Part 1 :Light and material بسم الله الر حمن الرحيم

Part 1 :Light and material

بسم الله الر حمن الرحيم

The Nature of Light

We all know a lot about light - it is the basis of our most important sensory function. But the question of what light “really is” ? Light is usually described in one of three ways:

• Rays• Electromagnetic Wave• Photons

Light as a stream of photons

Light is also a physical manifestation and consists of discrete particles.Such particles have been designated as photons.Some of these characteristics are ;(1) Any single ray of light has a fixed, discrete energy level.(2) Each color of light has its own unique energy level. It is notpossible to increase or decrease the energy of that single ray of light,except to absorb it completely and thereby end its existence.(3) The intensity of visible light can be increased or decreased only bychanging the number of rays of light present.(4) Light can exert a measurable pressure on physical objects.Viewed as a particle rather than a wave, light still does not change itsbasic behavior. These particles are electrically neutral, so they tend totravel in straight lines, without being affected by either magnetic fieldsor electrical fields.

Energy level diagram

All matters ultimately consist of atoms. Each atom consists ofa nucleus surrounded by electrons.• Bohr’s model assumes that electrons rotate on stationaryorbits and therefore posses a stationary value of energy.Bohr’s breakthrough was the assumption that rotatingelectrons do not radiate; that is they do not change theirenergy during rotation.• Any change in energy occurs only discretely, such as whenelectron jump from one orbit to another. This implies that anentire atom posses discrete amount of energy.• An energy level diagram is a convenient model to show this:

Atoms aspire to exist at the lowest possible energylevel.• To induce atoms to jump to the upper energy levels,we feed them energy from an external source, aprocess called ‘pumping’.• When atoms leap to the upper energy levels, theyabsorb an exact amount of energy from an externalsource. This amount is equal to the energy differencebetween the upper and lower levels between which thejump occurred.• When atoms drop from an upper energy level to alower level, they radiate quanta of electromagneticenergy called photons.

Photons

A photon is an elementary particle that travels as a speed of light, c,and carries a quantum of energy, Ep=hf, where h is Plank’sconstant (6.626 x 10-34 J.s) and f is the photon’s frequency.• Light is a stream of photons. Its color is determined by the photon’sfrequency, f (the photon wavelength, λ).• A photon’s energy, Ep, is equal to the energy gap between theradiating upper and lower energy levels. This implies that aphoton’s frequency (wavelength) is determined by the energylevels-that is, the material-used.• Energy levels exist naturally; therefore, we can get different colorsof light either by using different energy levels of the same materialor by using different materials.• Photons are absorbed by the material whose energy level gaps areequal to the photon’s energy.

Problem 1:

suppose a laser diode radiates red light withλ=650nm. What is the energy of single photon?

Energy of a single photon = Ep = hf =hc/λ= {[6.6x10-34J.s]x[3x108m/s]/650x10-9m]

=3.04x10-19J

So a single photons carries an extremely small amountsof energy but light radiated by a sources consists of anumber of photons.

Pumping

Atoms want to exist at the lowest possible energylevels; that’s the law of nature.• To raise them to higher levels, which is necessary foratoms to be able to jump down to produce lightradiation, we must energize them from an externalsource.• When atoms absorb external energy, they jumps tohigher energy levels and then drop to the lower levels,radiating photons- that is light.• The process of making atoms jump to higher levelsby feeding them external energy is called pumping.

Pumping process

Radiation

Relationship between a photon’s energy Ep and theenergy different, ΔE = E3-E2.

•A photon was created when an atom jumpedfrom E3 to E2 and release energy (E3-E2).

•ThereforeEp = ΔE = E3-E2

•andλ = ch/(E3-E2).

The wavelength (the color) of radiated light isdetermined by the energy levels of the radiatingmaterial. If Ep is not equal to ΔE, the photon will pass by the material without interaction.

Luminescence

Luminescence is light that usually occurs at low temperatures, and is used to describe the emission of radiation from a

solid .

