CHAPTER 6
Optical sources 1: the laser
Optical sources:
Its fundamental function is to convert electrical energy in the form of
a current into optical energy (light) in an efficient manner. Three main
types of optical light source are available. These are:
(a) wideband ‘continuous spectra’ sources (incandescent lamps);
(b) monochromatic incoherent sources (light-emitting diodes, LEDs);
(c) monochromatic coherent sources (lasers).
The major requirements for an optical fiber emitter:
The light source should be compatible in size and configuration to
launch light efficiently into the fiber, with a preference for highly
directional output.
It should accurately track the electrical input signal to minimize
distortion and noise, ideally being linear.
The light should emit at wavelengths where the fiber has low loss and
dispersion, and where detectors are efficient.
Simple signal modulation (direct modulation) should be possible over a
wide bandwidth, extending from audio frequencies to gigahertz range.
The source must provide enough optical power to overcome fiber
attenuation, connector losses, and still drive the detector effectively.
It should have a narrow spectral bandwidth (linewidth) to reduce
dispersion in the fiber.
Stability in optical output is essential, with minimal sensitivity to
ambient conditions (e.g., temperature changes).
The source must be cost-effective and highly reliable to compete with
conventional transmission methods.
Basic concepts:
The laser is a device which amplifies light – hence the derivation of the
term LASER as an acronym for Light Amplification by Stimulated
Emission of Radiation.
However, lasers are not typically used as amplifiers in practice. The reason
lies in the challenges of achieving high gain (intense amplification) without
causing oscillations (feedback of energy that leads to instability).
Oscillations can interfere with the desired output, so the laser is more
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practically used as an optical oscillator, which produces light by continually
circulating the energy within a confined space.
Absorption and emission of radiation
The interaction of light with matter at a fundamental level is governed by
quantum theory, which describes energy as being exchanged in discrete
packets called photons. These photons carry specific amounts of energy,
and the behavior of light and its interaction with atoms or molecules can be
understood through these quantum concepts.
Discrete Energy States of Atoms:
Atoms (and molecules) don't exist in a continuous range of energy levels;
rather, they have specific, discrete energy states. These states are
quantized, meaning that an atom can only exist at certain energy levels, not
in between. The quantum theory suggests that an atom can transition
between these energy states by either absorbing or emitting light.
Absorption (when an atom takes in light) and emission (when an atom
releases light).
When an atom absorbs a photon, it jumps from a lower energy state
(E₁) to a higher energy state (E₂).
Conversely, when an atom emits a photon, it moves from a higher
energy state (E₂) to a lower energy state (E₁).
The Energy-Frequency Relationship:
The frequency of the absorbed or emitted radiation f is related to the
difference in energy E between the higher energy state E ₂ and the lower
energy state E₁ by the expression:
E= E ₂−E ₁=hf
Where h =6.626*10−34 J s (Joules second) is Planck’s constant.
E₂ is the energy of the higher state
E₁ is the energy of the lower state
f is the frequency of the emitted or absorbed radiation.
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Figure 6.1 Energy state diagram showing: (a) absorption; (b) spontaneous
emission; (c) stimulated emission. The black dot indicates the state of the
atom before and after a transition takes place.
Figure 6.1(a) shows a two-energy-state atomic system, where an atom starts
in the lower energy state E ₁. When a photon with energy E ₂−E ₁ strikes the
atom, it may be excited to the higher energy state E ₂ through stimulated
absorption.
Alternatively, when the atom is in the higher energy state E ₂, it can
transition to the lower state E ₁ by emitting a photon at a frequency
corresponding to E ₂−E ₁. This emission can occur in two ways:
1. Spontaneous emission: The atom returns to the lower energy state
randomly, emitting a photon in an unpredictable direction.
2. Stimulated emission: A photon matching the energy difference between
the two states ( E ₂−E ₁) interacts with the atom in the upper state, causing
it to emit a second photon.
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Figures 6.1(b) and (c) illustrate these emission processes. Spontaneous
emission leads to incoherent radiation due to the randomness of the
emitted light. A similar process in semiconductors is used in LEDs, where
light is generated through spontaneous emission.
The stimulated emission process is what gives a laser its unique properties
as an optical source. Key characteristics include:
1. Photon identity: The photon produced by stimulated emission has the
same energy as the photon that caused it, so the emitted light has the
same frequency.
