Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers

PHYS5320 Chapter Seven 1 Optical Resonators When two mirrors are aligned to be perfectly parallel, light wave reflections between the two mirrors lead to interference of the waves within the cavity. The result is a series of stationary or standing EM waves. Since the electric field at the mirrors (metal coated) is zero, only an integer number of half wavelength of the waves can be fit in.     c  m   L  m  m   m f  2   2L 

m = 1,2,3,…  m  m1  m  f

Each particular allowed m for a f is known as the free given m defines a cavity mode. spectral range. PHYS5320 Chapter Seven 2 Optical Resonators

Charles Fabry (18671945), left Alfred Perot (18631925), right

This simple optical cavity with two mirrors, etalon, serves to store radiation energy only at certain frequencies and it is called a Fabry- Perot optical resonator.

The mode peaks become broader as the reflection loss at the mirrors is increased.

PHYS5320 Chapter Seven 3 Optical Resonators Consider a wave A traveling to the right. After one round trip this wave will be traveling again towards the right, but now as wave B, and so on. If the two mirrors are identical and have a reflection coefficient of magnitude r, then B has one round-trip phase difference of k(2L) and a magnitude r2 (two reflections) with respect to A. 𝐵𝐴𝑟𝑒𝑥𝑝 𝑗2𝑘𝐿

𝐸 𝐴𝐵⋯

𝐸 𝐴𝐴𝑟 exp 𝑗2𝑘𝐿 𝐴𝑟 exp 𝑗4𝑘𝐿 ⋯ 𝐴 𝐸 1𝑟exp 𝑗2𝑘𝐿

PHYS5320 Chapter Seven 4 Optical Resonators 2 2 2 Let R  r Icavity  Ecavity I0  A I I  0 cavity 1 R 2  4Rsin 2 kL  I I  0 k L  m max 1 R 2 m The spectral width (full width at half maximum) of the Fabry-Perot etalon of an individual mode intensity can be calculated by  R1/ 2   f F  m F 1 R F is called the finesse of the resonator. Finesse is the ratio of mode separation (m = f) to spectral width (m). PHYS5320 Chapter Seven 5 Optical Resonators The Fabry-Perot optical cavities are widely used in lasers, interference filters, and spectroscopic applications. For interference filters, mirrors are replaced with plates that are partially reflecting and transmitting. If the incident beam has the wavelength corresponding to one of the cavity modes, it can sustain oscillations in the cavity and lead to a transmitted beam. 1 R 2 I  I transmitted incident1 R 2  4Rsin 2 kL 

PHYS5320 Chapter Seven 6 Example: Consider a Fabry-Perot optical cavity of air of length 0.1 mm. The mirrors have a reflectance of 0.9. Calculate the cavity mode nearest to 900 nm, the separation of the modes, and the spectral width of each mode. 2𝐿 2 10 2L 2104 𝑚 222.22 222     900.90nm 𝜆 910 m m 222 8  c 310 12  m  f   4 1.510 Hz  2L 210 1/ 2 1/ 2 12 R  0.9  f 1.510 F    29.8     5.031010 Hz 1R 1 0.9 m F 29.8    2 9 2  c  c 900.9010      m   5.031010  0.136nm m   2 m m 8  m  m c 310 The above derivation can be extended to a medium with a refractive index n. If the incidence angle at the mirrors is not normal, we can resolve k to be along the cavity length direction.

PHYS5320 Chapter Seven 7 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers

PHYS5320 Chapter Seven 8 Stimulated Emission and Photon Amplification

In stimulated emission, the emitted photon is in phase with the incoming photon, it is in the same direction, it has the same polarization, and it has the same energy.

Stimulated emission is the basis for obtaining photon amplification since one incoming photon results in two outgoing photons that are in phase with each other.

