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Photonics and Optical Communication (Course Number 300352) Spring 2007 Optical Source Dr. Dietmar Knipp Assistant Professor of Electrical Engineering

http://www.faculty.iu-bremen.de/dknipp/

Optical Sources 1 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

Photonics and Optical Communication

5 Optical Sources 5.1 Introduction 5.2 Absorption and Emission of light 5.2.1 5.2.2 5.3 Light emitting versus diodes 5.4 Introduction to 5.4.1 Structural Properties of Semiconductors 5.4.2 Energy Bands in Semiconductors 5.4.3 The pn-junction 5.4.4 Diodes under forward bias 5.5 Light emitting diodes (LEDs) 5.5.1 Direct and indirect Semiconductors 5.5.2 Device structures 5.5.3 Application of Light emitting Diodes 5.6 5.6.1 Spontaneous Emission 5.6.2 5.6.3 Three and four energy level systems 5.6.4 Optical feedback and laser resonators

Optical Sources 2 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.5 Threshold condition for laser oscillation 5.6.6 Requirements for lasing 5.7 Lasers 5.7.1 Stimulated emission and lasing in Semiconductors 5.7.2 Semiconductor Materials for lasing applications 5.7.3 Efficiency of LEDs and laser diodes 5.7.4 Laser structures 5.7.4.1 Fabry Perot Homojunction 5.7.4.2 laser diode 5.7.4.3 lasers 5.7.4.4 Distributed Feedback (DFB) Lasers 5.7.4.5 Vertical Cavity Surface Emitting Lasers (VCSELs)

References

Optical Sources 3 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.1 Introduction The success of optical communication technology is stimulated by the development of optical fibers and technology on one side and the invention of solid state lasers and laser diodes on the other side. Solid state lasers are compact, reliable and inexpensive. Optical communication systems with very high bandwidth-distance products can only be implemented by using lasers or laser diodes.

Laser diode package and micrograph of inside of a laser package. Ref.: Infineon

Optical Sources 4 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.1 Introduction In general the generation of light is caused by the transition of an form an energetically higher energy state to a lower energy state. The energy difference due to the transition of the electron leads to a radiative or a non- radiative process. We are of course interested in radiative processes as we like to “build” an optical source. The non-radiative processes typically lead to the creating of heat. The energy is simply dissipated by heat. In the case of a radiative process photons are emitted. The emission of light, can take place either spontaneously or it can be stimulated by the presence of another photon of the “right” energy. In order to understand the processes of light-generation, it is necessary to consider fundamental processes like structural and optical properties and energy levels in materials and the electronic device concepts. An understanding of the structural and optical properties is needed to actually understand the process of light generation and an understanding of the devices is needed to make use of such an effect.

Optical Sources 5 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.2 Absorption and Emission of light The interaction of light and matter in the form of absorption and emission requires a transition from one discrete energy level to another energy level. The frequency and the of the emitted or absorbed photon is related to the difference in energy E, between the two energetic states, where h is the Planck constant h=6.626 x 10-34J, f is the frequency and λ is wavelength of the absorbed or emitted light.

hc E = E − E = hf = Photon energy 2 1 λ

Optical Sources 6 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.2 Absorption and Emission of light

The figure illustrates transitions between two energy states. When

a photon with the energy (E2-E1) is incident on the material an electron may be excited from the energy

state E1 into an higher energy state E2 through the absorption of the photon. Alternatively, when the electron is initially on a higher energy level it can make a transition to a energetically lower state and the provided energy loss leads to the emission of a photon. Here the transition is assumed to be a radiative transition. Energy state diagram showing (a) absorption, (b) spontaneous emission, (c) stimulated emission. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 7 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.2 Absorption and Emission of light We have to distinguish between radiative and non-radiative processes. In the case of a non-radiative process the energy is dissipated as heat. The question whether a transition is non-radiative or radiative depends on the involved species of carriers, the material itself, the level of impurities in the material, the temperature and the device structure. In the case of radiative emission we can than distinguish between spontaneous and stimulated emission.

Optical Sources 8 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.2.1 Spontaneous Emission For most of the light sources the photons are emitted spontaneously (sun light, light bulb, halogen lamp). In a first step an electron is elevated to an energetically higher state which is usually unstable. In the second step the electron will spontaneously return to an energetically more stable state (which is typically the energetically lower state). This process is a statistical process which can happen very fast. As a consequence the spontaneously (or randomly) emitted photons are incoherent (very short time) and the emitted spectrum has broad spectral width.

Energy state diagram for spontaneous emission of a photon. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 9 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.2.2 Stimulated Emission The operating principle of a laser is based on stimulated emission. We speak about stimulated emission if the electron which enters an energetically higher state (excited state) remains in this state until it is “stimulated” by the presence of a photon to leave this higher energetically state and return to the more stable lower energetically state (ground state). One of the requirements for stimulated emission is that the electron can stay in its excited state a relatively long period of time (a few microseconds) before it changes its state spontaneously. In the case of spontaneous emission the electron stays in this excited state usually for a shorter period of time (picoseconds). In the case of stimulated emission the electron can be “stimulated” by the presence of a photon to emit its energy in the form of another photon.