2. Coherent radiation: The light associated with both the stimulating
and stimulated photons is in phase and has the same polarization,
leading to coherent radiation. This is different from spontaneous
emission, which produces incoherent light.
3. Amplification: When an atom is stimulated to emit light by an
incident wave, the emitted energy can combine constructively with
the wave, resulting in amplification of the light.
Optical emission from semiconductors
The p–n junction
To understand semiconductor optical sources, it's important to review
properties of semiconductor materials, particularly the p-n junction. A
perfect semiconductor crystal with no impurities or defects is called
intrinsic. The energy band structure of an intrinsic semiconductor, shown
in Figure 6.8(a), includes the valence band and the conduction band,
separated by an energy gap (bandgap, Eg). The width of this gap varies
among semiconductor materials.
At temperatures above absolute zero, thermal excitation raises electrons
from the valence band into the conduction band, leaving holes in the valence
band. These thermally excited electrons in the conduction band and holes in
the valence band are called carriers, and they enable conduction through
the material.
In thermal equilibrium, the energy-level occupation follows the Fermi–
Dirac distribution (not the Boltzmann distribution). The probability P(E)
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that an electron will occupy a particular energy level E at temperature T is
given by the Fermi–Dirac distribution.
where K is Boltzmann’s constant and E F is known as the Fermi energy or
Fermi level. The Fermi level is only a mathematical parameter but it gives
an indication of the distribution of carriers within the material.
Figure 6.8 (a) The energy band structure of an intrinsic
semiconductor at a
temperature above absolute zero, showing an equal number
of electrons and holes in the conduction band and the
valence band respectively. (b) The Fermi–Dirac probability
distribution corresponding to (a).
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Figure 6.9 Energy band diagrams: (a) n-type semiconductor; (b) p-type
semiconductor
The Fermi level is a mathematical concept that indicates the distribution of
carriers (electrons and holes) within a material. In an intrinsic
semiconductor, the Fermi level is at the center of the bandgap, suggesting
a low probability of electrons occupying the conduction band and
corresponding holes in the valence band (Figure 6.8(b)).
To create an extrinsic semiconductor, the material is doped with impurities
that either add free electrons (donor impurities) or holes (acceptor
impurities):
Donor impurities create energy levels just below the conduction
band, allowing electrons to move into the conduction band and
resulting in an n-type semiconductor (majority carriers are electrons).
The Fermi level shifts above the center of the bandgap (Figure 6.9(a)).
Acceptor impurities create energy levels just above the valence band,
leading to electrons being raised to these levels, leaving holes in the
valence band, and forming a p-type semiconductor (majority carriers
are holes). The Fermi level shifts below the center of the bandgap
(Figure 6.9(b)).
A p–n junction diode is formed by joining p-type and n-type
semiconductor layers in a single crystal (Figure 6.10(a)). At the junction, a
depletion region forms where mobile charge carriers recombine, leaving the
region free of carriers. This creates a potential barrier that prevents the
flow of majority carriers between the p- and n-type regions (Figure 6.10(b)).
In equilibrium, with no external voltage applied, no current flows as the
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potential barrier restricts carrier movement, and the Fermi level for both
regions aligns.
Figure 6.10 (a) The impurities and charge carriers at a p–n
junction. (b) The energy band diagram corresponding to (a)
The width of the depletion region and the magnitude of the potential
barrier in a p-n junction diode depend on the carrier concentrations
(doping levels) in the p- and n-type regions, as well as any external voltage
applied. When a positive external voltage is applied to the p-type region
relative to the n-type region, the depletion region narrows and the potential
barrier is reduced. This is called forward biasing.
In forward bias, electrons from the n-type region and holes from the p-type
region can flow more easily across the junction into the opposite region.
These minority carriers are injected across the junction by the applied
voltage, leading to a continuous current flow as they diffuse away from the
junction. In suitable semiconductor materials, this process can result in
carrier recombination, which emits light.
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Spontaneous emission
In a forward-biased p-n diode, the increased concentration of minority
carriers in the opposite type region leads to carrier recombination across
the bandgap. In a direct bandgap semiconductor (Figure 6.11), electrons
in the conduction band of the p-type material and holes in the valence band
of the n-type material recombine. The energy released during this electron-
hole recombination is approximately equal to the bandgap enesrgy ( E g).
