyused metals as reflectors, although at a much larger aperture sizewithout the surrounding sidewall metal. The successful opera-tion of electrical-injection plasmonic nanolasers was demon-

Manuscript received November 29, 2010; revised February 21, 2011; ac-cepted February 22, 2011. Date of publication April 7, 2011; date of currentversion December 7, 2011. This work at University of Illinois at Urbana-Champaign, Urbana, IL, was supported by the Defense Advanced ResearchProjects Agency NACHOS Program under Grant W911NF-07-1-0314. Thework at Technische Universitat Berlin, Berlin, Germany, was supported byDeutsche Forschungsgemeinschaft in the frame of SFB 787. The work of S. L.Chuang was supported by the Humboldt Research Award. The work of S.-W.Chang was supported by the research project from the Research Center for Ap-plied Sciences, Academia Sinica, Taipei, Taiwan.

S.-W. Chang was with the University of Illinois, Urbana, IL 61801USA. He is now with the Research Center for Applied Sciences,Academia Sinica, Nankang, Taipei 11529, Taiwan (e-mail: [email protected]).

C.-Y. Lu and S. L. Chuang are with the Department of Electrical and Com-puter Engineering, University of Illinois at Urbana-Champaign, Urbana, IL61801 USA (e-mail: [email protected]; [email protected]).

T. D. Germann, U. W. Pohl, and D. Bimberg are with the Insti-tut fur Festkorperphysik, Technische Universitat Berlin, Berlin 10623,Germany (e-mail: [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTQE.2011.2121894

strated at liquid-nitrogen temperature so that the significantoptical loss from metals at the room temperature could be re-duced [2]. Despite the general belief that metal loss at room tem-perature is unfavorable to lasers, room-temperature operationsof plasmonic nanolasers under pulse electrical injection [3] andoptical pumping [4] at telecommunication wavelengths werealso realized. In fact, the Fabry–Perot (FP) lasers with a 2-μmcore width and metal-coated sidewalls can exhibit compara-ble performance to that of conventional uncoated semiconduc-tor FP lasers [5], [6]. Recently, an electrical-injection metal-cavity surface-emitting microlaser with the room-temperatureand continuous-wave operation was successfully demonstrated[7]. An output power in the microwatt range is achieved eventhough the whole device is covered by metal. This demonstrationis the precursor of an electrical-injection plasmonic nanolaserunder the same operation condition. So far, the operation of thesmallest plasmonic nanolasers with top-down fabrication [8] orthose with bottom-up synthesis [9] still requires optical pump-ing. Nevertheless, the recent demonstration of the metal-cavitysurface-emitting microlaser will pave the way for the more prac-tical applications of plasmonic nanolasers such as high-densitylaser arrays in photonic integrated circuits without crosstalkand high-speed direct electrical modulation, in which smallerdevices have great potential [10].

The fundamental issue of nanolasers is whether the gain-lossbalance condition is achievable. The loss reduction, includingthe blocking of radiation loss, is thus advantageous to the op-eration of nanolasers. In this paper, we formulate the metalcavity with a bottom distributed Bragg reflector (DBR) similarto that of a conventional VCSEL with the following modifi-cations: 1) the complex propagation constant in the presenceof metal plasma coating (complex permittivity with a negativereal part) and an insulator layer surrounding the semiconductorcore region are taken into account for each layer. We note thatthe effective index of each layer becomes a strong function ofthe core diameter below the micrometer scale and affects theround-trip phase-matching condition and quality factor signifi-cantly; 2) the energy confinement factor taking into account thedispersive nature of the metal plasma is adopted in a rigorousframework of the nanoplasmonic lasers to predict the thresh-old [11]; 3) the spontaneous emission coupling into the lasingmode and the spontaneous emission loss into the continuum areincluded as they are important in microcavity lasers.

In this paper, we present a comprehensive theoretical modelof the metal-cavity surface-emitting microlaser experimentallydemonstrated in [7]. Similar structures with metals as the sub-strate or high-reflection mirrors have appeared in the literature

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1682 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 17, NO. 6, NOVEMBER/DECEMBER 2011

Fig. 1. (a) Layer structure of the metal-cavity surface-emitting microlaser. Thewhole device is covered by silver. (b) Field profile along the growth direction(obtained by the transfer-matrix method with the effective index of HE11 modetaken into account). The inset shows the transverse profile of the mode in theGaAs QW region.

[12], [13]. Nevertheless, the device considered in this studyhas the full metal coverage including the sidewall and is evenmore compact. The device structure is depicted in Fig. 1(a). Thewhole structure is about 2.5 μm in height and 2 μm in diam-eter, and the active region consists of 14 GaAs/Al0.2Ga0.8Asquantum wells (QWs). A thin SiNx insulator layer is depositedon the device sidewall for the purpose of current isolation. Theoptical feedback is provided by the silver (Ag) layer as the topreflector and a bottom distributed-feedback reflector with 17.5pairs of quarter-wavelength layers. Another 10-nm bottom sil-ver coating (z = zd ) on the In0.5Ga0.5P etch-stop layer furtherenhances the reflectivity from the DBR. The silver coating onthe SiNx layer then provides the lateral field confinement. Formore details about the device and growth, see [7] and [14]. InFig. 1(b), we show the squared field magnitude of the cavitymode of interest along the growth direction. This mode has atransverse profile of the fundamental HE11 waveguide mode[see the inset of Fig. 1(b)]. It has 4.5 standing-wave periods inthe active region, and decays quickly toward the metal side. Inthe following sections, we will first address the design rule ofthis metal-cavity surface-emitting laser and discuss the materialgain and emission spectra of the QWs. The silver permittivity isadopted from [15]. The effect of metal cavities will be includedusing the transfer-matrix method [16] with the effective index ofthe HE11 mode of each layer, which is surrounded by the metal-lic sidewall, as inputs. The theoretical models for the quality (Q)factor, the amplified spontaneous emission (ASE) spectra, and

Fig. 2. Layer structure (region between two dashed lines) to which the lasingconditions are applied. This region contains the QWs, barriers, p-type cladding,and is sandwiched between the DBR and silver layers.

light output power versus current (L–I) curve will be presented,which show good agreement between our theoretical results andexperimental data. Finally, we discuss possible approaches tofurther reduce the size and threshold of this metal-cavity micro-laser.