PHYS5320 Chapter Seven 9 Stimulated Emission and Photon Amplification For light amplification to occur, the majority of the atoms must be at the energy level E2, which is called a population inversion. We can never achieve population inversion if there are only two energy levels because in the steady state, incoming photons will cause as many upward excitations as downward stimulated emissions.

LASER: Light Amplification by Stimulated Emission of Radiation PHYS5320 Chapter Seven 10 Stimulated Emission Rate and Einstein CoefficientsThe image part with relationship ID rId3 was not found in the file.

A useful laser medium must have a higher efficiency of stimulated emission compared with the efficiencies of spontaneous emission and absorption. Consider a

medium with N1 atoms per unit volume with energy E1 and N2 atoms per unit volume with energy E2. The upward and downward transition rates will be h  E E R12  B12 N1h R21  A21N2  B21N2 h 2 1

B12 is for absorption. A21 is for spontaneous emission. B21 is for stimulated emission. They all known as the Einstein coefficients. (h) is the photon energy density per unit frequency, representing the number of photons per unit volume with an energy h. To find the Einstein coefficients, we consider the medium in thermal equilibrium.

There is no net change in the populations at E1 and E2. N  E  E  2  exp 2 1  R12  R21   N1  kBT  PHYS5320 Chapter Seven 11 Stimulated Emission Rate and Einstein Coefficients In thermal equilibrium, (h) is given by Planck’s black body radiation  distribution law: 8 h 3 h    h   c3exp  1     kBT   R R N  12 N  21 1  2  B12 h A21  B21 h   B h  E  E    12  exp 2 1      A21  B21 h  kBT 

A 8h 3 / c3 h  21  E2 E1 / kBT h / kBT B12e  B21 e 1

PHYS5320 Chapter Seven 12 Stimulated Emission Rate and Einstein Coefficients We obtain from the equation on the previous slide:  3 3 B12  B21 A21 / B21  8 h / c Consider the ratio of stimulated emission to spontaneous emission and the ratio of stimulated emission to absorption:

3 R stim B h c R21stim N2 21  21    h   3 R absorp N R21 spon A21 8 h 12 1 There are two important conclusions. For stimulated emission to exceed photon absorption, we need to achieve population inversion. For stimulated emission to far exceed spontaneous emission, we must have a large photon concentration, which is achieved by building an optical cavity to contain the photons. The population inversion means that we depart from thermal equilibrium. The laser principle is based on non-thermal equilibrium.

PHYS5320 Chapter Seven 13 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers

PHYS5320 Chapter Seven 14 Optical Fiber Amplifiers A light signal traveling along an optical fiber over a long distance suffers attenuation. It is necessary to regenerate the light signal at certain intervals for long haul communications (>1000 km). Instead of regenerating the signal by photodetection, conversion to an electrical signal, amplification, and then conversion back from electrical to light energy by a laser diode, it is more practical to amplify the signal directly by using an optical amplifier.

One practical amplifier is erbium ion (Er3+) doped fiber amplifier (EDFA).

PHYS5320 Chapter Seven 15 Optical Fiber Amplifiers

The erbium doped fiber is inserted into the fiber communication line by splicing. It is pumped from a laser diode through a wavelength-selective coupler that allows only the pumping wavelength to be coupled. In the absence of the pumping light, erbium ions will absorb 1550-nm photons and act as an attenuator. The optical isolators inserted at the entry and exit end allow only the optical signals at 1550 nm to pass in one direction and prevent the 980 nm pumping light from the propagation into the communication system. PHYS5320 Chapter Seven 16 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers

PHYS5320 Chapter Seven 17 Gas Lasers: the He‐Ne Laser

The HeNe laser consists of a gaseous mixture of He and Ne atoms in a gas discharge tube. An optical cavity is formed by end mirrors so that reflection of photons back into the lasing medium builds up the photon concentration in the cavity. By using dc or RF high voltage, electrical discharge obtained within the tube causes the He atoms to become excited by collisions with drifting electrons.