The following are types of luminescence:

Photoluminescence: excitation arises from the absorption of photons

Cathodoluminesence: excitation is by bombardment with a beam electrons

Electroluminescence: excitation results from the application of an electric field

Light as an Electromagnetic Wave

Optical Sources

• Light Production

• Light Emitting Diodes (LEDs)

• Lasers

LasersLASER is an acronym for “Light Amplification by the Stimulated Emission of Radiation”. Lasers produce far and away the best kind of light for optical communication.

Ideal laser light is single-wavelength only. This is related to the molecularcharacteristics of the material being used in the laser. It is formed in parallelbeams and is in a single phase. That is, it is “coherent”.This is not exactly true for communication lasers. See the discussion under“Linewidth” below.. Lasers can be modulated (controlled) very precisely (the record is a pulselength of 0.5 femto seconds).. Lasers can produce relatively high power. Indeed some types of laser canproduce kilowatts of power. In communication applications, semiconductorlasers of power up to about 20 milliwatts are available. This is many timesgreater power than LEDs can generate. Other semiconductor lasers (such asthose used in “pumps” for optical amplifiers) have outputs of up to 250milliwatts.

Principle of the LASER

1. An electron within an atom (or a molecule or an ion) starts in a low energystable state often called the “ground” state.

2. Energy is supplied from outside and is absorbed by the atomic structurewhereupon the electron enters an excited (higher energy) state.

3. A photon arrives with an energy close to the same amount of energy as theelectron needs to give up to reach a stable state. (This is just another way ofsaying that the wavelength of the arriving photon is very close to the

wavelength at which the excited electron will emit its own photon(.4. The arriving photon triggers a resonance with the excited atom. As a result

the excited electron leaves its excited state and transitions to a more stable state giving up the energy difference in the form of a photon.

The critical characteristic here is that when a new photon is emitted it hasidentical wavelength, phase and direction characteristics as the excitingphoton.

Note: The photon that triggered (stimulated) the emission itself is notabsorbed and continues along its original path accompanied by the newlyemitted photon.

Spontaneous Emission

We use different terms to describe spontaneously emitted light depending on howthe energy was supplied:

Incandescent light is any light produced as a result of heating the material.Fluorescent light is light produced by spontaneous emission from an energysource that is not heat. The term fluorescence is used if the emission stops

when the external source of energy is removed .Phosphorescent light is also produced from an energy source that is not heat but

where the emission continues for some time after the external source ofenergy is removed.

Energy States of a typical 4-Level Material. A material which has 4 energylevels involved in the lasing process is significantly more efficient than one with only 3 levels.A 4-level system is where the radiative transition ends in an unstable state and another transition is needed to attain the ground state. A 3-level system is where the radiative transition achieves the ground state directly.

Lasing

Need for Population InversionThe requirement for a population inversion to be present as a precondition forstimulated emission is not at all an obvious one. Electrons in the high energystate will undergo stimulated emission regardless of how many electrons are inthe ground state. The problem is that an electron in the ground state will absorb photons at

exactly the wavelength at which electrons in the higher energy state willundergo stimulated emission! You must have a greater probability of stimulatedemission than absorption for lasing to occur.It happens that the probability that an electron in the ground state will absorb anincoming photon is usually different from the probability that an electron in theexcited state will undergo stimulated emission. So what you really need is notan inversion in the numbers of electrons in each state. Rather you need theprobability that an incoming photon will encounter an excited electron andstimulate emission to be greater than the probability that it will encounter anelectron in the ground state and be absorbed.So an inversion takes place when the number of electrons in the excited statemultiplied by the probability of stimulation by an incoming photon exceeds thenumber of electrons in the ground state multiplied by the probability ofabsorption of an incoming photon.

In summary, to make a laser you need:

1. A material that can enter a high energy metastable state. It should have abandgap energy of the right magnitude to produce light of the requiredwavelength. (There must be an available energy transition or sequence oftransitions from the high energy metastable state to a lower energy state that

will emit light at the desired wavelength(.2. A way of supplying energy to the material.

3. A suitable method of confinement of the material and of the emitted light.4. A pair of parallel mirrors at each end of the cavity.