II. DESIGN RULES OF METAL-CAVITY

SURFACE-EMITTING LASERS

The threshold material gain and lasing wavelength are twoimportant characteristics for a small laser. To obtain these twoparameters, let us consider the lasing condition in a layer struc-ture consisting of QWs and p-type cladding (see Fig. 2). Similarto the FP round-trip condition, we define an approximate round-trip phase Φ(ω) and gain G(g) of a particular transverse mode

Φ(ω) = φDBR(ω) + φAg(ω) + 2NQW hQW k(QW)R

+ 2(NQW + 1)hbk(b)R + 2hpk

(p)R (1a)

G(g) =[ ∑

n∈QWs

2hnΓL,n (ω)gM ,n

−∑

n

2hnΓL,n (ω)αi,n (hω)

− ln(

1|rDBR(ω)|2 |rAg(ω)|2

)]∣∣∣∣Φ(ω )=2mπ

(1b)

where ω is the photon frequency; φDBR(ω) and φAg(ω) arethe phases of reflection coefficients rDBR(ω) and rAg(ω) atthe DBR side (z = 0+ ) and silver side (z = z−u ), respectively;NQW (=14) is the number of QWs; hn , hQW , hb , and hpare the length of segment n, QW width, barrier width, andp-cladding width, respectively; k

(QW)R , k

(b)R , and k

(p)R are the

real parts of the propagation constants in the QWs, barri-ers, and p-type cladding, respectively; g is the QW materialgain; ΓL,n (ω) is an effective longitudinal confinement fac-tor due to the standing-wave pattern in segment n; gM ,n (hω)and αi,n (hω) are the modal gain and intrinsic modal loss,which are related to the imaginary part kn,I of the propaga-tion constant kn (kn,I = [αi,n (hω) − gM ,n (hω)]/2); and m isan integer. The modal gain gM ,n (hω) is proportional to thematerial gain through the waveguide confinement factor [11].

CHANG et al.: THEORY OF METAL-CAVITY SURFACE-EMITTING MICROLASERS 1683

The calculation of round-trip gain G(g) in (1b) is carried outnear possible frequencies at which the round-trip phases aremultiples of 2π. Also, mode mismatch across neighboring in-terfaces is neglected in (1a) and (1b), and we assume that there isan approximate one-to-one correspondence of transverse modesthroughout each segment. The resonance frequency ωcav of acertain cavity mode and the corresponding threshold materialgain gth satisfy the following lasing conditions:

Φ(ωcav ) = 2mπ

G(gth) = 0. (2)

While the conditions in (1a), (1b), and (2) are approximate,we point out some useful design concepts. First, the cavity fre-quency ωcav can be tuned by adjusting hQW , hb , hp , and sizeof waveguide (size-dependent propagation constant kn or effec-tive index neff ,n = kn/k0) for a fixed phase 2mπ. Usually, theselengths are chosen such that the corresponding frequency ωcavbrings about high reflectivities |rDBR(ωcav )|2 and |rAg(ωcav )|2 ,which reduce the mirror loss [the last term on the right-handside of (1b)]. While the QW width hQW has to be designedaccording to the emission window of interest, one can adjustthe barrier width hb , p-cladding width hp , and core size of thewaveguide to tune the frequency ωcav and reduce mirror loss.The optimization of this condition usually corresponds to a cav-ity frequency near the center of DBR stopband at which thereflectivity is maximal. Second, in (1b), to utilize the modalgain gM ,n (ωcav ) at resonance efficiently, most QWs should beplaced near standing-wave peaks where the longitudinal con-finement factor ΓL,n (ωcav ) has a maximum of about 2. This canbe achieved by redistributing QWs near standing-wave peaks.For the sample in experiment, QWs are uniformly distributedwithout the optimization of this condition. The improvement oflaser performance is expected if the layout of QWs is redesigned.

To more accurately obtain the resonance and threshold con-ditions in experiment, we use the transfer-matrix method withthe complex effective indices (complex propagation constants)as inputs to obtain ωcav and gth . If the forward- and backward-propagating amplitudes F (z−u ) and B(z−u ) are present at z = z−u ,the corresponding amplitudes F (0+) and B(0+) at z = 0+ canbe obtained by a backward transfer matrixB, which incorporatesthe effects of transmission, reflection, propagation, amplifica-tion (attenuation), and standing-wave pattern in these layers intoits matrix elements[

F (0+)B(0+)

]= B

[F (z−u )B(z−u )

]=

(B11 B12B21 B22

)[F (z−u )B(z−u )

]. (3)

Substituting backward-propagating amplitudes B(z−u ) =rAg(ω)F (z−u ) and B(0+) = rAg(ω)F (0+), where rAg(ω) isthe transformed reflection coefficient of rAg(ω) at z = 0+ , into(3), we obtain

rAg(ω) =B21 + B22rAg(ω)B11 + B12rAg(ω)

. (4)

Lasing oscillation requires the unity round-trip condition

rDBR(ω)rAg(ω)|ω=ω c av ,g=gt h= 1. (5)

Fig. 3. (a) Reflectivities |rDBR (ω)|2 and |rAg (ω)|2 of the HE11 mode as afunction of wavelength. The asymmetric stopband of DBR reflectivity is causedby the 10-nm Ag coating on the output side of DBR. (b) Round-trip phases ofthe layer structure in Fig. 2. The arrows indicate the resonance wavelengths ofcavity modes with different waveguide diameters.

Denote the round-trip phase Φ(t.m .)(ω) and gain G(t.m .)(g)from the transfer-matrix method as

Φ(t.m .)(ω) = φDBR(ω) + φAg(ω) (6a)

G(t.m .)(g) = − ln[

1|rDBR(ω)|2 |rAg(ω)|2

]∣∣∣∣Φ(t . m . ) (ω )=2mπ

(6b)

where φAg(ω) is the phase angle of rAg(ω). Lasing occurs ata frequency ωcav and threshold material gain gth of QWs suchthat

Φ(t.m .)(ωcav ) = 2mπ

G(t.m .)(gth) = 0 (7)

where the superscript “t.m.” indicates that the transfer-matrixmethod is used.

Fig. 3(a) shows the reflectivities |rDBR(ω)|2 and |rAg(ω)|2for the HE11 mode at a diameter of around 2 μm. The DBR re-flectivity does not show a symmetric profile with respect to thecenter of the stopband. This is caused by the 10-nm Ag coatingon the output side of DBR, which enhances the DBR reflectivityaround the cavity resonance. While the DBR reflectivity exhibits


the features from multiple reflections of quarter-wavelength lay-ers, the reflectivity |rAg(ω)|2 is flat in a broadband and has avalue of about 0.9 around the cavity resonance. The relativelylower reflectivity of metal than that of DBR is the main cause ofa high-threshold carrier density in this device. A better feedbackscheme such as the insertion of a few DBR pairs between metaland active region may relax this constraint of high threshold.On the other hand, if a layer structure is fixed, it is easier totune the resonance frequency of the cavity mode with the sizeof waveguide core. In Fig. 3(b), we show the round-trip phaseΦ(t.m .)(ω) (shifted to the ±π range) as a function of the wave-length with different diameters. Possible resonance wavelengthsof the cavity modes are indicated by arrows, while other spectralpositions of zero crossings correspond to resonant modes withfrequencies away from the stopband, which exhibit standing-wave-like rather than exponentially-decaying envelopes in theDBR region. As the size of waveguide core decreases, the res-onance wavelength blueshifts, and the amount of blue-shift issignificant at a small diameter. On the other hand, the resonancewavelength does not change much at a larger diameter, as shownin Fig. 3(b) for the cases of 2.5- and 2-μm diameters. The blue-shift reflects the fact that a smaller cavity usually has a higherresonance frequency. Note that as the radius of the waveguidecore decreases, the center of DBR stopband also shifts to theshorter wavelength side. Thus, in the design of a metal-cavitysurface-emitting laser with a small waveguide size but fixed QWemission window, the total length of the resonance structure andDBR periods need reexamination so that a high DBR reflectivityis still available at the resonance wavelength of interest.

