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’)

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’)

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

Photonic Crystals Improving LED Efficiency Incorporating a photonic crystal into an indium- gallium-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 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 Pockels effect: Kerr effect:

Phase Modulators Phase shift =, where V π (the half- wave voltage) is the voltage applied to achieve a phase shift of π radians.

Mach-Zehnder Modulator to Modulate Amplitude of Light Output Intensity: Consider the case of φ 0 =0. If V=V π, then I out =I in is the maximum, else if V=0, then I out =0 is the minimum.

Characteristics of Optical Modulators/Switches Extinction Ratio: η=(I 0 -I m )/I 0 if I m ≦ I 0 and η=(I m - I 0 )/I m if I m ≧ I 0, where I m is the optical intensity when the maximum signal is applied to the modulator and I 0 is the optical intensity with no signal applied. Insertion Loss: Li=10log(I t /I m ), where I t is the transmitted intensity with no modulator and I m 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 AO modulator: sinθ B = /2  Raman-Nath type AO modulator: sinθ m =m /2 , m: integer Bragg-type: Width >>  2 / Raman-Nath-type: Width <<  2 / : wavelength of light  : wavelength of acoustic wave

Bragg-type AO Modulator as Spectrum Analyzer Bragg angle: : wavelength of light  : wavelength of acoustic wave Operations of Bragg-type AO modulator: — Bragg diffraction effect — Driving frequency: 1MHz ~ 1GHz — Rise time: 150 ns (1-mm diameter laser) Acousto-optic materials: Visible and NIR — Flint glass, TeO 2, fused quartz Infrared — Ge High frequency — LiNbO 3, GaP

Direct Coupling from Laser/Fiber to Waveguide Direct Coupling Efficiency: where is the laser/fiber mode and is the waveguide mode.

Coupling Efficiency from Laser/Fiber to Waveguide

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, E F : 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) : wavelength of radiation (nm) e.g. GaAs  =1.43 ev, find the radiation wavelength

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 → I th ↓ 2. reduced emission area, easier coupling to optical fibers Typical W ~ a few μm, I th ~ 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 TEM 00 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 Principles of photodetection  External photoelectric effect Eg. vacuum photodiode photomultiplier  Internal photoelectric effect Eg. p-n junction photodiode PIN photodiode avalanche photodiode Classification by spectral response  wide spectral response  narrow spectral response

Characteristics of Light Detectors

External Photoelectric Detector  Vacuum Photodiode

External Photoelectric Detector  Photomultiplier

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 GaAs 0.35 P 0.65 → 632 nm N in GaAs 0.15 P 0.85 → 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

Output spectra Note : response time ~ 90ns (yellow and red LED) ~ 500ns (green LED) Radiation pattern