5. It seems obvious but its very important that the material in the cavity of thelaser should be transparent (should not absorb light) at the wavelengthproduced. This is partially the “population inversion” requirement. The lasingmedium does absorb light at the wavelength produced. To overcome this weneed to have more atoms in the excited stated state than in the ground stateso that lasing produces more photons than absorption removes. However, it isalso very important that other materials (dopants for example) should notabsorb light of the required wavelength.

* Lasing medium - gas, liquid, solid state or semiconductor (suitable optical fibre systems) - same basic principle of operation* Lasing processes - photon absorption, spontaneous emission and stimulated emission* Quantum theory - atoms exist only in certain discrete energy states* Planck’s law - transition between two states involves absorption or emission of a photon of energy hv12 = E2 – E1

* Spontaneous emission - excited atom (in unstable upper state) returns to the ground state - occurs without any external stimulation - isotropic and random phase (incoherent)* Stimulated emission - excited electron is stimulated to drop to the ground state by an impinging photon - emit photon with an identical energy, same optical frequency v, in phase and same polarization.

Initial state Final state

Absorption

Spontaneousemission

Stimulatedemission

E1

E2

E1

E2

E1

E2

Initial state Final state

Absorption

Spontaneousemission

Stimulatedemission

E1

E2

E1

E2

E1

E2

* Thermal equilibrium - absorption and spontaneous emission dominate* Population inversion - population (excited state) > population (ground state) - stimulated emission dominates - achieved through pumping technique (carrier injection)* Properties of laser diodes - response times less than 1 ns (modulation bandwidth > 200 MHz) - tens of milliwatts output power and optical bandwidth < 2 nm - more complex construction * Optical feedback - gain mechanism that compensates for optical losses in the medium (amplification) - basic structure of two parallel partially reflecting mirrors (Fabry-Perot resonator), or Bragg reflectors - sides of cavity are roughened* Losses in cavity - absorption and scattering in the amplifying medium - absorption, scattering and diffraction at the mirrors - non-useful transmission through the mirrors

* Radiation intensity:

where is the optical field confinement factor, is the effective absorption coefficient* Lasing - occurs when the gain exceed the optical loss during one round trip - amplification through repeated passes through the cavity* Fabry-Perot resonator

-

0 expI z I g z

1 22 0 exp 2I L I R R L g * Lasing threshold - magnitude and phase of the returned wave must be equal to the original wave. - and -

* Threshold current density - where β is a constant that depends on the specific construction - below threshold, spontaneous emission

2 0I L I 2 1j Le

1 2

1 1ln

2thgL R R

1

thJ

* Gain curve - broadened energy level, thus finite linewidth - oscillations are sustained over a narrow range of frequencies (gain > net loss)* Longitudinal or axial modes - emitted EM wave forms a standing wave between the two mirrors - 2 1 2 2

2j L m

e L m Ln

* Mode separation - separation between resonant frequencies -

* Multimode laser - consists of several modes - oscillations are sustained only for those modes which lie within the gain curve of the broadened laser transition line

2

cv

nL

* Tranverse modes - due to oscillation in a direction which is transverse to the axis of the cavity - designated by TEMlm where the integers l and m indicate the number of minima horizontally and vertically respectively - give rise to a pattern of spots at the output - TEM00 (the lowest) mode gives the greatest degree of coherence, and the highest level of spectral purity, as all parts of the propagating wavefront are in phase.

- When a forward bias voltage is applied, an active region with inverted population exists near the depletion layer- electromagnetic radiation of frequency, which is confined to the active region will be amplified

g Fc FvE h v E E h

* Stimulated Emission in Semiconductor Diode - Population inversion may be obtained at a p-n junction by heavy doping of both the p and n type material - Heavy doping causes the Fermi level to enter the conduction band of the n-region and lowering the Fermi level into the valence band in p region