The resonance wavelength λcav of a 2-μm-diameter deviceis around 869.02 nm, which agrees well with the experimentalresult of the resonance peak. At this wavelength, we calculate theround-trip gain G(t.m .)(g) as a function of the QW material gain,and the threshold material gain gth is around 7740 cm−1 , whichis high compared with typical VCSELs in the same wavelengthrange, mainly due to the relatively low metal reflectivity. Notethat the calculation of gth in (7) has automatically taken the fieldconfinement of cavity mode into account.

III. MATERIAL GAINS AND FREE-SPACE SPONTANEOUS

EMISSIONS OF QWS

The gain medium of metal-cavity lasers consists of 14 GaAsQWs (5.5 nm) separated evenly by the Al0.2Ga0.8As barriers(23.5 nm). The low-intensity room-temperature photolumines-cence (PL) measurement with an Argon laser as the pump isapplied to the bare sample. The emission spectrum is collectedat the top of the sample surface and indicates a superposition oftwo Lorentzian lineshapes due to the heavy-hole (HH) and light-hole (LH) exciton transitions between the respective groundsubbands (see Fig. 4). The transition at 840.83 nm correspondsto the HH exciton, and the other at 831.93 nm corresponds tothe LH exciton. The Lorentzian fitting to the emission line-shapes indicates that the relative strength of the two transitionis roughly 3:1, consistent with the ratio between the squaredin-plane dipole moments of HH and LH transitions. At higher

Fig. 4. Experimental data of low-intensity PL (symbol) at room temperature.The emission spectrum can be fitted well by two Lorentzians corresponding tothe HH and LH exciton transitions at 840.83 nm and 831.93 nm, respectively.

pumping intensities, the emission peak redshifts to 845–860 nmdue to the bandgap renormalization and thermal effect.

We use the four-band Luttinger–Kohn Hamiltonian with theaxial approximation to calculate the valence subband struc-tures [16]. The conduction subband structure is obtained withthe single-band effective-mass approximation. We compare ourtheoretical bandedge energy between the conduction and HHsubbands with the low-intensity PL data. After about 10-meVcorrection of the HH exciton binding energy, we obtain a 9-meVdeviation between the theoretical calculation and experimentaldata, which indicates a reasonable accuracy of our calculation.We, therefore, slightly change the bandgap of the GaAs QWs tocomply with the low-intensity PL spectrum.

Since the metal-cavity laser is operated with a high-densitycurrent injection, the spectral characteristics of the QWs are sig-nificantly influenced by thermal shrinkage of the bandgap andbandgap renormalization. These effects lead to the red-shifts ofemission and gain spectra and have to be taken into accountwhen designing the resonance wavelength for a conventionalVCSEL. In our case, the red-shift is necessary for lasing be-cause the resonance wavelength is significantly longer than theintrinsic bandedge wavelength of QWs by over 30 nm. If therewere no red-shift from the thermal effect and bandgap renor-malization, the cavity mode could not have overlapped with thegain spectrum and would not have lased.

Fig. 5(a) and (b) shows the transverse-electric (TE) materialgain and free-space spontaneous emission spectra of QWs. Dueto the bandgap shrinkage from the thermal effect and bandgaprenormalization, we model the reduction of energy differenceΔEg between quantized subbands as follows:

ΔEg = −ΔEBR n1/3 − (ΔEAn + ΔEC n3) (8)

where n is the normalized surface carrier density (relative to1012 cm−2) of a single QW; ΔEBR (=21 meV) is a parameterfor the bandgap renormalization modeled as a cubic-root de-pendence on the carrier density [17]; and ΔEA (=3.65 meV)and ΔEC (=7.54 × 10−3 meV) are two energy parametersmodeling the heat generation due to the defect/surface recom-bination and Auger recombination. Although the band fillingtends to blueshift the gain and spontaneous emission spectra, the


Fig. 5. Theoretical room-temperature (a) TE gain spectra and (b) TE sponta-neous emission spectra of a single GaAs/Al0 .2 Ga0 .8 As QW at different surfacecarrier densities from 1012 (bottom) to 1013 cm−2 (top). The red-shifts of thetwo spectra at high surface carrier densities are due to the bandgap shrinkage in(8).

red-shift from bandgap shrinkage in these calculations finallyexceeds the blue-shift, and thus the gain and spontaneous emis-sion peaks both exhibit a monotonic red-shift in Fig. 5(a) and (b)at a large carrier density. Experimentally, even under the low-density current injection, red-shift is observed in a light-emittingdiode (LED) with an edge-emitting geometry (emission spectraare less interfered by the DBR) made from the same sample.In addition to the heat generation due to nonradiative recombi-nations in the active region, the significant red-shift may alsooriginate from the proximity of the p-side metal contact withthe active region (separated by only 96 nm). A considerableamount of heat may be generated due to the contact resistanceunder a high-density current injection, which further shrinks thebandgap.

The experimental ASE spectra observed at the output of themetal-cavity laser are the QW emission spectrally filtered bythe DBR and are related to the free-space spectra shown inFig. 5(b). In the next section, we calculate the ASE spectra atthe output, taking the distributions of the electron–hole pairs,both spectrally and spatially, and the multisectional waveguidestructure of the metal cavity into account.