PHYS5320 Chapter Seven 18 Gas Lasers: the He‐Ne Laser

electron impact

PHYS5320 Chapter Seven 19 Gas Lasers: the He‐Ne Laser

The molar ratio of He to Ne in He-Ne lasers is typically 5 to 1 with a pressure of several torrs. The lasing emission intensity increases with the tube length since more Ne atoms are then used in stimulated emission. The intensity decreases as the tube diameter is increased because Ne atoms in the 2p53s1 state can return to the ground state only by collisions with the walls of the tube. Brewster windows are typically used at the ends of the tube to allow only polarized light to be transmitted and amplified within the cavity so that the output radiation is polarized.

PHYS5320 Chapter Seven 20 The Doppler Broadening Effect The output radiation from a gas laser covers a spectrum of wavelengths with a central peak. One mechanism causing the line broadening is the Doppler effect. According to the kinetic molecular theory, gas atoms are in random motion with an average kinetic energy of (3/2)kBT. Suppose that these gas atoms emit radiation of frequency 0. When a gas atom is moving away from the observer, the observer detects a lower frequency. When a gas atom is moving towards the observer, the detected frequency will be larger.

 vx   vx  1  0 1   2  0 1   c   c  The relative velocity of the atom along the laser tube axis with respect to the observer can be estimated from 1 2 1 Mvx  kBT 2 2 The Doppler broadened linewidth can be estimated according to v  v2  v1 PHYS5320 Chapter Seven 21 The Doppler Broadening Effect If we consider the Maxwell velocity distribution of the gas atoms in the laser tube, 2kBT ln2 the full width at half maximum (FWHM) v1/ 2  2v0 Mc2 linewidth 1/2 in the output intensity versus frequency spectrum is given by

Δλm

Δλm PHYS5320 Chapter Seven 22 Example: Calculate the Doppler broadened linewidths in frequency and wavelength for the He-Ne laser transition for 632.8 nm if the gas discharge temperature is 127 C. The atomic mass of Ne is 20.2 g/mol. The laser tube length is 40 cm. What is the mode number m of the central wavelength, the separation between consecutive modes and how many modes do you expect within the Doppler broadened linewidth? 0.0202 M   3.361026 kg Ne 6.021023   1/ 2 1/ 2  k T  1.38 1023 127 273   B    1 vx       405.6ms   26  M Ne   3.3610 

 vx   vx  2 0vx 2vx 2405.6   0 1   0 1     9 1.282GHz  c   c  c 0 632.810  23 2 2kBT ln2 2 21.3810 400 ln 2  1/ 2   1.51GHz 9 26 0 M Ne 632.810 3.3610 PHYS5320 Chapter Seven 23       2 9 2  c  c 0 632.810 9  1/ 2      1/ 2  1/ 2  1.5110  0.00202nm    2 c 3108  0  2L 20.4 m0   9 1264222.5 0 632.810 2 2L 2L 2L 2 632.8109        0   0.501pm m m m1 m m 1 m2 2L 20.4  2.02 Modes  1/ 2   4.03 m 0.501

The number of modes will depend on how the cavity modes and the Doppler broadened spectrum coincide.

PHYS5320 Chapter Seven 24 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers

PHYS5320 Chapter Seven 25 Optical Gain Coefficient The attenuation coefficient is defined as the fractional decrease in the optical power per unit distance. 1 dP    P dx

Similarly, we can define an optical gain coefficient: P  c g  x  t  Px n  N n n N g  ph  ph Nph c t cNph t

PHYS5320 Chapter Seven 26 Optical Gain Coefficient Spontaneous emissions can be omitted because they are in random directions and do not contribute to the directional wave on average. dN ph  Net rate of stimulated photon emission dt  N2 B21h  N1B12  h    N2  N1 B21 h Normally the emission and absorption processes occur over a frequency interval. The spread can be due to the Heisenberg uncertainty principle and the Doppler broadening effect.  Nphh 0 h 0   n  B21nh0 g0  N2  N1 B21 h0  N2  N1

cNph PHYS5320 Chapter Sevenc 27 Threshold Gain

Consider a cavity containing a laser medium. At the steady state, an initial optical power at some point travels along the cavity, gets reflected by the end mirrors, and arrives at the same point after a round trip. Under steady state conditions, the initial optical power must be equal to the final optical power.