The rate equation that governs the number of photon,

The rate equation that governs the number of electron, n

stimulatedemission spontaneousemission

photon loss

spph

dCn R

dt

injection spontaneousemission

stimulatedemission

sp

dn J nCn

dt ed

Assuming Rsp is negligible and noting that when is small, we have

In the steady state (dn/dt = 0) when = 0, the threshold current density needed to maintain n = nth is

Rate equations

10

ph

Cn

d is the depth of the carrier-confinement region, C is a coefficient describing the strength of the optical absorption and emission interactions, Rsp is the rate of spontaneous emission, ph is the photon lifetime, sp is the spontaneous-recombination lifetime, J is the injection-current density

* At lasing threshold, - the combination of the electron and photon rate equations in the steady-state condition (dn/dt = 0, d/dt = 0) gives

- the first term is the number of photons resulting from stimulated emission - the second term gives the spontaneously generated photons

phs th ph spJ J R

ed

* The external differential quantum efficiency - the number of photons emitted per radiative electron-hole pair recombination above threshold

- i is the internal quantum efficiency (not a well-defined quantity ~ 0.6-0.7 at room temperature) - also calculated from the straight-line portion of P vs I curve

i thext

th

g

g

extg

e dP

E dI

• Electrons are injected into the device from the n-type side

• Diode laser commonly takes the form of a rectangular parallel piped >100m to 1mm

• Two of the sides perpendicular to the junction are purposely roughened so as to reduce their reflectivity

• The other two sides are made optically flat and parallel, by either cleaving or polishing

Semiconductor injection laser

• These two surfaces (air-semiconductor interface) form the mirrors for the laser cavity

• One of the reflecting surfaces may be coated to increase the reflectivity and to enhance laser operation.

• The thickness of the junction region is small, typically around 1 m • light traveling in the plane of the junction is amplified more than light

perpendicular to it• the laser emission is parallel to the plane of the junction.

* Beam profile• typically has an elliptical spatial profile• In the direction perpendicular to the

junction, the beam is confined by the narrow junction, ~ 1m and is spread by diffraction to an angle as large as several tens of degrees

• In the direction parallel to the junction, the beam is not confined so stringently and spreads less to around ten degrees

* Semiconductor laser materials• 630-680nm: AlxGayIn1–x–yP• 780-880nm: Al1–xGaxAs• 1150-1650nm: In1–xGaxAs1–yPy

• The properties of the material vary continuously as x or y vary (0 to 1).

Al1–xGaxAs

* Edge-emitting laser - the light emerges from the edge of the device, where the junction intersects the surface - the configuration is simple and easy to fabricate. Most diode lasers are edge-emitters - they suffer from the drawback that the volume of material that can contribute to the laser emission is limited and they are difficult to package as 2-D arrays

Classification of laser diodes

* Surface-emitting laser - the light emerges from the surface of the chip rather than from the edge - devices could be packed densely on a semiconductor wafer and it would be possible to fabricate 2-D arrays easily

* Homojunction laser- one type of semiconductor material is used in the junction with different dopants to produce the p-n junction. The index of refraction of the material depends upon the impurity used and the doping level- the lightly doped p-type material has the highest index of refraction. The n-type material and the more heavily doped p-type material both have lower indices of refraction. This produces a light pipe effect that helps to confine the laser light to the active junction region- In the homojunction the index difference is low and much light is lost* Single heterojunction laser - A fraction of the Ga in the p-type layer has been replaced by Al to reduce the index of refraction and results in better confinement of the laser light to the optical cavity - This leads to lower losses, lower current requirements, reduced damage, and longer lifetime for the diodes

Homojunction and single heterojunction

- only the junction region is composed of GaAs, both the p and n regions are of AlGaAs- better confinement of the optical standing wave on both sides of the optical cavity- the band-gap discontinuities that exist in DH laser confined the injected carriers in the GaAs layer and made to recombine in the active region- this confinement greatly reduces the optical loss, but leads to two additional difficulties

Double heterojunction laser

- very well optical confinement, thus the irradiance may easily reach the damage threshold, increasing the likelihood of catastrophic failure - the tight confinement of the beam also reduces the effective width of the output aperture of the laser. This increases the divergence angle in the direction perpendicular to the junction

- The difficulties in DH laser are overcome by a further development of a large-optical-cavity (LOC) laser and uses regions of AlGaAs of varying composition

- Each of the advances described has lowered the operating threshold of GaAs lasers. The typical current densities necessary to achieve the lasing threshold of the various junction types at 300° K.