IV. QUALITY FACTOR AND ASE SPECTRUM

The output powers 〈P (zd)〉 and 〈P (zu )〉 at zd and zu of themetal cavity are the sums of transmitted powers generated by

random dipole sources in QWs and carried by various modes:

〈P (zd)〉 ≈∑n,b

Tb,(d,n)P(z )b,n 〈|B

(1)b,n |2〉

〈P (zu )〉 ≈∑n,b

Tb,(u,n)P(z )b,n 〈|F

(2)b,n |2〉

P(z )b,n =

∫dρz · 1

2Re

[Eb,n (ρ) × H∗

b,n (ρ)]

(9)

where 〈...〉 is the ensemble average that takes the randomness ofspontaneous emission and symmetry of the semiconductor QWsinto account; Tb,(d,n) and Tb,(u,n) are the power transmissionsto outputs at zd and zu for mode b from QW segment n, whichinclude the composite effect of waveguide sections; P

(z )b,n is the

real power carried by mode b in segment n; and 〈|B(1)b,n |2〉 and

〈|F (2)b,n |2〉 are the squared magnitudes of the modes, which are

generated by the random dipoles in QWs and propagate towardthe outputs at zd and zu , respectively. If we use simple reflec-tion boundary conditions [see (17) in the Appendix] valid forweak mode mismatch across neighboring segments in waveg-uides with core sizes larger than the effective wavelength byseveral times, the squared magnitudes 〈|B(1)

b,n |2〉 and 〈|F (2)b,n |2〉

are proportional to the resonance factor (RF)

〈|B(1)b,n |2〉, 〈|F

(2)b,n |2〉 ∝ RF ≡ 1

|r(1)b,n r

(2)b,n e2ikb , n hn − 1|2

(10)

where r(1)b,n and r

(2)b,n are reflection coefficients of mode b at

two ends of QW segment n, which also include the compositeeffects of multiple waveguide segments toward the outputs, andkb,n,I is the imaginary part of the propagation constant kb,n .Equations (9) and (10) reveal that significant output powers canbe observed in two cases: 1) if the power transmissions Tb,(d,n)or Tb,(u,n) are large, which correspond to the pass bands in DBR;and 2) if the denominator of the RF in (10) becomes smaller,which indicates the fulfillment of FP round-trip condition, orthe formation of a resonance cavity mode such as the lasingmodes in VCSELs. This cavity resonance is consistent with theround-trip phase condition in (7). For details of the derivations,see the Appendix.

The full-width at half-maximum (FWHM) frequencylinewidth Δωcav (or wavelength linewidth Δλcav ) for a coldcavity indicates the intrinsic quality factor Q of the mode

Q =ωcav

Δωcav λcav

Δλcav. (11)

This FWHM linewidth can be obtained by the calculation of theoutput emission spectrum with a white spontaneous emissionnoise, which eliminates the interference of the QW emissionspectrum. Since the effect of gain medium is excluded in acold cavity, the interband absorption or gain has to be absentnear the wavelength of interest while the absorption loss (metaland free-carrier absorptions) and radiation loss still have to bekept in the calculation. The resonance photon energy of thefundamental HE11 mode in this metal-cavity laser is below theintrinsic absorption edge of QWs. Thus, we need not set the


Fig. 6. Output spectrum with a white spontaneous emission noise. The res-onance wavelength λcav is 869.02 nm, and the FWHM linewidth Δλcav is1.56 nm, corresponding to a Q factor of about 556.

interband absorption to zero. Fig. 6 shows the output emissionspectrum calculated with the transfer-matrix method, assuminga white spontaneous emission noise for the fundamental HE11mode. The resonance wavelength λcav (869.02 nm) is identicalto that obtained from the round-trip phase condition in (7), andthe FWHM linewidth Δλcav is 1.56 nm. The corresponding Qfactor is around 556, which is close to the experimental value580 when the mode just emerged on the spectrum.

The experimental emission spectrum is the ASE (but dissi-pated by metal as well), which is spectrally influenced by thematerial gain, carrier occupations in QWs, and cavity structure.Thus, the lineshape of the ASE spectrum reflects the convolvedeffects of these factors and does not often exhibit simple fea-tures. It is only with a sufficient material gain that the ASEspectrum is transformed into a narrow Lorentzian-like lasingpeak. In Fig. 7(a), we show our theoretical ASE spectra of thefundamental HE11 mode at the bottom silver facet (z = zd )under different surface carrier densities and compare them withthe experimental data of an LED in Fig. 7(b). These calculationsare obtained with the transfer-matrix method (using the effec-tive index of the HE11 mode as the input) and the light-emissionmodel in the Appendix. While the experimental data show anadditional red-shift due to the material index change and expan-sion of the DBR layer due to the thermal effect, which is nottaken into account in our model, our calculations have graspedmost of the characteristics of the experimental ASE spectra.When the effect of material gain is not significant (low injectioncurrents), the ASE around cavity resonance can be roughly re-garded as the product of the free-space spontaneous emission inFig. 5(b) and the cavity resonance in Fig. 6. Despite the largermagnitude of the QW emission at a higher carrier density, theincrement of the cavity ASE is mainly due to the red-shift ofthe QW emission spectrum toward the cavity wavelength as aresult of the bandgap shrinkage. The ASE spectra also exhibit anasymmetric lineshape with a high-energy tail. While the mainpeak is caused by the cavity resonance, the asymmetry origi-nates from the sharp change of the QW emission around theQW subband edge (step-like joint density of states). The longtail toward the short-wavelength side also reflects the Fermidistributions of electrons and holes even though the radiative

Fig. 7. (a) Theoretical calculation of output ASE spectra at different surfacecarrier density per QW. (b) Experimental ASE spectra of an LED. The experi-mental data show an additional red-shift due to the heat-up of DBR layer. Theemission of the cavity mode becomes more prominent as the emission spectrumof QWs redshifts toward the cavity wavelength at a high carrier density (high-current injection). The asymmetric emission lineshape is cause by the sharpchange of the QW emission around the QW subband edge.

emission is suppressed by the DBR stopband. For the lasingdevice in experiment [7], the more significantly redshifted gainand emission spectra of QWs make the resonance lineshape onthe ASE spectrum more symmetric and narrow, which marksthe precursor of lasing action. As the cavity mode is immerseddeeply into the gain and emission spectrum of QWs, only thesymmetric Lorentzian-like lasing spectrum is observed experi-mentally.

V. LIGHT OUTPUT POWER VERSUS CURRENT

The rate equations of carrier density n and photon density Sof the cavity mode are often used to model the output powers ofa laser

∂n

∂t= ηi

I

qVa− Rnr(n) − Rsp(n) − Rst(n)S (12a)

∂S

∂t= − S

τp+ ΓERst(n)S + ΓEβsp(n)Rsp(n) (12b)

Rnr(n) = An + Cn3 (12c)

Rst(n) = vg,ag(n) (12d)


where I is the injection current; ηi is the injection efficiency; Va

is the volume of the active region; Rnr(n) is the nonradiativerecombination, which is modeled with a defect recombinationcoefficient A and Auger coefficient C; Rsp(n) is the sponta-neous emission rate; τp = Q/ωcav is the photon lifetime; ΓE isthe energy confinement factor [11], [18]; βsp(n) is the density-dependent spontaneous emission-coupling factor into the cavitymode; and Rst(n) is the stimulated emission coefficient writtenas the product of the gain g(n) and material group velocity vg,a

of QWs. The energy confinement factor ΓE can be calculatedfrom the optical field E(r) of the cavity mode [11], [18] asfollows:

ΓE =

∫Va

dr ε04 {εg ,a(ω) + Re[εa(ω)]}|E(r)|2∫

V dr ε04 {εg(r, ω) + Re[ε(r, ω)]}|E(r)|2 (13)

where ε(r, ω) is the permittivity of the cavity; εg(r, ω) is thegroup permittivity defined as ∂Re[ωε(r, ω)]/∂ω, and the quan-tities with subscript “a” are related to the active region (GaAsQWs). The estimated energy confinement factor is about 7.8%for 14 QWs. Alternatively, it can be also calculated using the Qfactor, gth , and threshold condition from the rate equation of S.For details of various quantities, see [11] and [18].