Energy state diagram for stimulated emission. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 10 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.2.2 Stimulated Emission In this case the energy of the incident photon has to be very close to the energy of the excited electron. Stimulated emission takes place when the emitted photon has the same energy (the same wavelength), phase and direction as that of the photon which stimulated it! Stimulated emission is the inverse process of absorption!

5.3 Light emitting diodes versus laser diodes In order to observe spontaneous or stimulated emission we have to excite the first before they can return to a lower energetic states. Of course energy has to be provided to excite the electron. The energy can be provided by heat, absorption of photons (photoluminescence) or electrical current (electroluminescent). We are interested in the later case, where the energy is provided by an electrical current.

Optical Sources 11 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.3 Light emitting diodes versus laser diodes In both types of devices the recombination of carrier is used to provide a photon flux. However, the emission of light in a light emitting diode is a spontaneous process, whereas it is a stimulated process in a laser diode. Therefore, the description of an LED (light emitting diode) is different from the description of a laser diode. The description of an LED is by far simpler than the description of a laser diode. In both cases a semiconductor diode is used, which operates under forward bias conditions. Furthermore, the same structure can be used to build an optical .

Forward biased pn-diode operating as (a) LED, (b) semiconductor amplifier, (c) semiconductor injection laser. Ref.: Saleh & Teich, Fundamentals of Photonics

Optical Sources 12 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4 Introduction to semiconductors In order to get an understanding of semiconductor based optical light sources we have to review some of the basic semiconductor properties. We will concentrate in this lecture on the description of the basic operating principle of a pn-junction (pn diode) as the light emitting diode (LED) and the laser diode are based on such structure.

5.4.1 Structural Properties of Semiconductors First the structural properties of semiconductors will be discussed. The structural properties have a strong effect on the electronic and the optical properties of the material. In general we can distinguish semiconductors in terms of their structural properties. Semiconductors exist as crystalline or amorphous materials. Crystalline material exhibit a high degree of structural order, whereas amorphous materials are characterized by a random or partly random distribution of the atoms or molecules in the solid. We concentrate here only on crystalline materials.

Optical Sources 13 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.1 Structural Properties of Semiconductors We assume that the material has a perfect crystal structure, which means that the material has no structural defects (structural disorder) and they do no contain impurities. Based on the Bohr’s atom model we can derive the energy band structure of a semiconductor.

Different kinds of materials in terms of structural properties. Ref.: Saleh & Teich, Fundamentals of Photonics

Optical Sources 14 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.2 Energy Bands in Semiconductors The band structure of a single atom is characterized by allowed discrete energy levels. Electrons can stay on these energy levels. When moving from a single atom to a solid several of these energy levels overlap and discrete energy bands are formed. The conduction and the valence band are the two highest energy levels. The band structure of semiconductor is characterized by a valence band and a conduction band. The two bands are separated by the bandgap. The energetically states in the bandgap are forbidden due to Bohr’s atom model.

Energy bands in two semiconductors (a) , (b) Arsenide Ref.: Saleh & Teich, Fundamentals of Photonics

Optical Sources 15 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.3 The pn-junction A band structure for an intrinsic semiconductor is shown in the figure. Intrinsic means that the semiconductor is not doped. is the incorporation of impurities in the crystalline semiconductor. The intrinsic semiconductor is therefore considered to be a highly pure semiconductor. The fact whether the conduction band is occupied by an electron is described by the Fermi-Dirac statistic. The Fermi Dirac function is a probability function.

Energy bad structure of an intrinsic semiconductor at a temperature above absolute zero, and the Fermi-Dirac distribution for holes. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 16 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.3 The pn-junction The Fermi-Dirac statistic is closely related to the Fermi energy.

1 P()E = ()Fermi-Dirac Distribution 1+ exp[]E − EF kT

where k is the Boltzmann factor and EF is the Fermi energy. The Fermi-Dirac function P(E)=0.5 for E=EF. The Fermi-Dirac distribution is shown (on the previous slide) for a temperature above absolute zero. The excitation of an electron from the valance band to the conduction band leaves an empty state in the valence behind. A missing electron in the valence band is called a hole. Electrons can move in the conduction band and holes move in the valence band.

Optical Sources 17 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.3 The pn-junction The Fermi level is a measure of the distribution of carriers in the semiconductor. The Fermi level is almost in the middle of the bandgap for an intrinsic semiconductor. The Fermi level can be seen as a probability function, which describes whether the bands are occupied or not (by a carrier). As we are speaking about electrons and hole we can define a Fermi-Dirac distribution for electrons and holes. The probability that a state is occupied by an electron or hole is exact 50% for the Fermi energy.