Excess carrier population decreases due to recombination, which can be:
1. Radiative recombination: Energy is released in the form of a photon
with frequency corresponding to E=hf, where E≈Eg .
2. Nonradiative recombination: Energy is dissipated as heat through
lattice vibrations, instead of being emitted as light.
Figure 6.11 The p–n junction with forward bias giving spontaneous emission
of photons
This spontaneous emission of light from within the diode structure is known
as electroluminescence. The light is emitted at the site of carrier
recombination which is primarily close to the junction, although
recombination may take place through the hole diode structure as carriers
diffuse away from the junction region (see Figure 6.12). However, the
amount of radiative, recombination and the emission area within the
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structure is dependent upon the semiconductor materials used and the
fabrication of the device.
Figure 6.12 An illustration of carrier recombination giving spontaneous
emission of light in a p–n junction diode.
Carrier recombination
Direct and indirect bandgap semiconductors
To encourage electroluminescence, it's crucial to select an appropriate
semiconductor material. Direct bandgap semiconductors are most useful
because the electrons and holes on either side of the forbidden energy gap
have the same value of crystal momentum, allowing direct
recombination. In these materials, as shown in Figure 6.13(a), the energy
maximum of the valence band aligns closely with the energy minimum of
the conduction band. When electron-hole recombination occurs, the
momentum remains constant, and the energy released (equal to the
bandgap energy (Eg)) is emitted as light. This efficient transition leads to
short minority carrier lifetimes (around 10−8∧¿ 10−10 seconds). Common
direct bandgap materials are listed in Table 6.1.
In contrast, indirect bandgap semiconductors have the maximum and
minimum energies at different values of crystal momentum (Figure 6.13(b)).
For electron-hole recombination to occur, the electron must lose
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momentum to match the valence band's maximum energy, requiring the
emission or absorption of a third particle, a phonon.
Figure 6.13 Energy–momentum diagrams showing the types of transition:
(a) direct bandgap semiconductor; (b) indirect bandgap semiconductor
Table 6.1 Some direct and indirect bandgap semiconductors with calculated
recombination coefficients
The three-particle recombination process in indirect bandgap
semiconductors (which requires the involvement of a phonon) is much less
probable than the two-particle process in direct bandgap semiconductors.
As a result, recombination in indirect bandgap materials is slower, with
minority carrier lifetimes ranging from (10−2 ¿ 10−4 seconds). This slower
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recombination increases the likelihood of nonradiative transitions.
Nonradiative recombination, often caused by lattice defects or impurities
occurs more quickly and competes with radiative recombination.
Indirect bandgap emitters, like silicon and germanium, produce very low
levels of electroluminescence. This difference is reflected in the
recombination coefficient (Br) values for both direct and indirect bandgap
semiconductors.
The recombination coefficient is obtained from the measured absorption
coefficient of the semiconductor, and for low injected minority carrier
density relative to the majority carriers it is related approximately to the
radiative minority carrier lifetime τ r by
where N and P are the respective majority carrier concentrations in the n-
and p-type regions.
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Figure 6.14 Major radiative recombination processes at 300 K: (a)
conduction to valence band (band-to-band) transition: (b) conduction band to
acceptor impurity, and donor impurity to valence band transition; (c) donor
impurity to acceptor impurity transition; (d) recombination from an
isoelectronic impurity to the valence band.
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Summary of the Recombination Processes:
Energy
Process Description Photon Emission
Source
(a) Band-to-Band Electron in conduction Efficient, typically
Bandgap
(Conduction to band recombines with visible/infrared light
energy
Valence Band) hole in valence band (direct bandgap)
(b) Conduction to Impurity Less efficient than band-
Electron recombines with
Acceptor/Donor to energy to-band, lower energy
hole at impurity state
Valence levels light
Electron from donor Energy
(c) Donor Impurity to Lower energy photon or
recombines with hole at levels of
Acceptor Impurity non-radiative
acceptor impurity impurities
(d) Isoelectronic Impurity Light at characteristic
Recombination from
Impurity to Valence energy wavelengths depending on
impurity to valence band
Band levels impurity
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