Pf  PiR1R2 expg2L exp 2L  Pi  is the attenuation coefficient of the medium, representing all losses in the cavity and its walls, except light transmission losses through the end mirrors and absorption across the energy levels involved in stimulated emissions, which is incorporated into the optical gain coefficient. PHYS5320 Chapter Seven 28 Threshold Gain

The value of the gain coefficient that makes Pf = Pi under steady state oscillations is called the threshold gain. The threshold gain coefficient has to be obtained by suitably pumping the medium so that N2 is sufficiently greater than N1, corresponding to a threshold population inversion. 1  1  g    ln  th   2L  R1R2  c N2  N1 th  gth B21nh0

Until the pump rate can bring (N2 – N1) to the threshold value, there will be no coherent radiation output. When the pump rate exceeds the threshold value, then (N2 – N1) remains clamped at (N2 – N1)th. Additional pumping increases the rate of stimulated emissions and thus increases the optical output power. PHYS5320 Chapter Seven 29 Phase Condition and Laser Modes

There is an additional condition to ensure the self-replication rather than self- destruction of the EM wave traveling in the cavity.

roundtrip  m2 If the refractive index of the medium in the cavity is assumed constant, then

 m  nkm 2L  m 2  m   L  2n  PHYS5320 Chapter Seven 30 Phase Condition and Laser Modes The EM wave traveling in the cavity has been idealized as plane waves. A more accurate way of thinking about modes is to realize that a mode represents a particular electric field pattern in the cavity that can replicate itself after one round trip. A mode with a certain field pattern at a reflector can propagate to the other reflector and back again and return the same field pattern. All these modes can be represented by electric and magnetic fields that are nearly normal to the cavity axis. They are referred to as transverse modes or transverse electric and magnetic (TEM) modes. Each allowed mode corresponds to a distinct spatial field distribution at a reflector. These mode field patterns at a reflector can be described by three integers p, q, m and designated by TEMpqm. PHYS5320 Chapter Seven 31 Phase Condition and Laser Modes The integers p and q represent the number of nodes in the field distribution along the transverse directions. The integer m is the number of nodes along the cavity axis and is the usual longitudinal mode number. Each transverse mode with a given p and q has a set of longitudinal modes, the number of which (m) is usually very large (~106 in gas lasers) and is not written, though understood. Therefore, transverse modes are written as TEMpq and each has a set of longitudinal modes (m = 1,2,3,).

TEM00 is radially symmetric and has a Gaussian intensity distribution across the beam cross section. It has the lowest divergence angle. These properties make

TEM00 highly desirable.

PHYS5320 Chapter Seven 32 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers

PHYS5320 Chapter Seven 33 Principle of the Laser Diode Consider a degenerately doped direct bandgap semiconductor pn junction.

Under degenerately doping conditions, the Fermi level EFp in the p-side is in the valence band, and the Fermi level EFn in the n-side is in the conduction band. The depletion region is very thin.

without bias With bias, EFn – EFp = eV > Eg PHYS5320 Chapter Seven 34 Principle of the Laser Diode A population inversion is established between energies near Ec and those near Ev around the junction. There will be an optical gain, which depends on EFn – EFp = eV. The population inversion is achieved by the injection of charge carriers across the junction under a sufficiently large forward bias. This type of pumping is called injection pumping.

PHYS5320 Chapter Seven 35 Homojunction Laser Diodes

The ends of the crystal are cleaved to be flat and optically polished to provide reflection and hence form an optical cavity.

 m  L 2n

Each radiation with a particular frequency/wavelength satisfying the above relationship is essentially a resonance frequency of the cavity, that is, a mode of the cavity.