1 Fermi-Dirac Distribution P ()E = e ()for Electrons 1+ exp[]E − EF kT

1 P ()E = Fermi-Dirac Distribution h () 1+ exp[]EF − E kT for Holes

Pe ()E + Ph E ()= 1 Fermi-Dirac Distribution

Optical Sources 18 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.3 The pn-junction To create an the material is doped with impurities which either create free electrons (donors) or free holes (acceptors). When donor impurities are added to the material, the thermally excited electrons from the donor level are raised in the conduction band to create free carriers so to say electrons. Due to the increase of the electron concentration in the conduction band the Fermi level shifts closer to the conduction band. Is the semiconductor material doped with acceptors the number of free carriers in the valence band is increased which are in this case holes. Under such conditions the Fermi level shifts closer to the valence band.

Energy band diagram for an n-type and an p-type semiconductor Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 19 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.3 The pn-junction A pn-junction is realized by the formations of a semiconductor with adjacent p- and n-regions. As a consequence a depletion layer is formed by the recombination of free carriers in the vicinity of the pn- junction. Only the localized states are left behind which leads to the formation of a high electric field in the . The electric field distribution (potential barrier) leads to the limitation of the interdiffusion of the free carriers. In the absence of an applied bias voltage no net current is flowing Cross section and band diagram of a through the diode. The width of the pn-junction under thermal equilibrium. depletion layer and the magnitude of the electric field (potential barrier) Ref.: J.M. Senior, Optical Fiber depends on the doping level in the p- Communications and n-region.

Optical Sources 20 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.3 The pn-junction If now a voltage is applied to the pn-junction the potential barrier is either increased or lowered. For positive applied voltages the diode is forward biased and the potential barrier is lowered, whereas for negative voltages the diode is in reverse biased and the potential barrier is increased. As a consequence the electric field in the depletion layer is increased or decreased.

Optical Sources 21 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.4 Diodes under forward bias Under forward bias conditions electrons and holes are injected in the semiconductor via the contacts. Electrons are injected via the n-type region and holes are injected via the p-tpye region. The schematic operation behavior of a diode under forward bias conditions is shown in the figure. Due to injection of carriers the concentration of minority carriers will increase in the vicinity of the depletion region.

Pn-junction under forward bias. The recombination of pair leads to the spontaneous emission of photons. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 22 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.4.4 Diodes under forward bias Electrons are minority carriers in an p-type semiconductor and holes are minority carriers in an n-type semiconductor. The opposite of minority carriers are majority carriers. Therefore, electrons are majority carriers in an n-type semiconductor and holes are majority carriers in an p-type semiconductor. If we now increase the concentration of minority carriers in a semiconductor a lot of the carriers will recombine via the majority carriers in this material. For example the concentration of electrons in the p-region of a pn-diode can be increased by a applying forward bias to the diode. The concentration of minority carriers in the vicinity of the depletion region is increased due to the diffusion of carriers. We already discussed that the recombination can be radiative or non-radiative. In the case of non-radiative recombination the energy is dissipated by lattice vibrations (heating up of the sample).

Optical Sources 23 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5 Light emitting diodes (LEDs) In the case of radiative recombination the wavelength of the emitted photons is givenλ by,

c hc 1.24 = = = µm Wavelength f E E()eV

where c is the speed of light and h is the Planck constant. If a material (semiconductor) emits light as a consequence of the injection of charges (current) we speak about electroluminescence. The name implies that the emission is stimulated by electron injection. The alternative would be photoluminescene, where we shine light on a sample and the sample emits light (at a lower energy / higher wavelength). In both cases the emission is caused by the recombination of electron-hole pairs.

Optical Sources 24 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5 Light emitting diodes (LEDs) The efficiency of the recombination process, which leads to radiative recombination (light emission), depends on the semiconducting material itself, the level of impurities, the structural properties, the temperature and the device fabrication. Out of the list of important requirements for an efficient light emission process the material itself is the most important factor. The most important materials for the manufacturing of LEDs and laser diodes are out of the class of direct semiconductors, whereas indirect semiconductors usually exhibit very low efficiencies in converting electrical energy in light.

Schematic sketch of carrier recombination in a pn- junction. The recombination leads to the emission of photons (radiative process). Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 25 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.1 Direct and indirect Semiconductors Typical examples of direct semiconductors are (GaAs), (InP) or (GaN). Typical materials for indirect semiconductors are silicon (Si) or germanium (Ge). Therefore, the most important semiconductor (silicon) can not be used as an efficient light emitter. In order to understand the difference between a direct and an indirect semiconductor we have to look a little bit closer in the electronic structure of semiconductor materials. We already discussed that the bands (valence band and conduction bands) are formed by the superposition of the orbitals for each atom.