Fig. 8(a) shows the comparison between our theoretical cal-culation of the L–I curve and the experimental data. In thiscalculation, the defect recombination coefficient A is set to0.966 ns−1 , and the injection efficiency ηi is set to 0.419. TheAuger coefficient C is set to zero for simplicity since it is usu-ally small in the wide bandgap material, and we do not findquantitative changes of the L–I curve when varying this param-eter. We adjust the collection efficiency to match the theoreticaloutput power with that collected by the photon detector in ex-periment. An emission component from the background (QWemission not coupled to the lasing mode) is also included inthe calculation of L–I curve since the power of cavity mode isnot spectrally filtered out from experimental data. Experimen-tally, there is a kink on the L–I curve due to the emergenceof a second nearly degenerate HE11 mode at a high-currentinjection [7]. We thus focus on the range below 2.5 mA andconsider only a single lasing mode in the rate-equation model.The power below the threshold current Ith = 1.75 mA is mainlycontributed by the spontaneous emission power not coupled tothe lasing mode. The QW emission edge is far away from thelasing mode at a low-injection current, which effectively leadsto a low spontaneous emission factor βsp(n). Thus, a clear turn-ing point that marks the takeover of stimulated emission rateis present on the L–I curve. In addition to the turn-on behav-ior at Ith = 1.75 mA, the theoretical L–I curve shows anotherless significant change at a current ION = 0.5 mA. This currentION corresponds to the onset of the immersion of the cavityresonance into the redshifted QW emission window because thebandgap shrinkage increases with the injection current. In thisway, the photon emission through the potential lasing cavitymode becomes possible, and the theoretical L–I curve exhibitsa small kink at ION = 0.5 mA. In Fig. 8(b), we show the stim-ulated emission rate Rst(n)S and cavity spontaneous emissionrate βsp(n)Rsp(n). The nonradiative recombination rate Rnr(n)is shown in Fig. 8(c). Note that the scales of Fig. 8(b) and (c) are

Fig. 8. (a) Comparison between theoretical (solid curve) and experimental(symbol) light output power-versus-current (L–I) curves. The threshold currentIth is around 1.75 mA. (b) Stimulated emission rate Rst (n)S and spontaneousemission rate βsp (n)Rsp (n) of the cavity mode. (c) Stimulated emission rateRst (n)S and nonradiative recombination rate Rnr (n) are plotted as a functionof injection current. While the threshold current Ith = 1.75 mA marks theonset of lasing action, another smaller turn-on current ION at 0.5 mA [see thetheoretical L–I curve in (a) and two curves in (b)] is due to the immersion ofthe cavity resonance into the redshifted QW emission window as a result of thebandgap shrinkage when the injection current increases.

different. The stimulated emission rate Rst(n)S can be as smallas the low spontaneous emission rate βsp(n)Rsp(n) to the cav-ity mode below threshold, and of the same order of magnitudeas the significant nonradiative recombination rate Rnr(n) abovethreshold. Note that the turn-on behavior at ION = 0.5 mA canbe clearly observed in Rst(n)S and βsp(n)Rsp(n) as a func-tion of the injection current. Both βsp(n)Rsp(n) and Rnr(n)are pinned above the threshold due to the stimulated emission.The very significant nonradiative recombination rate indicatesthe inefficient usage of injected carriers because heat is needed


to bring the gain to the cavity mode. Also, since the resonancewavelength of the cavity mode is not within the QW emissionspectrum originally, the advantage of thresholdless operationexpected for a small laser has not been exploited in this device.The estimated spontaneous emission-coupling factor βsp(n) isaround 2.6% near threshold.

To further improve the performance of this metal-cavitysurface-emitting laser, a few approaches could be taken. First,the cavity resonance needs to be shifted back to the emissionwindow of QWs so that the material gain is available for thecavity mode even at a low-injection current. Also, the QWscan be redistributed near the standing-wave peaks of resonancemode profile so that the threshold material gain can be lowered.Another potential method to lower the threshold material gainis to increase the relatively low reflectivity of metal. The higherreflectivity may be obtained through the combination of metalcoating on the DBR. For example, a few (4-5) DBR pairs be-tween a thin metal coating and active region may significantlyincrease the reflectivity. This combination can be applied to bothsides of the active region, and even fewer DBR pairs than thosein the current design are needed. This can also reduce the devicesize and eliminate carrier-transport problems through the thickDBR regions.

When shrinking the size of this metal-cavity surface-emittinglaser, the approaches mentioned earlier in the reduction ofthreshold material gain are also applicable. However, for asignificant reduction of waveguide size, the effective indicesof guided modes can change significantly. The correspondingstopband of DBR may also not have enough reflectivity at thewavelength of interest. Thus, the redesign of the DBR that aimedat a particularly small waveguide core is necessary. This newdesign, with the combination of metal and DBR, may furtherreduce the laser size to the subwavelength regime.

To investigate the possibility of further shrinking the size of ananolaser fabricated from the same grown sample, we theoreti-cally consider a nanocavity structure with an 800-nm diameterand 8.5 bottom DBR pairs (the total height is 1.77 μm). Thelarger mirror loss due to fewer DBR periods is compensatedby a 50-nm silver coating on the DBR facet. The longitudi-nal field pattern of the HE11 mode with a cavity wavelengthλcav = 859.3 nm is shown in Fig. 9(a). The normalized totalcavity volume in the unit of λ3

cav is roughly 1.4. Compared withthe previously reported device, the cold-cavity quality factor Qis reduced to 494 while the energy confinement factor ΓE is im-proved to 8.6%. The corresponding threshold material gain gthis about 7550 cm−1 . The threshold material gain is comparableto (actually smaller than) that of the 2-μm-diameter microlasermainly due to the thicker silver coating (50 nm) that blocks themirror loss. To evaluate the performance of this laser device, wecalculate the L–I curve (power corresponding to the cavity res-onance, without collection loss from measurement setups) andvarious recombination rates, as shown in Fig. 9(b) and (c). Forsimplicity, we assume that the parameters such as nonradiativerecombination coefficient A or those for bandgap shrinkage in(8) remain unaltered, though the surface recombination whichis important for small devices may increase its value. FromFig. 9(b), the intrinsic output power of the cavity mode can be

Fig. 9. (a) Field profile along the growth direction. (b) Theoretical light outputpower-versus-current (L–I) curve. (c) Stimulated emission rate Rst (n)S andspontaneous emission rate βsp (n)Rsp (n) of the cavity mode. (d) Nonradiativerecombination rate Rnr (n) of the laser device with an 800-nm diameter. Al-though the thickness of silver coating (50 nm) is larger than that of the existingmicrolaser (10 nm), the intrinsic output power (assuming no collection loss)may be still in the microwatt range.


