NASA Technical Reports Server (NTRS) 20010071849: VCSEL Applications and Simulation

9 Pages·0.36 MB·English

by  NASA Technical Reports Server (NTRS)

:Outline :
• Introduction
- What isVCSEL?
TheVision
VCS_ SA_PAPLTIICOANTIONS AND/:
• VCSEL Applications
Op_caI Intcrconnectlon in Information l"echnoloKv
Dr. Samson Cheu_ Yh¢ Reason
Dr. Peter Goorjian • VCSEL Simulation
Dr. Jianzhong Li FormuJafion
Numeric Algorithm
Dr. Cun-zheng..=Ning )Lead)
Computation Resulta
hOp'J/www.n as.na.sa .gov/G roups/Sa Tech/qd m/index .htmt
• • • , • • • •
VCSEL is a Semiconductor Laser
• Any laser consists of two ingredients
active matenal
cavity
• Semiconductor laser based on electronic
transitions involving annihilation ofelectrons and
holes in asemiconductor, e.g. GaAs Gallium
INTRODUCTION Arsenide.
• WtlAT IS VCSEL? • The first VCSEI, ismade by Prot'. Iga from Tokyo
• TIlE VISION University.
• Focused on native oxide confined GaAs and
lnGaAs VCSELs, red VCSELs and 1.3 and 1.55
micron wavelength VCSELs.
WHAT IS VCSEL? ComparisOn with Edge.Emitting Laser
• VCSELs :Vertical-Cavity-Surface-Emitting Lasers
_A
• Vertical-Cavity means that the • Edge Emitting Diode Laser _l
- Light fromlhc edge
cavity is vertical to the
A+tigtmtie dixerging :ll+te
semiconductor u,afer.
Elli_icai beam
• Surface-Emitting means that
the light conies out fi'om the
surfiace of the wafer.
Light fromll_ stathce ;1_
• Distributed Bragg Reflectors (DBRs)
• VCSE_Lnraller divergence ,ingle
2t'*-_Opairsof semiconductor !a_e_s
circular i_am cvo$_ .,¢ction
:'effectivity().99S
/a,.er thickness :)+ldt=,,__d_=,L.4.
2-D VCSEL _ys
° Re_ereh_ Id experimemts
have been deme oa VCSEL in
rt.¢t_ Iyt_M.
• An ant is Iookiulg down at
VCSEL array.
• One array consists of 400
INTRODL'CTION
individual VCSELs.
• WHAT IS VCSEL':
• By A. Soberer, Harnessing the
Atom '_ Light, Scientific • TIlE VISION
_.m_r"w.a n. 1998.
! li a li | "
The Tera-Em Vision
Optoelctronic Integlated Circuit (OEIC)
According to a 1999 marketing study generated by Optoelect ronic_is themajor enabling technolo_ for the tera-era
ElectroniCast (Palo Alto, CA). there are four primary information technology according tothe NRC report.
OEIC application areas: datacom, telecom, military, and http://ww w.nap.ed u/eat alo#5954.h tml
specialty. • information Transmission: (Terabit-pee-second
The potential OEIC market is projected to be $1.1 backbone, ion8 haul networkst
Access r_twork openltxng at hundlt daof_bll_# s¢,2
billion by FY 2003 and over f_ billion by FY 2008. Local area rtetwod_ opemtan_ atrcnsofg_t bits.scc
- Gl_abd persecond tothed_sktop
Datacom OEICs are expected to be the most cost
• Informatio*l Proces_ng: (tern-operations per second
effective devices to manufacture because the majority
computersl
of the components will be serial (single element) Terabd per s_ond throughput switches
Mulh_lgahert2 clc-cks
devices which operate at 850nm (the ;Z)in multimode [nt_rconne¢ )onsopemtmg at hundreds ofglgablt _",ec
fiber networks. • Information Storage: _Terabyte data bankl
Mulhterbyt¢ disk dnses
tens, of_abyl¢ _111o_ chil_
: Advantages :
• Circular beam
. :deal for free spctce coupling toother optical elements
effectively taunched into optical fibers
• I,ow threshold current {< imA)
• 2-dimensional array capabilities
• Iiigh Bandwidth under modulation
VCSEL APPLICATIONS
- l_l_ GFIz
•OPTICAL INI"ERCONNECTION IN Easily integrated with traditional electronic devices
INFORMATION TECHNOLOGY
monolithically (like transistor)
•TIlE REASON heterogeneously by v,afer Ixmding _echnoh_gy with C,_lOS
circutt ,',3form SPA (Smart Pixel Arrayl
"• . . • . • • •
2
• MonoJitbl¢ VCSELJpbolodc4ector
array
• Photodetectors receive the optical •2-dimensional array capabilities
_ignal from the VCSEL.