Energy momentum diagram showing the emission of a photon for an direct (a) and an indirect (b) semiconductor. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 26 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.1 Direct and indirect Semiconductors However, the band diagram we are using so far is a drastically simplification of the real picture. If we consider the location of the individual atoms in a lattice we will get a more precise picture of the electronic structure. The 3 dimensional nature of a lattice is considered in the momentum energy diagram for a specific crystal orientation of the material. We speak about a direct semiconductor if the minimum of the conduction band and the maximum of the valence band are adjacent to each other and electron and the hole pairs can directly recombine. In the case of an indirect semiconductor an additional momentum of the electron is needed to recombine with a hole in the valence band.

Optical Sources 27 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.2 Device structures LEDs and laser diodes can be constructed based on surface emitting or edge- emitting device structures. The surface-emitting devices emit light from a face of the device, whereas the edge-emitting structure emits light from the edge. The edge emitting structure is usually applied for solid-state laser diodes. Most of the LEDs are based on a surface emitting structure. The different structures have clear advantages and disadvantages. The surface emitting structure is very well suited for lighting applications. Furthermore, it is possible to test devices on the wafer level. In the case of a surface emitting laser structure the cavity of the laser diode is short so that the reflectivity of the mirrors has to be high, but still the laser diodes can be tested on the wafer level.

Implementation of LED and laser structures, (a) Surface emitting Device, (b) Edge- emitting Device. Ref.: Saleh & Teich, Fundamentals of Photonics

Optical Sources 28 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.2 Device structures The photons are created by the electron-hole recombination in the vicinity of the depletion region. Therefore, the emission light occurs in this region. The efficiency of such a structure is relatively low. Such a structure is called a homojunction. The semiconductors in both regions of the pn diode have the same bandenergies so that not no discontinuity occurs in the bandgap. To improve the device performance and therefore the efficiency we have find a way of producing light in a more localized area, with a greater intensity. The situation can be improved by introducing a heterostructure.

Homejunction and double LED. Ref.: H. J.R. Dutton, Understanding optical communications

Optical Sources 29 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.2 Device structures A heterojunction is different from an ordinary homojunction. In such case a discontinuity in the band diagram is observed. In such a configuration the charge carriers (electrons or holes) are attracted over the barrier from the material of higher bandgap energy to the one of lower bandgap energy. As a consequence most of the recombination occurs in the region of lower optical bandgap. The situation can even be improved by using a double heterostructure.

Optical Sources 30 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.2 Device structures The double heterostructure is realized by introducing a layer of lower bandgap material in between two layers of higher bandgaps. A double heterojunction consists of two . Again the recombination of carriers is restricted to the low bandgap region which is called „the active region“ of the diode. An example of an energy diagram of a double heterojunction based on indium phosphide is shown in the figure.

Double Heterojunction LED. Ref.: H. J.R. Dutton, Understanding optical communications

Optical Sources 31 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.3 Application of Light emitting Diodes The manufacturing cost of LEDs is low in comparison to lasers diodes. However, LEDs are only used for very short range optical communication systems. The main advantage of LEDs based optical communication systems is the cost in implementing such systems. There are two reasons which limit the performance of LED based fiber communication systems

Incoherent Light: The light produced by a LED is incoherent. Furthermore, the light is not guided inside of the LED structure, therefore, the light is emitted in all directions. As a consequence it is difficult to couple light in a fiber. It is almost impossible to couple the light in a single mode fiber. Spectral Width: LEDs do not produce a single wavelength but rather a band of . The range (or band) of wavelengths emitted is defined by the “spectral width”. Depending on the material system and the emitted wavelength the spectral width is typically in the range of 20-80nm. The spectral width increases with the square of the wavelength.

Optical Sources 32 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.3 Application of Light emitting Diodes Optical Output Power The optical output power of a LED is typically much lower than the output power of a laser. If we compare semiconductor lasers with LEDs the optical output is comparable. In particular the output power of LEDs has been drastically increased due to the development of high brightness LEDs for lighting applications.

Applications of High Brightness LEDs in 2002. Ref.: www.lumileds.com

Optical Sources 33 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.3 Application of Light emitting Diodes The light extraction of a LED (high brightness LED) can be improved by the geometric design of the device structure.

Historical development of LED device design for high brightness LEDs. Ref.: www.lumileds.com

Optical Sources 34 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.5.3 Application of Light emitting Diodes Most of the LEDs (high brightness LEDs) are used for applications in the areas of signs, automotive and mobile appliances.

Applications of High Brightness LEDs in 2002. Ref.: www.lumileds.com

Optical Sources 35 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6 Lasers Laser stands for “Light Amplification by the Stimulated Emission of Radiation”. Optical Communication Systems with high Bandwidth-Distance products as high as 10Tbit/s wouldn’t be possible without the invention of the laser in the 1960’s and the semiconductor laser diode in the 1970’s.