Fig. 10. Schematic of a multisectional waveguide. The random dipole currentJn (r) in the nth segment generates the output spontaneous emission spectra atz0 and zN +1 .

over 1 μm, even though about 78.5% of the outgoing power isdissipated in the 50-nm silver coating. The stimulated emissionrate Rst(n)S shows a turn-on behavior at ION = 0.06 mA [seeFig. 9(c)], while the threshold current Ith is around 0.28 mA[see Fig. 9(d)]. The nonradiative recombination rate Rnr(n) ofthis device is pinned at a fixed level once the stimulated emis-sion rate Rst(n)S begins to dominate, as shown in Fig. 9(d).These calculations indicate that with the same sample, a laser inthe subwavelength regime with a decent output power may bepossible by scaling down the size of the existing microlaser ateach dimension.

VI. CONCLUSION

We have developed a theoretical model for the metal-cavitysurface-emitting nanolasers. The design rules of this metal-cavity surface-emitting laser are presented. Our theory explainsthe experimental phenomena, such as the asymmetric ASE line-shape well. By utilizing the effective indices of waveguidemodes, the simple transfer-matrix method gives a quantitativeand reasonably good description of device characteristics. Theperformance of current micro-cavity device (2-μm diameter) ismainly limited by the large wavelength detuning between thecavity resonance and the QW gain spectrum at an injection levelnot high enough. We also discuss the possible approaches to re-duce the threshold material gain. These approaches, togetherwith the combination of DBR and metal, and redesign of DBR,may further shrink the device size to the subwavelength regime.

APPENDIX

LIGHT EMISSION IN MULTISECTIONAL WAVEGUIDES

Let us consider the light emission due to the random-dipolesources in a multisectional waveguide shown in Fig. 10. Thenth segment begins at z = zn and ends at z = zn+1 = zn + hn ,where hn is the length of the section. We first obtain the field dueto the random dipole current Jn (r) existing only in segment n.Later, the linear superposition principle can be used to obtain thetotal output radiation due to random dipole sources in differentsegments.

In segment n, since the random dipole current Jn (r) is atransverse current that does not generate a macroscopic chargedensity, we can use the waveguide modes obtained with zerodivergence condition of the displacement field (∇ · D = 0) toexpand the electric field En (r) and the magnetic field Hn (r)

inside the segment:

En (r) =∑

b

[Eb,n (ρ)Fb,n (z) + Eb,n (ρ)Bb,n (z)]

Hn (r) =∑

b

[Hb,n (ρ)Fb,n (z) + Hb,n (ρ)Bb,n (z)] (14)

where Eb,n (ρ) and Eb,n (ρ) are the electric-field profiles offorward- and backward-propagating mode b in segment n, andHb,n (ρ) and Hb,n (ρ) are the corresponding magnetic-field pro-files. These field profiles can be written in terms of the associatedtransverse and z components as [19]

Eb,n (ρ) = E(t)b,n (ρ) + zE

(z )b,n (ρ)

Eb,n (ρ) = E(t)b,n (ρ) − zE

(z )b,n (ρ)

Hb,n (ρ) = H(t)b,n (ρ) + zH

(z )b,n (ρ)

Hb,n (ρ) = −H(t)b,n (ρ) + zH

(z )b,n (ρ). (15)

The amplitudes Fb,n (z) and Bb,n (z) are then obtained by theorthogonality condition of waveguide modes and reciprocitytheorem [19] as follows:

Fb,n (z) = eikb , n (z−zn + 1 )F(2)b,n +

1

4P(z )b,n

×∫ zn + 1

z

dz′∫

dρ′e−ikb , n (z ′−z )Eb,n (ρ′) · Jn (r′)

Bb,n (z) = e−ikb , n (z−zn )B(1)b,n +

1

4P(z )b,n

×∫ z

zn

dz′∫

dρ′eikb , n (z ′−z )Eb,n (ρ′) · Jn (r′)

P(z )b,n =

∫dρ′z · 1

2

[E(t)

b,n (ρ′) × H(t)b,n (ρ′)

](16)

where F(2)b,n = Fb,n (zn+1) and B

(1)b,n = Bb,n (zn ) are amplitudes

at the boundaries (superscripts (1) and (2) refer to quantities atzn and zn+1 , respectively), and P

(z )b,n is the complex power of

mode b. We adopt reflection boundary conditions at zn and zn+1(neglect mode mismatch, valid for waveguides with core sizeslarger than the effective wavelength by several times)

r(1)b,n =

Fb,n (zn )Bb,n (zn )

r(2)b,n =

Bb,n (zn+1)Fb,n (zn+1)

. (17)

With these conditions, the amplitudes F(2)b,n and B

(1)b,n are ob-

tained as follows:

F(2)b,n =

eikb , n hn

r(1)b,n r

(2)b,n e2ikb , n hn − 1

1

4P(z )b,n

×∫ zn + 1

zn

dz′∫

dρ′[r

(1)b,n eikb , n (z ′−zn )Eb,n (ρ′)

+ e−ikb , n (z ′−zn )Eb,n (ρ′)]· Jn (r′)


B(1)b,n =

eikb , n hn

r(1)b,n r

(2)b,n e2ikb , n hn − 1

1

4P(z )b,n

×∫ zn + 1

zn

dz′∫

dρ′[eikb , n (z ′−zn + 1 )Eb,n (ρ′)

+ r(2)b,n e−ikb , n (z ′−zn + 1 )Eb,n (ρ′)

]· Jn (r′). (18)

The single-mode reflections in (17) imply that different modesdo not significantly mix at waveguide boundaries, which is validif there is an approximate one-to-one correspondence betweenthe modes at two sides of boundaries, and their transverse pro-files do not differ much.

