Lasers

AS UNIT 2 Electricity and light 2.8 Lasers Learners should be able to demonstrate and apply their knowledge and understanding of:
a)	the process of stimulated emission and how this process leads to light emission that is coherent
b)	The idea that a population inversion ([math]N_2 > N_1[/math] ) is necessary for a laser to operate
c)	The idea that a population inversion is not (usually) possible with a 2-level energy system
d)	How a population inversion is attained in 3 and 4-level energy systems
e)	The process of pumping and its purpose
f)	The structure of a typical laser i.e. an amplifying medium between two mirrors, one of which partially transmits light
g)	The advantages and uses of a semiconductor laser i.e. small, cheap, far more efficient than other types of laser, and it is used for CDs, DVDs, telecommunication etc

a) Stimulated Emission and Coherent Light
A. Basic Process of Stimulated Emission
In an atom or molecule, electrons occupy discrete energy levels. When an electron in an excited state (higher energy level, often labeled [math]E_2[/math]) encounters a photon whose energy exactly matches the energy difference between [math]E_2[/math] and a lower energy level [math]E_1[/math] (with ΔE=[math]E_2 – E_1[/math] ), it can be induced to drop to the lower state by emitting a second photon. This process is called stimulated emission. The key points are:
1. Photon Energy Matching:
– The incident photon must have an energy [math]E = hf[/math] equal to the energy gap between the excited state and the lower state.
2. Emission of a Second Photon:
– The excited electron, upon being stimulated by the incident photon, emits a photon and returns to the lower energy level.
Figure 1 Coherent Light waves
3. Properties of the Emitted Photon:
Identical Frequency:
– The emitted photon has the same energy (and thus frequency f) as the stimulating photon.
Identical Phase:
– The emitted photon is in phase with the incident photon.
Identical Direction and Polarization:
– It travels in the same direction and has the same polarization.
These properties are what make the process unique: the emitted light is coherent with the stimulating light.
B. Coherence and Its Importance
Coherence means that the electromagnetic waves have a constant phase relationship, identical frequency, and, in many cases, the same direction of propagation. In stimulated emission:
– Temporal Coherence: Since the photons share the same frequency and phase, the light is temporally coherent, meaning that its phase remains correlated over time.
– Spatial Coherence: Because the photons are emitted in the same direction, the resulting light beam is highly directional, which is a hallmark of laser light.
Coherent light is essential for many laser applications, including high-resolution imaging, precise cutting or welding, and interferometric measurements, because it allows the light waves to add constructively over long distances and through complex optical systems.
b) Population Inversion and Laser Operation
A. Definition of Population Inversion
In a typical thermal equilibrium situation, more atoms or molecules reside in the ground state [math]E_1[/math] than in any excited state [math]E_2[/math]. A population inversion is a non-equilibrium condition in which the number of particles in a higher energy state ( [math]N_1[/math]) exceeds the number in a lower energy state ([math]N_2[/math] ); that is:
[math]N_2 > N_1[/math]
Figure 2 Properties of laser
B. Why Population Inversion is Necessary
For stimulated emission to dominate over absorption (the process in which an electron absorbs a photon and moves from [math]E_1[/math] to [math]E_2[/math]), the medium must have more particles in the excited state than in the lower state.
In thermal equilibrium, absorption is typically more likely than stimulated emission because there are far more atoms in the ground state. Therefore, achieving a population inversion is critical because:
Net Gain in Photons:
– With more excited atoms available, an incident photon is more likely to stimulate emission (producing an extra photon) rather than be absorbed by an atom in the ground state.
Amplification of Light:
– This net gain leads to an optical amplification Each stimulated emission event produces a photon coherent with the stimulating light, reinforcing the beam and allowing it to build in intensity as it traverses the active medium.
Threshold for Lasing:
– In a laser, the gain must overcome losses (like absorption, scattering, and transmission losses through the mirrors) in the optical cavity. Population inversion is the first step to achieving that net gain.
C. Creating a Population Inversion
Because a natural thermal distribution does not favor inversion, various techniques are used to create and maintain a population inversion in the laser medium. These include:
Optical Pumping:
– Using light from another source (such as a flashlamp or another laser) to excite electrons to higher energy levels.