Advantages of Lasers: • Extreme narrow spectral width (Linewidth) • Source of coherent light • Laser can be modulated very fast • Compact and inexpensive (laser diodes)

Disadvantages of lasers: • Lasers need temperature and output power control (high cost). • For optical communication systems a cooler “peltier effect” is needed. • Analog modulation is difficult due to the non linearity of the output power (e.g. current threshold)

Optical Sources 36 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.1 Stimulated Emission The operating principle of a laser is based on stimulated emission. We speak about stimulated emission if the electron which enters an energetically higher state (excited state) remains in this state until it is “stimulated” by the presence of a photon to leave this higher energetically state and return to the more stable lower energetically state (ground state). One of the requirements for stimulated emission is that the electron can stay in its excited state a relatively long period of time (a few microseconds) before it changes its state spontaneously. In the case of spontaneous emission the electron stays in this excited state usually for a shorter period of time (picoseconds). In the case of stimulated emission the electron can be “stimulated” by the presence of a photon to emit its energy in the form of another photon.

Energy state diagram for stimulated emission. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 37 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.1 Stimulated Emission

Let‘s assume that we start our discussion on stimulated emission by introducing a two level atomic system. In general three different transition processes exist in a two level atomic system: Absorption, the spontaneous emission and the stimulated emission. In 1927 Albert Einstein demonstrated that these processes are mathematically related. We will not discuss a mathematical description of these transition processes here. In general, due to thermal equilibrium the rate of upwards transitions has to be equal to the rate of downwards transitions. Rate equations can be defined, which describe the probability of a transition from level 1 (lower energetic state or ground state) to level 2 (higher energetic state) and vice versa. For the level 1 rate equation we have to considered only the absorption, whereas for the level 2 rate equation we have to consider spontaneous and stimulated emission. This leads to the following relationship:

Spon taneous emission rate 1 = Stimulated emission rate  hf  exp  −1  kT 

Optical Sources 38 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.1 Stimulated Emission For most of the systems in thermal equilibrium spontaneous emission is by far the dominate process. Therefore, the emission of an ordinary light source in the visible spectrums occurs in a random fashion, which as a consequence leads to incoherent light. The spontaneous emission term of the rate equation of level 2 is much larger than the term of stimulated emission. In order to produce coherent light the stimulated term has to be drastically increased.

5.6.2 Population inversion In the case of a two level system in thermal equilibrium, which can be

described by a Boltzmann distribution, the lower energy level E1 contains more atoms than the upper energy level. This situation is normal for structures at room temperature. To achieve optical amplification (stimulated emission) it is necessary to create a non-equilibrium distribution of atoms. The population of atoms in the higher energetic state has to be (significantly) higher than the population of atoms in the lower energetic state. Optical Sources 39 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.2 Population inversion This situation is called population inversion.

Population in two energy level system: (a) Boltzmann distribution for a system in thermal equilibrium, (b) Non-equilibrium distribution indicating the population inversion. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 40 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.2 Population inversion

In order to achieve population inversion it is necessary to excite atoms into the higher energetic state and hence achieve population inversion. This process is usually called “pumping”. We can distinguish between electrical and . The medium is optically pumped for gas lasers (e.g. HeNe lasers) or crystal lasers (e.g. ) where the atoms are excited by an external optical source. The systems are usually pumped by an intensive radiation source like a flash lamp. The intense radiation leads to the transition of the atoms from the lower to the energetically higher states which we would normally be called absorption, but we can even call it “stimulated absorption” The term “stimulated emission” indicate the similarities between the absorption and the stimulated emission. (The stimulated emission is the inversion of the (stimulated) absorption.) However, so far we discussed the behavior of two level systems which are not suitable for population inversion. The probability of absorption and emission can be in the best case to be equal. Population inversion however, can be observed in certain three or four energy level systems.

Optical Sources 41 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.3 Three and four energy level systems The principle transition for a three level system is illustrated in the figure. The

three level system consists of a ground level E0, a stable level E1 and a third level E2 which is again metastable. Initially (before pumping) the system is in thermal equilibrium and the atomic distribution can be described by a Boltzmann distribution.

Energy diagrams showing population inversion for a three level system (ruby crystal). Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 42 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.3 Three and four energy level systems

Due to pumping electrons get excited from the ground level to the level 2. The level 2 is considered to be a “normal” energy level so that the electrons rapidly decay in the lower energetic state 1. Of course a certain number of electrons will directly go back to the energy level 1, but most of the electrons will end up on level 1. As a consequence empty states will be always available on level 2. The lifetime of the electrons on level 1 is however much longer than the lifetime of the carriers on level 2, so that a large number of electrons is accumulated on level 1. The long lifetime of the carriers on level 1 leads to the population inversion between level 1 and the ground level. The stimulation of an electron on level 1 leads now to lasing. The disadvantage of a three level system is that it needs very high levels of pumping power. More than half the electrons in the ground state have to pumped in order to achieve population inversion. A more efficient system is a four level system as it was shown for a HeNe laser system. Here much lower pumping power is needed. In this case an atom is pumped from the ground state into the highest energetic state on level 3.

Optical Sources 43 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.3 Three and four energy level systems Again the transition from level 3 to level 2 is a rapid decay, because the lifetime of the carriers on level 3 is short. The lifetime of carriers on level 2 however is much longer (several orders of magnitude) so that population inversion is observed for the level 2. As a consequence lasing is detected between the levels 3 and 2.