PHYS5320 Chapter Seven 36 Homojunction Laser Diodes

Lasing oscillations occur only when the optical gain in the medium can overcome the photon losses from the cavity, that is, when the optical gain g reaches the threshold gain gth. Accordingly there is a threshold current Ith. The number of modes in the output spectrum and their relative strengths depend on the diode current. The main problem for homojunction lasers is that the threshold current (~500 A mm‒2) is too high for practical uses.

PHYS5320 Chapter Seven 37 Heterostructure Laser Diodes The reduction of the threshold current to a practical value requires improving the rate of stimulated emission and also improving the efficiency of the optical cavity, that is, we need both carrier confinement and photon confinement. For carrier confinement, we can confine injected electrons and holes to a narrow region around the junction. This narrowing of the active region means that less current is needed to establish the necessary concentration of carriers for population inversion. For photon confinement, we can build a waveguide around the optical gain region to increase the photon concentration and hence the probability of stimulated emission. Both of these requirements are achieved by the use of a double heterostructure device. PHYS5320 Chapter Seven 38 Heterostructure Laser Diodes Refractive index

A wider bandgap semiconductor generally has a smaller refractive index. AlGaAs has a lower refractive index than GaAs. The change of the refractive index defines an optical dielectric waveguide that confines photons to the active region of the optical cavity and thereby reduces photon losses and increases the photon concentration. Without double heterostructure devices, we would not have practical solid state lasers that can be operated continuously at room temperature. PHYS5320 Chapter Seven 39 Heterostructure Laser Diodes

Such lasers are called gain guided.

The contact on p-GaAs is in a stripe geometry. The current density is non- uniform laterally. It decreases from 1 to 2 and 3. Two advantages: (1) reduce the threshold current Ith; (2) coupling to optical fibers easier. The laser efficiency can be increased by reducing the reflection loss at the side facets. Dielectric mirrors can be fabricated at the side facets. PHYS5320 Chapter Seven 40 Heterostructure Laser Diodes

The active region is bound both vertically and laterally by AlGaAs with a larger bandgap energy and a lower refractive index. The structure is hence called buried double heterostructure laser diode. Since the optical power is confined to the waveguide defined by the refractive index variation, these diodes are called index-guided. If only the fundamental mode can exist in the waveguide structure, then we will have a single-mode laser diode. The laser diodes based on GaAs and AlGaAs have a wavelength of 900 nm. For operation in the optical communication wavelengths of 1300 nm and 1500 nm, typical heterostructures are based on InP (substrate) and quaternary alloys InGaAsP. PHYS5320 Chapter Seven 41 Low‐Pumping‐Current Lasers

SEM image

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, Y.-H. Lee, Science 2004, 305, 1444.

PHYS5320 Chapter Two 42 Low‐Pumping‐Current Lasers

Radii of air holes: 0.28a (I) Designed according Electric field intensity profile 0.35a (II) to FDTD (finite- 0.385a (III) difference time- 0.4a (IV) domain) calculations

0.41a (V) PHYS5320 Chapter Two 43 Low‐Pumping‐Current Lasers

These low-threshold-current, highly-efficient lasers can function as single-photon sources, which are useful for cavity quantum electrodynamics and quantum information processing.

PHYS5320 Chapter Two 44 Elementary Laser Diode Characteristics The output spectrum of a laser diode depends on (1) the nature of the optical resonator and (2) the optical gain curve. The optical resonator is essentially a Fabry-Perot cavity, which is defined by the length L, width W, and height H. The length determines the longitudinal modes and the width and height determine the lateral modes or transverse modes. The emerging laser beam exhibits divergence due to diffraction at the cavity ends.

PHYS5320 Chapter Seven 45 Elementary Laser Diode Characteristics

The actual modes existing in the output spectrum depend on the optical resonator structure and the pumping current level.