•single longitudinal mode optical output
• OptiComp Corporation, Nevada
•very small size
•very low threshold current A _ch_ed CSEM
VCSEL array _*th the
cap removed. "['helauerl
e_ttt verttcaUy fromthe
chip _urftce.
p
h[tp: ',_,',vw.d a',vnO_akc r.co mma,. _.t_nefi ngs_ o_d¢omp.html
Optoelectmnics and IT
VCSELs applied to Information Technology:
• Smalle_l semiconductor lase¢
/i¸i_!/i/iii!:_!_//_ii!i :_ i : : !
• Peta-flop compuling with VCSEL-based
optical interconnect
• lnterprocesaor communication
• _',lulti-gigabit Ethernet
"31C] .. ii 0,0,... VCSEL APPLICATIONS
.l-U-k ._.JZrl. • OPTICAL INTERCONNECTION 1N
INFORMATION TECIINOLOGY
Electronic
Electronic _ TOrpa_rmm l[e_mUotn Output • TIlE REASON
l.put rraz_nUtter recaller
David Miller :lnt J.Optoelectronics Vol. II, p.t55 (19973
• * • , • • o 0
Electrical and Optical: Similarities :Electrical and Optical Differences
• hlfornmtJou carried via electromagnetic physic,;
_lgt_als in '_ires _on't propaga:e at the electren velocity Very short wavelength)
,IC_r_ s)
500 nm | k= c/v
• lake electronic logic devices, optical logic devices electronic 3cm-30m )
ttse electrons to effect the necessary switching
_,nol tt_ V Vh/e
0 _ o ~3.0e_8 rTVS High oarrier frequency 1 arge photon energy
500 THz [ 2 eV
electronic 10MHz-10GHz) lectronic 40neV_OmeV
1- 'T" << 3,0e_.B rr_s
r_cMaac_'c._ clanc_
i a | a I - . .
• High frequency Bits per second ~ B0
- solves difficulty of_'high aspect ratio" archJ_tums B0- 10i5 for cables rt
allows short op_cal pulses usage
B0- 1016 for on-chip lines
allows muitipte different frequency carriers
B0~ 10ns for equalized lines
• Short wavelength _ILA
(How can we reach l"b/s ?!)
alloy, sfrte-space multi-chart:el imaging interconnets
allows beamsplitters without _ck retlec_on Architecture
. Large photon energy Telecommunication switching -- I r_sot
ailow_ voltage isolal3on Servers
aito'_,s quantum impedance coave_
Noee: can elceed the limil by codin_ repeating,
or multilevel modulation
No_ tim_ivo formalinien_ fundamental.
Optical lntercormections sho t
• No aspect-ratio problem Free-'_pace electri¢_l| interconneclio,'ls are not practical b(_cause
Ihewavelength nf signal istoo long --longer than achip. It is
• No modulation-frequency-dependent loss hard to focus awave toadimension smaller than its
• Loss in optical giber is low (0.2dB/km) wavelength
• Dispersion is weaker in optical fiber than cable
In optics, bycontrast, common to
less than l,10clock period, of,Lispersion fora6GHz image thousands ofoutputs onone
bandwidth slgr_al over Ikm ,fffiber surface tothousands of inputs on
• Optical fiber can be small ~12.Smicrons in diameter another via "free space"; e.g. using
lens.
Note: Free spalce ill¢er_llaecllo_ _n beopen SpiCe or mtirely take pl_ce wlt ItJ _olld
or rigid g_ _rmcrare
Note: stin ulcter reae_cb
Voltage Isolation
Detection ofphoton allows _s togenerate current and
voltage but carries no information (orinterference) from the
d.c. level inthe source circuit.