Homojunction 40,000 A/cm2 Single heterojunction 10,000Double heterojunction 1,300Double heterojunction, large optical cavity 600

• The DH laser structure provides optical confinement in the vertical direction through the reflective index step at the heterojunction interfaces

• If the top electrode covers the entire top surface of the p-type material and allows current flow across the full width of the diode, which is typically several hundred microns

• Lasing takes place across the whole width of the device• The current density, and thus the gain, can be greatly increased if current flow

is confined to a narrow strip of the junction. This does not greatly reduce the maximum current that can be used, as the current limitation is the heating effect in the material

A broad area DH injection laser

• a stripe geometry for the current confinement

• the stripe is formed by the creation of high resistance areas on either side by techniques such as proton-bombarded,p-n junction isolation or oxide isolation

• The current flows only in the region where the metallization contacts the semiconductor and confines the current and defines the area where laser operation will occur

DH Laser - Stripe Geometry

• The optical gain of stripe geometry injection lasers are determined by the carrier distribution along the junction plane

• The optical mode distribution along the junction plane (longitudinal modes) is decided by the optical gain and therefore these devices are said to be gain-guided laser structures

Gain-guided lasers• Fabrication of multimode injection

lasers with a single or small number of transverse modes is achieved by use of stripe geometry

• The figures show the typical output spectrum for a broad area junction laser with multi-transverse modes.

• The spacing of these modes is dependent on the optical cavity length and are generally separated by a few tenths of a nanometre

• The correct stripe geometry inhibits the occurrence of the higher order transverse modes by limiting the width of the optical cavity leaving only a single transverse mode, where only the longitudinal modes may be observed

• Employ steps in the index of refraction both parallel and perpendicular to the junction to confine the light

• The optical confinement perpendicular to the junction is achieved through the heterojunctions

• Index-guided lasers also have a change in the index of refraction in the plane of the junction to reduce spreading of light within the junction

• In the ridge waveguide laser, the active region waveguide thickness is varied by growing it over a channel or ridge which not only provides the loading for the weak index guiding but also act as a narrow current confining stripe

• The threshold currents for such weakly index guided structures are in the range 40 to 60 mA as compare to oxide stripe gain guided device 100 to 150mA

• strong index-guided laser• the active volume is completely buried

in a material of wider bandgap and lower refractive index

• the optical field is well confined both in the transverse and lateral directions within these lasers, providing strong index-guiding of the optical mode together with good carrier confinement

Buried heterostructure lasers

• The higher bandgap, low reflective index confinement material is AlGaAs for GaAs and it is InP in InGaAsP lasers

• Confinement of the injected current to the active region is obtained through the reverse biased junctions of the higher bandgap material

• The strong lateral optical and current confinement provided by these devices lead to lower threshold currents ~10 to 20mA

Double channel planar BH InGaAsP/InP laser

- For single mode operation, the optical output from laser must contain only a single longitudinal and single transverse mode- Single transverse mode operation may be obtained by reducing the aperture of the resonant cavity (<0.4mm) such that only the TEM00 mode is supported

Single mode lasers

- A straightforward method of achieving single longitudinal mode operation is to reduce the length L of the cavity until the frequency separation of the adjacent modes given by is larger than the laser transition linewidth or gain curve- Only the single mode which falls within the transition linewidth can oscillate within the cavity- The conventional cleaved mirror structures are difficult to fabricate with cavity lengths below 50mm and therefore configurations employing resonators have been utilized

2v c nL

DFB lasers use Bragg reflection to suppress undesirable modes, where a periodic variation in refractive index is fabricated into the laser heterostructure waveguide along the direction of wave propagation Light reflection occurs not at a single point (a mirror as in Fabry-Perot laser) but a portion of light reflected at each slope of the corrugated grating When the period of the corrugation , where l is the integer order of the grating, B is the Bragg wavelength and ne is the effective refractive index of the waveguide, then the only mode near the Bragg wavelength is reflected constructively.