PHYS5320 Chapter Seven 46 Elementary Laser Diode Characteristics The LD output characteristics is temperature-sensitive. As the temperature increases, the threshold current increases rapidly.

Slope efficiency: Conversion efficiency (up to 30 – 40%): 𝑃o 𝑃o 𝜂 𝜂slope conversion 𝐼𝑉 𝐼𝐼th PHYS5320 Chapter Seven 47 Elementary Laser Diode Characteristics

The output spectrum also changes with temperature. In the case of a single mode LD, the peak emission wavelength exhibits certain jumps at certain temperatures. A jump corresponds to a mode hop in the output, which means at a new operation temperature, another mode fulfills the laser oscillation condition. Between mode hops, the wavelength increases slowly with the temperature due to the slight increase in the refractive index and the cavity length with the temperature. If mode hops are undesirable, the device structure must be designed to keep the modes sufficiently separated. PHYS5320 Chapter Seven 48 Steady State Semiconductor Rate Equations

d is the thickness of the active layer.

I n Under steady state conditions, the rate of   CnNph electron injection by current is equal to the sum edLW sp of the rate of spontaneous emissions and the n: electron carrier rate of stimulated emissions (neglecting non- concentration radiative emissions). PHYS5320 Chapter Seven 49 Steady State Semiconductor Rate Equations Nph is the coherent photon concentration in the active layer. Under steady state conditions, the rate of coherent photon loss in the cavity must be equal to the rate of stimulated emissions. Nph  CnNph ph

ph is the average time for a photon to be lost from the cavity due to transmission through the end faces, scattering and absorption in the semiconductor.

The threshold electron concentration nth and threshold current Ith refers to the condition when the stimulated emission just overcomes the spontaneous emission and the total loss mechanisms in ph. Therefore, we have

1 This is the point when coherent radiation gain by nth  stimulated emission just balances all the cavity losses C ph (represented by ph) plus losses by spontaneous emission.

PHYS5320 Chapter Seven 50 Steady State Semiconductor Rate Equations When the current exceeds Ith, the output optical power increases sharply with the current. We can just take Nph = 0 when I = Ith. nthedLW Ith  sp

When the current exceeds the threshold current, the excess carriers above nth brought in by the current recombine by stimulated emission because above threshold, the active layer has optical gain and therefore builds up coherent radiation quickly and stimulated emission depends on Nph. The steady state electron concentration remains constant at nth though the rates of carrier injection and stimulated recombination have increased. I  Ith  Cnth Nph edLW 1 I n  ph J  th Nph  J  Jth LW C ph ed PHYS5320 Chapter Seven 51 Steady State Semiconductor Rate Equations To find the optical output power, consider that it takes t = nL/c for photons to cross the laser cavity length L. Only half of the photons in the cavity volume would be moving towards the output face. Only a fraction (1R) of the radiation power will escape. 1 𝑁 𝑉 ℎ𝜈 2 ph cavity 𝑃o 1𝑅 This is called the laser Δ𝑡 diode equation. 𝜏ph𝑑𝐿𝑊ℎ𝑐𝑐 𝑃 𝐽𝐽 1𝑅 o 2𝑒𝑑𝜆𝐿𝑛 th

ℎ𝑐 𝜏ph𝑊 1𝑅 𝑃 𝐽𝐽 o 2𝑒𝑛𝜆 th

PHYS5320 Chapter Seven 52 Light Emitters for Optical Fiber Communications

Current efforts are to achieve single frequency operation, for which  is less than 0.01 nm.

PHYS5320 Chapter Seven 53 Single Frequency Solid State Lasers There are several methods to ensure a single mode of radiation in the laser cavity. One is to use frequency-selective dielectric mirrors at the cleaved surfaces of the semiconductor. One of such mirrors is the distributed Bragg reflector (DBR).

