Transcript Approximate Theory of Rectangular Optical Waveguides

6. Optoelectronic Devices
Optical Waveguides
(a) A buried-in rectangular waveguide, (b) a buried-in rib waveguide,
(c) a strip-loaded waveguide, and (d) a diffused waveguide
Some Fabrication Processes of
Optical Waveguides
Basic Theory of Waveguides
Theory of Planar Optical Waveguides
Approximate Theory of Rectangular Optical
Waveguides Surrounding by a Uniform Medium
Approximate Theory of Rectangular Optical
Waveguides Surrounding by a Uniform Medium (Cont’)
Approximate Theory of Rectangular Optical
Waveguides Surrounding by a Uniform Medium (Cont’)
Applications of Y-Branches and Bends of
Conventional Optical Waveguides
Multimode Interference (MMI) Devices
Example of Optical Performance
of MMI Device
1×n MMI Optical Splitters
All-optical Logic Gate Based on
MMI Waveguide
All-optical Logic Gate Based on
MMI Waveguide (Cont’)
All-optical Logic Gate Based on
MMI Waveguide (Cont’)
Photonic Crystals
Square-lattice and Triangular-lattice
Photonic Crystals
Band Structures of Photonic Crystals
Eg. The band structures of the 2D square-lattice photonic crystal with the lattice constant is a=0.5μm. The radius of the
pillar is Rc=225nm. And the refractive index of the pillar is 3.16227766.
Photonic Crystals Improving
LED Efficiency
• Incorporating a photonic
crystal into an indiumgallium-nitride (InGaN)
LED increases both the
internal quantum
efficiency and the amount
of light extracted. The
light is produced in the
quantum-well (QW) active
region.
Photonic Crystals Improving
LED Efficiency (Cont’)
Far-field emission patterns from a conventional (left) and a photonic-crystal
LED (right) are very different. The latter has a strongly-modified emission
pattern due to the scattering of waveguided modes out of the LED chip.
Photonic Crystal Waveguides (PCWGs)
Comparison between the Conventional
Waveguides and the PCWGs
•
•
The conventional optical waveguides are
weakly guided. There exist large power losses
in the wide-angle bends/branches. However,
the same structures made of line-defect
photonic crystals give little losses because the
lights were trapped by the defects of the
photonic crystals.
Most of the conventional optical waveguide
devices can be easily modulated by EO effect,
AO effect, and so on. But only a few photonic
crystal waveguide devices can be modulated.
Periodical Dielectric Waveguides
(PDWGs)
Electro-Optic (EO) Effect
Pockels effect:
Kerr effect:
• The electro-optic (EO) effect is
a nonlinear optical effect that
results in a refractive index that
is a function of the applied
electric field (voltage)
• Examples of Pockels effect :
Ammonium dihydrogen
phosphate (ADP), Potassium
dihydrogen phosphate (KDP),
Lithium Niobate, Lithium
Tantalate, etc.
• Examples of Kerr effect: Most
glasses, gases, and some
crystals
Phase Modulators
• Phase shift =
, where Vπ (the halfwave voltage) is the
voltage applied to
achieve a phase shift
of π radians.
Mach-Zehnder Modulator to
Modulate Amplitude of Light
Output Intensity:
I out

V 
1  cos0 
V 

 I in 
2
Consider the case of φ0=0. If V=Vπ, then Iout=Iin is the maximum, else if V=0, then Iout=0 is the minimum.
Characteristics of Optical
Modulators/Switches
• Extinction Ratio: η=(I0-Im)/I0 if Im≦I0 and η=(ImI0)/Im if Im≧I0, where Im is the optical intensity when
the maximum signal is applied to the modulator and
I0 is the optical intensity with no signal applied.
• Insertion Loss: Li=10log(It/Im), where It is the
transmitted intensity with no modulator and Im is the
transmitted intensity when the maximum signal is
applied to the modulator.
• Bandwith: △f=2π/T, where T is the switching time.
Optical Directional Coupler as a
Channel Switch
A Complicated Optical Directional Coupler
3dB-Directional Coupler as a Beam Splitter
Coupled-Mode Equations to
Analyze Directional Coupler
Coupled-Mode Equations (Cont’)
•
•
The coupling length is Lc=π/2κ.
Both Lc and κ depend on the
refractive index distribution of
guide.
While the waveguiding mode
traverses a distance of odd
multiple of the coupling length (Lc,
3Lc, …, etc), the optical power is
completely transferred into the
other waveguide. But it is back to
the original waveguide after a
distance of even multiple of the
coupling lengths (2Lc, 4Lc, …,
etc). If the waveguiding mode
traverses a distance of odd
multiple of the half coupling length
(Lc/2, 3Lc/2, …, etc), the optical
power is equally distributed in the
two guides.
Acousto-Optic (AO) Modulators
Bragg-type: Width >> 2/
Raman-Nath-type: Width << 2/
: wavelength of light
: wavelength of acoustic wave
Bragg-type AO modulator: sinθB=/2
Raman-Nath type AO modulator:
sinθm=m/2, m: integer
Bragg-type AO Modulator as Spectrum
Analyzer
Acousto-optic materials:
Visible and NIR — Flint glass, TeO2,
fused quartz
Infrared — Ge
High frequency — LiNbO3, GaP
Operations of Bragg-type AO modulator:
— Bragg diffraction effect
— Driving frequency: 1MHz ~ 1GHz
— Rise time: 150 ns (1-mm diameter laser)
  
Bragg angle: d  sin 1 

 2 
: wavelength of light
: wavelength of acoustic wave
Direct Coupling from Laser/Fiber to Waveguide
• Direct Coupling Efficiency:


 

 

 