2B el n

Distributed Feedback (DFB) lasers

The period of the periodic structure determines the wavelength of the single mode light output First order Bragg wavelength (l = 1),

2B en

The cavity length of VCSELs is very short typically 1-3 wavelengths of the emitted light. As a result, in a single pass of the cavity, a photon has a small chance of a triggering a stimulated emission event at low carrier densities

Vertical Cavity Surface Emitting Lasers (VCSEL)

VCSELs require highly reflective mirrors to be efficient. For VCSELs, the reflectivity required for low threshold currents is greater than 99.9%. VCSELs make use Distributed Bragg Reflectors (DBRs). These are formed by laying down alternating layers of semiconductor or dielectric materials with a difference in refractive index Advantages over the edge-emitting lasers: (i) Its design allows the chips to be manufactured and tested on a single wafer (ii) Large arrays of devices can be created exploiting methods such as 'flip' chip optical interconnects (iii) optical neural network applications to become possible. In the telecommunications industry, the VCSEL's uniform, single mode beam profile is desirable for coupling into optical fibres

* Threshold current temperature dependence• Generally, the threshold current tends to increase with temperature, the

temperature dependence of Jth being approximately exponential for most common structures:

where T is the device absolute temperature and T0 is the threshold temperature coefficient, which is a characteristic temperature describing the quality of the material, but which is also affected by the structure of the device

0

expth

TJ

T

Laser diode performances

* Threshold current temperature dependence• For AlGaAs devices,

T0 ~ 120 to 190 K. • For InGaAsP devices,

T0 ~ 40 to 75 K. • This emphasizes the

stronger temperature dependence of InGaAsP structures

AlGaAs laser.

InGaAsP laser.

* Dynamic response• The application of a current pulse, IP, to the laser results in a switch-on

delay, often followed by high frequency (of the order of 10GHz) damped oscillations known as relaxation oscillations (RO).

• The switch-on delay, td is needed to achieve the population inversion necessary to produce a gain that is sufficient to overcome the optical losses in the lasing cavity

• The switch-on delay, td is given by,

where IB is the bias current and is the average lifetime of the carriers in the device when is close to Ith. td can be eliminated by dc-biasing the diode at the lasing threshold current

• The RO depends on both the spontaneous lifetime and the photon lifetime.

ln P

dP B th

It

I I I

P BI I I

* Dynamic response (cont.)• In a Fabry-Perot cavity, the photon life time is

• Theoretically, assuming a linear dependence of the optical gain on carrier density, the RO occurs approximately at

1

1 2

1 1ln

2ph th

c cg

n L r r n

1 2

1 2

1 11

2 thsp ph

If

I

• Since and for a 300mm long laser, then when the I = 2Ith, the RO ~ gigahertz.

• When using a directly modulated laser diode for high-speed transmission systems, the modulation frequency can be no larger than the frequency of the relaxation oscillations of the laser field

1nssp 2psph

* Laser Diode Damage• Catastrophic optical damage to the output facets as a result of excessive

optical power• Gradual aging, manifested by decreasing light output and increased

current to maintain operation at a specified output• Operation at excessive temperature• Electrostatic discharge• Transient current pulses during operation

* Laser Lifetime• The operating lifetime of a laser diode is reduced significantly by

operation at elevated temperature• The lifetime is reduced by a factor that varies with absolute temperature

T as exp(Ea/kT), where Ea is an activation energy, typically around 0.5 to 0.7 eV, and k is Boltzmann’s constant

• According to this dependence, an increase in operating temperature of 40 Celsius degrees will decrease the lifetime by a factor around 30

• The figure shows the percentage of a typical 5-mW Al1–xGaxAs laser diodes laser that have failed as a function of operating time, for various operating temperatures. At 20° C, the mean time before failure is 770,000 hours, but at 70° C, it has fallen to 27,000 hours.