Let us consider the output spectrum at z = z0 . The field atz = z0 is the sum of the output fields due to sources in differ-ent segments, and therefore, the corresponding output P (z0 , ω)is a bilinear sum of backward-propagating amplitudes {B(1)

b,n}(bilinear functional of {Jn (r)})

P (z0 , ω) =∫

dρ(−z) · 12Re [E(ρ, z0) × H∗(ρ, z0)]

=∑

(n ′,b ′),(n,b)

c(n ′,b ′),(n,b)B(1)∗n ′,b ′B

(1)n,b

=∑

(n ′,b ′),(n,b)

c(n ′,b ′),(n,b)

∫ zn + 1

zn

dz′∫

dρ′∫ zn + 1

zn

dz

∫dρ

×∑

α ′,α=x,y ,z

[...] J∗n ′,α ′(r′)Jn,α (r) (19)

where c(n ′,b ′),(n,b) is a factor related to power coupling, and [...]is part of the integrand unrelated to Jn ′,α ′(r′) and Jn,α (r). Wesimplify (19) based on the ensemble average as

〈J∗n ′,α ′(r′)Jn,α (r)〉 = δn ′nδ(r′ − r)

∑c,v

Dcvn (r)

×[−2iωqdcv ,α ′ ]∗[−2iωqdcv ,α ] (20)

where c and v are the labels of conduction and valence subbandsfor interband transitions; Dcv

n (r) is the corresponding dipoledensity; and qdcv ,α is the dipole moment of transition (c, v) inthe α-direction. We further drop the coupling of distinct modesin (19) and recast it into a more physical form

〈P (z0 , ω)〉 ≈∑n,b

Tb,(0,n)P(z )b,n 〈|B

(1)b,n |2〉

〈|B(1)b,n |2〉 =

e−2kb , n , I hn

|r(1)b,n r

(2)b,n e2ikb , n hn − 1|2

(ω

2

)2 ∑c,v

Dcvn (r)

× 1

|P (z )b,n |2

∫ zn + 1

zn

dz

∫dρ

∣∣∣[eikb , n (z−zn + 1 )Eb,n (ρ)

+ r(2)b,n e−ikb , n (z−zn + 1 )Eb,n (ρ)

]· qdcv

∣∣∣2 (21)

where Tb,(0,n) is the power transmission to output at z0 for modeb from segment n. Similarly, we can write out the ensemble-

averaged output spectrum 〈P (zN +1 , ω)〉 at z = zN +1 as

〈P (zN +1 , ω)〉 ≈∑n,b

Tb,(N +1,n)P(z )b,n 〈|F

(2)b,n |2〉

〈|F (2)b,n |2〉 =

e−2kb , n , I hn

|r(1)b,n r

(2)b,n e2ikb , n hn − 1|2

(ω

2

)2 ∑c,v

Dcvn (r)

× 1

|P (z )b,n |2

∫ zn + 1

zn

dz

∫dρ

∣∣∣[e−ikb , n (z−zn )Eb,n (ρ)

+ r(1)b,n eikb , n (z−zn )Eb,n (ρ)

]· qdcv

∣∣∣2 (22)

where Tb,(N +1,n) is the power transmission to output at zN +1for mode b from segment n.

For a uniform dipole density in a [0 0 1] QW (denoted assegment n), in which there are no TE and TM cross terms in(20), we can simplify 〈|B(1)

b,n |2〉 as

〈|B(1)b,n |2〉=

η0hnω2

2P

(z )b,n

|P (z )b,n |2

e−2kb , n , I hn

|r(1)b,n r

(2)b,n e2ikb , n hn − 1|2

×{[(

ekb , n , I hn +∣∣∣r(2)

b,n

∣∣∣2e−kb , n , I hn

) sinh(kb,n,Ihn )kb,n,Ihn

+ 2∣∣∣r(2)

b,n

∣∣∣ cos(kb,n,Rhn + φ

(2)b,n

) sin(kb,n,Rhn )kb,n,Rhn

]

×Γ(t)

wg ,b,n

n(t)n,R

[∑c,v

Dcvn |qd(TE)

cv |2]

+[(

ekb , n , I hn +∣∣∣r(2)

b,n

∣∣∣2e−kb , n , I hn

) sinh(kb,n,Ihn )kb,n,Ihn

− 2∣∣∣r(2)

b,n

∣∣∣ cos(kb,n,Rhn + φ

(2)b,n

) sin(kb,n,Rhn )kb,n,Rhn

]

×Γ(z )

wg ,b,n

n(z )n,R

[∑c,v

Dcvn |qd(TM)

cv |2]}

Γ(t)wg ,b,n =

1

P(z )b,n

n(t)n,R

2η0

∫Aa , n

dρ|E(t)b,n (ρ)|2

Γ(z )wg ,b,n =

1

P(z )b,n

n(z )n,R

2η0

∫Aa , n

dρ|E(z )b,n (ρ)|2 (23)

where η0 is the intrinsic impedance, kb,n,R is the real part of

kb,n , and φ(1)b,n and φ

(2)b,n are the phase angles of r

(1)b,n and r

(2)b,n ,

respectively; Γ(t)wg ,b,n and Γ(z )

wg ,b,n are the transverse and z wave-guide confinement factors, respectively; Aa,n is the QW area,

n(t)n,R and n

(z )n,R are the corresponding refractive indexes in the

QW active region, Dcvn is the uniform dipole density, and qd

(TE)cv

and qd(TM)cv are TE and TM dipole moments, respectively. The

quantity 〈|F (2)b,n |2〉 can be obtained by replacing (|r(2)

b,n |, φ(2)b,n )

with (|r(1)b,n |, φ

(1)b,n ) in (23). The material properties of QWs come


into play through the TE and TM dipole moments:

∑c,v

Dcvn |qd(TE/TM)

cv |2 ≡ 1hn

∑c,v

∫dkt

(2π)2

∣∣∣∣∣qP

(TE/TM)cv ,kt

m0

∣∣∣∣∣2

× fc,kt(1 − fv,kt

)

× L(Ec,kt − Ev,kt− hω) (24)

where kt is the wave vector of carriers, P (TE/TM)cv ,kt

is the TE/TMmomentum matrix element, fc,kt

and fv,ktare the Fermi occu-

pation numbers at energies Ec,ktand Ev,kt

, respectively, andL(E) is a lineshape function centered at E = 0 and is modeledas a Gaussian function.

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Shu-Wei Chang (M’09) received the B.S. degreein electrical engineering from the National TaiwanUniversity, Taipei, Taiwan, in 1999, and the M.S.and Ph.D. degrees from the University of Illinoisat Urbana-Champaign, Urbana, in 2003 and 2006,respectively.

From 2008 to 2010, he was a PostdoctorateAssociate in the Department of Electrical and Com-puter Engineering, University of Illinois at Urbana-Champaign. Since 2010, he has been an AssistantResearch Fellow at the Research Center for Applied

Sciences, Academia Sinica, Taipei, Taiwan. His current research interests in-clude fundamental and applied physics of semiconductor photonics includingtunneling-injection quantum-dot–quantum-well coupled system, slow and fastlight in semiconductor nanostructures, spin relaxation in strained [1 1 0] and[1 1 1] semiconductor quantum wells, group-IV direct-bandgap semiconductorlasers, active and passive plasmonic devices, semiconductor nanolasers, and ap-plications of metamaterials, both chiral and nonchiral, to semiconductor activedevices.

Dr. Chang is a member of the Optical Society of America. He was the recipientof the John Bardeen Memorial Graduate Award from the Department of Elec-trical and Computer Engineering, University of Illinois at Urbana-Champaign,in 2006.