Energy diagram showing population inversion for a four level system. Ref.: H. J.R. Dutton, Understanding optical communications

Optical Sources 44 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.4 Optical feedback and laser resonators Stimulated emission and therefore lasing occurs when a photon stimulates the emission of another photon and then both photons continue to stimulate the release of further photons. In order to generate coherent light the stimulation process has to be continuous and effective. An amplification due to the stimulated multiplication of photon is necessary to accomplish coherent emission. To ensure that the emitted light is coherent the laser medium is placed in a laser resonator which can be formed by two mirrors. The laser medium and the two mirrors form a laser cavity. Hence the emitted light is reflected at the mirrors and fed back into the resonator to simulate more photons. Such a structure is called a Fabry Perot resonator.

Schematic cross section of a laser structure based on a laser medium and two partially transmissive mirrors. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 45 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.4 Optical feedback and laser resonators The amplification of the signal after one roundtrip is usually relatively small, but after several roundtrips the net amplification of the structure can be large. Typically the mirrors of such a Fabry Perot resonator are not perfect. A small fraction of the light is transmitted through the mirrors. As the mirrors typically consist of a semiconductor layer stack rather than a metal mirror the transmission of the mirror can be controlled very precisely by the manufacturing process. Therefore, the mirrors are partially transmissive. A continuous and stable optical output signal can be achieved when the of the structure is higher than the loss of the structure. Loss is caused by the absorption and the scattering of light in the cavity and absorption losses in the partially transmissive mirrors. Furthermore, the light has to be guided inside the structure which leads to further losses. The wavelength of the emitted light depends on the radiative transitions in the laser medium. However, it is clear that the emitted light is not perfectly monochromatic, moreover, a narrow spectrum of wavelengths is emitted. The emission spectrum follows the frequency range determined by the gain curve of the structure.

Optical Sources 46 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.4 Optical feedback and laser resonators

Due to the formation of the laser cavity a sufficient population inversion exists in the laser medium. The superposition of the back and forth propagating waves leads to the formation of a standing wave in the resonator. The standing wave exists only for wavelengths for which the distance of the mirrors is an integral number of the half of the wavelength.

λ L = k ⋅ Resonance condition 2n

Relative amplification in a laser cavity showing the broadening of the laser gain. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 47 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.4 Optical feedback and laser resonators

where n is the of the laser medium, k is an integer and λ is the wavelength of the emitted light. Based on the resonance condition the spectral width of the amplified signal can be determined to be λ λ2 ∆ = Spectral width 2nL Based on the equation it can be seen that the spectral width can be reduced by increasing the length of the cavity. However, at the same time the number of modes which can propagate in the cavity is increased. The number of mode can be calculated by:

2nL k = Propagating modes λ

Optical Sources 48 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.4 Optical feedback and laser resonators The propagation of modes in the laser resonator is illustrated in the figure. The spectral output of the laser is defined by the gain curve.

Propagating modes in a laser cavity and modes in the laser output. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 49 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.5 Threshold condition for laser oscillation Lasing only occurs when the gain in the amplification medium equals the overall losses of the laser structure. Therefore, population inversion alone is not sufficient to achieve laser operation. A minimum or a threshold gain has to be overcome to initiate and sustain laser emission. In the following we will derive a simple expression for the required threshold gain. In the first step we assume that the overall losses of the structure can be described by a loss (or absorption) coefficient per unit length.

α Loss coefficient per unit length The length of the cavity is given by L and the reflectivity of the mirrors is

provided by R1 and R2. Based on the given parameters we can calculate the loss for a round trip:

Fractional loss Fractional loss = R1R2 exp(− 2α ⋅ L)

Optical Sources 50 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.5 Threshold condition for laser oscillation Not only the absorption but also the gain of a round trip can be described by a power law, Fractional gain = exp(2g ⋅ L) Fractional gain where the gain coefficient per unit length is given by:

g Gain coefficient per unit length In the case of threshold the fractional losses have to be equal to the fractional gain so that we can define a threshold gain by 1  1    Threshold gain gth = α + ⋅ln  2L  R1R2  Hence, the threshold gain corresponds to the absorption losses plus the light that is transmitted through the partially transmissive mirrors.

Optical Sources 51 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.6.6 Requirements for lasing

In summary, the following requirements have to be fulfilled to realize a laser.

1. Population inversion is required to achieve stimulated emission. 2. A material system which exhibits several energy states of which a high energy state has to be metastable. The wavelength of the emitted light will be than defined by the energy difference between the higher metastable energy state and the next lower energy state. 3. The material (system) has to be transparent for the emitted light. Otherwise the light can not leave the material. 4. Confinement of the material and the light by a resonator. 5. The threshold gain has to be larger than the fractional losses plus the emitted light.