Electrical Discharge:
– Passing an electrical current through the medium (common in gas lasers) to excite the atoms or molecules.
Chemical Reactions:
– In chemical lasers, energy released from exothermic reactions is used to produce the population inversion.
Once a sufficient population inversion is established, even a weak light signal can stimulate the emission of additional coherent photons, leading to laser oscillation.
c) Why a Population Inversion is Not (Usually) Possible with a 2-Level Energy System
In a two-level system there are only two energy states:
Ground State (Level 1)
Excited State (Level 2)
1. Equal Likelihood of Absorption and Emission:
– In a 2-level system, when you illuminate the medium (pump it), electrons can be excited from the ground state (level 1) to the excited state (level 2) by absorbing photons.
– However, the same photons can also stimulate electrons already in the excited state to return to the ground state (stimulated emission).
Because the probability of absorption and stimulated emission is comparable, you quickly reach a situation where the rate of excitation is balanced by the rate of de-excitation.
Figure 3 Absorbance and emission of photons
2. Thermal Equilibrium and Boltzmann Distribution:
– Under steady pumping, the system tends to achieve thermal (or quasi-thermal) equilibrium, where the maximum possible population in the excited state can only approach, but not exceed, 50% of the total population.
– A population inversion requires more electrons in the excited state than in the ground state (i.e., [math]N_2 > N_1[/math]). In a 2-level system, it is nearly impossible to exceed a 50:50 ratio because every photon that promotes an electron upward also increases the chance of stimulated emission, thereby driving electrons back to the ground state.
Figure 4 Boltzmann Distribution
3. Reabsorption:
– Photons produced by spontaneous or stimulated emission from electrons in the excited state can be reabsorbed by electrons in the ground state. This further inhibits the build-up of a population inversion.
⇒ Conclusion:
A simple 2-level system cannot practically achieve the necessary condition of [math]N_2 > N_1[/math] (population inversion) because the processes of absorption and stimulated emission inherently tend to equalize the populations rather than invert them.
d) How a Population Inversion is Attained in 3- and 4-Level Energy Systems
⇒ Three-Level Systems:
1. Energy Level Structure:
– Level 1: Ground state.
– Level 3: A high-energy level that electrons are excited into by an external pump.
– Level 2: A metastable state (longer-lived) located below level 3 but above the ground state.
2. The Process:
Pumping:
– Electrons are excited from the ground state (Level 1) to the high-energy Level 3.
Non-Radiative Decay:
– Electrons quickly decay (usually by phonon interactions or collisions) from Level 3 to the metastable Level 2. This decay is fast and non-radiative, so it does not produce photons that can interfere with the lasing process.
Laser Transition:
– The stimulated emission occurs as electrons drop from Level 2 to the ground state (Level 1).
Population Inversion:
– Because the metastable state (Level 2) is long-lived, electrons accumulate there, allowing [math]N_2[/math](the population in Level 2) to exceed [math]N_1[/math](the ground state population) temporarily. However, in a three-level system, since the ground state is heavily populated in the beginning, a relatively high pumping rate is needed to achieve inversion.
⇒ Four-Level Systems:
1. Energy Level Structure:
– Level 0: Ground state.
– Level 3: The pump level where electrons are initially excited.
– Level 2: A metastable level where electrons quickly decay non-radiatively from Level 3.
– Level 1: The lower laser level, which is above the ground state and has a very short lifetime, so electrons quickly leave Level 1 (typically by fast non-radiative decay) and return to the ground state.
2. The Process:
– Pumping: Electrons are excited from the ground state (Level 0) to Level 3.
– Rapid Decay: Electrons then rapidly decay to the metastable Level 2.
– Laser Transition: Stimulated emission occurs when electrons drop from Level 2 to Level 1. Because Level 1 is quickly depopulated (electrons rapidly relax back to the ground state), it remains nearly empty.
– Achieving Inversion: The population in the metastable Level 2 can then be much greater than in Level 1, easily achieving population inversion ([math]N_2 > N_1[/math] ).
Figure 5 Four energy level system
3. Advantages of 4-Level Systems:
Lower Threshold:
– Since the lower laser level (Level 1) is quickly depopulated, it requires much less pumping to achieve and maintain inversion.