The so-¢alled "oplo-isolator" so_ves an important pxoblem in _i:_ _ _ _i!_i_ _ _ii_:!_ _
electrical systems
'.ightemitting
diode
VCSEL FORMULATION
pho
4
Semiconductor Bloch Equations _iiii
2 2
_t*=-iakpk-_<._ +n_-I)+_ atI,,,, e_ = '_ k Carrier Particle Energy
2ma
3
--at ------'ynnk -s- Pit at tc-¢ at Ic-p. •Va _---V ,_ nak Total Carrier i)ens_ty
2
Wa =_-_e_n Total Energy
7_ carrier re_ombinat ion rate
Ak electronic pumping
• Parabolic energy band
Att detuninlt t¢,rm
nt Coulomb effect • N" = Nh= N
c - c carrier -orrie_eattering • ._ is described by Fermi-Dirac distribution
c - ph carrier -phonon scattering
I i I n - " "
Bottom-Up Approach: Calculation of Optical Susceptibility
A Simp|ified Model
• Solve the Bloch equations for some N to obtain the
induced polarization PtO
=t • Obtain the optical susceptibility XIt_,N) from
Fourier Transforms of E and P:
P(¢o) = %e_(_,N) E(_
OPTICAL • Then refractive index and optical gain follow
X(co_V) -(21nb)fn(co,N) -(i/K)G(osV)
• For each value of N, obtain Lorentzian oscillator
and background Xo to approximate
X({o,,N) = go (N) +AiN)/IiA(N)+t_+cx._5(,V)]
l I I | I " |
Polarization (Matedal) : ::
The polarization dynamics ha.';a femtosecond time scale, much Treat Electric field as ascalar quantity. Within the slowly
faster than the dynamics of Ihe electric field and the carrier varying envelope approximation, the time dependence of the
density, and can often be a_ume,d to adjust instantaneously on electric field (E-field) envelope is governed by
the time scale of the latter processes. The polarizalion can be _r
approximated by P{D = P0itl *PI_._where,
l_(t) =_)nb Z,)l N.Tp.Tt lE r
nb , n% refractiveindex :phase, group
8 s(x, y ) derivation of refractive index profile
03c cavity resonance frequency
nO permiltivity of vacuum
= Icl 2Ln _ lint I r_ ) _=_,_ (reflectivityoflaand2 "dmirror
wherelm, A,8, and, t.arefillin_ paralnelersapproximalng • r = ,8L,. /L L= cavity length, /.,i =width of acliveregion
=effective coupling cort_ant
:_er Density Equation :
The dynamics of carrie¢ density is g_vernment by the Bloch
equation
carrtef d_mity
_vt_,V =V _Dv VNi÷D,-rIVT,)>-,_.¥+_--_Im(P'E)
J(x. y) pumping clrrent profile
f_ plasma temperature
y_ non -radiative carrier r_combinat ion rate
D_N. Dr,_ diffusion ,-oefllcients due to N and T_,
e elect ro4n chaise _
h= h 2_ h =plank ¢ot'6tant
I a I i I
Thermal-Electronic-Optical Couplin_ : PlasmaTemperature
The tem peralure Lqderived from the energy (W_ equation
._rrler .[en_ity aw_ aw awaN
i _ja,:_ aNa,
t _W
InFctkm healm_ ermsslon with _'- = 7Jw - #r (T/, - TI)+Rw
rphonon Therefore.
m 9tl_rre on_
_-_J_7"=V(nrNtVN_+Orr_Vr.,-Vr(r,-1",)
., k_'" ) --_- R v
Hasma Temperature (conts.) : ..... The M_I
• Modeling transverse mode dynamics of VCSEI.s
• No a_umptions are nmde about about the type or
where
{ - o! 1t number ofspatial (transverse) modes
-- tWa-W0 +n-Er'/_-L'ra ozc-iy2'- P*E-iP*E • Nonlinear carrier density dependence of the optical
gain and refractive index
R,_ =_¢n,V ÷ , -T._.f-i_tLm (P .E) • Wavelength dependent dispersion effecLs on the
O'r.'_ , D/-r diffusionco¢mcients due to ,V andTp optical gain and refractive index
-_ plasmacoolmgrate • The 0ptical'Susceptibility is based on suhltions of
the semiconductor BIoch equations
yz polar izativn dephasingraie
includes many-body efflcts
includes device details (qw _l'rucruoe -- [n(;a,\s_GaAs)
I i i i i i
• Seleacftew
transverse modt_ beforehand and then
solve their time evolution (either by ordinary or
partial differential equations)
• Solve an eigenvalue problem [or the Helmholtz
equation, which is uncoupled to the material
equations
• Solve time independent, coupled rate equation NL_IERICAL ALGORITHM
methods, which contain diffractive terms (in the
wave equation) and dillMsive transverse terms (in
the carrier density equation)
: ..**oo.°
Effective Maxwell BIoch Equations Alternating Direction: Implicit (ADI)
ql)
DE_ ic z VeE_(_ 3n(x.y)C_C)E+ i_cF p - • Sweepin xdirection
_t 2n_nb_ c ng 2ngnbe o _ • advance from tto t+_/2
I <
• implicit differences are used
a__[-,vl_c_frov, o,.:_FNll FNI for derivative of x.