Optical Sources 52 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7 Semiconductor Lasers So far we discuss the concept of lasing on a generic level. For example population inversion is necessary for all kinds of lasers. It does not matter whether the laser structure is a gas, a crystal laser or a semiconductor laser which is electrically or optically pumped. The same is true for the resonator structure. The gain of the laser structure has to be higher than the overall losses.

5.7.1 Stimulated emission and lasing in Semiconductors Now we will concentrate on semiconductor laser diodes. We will extend the discussion we already started as part of the LED presentation. A major requirement for the stimulated emission is the carrier population inversion which is achieved in an intrinsic (undoped) semiconductor by the injections of electrons in the conduction band and holes in the valence band. However, under “normal” conditions the number of injected carriers is not high enough to get stimulated emission. The recombination of carriers will lead to spontaneous emission as we already discussed for the LED structure.

Optical Sources 53 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.1 Stimulated emission and lasing in Semiconductors In order to achieve population inversion the concentration of carriers in the bands has to be significantly increased. One way to increase the concentration of carriers in the bands is doping. So far we assumed that the p- and the n-regions of the laser diode are “normally” doped, which leads to a shift of the Fermi level.

Filled electron states in a direct bandgap semiconductor in equilibrium and at high carrier injection. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 54 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.1 Stimulated emission and lasing in Semiconductors In the case of n-type doping the Fermi level shift towards the conduction band and in the case of p-type doping the Fermi level shift towards the valence band. The higher the doping concentration the closer the Fermi energy will be to the bands. Population inversion in a pn-junction can only be reached if the p- and the n-type material is very heavily doped. Such heavy doping is called degenerated doping. The doping level is so high that the Fermi levels shift into the conduction and the valence band.

Degenerated pn-junction in thermal equilibrium. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 55 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.1 Stimulated emission and lasing in Semiconductors

An incident photon with an energy of higher than Eg but less than Eq cannot be absorbed, because the necessary states in the conduction band are already occupied by electrons. However, this photon can stimulate a downward transition of an electron from the filled conduction band states to the empty valence band state. The basic condition for stimulated emission is therefore given by the following relationship:

EFC − EFV = Eq > hf > Eg Condition for stimulated emission

Instead of using the occupation of states in the conduction and valence band we can describe stimulated emission in terms of quasi Fermi levels. So far we used only the term “Fermi level”. The term Fermi level, however, describes the probability of states being occupied by electrons or holes in thermal equilibrium.

Optical Sources 56 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.1 Stimulated emission and lasing in Semiconductors In the case of non thermal equilibrium which occurs under forward or reverse bias conditions the Fermi level splits up so that we can define separate Fermi levels for electrons and holes. Population inversion is observed if the quasi Fermi levels shift into the band so that an incident photon cannot excite an electron form the valance band to the conduction band because the states in the conduction band are already occupied. As a consequence an downward transition will be observed.

Degenerated pn-junction under strong forward bias so that the separation of the quasi Fermi level in the active region is higher than the energy of the emitted photons. Therefore, stimulated emission is obtained. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 57 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.1 Stimulated emission and lasing in Semiconductors In order to obtain stimulated emission in the active region of the laser diode a high forward bias has to be applied so that the separation of the quasi Fermi level in the active region is higher than the energy of the emitted photons. As consequence the incident photon stimulates emission rather than excites an electron form the conduction band to the valence band (absorption). Only if all these requirements are satisfied stimulated emission can be observed for a semiconductor laser diode. For current levels below the threshold the emission of the laser diode is spontaneous emission. Only for current levels higher than the current threshold the emission is stimulated.

Ideal light output curve of a laser diode against the injected current. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 58 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.2 Semiconductor Materials for lasing applications As we already learned the materials applied for the manufacturing of laser diodes have to fulfill several requirements. The list of materials suitable for the realization of laser diodes is almost identical with the list of materials used for LEDs. In general only direct semiconductors are used for the realization of laser diodes. A detailed list of the materials can be found in literature. The requirements in terms of the material quality and the mirror are much higher for a laser than for a LED structure (A LED usually does not even have mirrors). The fact that the materials are sufficiently good for an LED structure does not mean it is sufficiently good enough for a laser diode.

Optical Sources 59 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.3 Efficiency of LEDs and laser diodes The efficiency of a LED or a laser diode can be defined by different ways. We will start with the internal efficiency which can be calculated by:

number of emitted photons η = Internal efficiency i number of injected electrons

The internal efficiency can be very high. Depending on the material quality and the devices structure the efficiency can be close to 100%. The external efficiency can be determined by,

number of output photons Pop ηex = = External efficiency number of injected electrons I ⋅ Eg

where Pop is the emitted optical power which changes linearly with the injected current I greater than the threshold current Ith.