Chien-Yao Lu (S’05) received the B.S. and M.S.degrees in electrical engineering from NationalTaiwan University, Taipei, Taiwan, in 2003 and2005, respectively. He is currently working towardthe Ph.D. degree in the Department of Electricaland Computer Engineering, University of Illinois atUrbana-Champaign, Urbana.

He is conducting research on the design, fab-rication, and characterization of nanophotonic andplasmonic devices. During his Ph.D. study, he hasdesigned and fabricated several metal-cavity lasers,

including the device used in this paper.Mr. Lu won the Best Poster Award (1st place) in the International Nano-

Optoelectronics Workshop (i-NOW) 2010 for his work on substrate-free metal-cavity microlasers. He received the Nick and Katherine Holonyak OutstandingResearch Award for the University of Illinois in 2011.


Shun Lien Chuang (S’78–M’82–SM’88–F’97)received the B.S. degree from National Taiwan Uni-versity, Taipei, Taiwan, in 1976, and the M.S., E.E.,and Ph.D. degrees from the Massachusetts Instituteof Technology, Cambridge, in 1980, 1981, and 1983,respectively, all in electrical engineering.

In 1983, he joined the Department of Electricaland Computer Engineering, University of Illinois atUrbana-Champaign, Urbana, where he is currentlythe Robert MacClinchie Distinguished Professor. Hewas a Visitor at AT&T Bell Laboratories (1989), the

SONY Research Center (1995), and NTT Basic Research Laboratories (1997).He was also a Visitor at the NASA Ames Research (1999), Fujitsu Research Lab-oratories (2000), Cavendish Laboratory at the University of Cambridge (2002),and the Technical University of Berlin (2009). He contributed to the theory ofstrained quantum well, band structures and optical gain models. He is conduct-ing research on nanolasers, plasmonics, strained semiconductor quantum-welland quantum-dot lasers, and superlattice photodetectors. He is the author ofPhysics of Photonic Devices (Wiley, 2009, second edition) and Physics of Op-toelectronic Devices (Wiley, 1995, first edition). He has published more than300 journal and conference papers and given many invited talks at conferencesand institutions.

Dr. Chuang is a Fellow of the American Physical Society and the OpticalSociety of America. He has been cited many times for Excellence in Teachingat the University of Illinois. He was also awarded a Fellowship from the JapanSociety for the Promotion of Science to visit the University of Tokyo in 1996.He received the Engineering Excellence Award from the Optical Society ofAmerica in 2004, the IEEE Lasers and Electro-Optical Society (LEOS) Distin-guished Lecturer Award for 2004–2006 for two terms, and the William StreiferScientific Achievement Award from the IEEE (LEOS) in 2007. He received theHumboldt Research Award for Senior U.S. Scientists in 2008–2009. He waselected as a member of the Board of Governors for the IEEE Photonics Societyfor 2009–2011. He served as an Associate Editor of the IEEE JOURNAL OF

QUANTUM ELECTRONICS (1997–2002) and the JOURNAL OF LIGHTWAVE TECH-NOLOGY (2007–2008). He was a General Co-Chair for Slow and Fast LightMeeting of the Optical Society of America, July, 2008 and has served in manytechnical program committees of the IEEE and the Optical Society of America.He was a Feature Editor for a special issue in Journal of Optical Society ofAmerica B on Terahertz Generation, Physics and Applications in 1994. He alsoedited a feature section on Mid Infrared Quantum-Cascade Lasers in the June2002 issue of the Journal of Quantum Electronics.

Tim D. Germann studied at Konstanz Univer-sity, Germany Uppsala University, Uppsala, Sweden,and the Technische Universitat (TU) Berlin, Berlin,Germany. He received the Diplima degree in appliedphysics from the TU Berlin in 2007. Currently he isworking toward the Ph.D. degree in the Departmentof Solid State Physics at TU Berlin.

He is conducting research on the epitaxial growth,design and fabrication of nanophotonic and plas-monic devices. During his Ph.D. study, he has de-signed, epitaxially grown and realized several novel

photonic device concepts, including the metal-cavity laser device used in thispaper. He has authored more than ten research papers. His research interestinclude the epitaxial realization of novel III-V semiconductor applications. Hespecialized in the realization of quantum dots and novel nanostructure conceptsfor optical devices such as high-speed and high-brilliance lasers, micro- andnanolasers and single photon emitters.

Mr. Germann won the Best Poster Awards 2nd place in International Nano-Optoelectronics Workshop (i-NOW) 2008, Japan and 1st place i-NOW 2010,China, and received the Dimitris N. Chorafas Foundation Award 2010 for hisdoctoral research. He is a member of the German Physical Society.

Udo W. Pohl received the B.S. degree from the Tech-nical University of Aachen, Aachen, Germany, in1978, and the M.S. (Diploma) and Ph.D. degrees fromthe Technical University of Berlin, Berlin, Germany,in 1983 and 1988, respectively, all in physics.

He is currently the Chief Operating Officer ofthe Center for Nanophotonics, Institute of Solid StatePhysics, Technical University of Berlin. In 2009, hewas appointed as an Adjunct Professor of Physics atTechnical University of Berlin. He has authored about200 journal articles and conference papers, nine book

contributions and two patents. His current research interests include epitaxy andphysics of semiconductor nanostructures and devices.

Dieter Bimberg (M’92–SM’08–F’10) received theDiploma degree in physics and the Ph.D. degree fromGoethe University, Frankfurt, Germany, in 1968 and1971, respectively.

He is currently with the Institut furFestkorperphysik, Technische Universitat (TU)Berlin, Berlin, Germany. From 1972 to 1979, he heldthe position of Principal Scientist at the Max Planck-Institute for Solid State Research, Grenoble, France,and Stuttgart, Germany. In 1979, he was appointedas a Professor of Electrical Engineering, Technical

University of Aachen, Aachen, Germany. Since 1981, he has been the Chair ofApplied Solid-State Physics at TU Berlin. He was elected in 1990 and succes-sively reelected as Executive Director of the Solid State Physics Institute at TUBerlin. In 2006, he was elected Chairman of the Board of the German NationalCenters of Excellence of Nanotechnologies. He has authored more than 800research papers and several books, and has been awarded many patents, re-sulting in more than 16 000 citations worldwide. His current research interestsinclude the growth and physics of nanostructures and photonic devices, such asquantum-dot lasers and amplifiers, singlephoton emitters, wide-gap semicon-ductor heterostructures, and ultrahigh speed photonic devices.

Dr. Bimberg is a winner of the Russian State Prize in Science and Tech-nology in 2001, the Max-Born Award and Medal in 2006, which is awardedjointly by the Institute of Physics and the German Physical Society, and theWilliam-Streifer Award of the Photonics Society of the IEEE in 2010. In 2004,he was elected to the German Academy of Sciences (Leopoldina) and becamea Fellow of the American Physical Society.

Documents

Theory of Metal-Cavity Surface-Emitting Microlasers and Comparison With Experiment