 
 ( x, y )  ( x, y )dxdy
 ( x, y ) dxdy 
2



 
2
 ( x, y ) dxdy
2
where  (x) is the laser/fiber
mode and  (x) is the waveguide
mode.
Coupling Efficiency from Laser/Fiber to
Waveguide
Coupling Efficiency from Laser/Fiber to
Waveguide (Cont’)
Coupling Efficiency from Laser/Fiber to
Waveguide (Cont’)
Simulation Results Coupling Efficiency
from Laser/Fiber to Waveguide
For given waveguide’s fundamental
mode, one can obtained the optimal
coupling efficiency by selecting the
values of w and c.
Typical Optical Disks
DVD Disks
Lasers in DVD Players
Optoelectronic Devices in DVD Players
Band Theory of Semiconductor
Devices
• Metal: The conduction band
and the valence band may
overlap.
• Semiconductor: The bandgap
between the conduction band
and the valence band is very
small. The electron can be
easily excited into the
conduction band to become a
free electron.
• Insulator: The bandgap
between the conduction band
and the valence band is very
large. The electron is hardly
excited into the conduction
band to become a free electron.
Semiconductor
Fermi energy level, EF: the highest
energy level which an electron can
occupy the valance band at 0°k
Bandgap Theory of Diode
Bandgap Theory of Tunnel Diode
Bandgap Theory of n-p-n
Transistor
Radiation from a Semiconductor Junction
wavelength of radiation:  
where  : energy gap (ev)
1240
(nm)
E (ev)
 : wavelength of radiation (nm)
e.g. GaAs  =1.43 ev, find the radiation wavelength

1240
 876(nm)  Near Infrared (NIR)
1.43
Homojunction Laser Diode
Formation of Cavity in Laser Diode
Threshold Current
Heterostructure Laser Diodes
Stripe AlGaAs/GaAs/AlGaAs LD
• Advantages of stripe
geometry :
1. reduced contact area
→ Ith↓
2. reduced emission
area, easier coupling to
optical fibers
• Typical W ~ a few μm, Ith~
tens of mA
• Poor lateral optical
confinement of photons
Buried Double Heterostructure LD
• Good lateral optical
confinement by lower refractive
index material →stimulated
emission rate ↑
• Active region confined to the
waveguide defined by the
refractive index variation →
index guided laser diode
• Buried DH with right
dimensions compared with the
λ of radiation → only
fundamental mode can exist→
single mode laser diode
• DH AlGaAs/GaAs LD
• → ~ 900 nm LD
• DH InGaAsP/InP LD →
1.3/1.55 μm LD
Output Modes of LD
• Output spectrum depends on
1. optical gain curve of the
active medium
2. nature of the optical
resonator
• L decides longitudinal mode
separation. W & H decides
lateral mode separation
• With sufficiently small W &
H→only TEM00 lateral mode
will exist ( longitudinal modes
depends on L )
• Diffraction at the cavity ends
→laser beam divergence
( aperture ↓→diffraction ↑)
Current Dependence of Power
Spectrum in LD
• Output spectrum depends
on
1. optical gain curve of
the active medium, and
2. nature of the optical
resonator
• Output spectrum from an
index guided LD
low current →multimode
high current →single
mode
Light Detectors
Classification by spectral response
 wide spectral response
 narrow spectral response
Principles of photodetection
 External photoelectric effect
Eg. vacuum photodiode
photomultiplier
 Internal photoelectric effect
Eg. p-n junction photodiode
PIN photodiode
avalanche photodiode
Characteristics of Light Detectors
Responsivit y : rat ioof out put t oradiant input

Vo
I
or o
I
I
 I : appliedradiant or liminousflux (W or lm)
Vo : out put volt age from t hedet ect or(V)
I o : out put current from t hedet ect or(A)
Quantumefficiency
number of emittedelectrons

number of incident photons

 1.24

 : wavelength of theradiation( m)
External Photoelectric Detector  Vacuum Photodiode
P hot ocurre
nt
eP
i
hc
External Photoelectric Detector Photomultiplier
P hot ocurrent
eP
hc
 : gain at each dynode
i  N
N : number of dynodes
Internal Photoelectric Detector (Semiconductor Photodiode)
P-N photodiode
PIN and Avalanche Photodiodes
Operating modes:
(1) photoconductive mode (reverse biased)
(2) Photovoltaic mode (forward biased)
Typical Characteristics of Photodetectors
Principle of OP Circuit for
Photodiodes
Light Emitting Diode (LED)
Construction
Optical design
Choice of LED Materials
Typical Choice of Materials for LEDs
Radiative Transition Through
Isoelectronic Centers
• For indirect band-gap semiconductors→use
recombination of bound excitons at isoelectronic centers
to generate radiative recombination
• Isoelectronic center : produced by replacing one host
atom in the crystal with another kind of atom having the
same number of valence electrons
• Isoelectronic center attract electron and hole pair →
exciton radiative recombination can occur without
phonon assistance → hυslightly smaller than bandgap
energy Eg
• Common isoelectronic centers :
• N in GaP → 565 nm
• N in GaAs0.35P0.65 → 632 nm
• N in GaAs0.15P0.85 → 589 nm
• ZnO pair in GaP ( neutral molecular center ) → 700 nm
Choice of Substrates for Red and Yellow LEDs
Material System for High
Brightness Red/Yellow LEDs
Choice of Substrates for Blue
LEDs
• Choices of light
emitting material for
blue LEDs ( before
1994 ) : GaN system,
ZnSe system, SiC,
etc. And the winner
is : GaN
Earlier LED Structures
Basic Structures of High
Brightness Visible LEDs
High Brightness Blue LEDs
Radiation pattern
Output spectra
Note : response time
~ 90ns (yellow and red LED)
~ 500ns (green LED)