Optical Sources 60 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.3 Efficiency of LEDs and laser diodes The external efficiency can be calculated by

η   η   External efficiency  1   Ith  ex = i   ⋅ 1−   2α ⋅ L   I  1+        ln()1 R1R2 

The external optical power efficiency can be determined by: η P  E  op  g  External optical power op = = ηex ⋅   Pe  eV  efficiency

Optical Sources 61 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.4 Laser Diode structures 5.7.4.1 Fabry Perot Homojunction laser diode A schematic diagram of an early GaAs laser diode is shown on this slide. The cavity of the laser is formed by a Fabry Perot structure. The cleaved edges of the structure act as partially transmissive mirrors. The device structure itself consists of a homojunction GaAs pn-junction. The threshold current of such a structure is very high, because the reflection of the partially transmissive mirrors is relatively low and the standing wave inside of the cavity is not confined. The confinement problem could be solved by using a double heterostructures.

Schematic diagram of a GaAs homojunction laser diode based on a Fabry Perot cavity. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 62 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.4.2 Double heterostructure laser diode The double heterostructure provides an electrical and an optical confinement within the laser diodes which leads to a drastically increase of the efficiency. However, the structure is only confined in the vertical direction, but lasing occurs along the entire width of the structure. To solve this problem the active region has to be confined along the active region. This problem is usually solved by guiding the light parallel to the lasing direction.

Directing and guiding light in a Fabry Perot laser structure. Ref.: H.J.R. Dutton, Understanding Optical Communications

Optical Sources 63 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.4.2 Double heterostructure laser diode The easiest way to confine the light in lateral direction is a gain guided structure. In this case the laser structure is electrically confined. A region of high gain is created by the patterning or definition of the electrodes or contacts of the laser diode. As a consequence carriers are only injected in certain parts of the device so that the light is defined by the region of high gain. A more efficient structure is an index guided structure, where the light is guided optically. Similar to a wave structure regions of high and low refractive index are created which guide the light. If the optical guidance is combined with an electrical confinement of the laser cavity an efficient laser diode can be formed.

Optical Sources 64 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.4.3 Quantum well lasers The fabrication technique of lasers has been improved drastically throughout the last 20-30 years so that the layer thickness can now be controlled down to the sub nanometer range. This offers the possibility of manufacturing double heterostructure lasers with very thin active regions of around 10nm. If the dimension of the active region is reduced to that range the carrier motion normal to the active region of the laser gets restricted. Instead of having well defined electronic bands we have well defined discrete energy level like it is predicted by quantum mechanics. We get quantized energy levels.

Energy band diagrams showing various types of quantum well structures, (a) single quantum-well structure, (b) multiple quantum well structure (c) modified quantum well structure. Ref.: J.M. Senior, Optical Fiber Communications

Optical Sources 65 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.4.3 Quantum well lasers In such a case we speak about a quantum well like it is shown in figure a on the previous slide. In figure a only single quantum well is shown therefore the structure is called single quantum well structure. This effect can be used for lasers, because these quantum well structures exhibit the fundamental advantages that high gain can be accomplished at low carrier densities and therefore a significant lower threshold currents. Instead of using a single quantum well a series of quantum well can be used and we use the general term of a quantum well structure. Nowadays this process has to been optimized leading to modified quantum well structures.

5.7.4.4 Distributed Feedback (DFB) Lasers Fabry Perot lasers exhibit significant problems if they are used for long distance communication. Wavelength Division Multiplexed (WDM) systems require the transmission of several channel in a single fiber. To do this it is important for each signal/channel to have a narrow spectral width. The spectral width of a Fabry Perot lasers however is too high for such applications.

Optical Sources 66 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

5.7.4.4 Distributed Feedback (DFB) Lasers Distributed Feedback (DFB) lasers are much more suitable for long distance communication. The idea is that a Bragg grating is put into the laser cavity of an index-guided Fabry Perot laser. The operation and the device structure will be presented later on (Student Presentation).

5.7.4.5 Vertical Cavity Surface Emitting Lasers (VCSELs) Vertical Cavity Surface Emitting Lasers (VCSELs) got very popular during the last 5-10 years. VCSELs are very attractive light sources for metropolitan networks, where the requirements in terms of stability, output power, cost and mode propagation are different from wide area networks. However, the advantages of a VCSEL structure are clear. The lasers exhibit low threshold current and the structures can be tested on the wafer level. The operation and the device structure will be presented later on (Student Presentation).

Optical Sources 67 Photonics and Optical Communication, Spring 2007, Dr. D. Knipp

References: John M. Senior, Optical Fiber Communications, Prentice Hall Series in Optoelectonics, 2nd edition, 1992. Bahaa E.A. Saleh, Malvin Carl Teich, Fundamentals of Photonics, Wiley-Interscience (1991) Harry J. R. Dutton, Understanding Optical Communications, Prentice Hall Series in Networking, 1998. (Formerly freely available as a book on the IBM red book server. Stamatios V. Kartalopoulos, DWDM, Networks, Devices and Technology, IEEE press and Wiley Interscience, 2003. Joseph C. Palais, Fiber Optic Communications, Prentice Hall Series, 1998. 4th edition.

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