 2n  B is called the Bragg wavelength, and  2  2q q is called the diffraction order.    B  Only those Fabry-Perot cavity modes close to B can lase and exist in the 2n output. B  𝑞 1,2,3, ⋯ q

PHYS5320 Chapter Seven 54 Single Frequency Solid State Lasers The second method is to use a corrugated layer (guiding layer) next to the active layer. The corrugations in the refractive index act as optical feedback over the length of the cavity by producing partial reflections. Optical feedback is distributed over the cavity length. This is called the distributed feedback laser (DFB). Because partially reflected waves experience gain, the left and right traveling waves can only coherently couple to set up a mode if their frequency is related to the corrugation periodicity.  2  B m  B  m 1 𝑚 1,2,3, ⋯ 2nL

PHYS5320 Chapter Seven 55 Single Frequency Solid State Lasers The third method is to use two coupled laser optical cavities with different cavity lengths, which is called the cleaved-coupled-cavity (C3). Only those waves that can exist as modes in both cavities are allowed. If one mode separation is larger than the other one, then these two different sets of modes coincide only at far spaced intervals.

PHYS5320 Chapter Seven 56 Quantum Well Devices A quantum well structure has a very thin (typically less than 50 nm) narrow bandgap semiconductor sandwiched between two wider bandgap semiconductors. For GaAs/AlGaAs,

Ec  60%Eg

Ev  40%Eg

PHYS5320 Chapter Seven 57 Single Quantum Well (SQW) Devices 2 2 2 2 2 2 h n h ny h nz E  Ec    * 2 * 2 * 2 8med 8meDy 8meDz The energy is mainly determined by the term associated with motion along x. The density of states for the two dimensional electron system is constant and does not depend on the energy. Since at E1 there is a finite and substantial density of states, the electrons in the conduction band do not have to spread far in energy to find states. Under a forward bias electrons are injected into the conduction band. The injected electrons readily populate the ample number of states at E1, which means that the electron concentration at E1 increases rapidly with the current and hence population inversion occurs quickly. Two advantages for lasers: (1) The threshold current is markedly reduced. (2) The linewidth is substantially narrower than that in bulk semiconductor lasers.

PHYS5320 Chapter Seven 58 Multiple Quantum Well Devices

A 1550 nm MQW-DFB InGaAsP laser diode pigtail-coupled to a fiber

PHYS5320 Chapter Seven 59 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers

PHYS5320 Chapter Seven 60 Vertical Cavity Surface Emitting Lasers (VCSELs)

There are dielectric mirrors on the top and bottom to form an optical cavity. The mirrors are essentially distributed Bragg reflectors (DBRs).

PHYS5320 Chapter Seven 61 Vertical Cavity Surface Emitting Lasers (VCSELs) VCSELs are generally circular and therefore the emitted beam has a circular cross- section. The height can be as small as a few m, which makes the longitudinal mode separation sufficiently large to allow only one longitudinal mode to operate. When the cavity diameter is less than 8 m, there will be only one lateral mode. Such a laser is referred to as a microlaser. Microlasers can be arrayed to construct a matrix emitter. Such laser arrays have important potential applications in optical interconnect and optical computing technologies.

PHYS5320 Chapter Seven 62 Chapter 7: Laser Diodes Optical resonators Stimulated emission and photon amplification Optical fiber amplifiers Gas lasers Laser oscillation conditions Laser diodes Vertical cavity surface emitting lasers Optical laser amplifiers

PHYS5320 Chapter Seven 63 Optical Laser Amplifiers

Traveling wave amplifier Fabry-Perot amplifier

Fabry-Perot amplifiers can have a higher gain than traveling wave amplifier, but they are less stable.

A 1550 nm semiconductor optical amplifier using an InGaAsP chip PHYS5320 Chapter Seven 64 Reading Materials

S. O. Kasap, “Optoelectronics and Photonics: Principles and Practices”, Prentice Hall, Upper Saddle River, NJ 07458, 2001, Chapter 4, “Stimulated Emission Devices LASERS”.

PHYS5320 Chapter Seven 65