12)
• S_,eep iny direction
• advance from t+6_2 to t+6t
P_(t) =e,n_znE(t) [
• implicit differenc_l are usc{I
dP1 ={-:_(N)}P(t)-=:(N IE(t)J ODE t t+/I.¢2 [or derivali ce of y.
AD[ Illustration ....:
Consider
=GV E+F I-GAt([- f)(V2* +V2Y)I_(n+I) =
,,:,,.tn_./I ,r72__1_'1 ..r(n÷l/2)
At the nta time level method I fully implicit Cmnk-Nicolson explicit
._)_e I O fL5 t -
To alarge system implicitly in Iloth tile xand ydirections
• ._ . =GII_f)V,EL )+GJV_E ( ) is computationally intensive. As an alternative...
At
Sweep in x-direction
Sweep in y.direction
...... s 2, -.eq. ,.rf "+l_z) i_,.,i #_t,.r2 _ln+l) (n+[: 2_ r,,,i .'x¢72 _(/_)
7
• The above set of equations describe the lasing
environment
+AtF ('+1'2) +O(_t2&r2&y:)(_._-) • TheapproximatiolofLorantzian for Polarization
is not good for absorption
• At the region where N is small (l0 jz l/ra J)
Second order accurate in time and space
Solving Y(M-i} _ of IM-I} Iridin_onal equatioets
W = 2k_Fsv
ps.u2) isobtained by Taylor Stq-ies
E=p=_I
p_.tm. F,s,+At 8 P'V'_
Simplified ,"_and '_requations
i | " "
The Experiment
Two.elemenl phased array of anliguided vertical-cavity in_ers
by D. K. Serkland, et. al.
Applied Physic_q Letters, Vol. 75. No. 24, De¢_ i999.
• Zadjacent VCSELs z,_ ...... "_/_._-_.
1 _
O High optical index ,,........_..........._.............................
COMPUTATION RESULTS between the 2VCSELs " )
• Emitted light ...... pied :,...... _! "_""_Z.: :.g:.:q_'X_'_: )'" _
a,nod,_VhCSEoLtsherinterfered L__L_ / _X' i .
m | | t ii -
:: :_e Computational Grid
• near-field (I) and far-field
121images
• 8(a) and 20 Ibl micron_
separations
(a) _b)
• The far field
peak at the center for the 8-
rnictotlseparation
nopeak at thecenter tbrthe
-_O-mlcm ii_ep_CallOlk
| -
Near-Field Sotution
_a)
" i!ii!i_i_i:_!i:i:i:i:i!i_:!?i.!ii:!i:ii!iii!.ti:i!i_i!i
:i...... ii'i'i
P
ii | | - " -_
Maximum Power
Guiding Index and Central Current:
85% 75% 65% 55% Central
When do we have phase-locking (resonance)? Current
When do we have maximum intensity output?
0.005
8.(x_v)
t j _ J 9.7e+7Amp_m '_ _ 0.006
0.007
0.008
vcs FA_
Conclusion :: i
• Changing Index
affects on the [ar-_ield parterre.
for lndexffi(_._6, no phase-l¢cx_ng, rest_ts are ume
averaged, transttlon stage from )_l.x_ts to_ _ts
increase the index, increase the ;'_attem at _e :truer edge of
IheVCSEL
• Changing Central Current
alfec_ on _he rear-fleld pattet_
g5% of J alone doesn't create _asing envit_nmerit
Increase the cur'_nt, increase "_e intensity
Increase the cuY'r_nl, increase ,2_e _nterference at ",hecenlcr