Efficient Lasing:
– Four-level lasers typically exhibit higher efficiency and lower threshold pumping requirements compared to three-level lasers.

e) The Process of Pumping and Its Purpose
Pumping is the method by which energy is supplied to the laser medium to create a population inversion. It is essential for achieving laser action.
⇒ Types of Pumping:
1. Optical Pumping:
– Light (usually from a flashlamp or another laser) is used to excite electrons from a lower energy state to a higher energy state.
– Common in solid-state lasers and some gas lasers.
2. Electrical Pumping:
– An electrical current is passed through the laser medium (for example, in semiconductor lasers or gas-discharge lasers) to excite electrons.
– In semiconductor lasers, a forward bias causes electrons and holes to recombine and emit light.
3. Chemical Pumping:
– Energy from an exothermic chemical reaction is used to excite the electrons in the laser medium.
– Used in chemical lasers.
⇒ Purpose of Pumping:
1. Establish Population Inversion:
– The primary goal of pumping is to increase the number of electrons in an excited state (or metastable state) above the number in the lower energy state, achieving the condition
[math]N_{upper} > N_{lower}[/math]
– Without pumping, most electrons remain in the ground state due to thermal equilibrium, and stimulated emission (and hence laser action) would not be possible.
2. Sustain Laser Action:
– Continuous or pulsed pumping maintains the population inversion, allowing the process of stimulated emission to occur repeatedly.
– As electrons emit photons through stimulated emission, pumping replenishes the excited state population to keep the laser “lasing.”
3. Control Laser Output:
– The intensity and quality of the laser beam can be controlled by adjusting the pumping rate.
– Efficient pumping is essential for achieving high output power, beam quality, and overall efficiency of the laser.
f) The Structure of a Typical Laser
A typical laser consists of several key components arranged in a configuration that allows for light amplification and the generation of a coherent beam. The main parts include:
1. The Active (Gain) Medium
Definition:
– The active or amplifying medium is a material (solid, liquid, or gas) whose atoms or molecules can be excited to higher energy levels.
Function:
– When pumped with energy (via electrical current, another light source, or chemical reactions), the medium achieves a population inversion where more particles are in an excited state than in the lower state. This is crucial for stimulated emission to dominate over absorption.
2. The Pumping Mechanism
Purpose:
– The pump supplies energy to the active medium to excite electrons from lower energy levels to higher ones.
Methods:
– Optical Pumping: Using another light source (e.g., flashlamp or another laser).
– Electrical Pumping: Passing an electric current (common in semiconductor lasers).
– Chemical Pumping: Energy from chemical reactions (used in chemical lasers).
3. The Optical Resonator (Cavity)
⇒ Components:
The resonator is typically formed by two mirrors placed at either end of the active medium.
⇒ Highly Reflective Mirror (HR):
This mirror reflects almost all the light back into the medium, ensuring that photons have many chances to stimulate further emission.
⇒ Output Coupler (Partially Transmitting Mirror):
This mirror is partially reflective, allowing a small fraction of the light to exit as the laser beam while reflecting the rest back into the cavity.
⇒ Function:
The optical cavity ensures that the light travels back and forth through the gain medium, undergoing multiple stimulated emission events. This feedback loop amplifies the light and forces it to be coherent (same phase, frequency, and direction).
4. Mode Selection and Beam Shaping
Longitudinal and Transverse Modes:
– The cavity supports specific optical modes that satisfy the boundary conditions (i.e., the light wave must reproduce itself after a round trip in the cavity).
Beam Quality:
– The design of the resonator (mirror curvature, spacing, etc.) helps control the spatial profile and divergence of the output beam.
Figure 6 Structure of the laser
⇒ Overall Operation
1. Pumping: Energy is supplied to the gain medium, creating a population inversion.
2. Stimulated Emission: Photons stimulate the emission of identical photons, leading to the amplification of light.
3. Resonance: The optical cavity forces the light to oscillate between the mirrors, building up intensity.
4. Output: A fraction of the coherent light escapes through the output coupler as the laser beam.
This arrangement results in a laser that emits a highly coherent, monochromatic, and directional beam of light.
g) Advantages and Uses of a Semiconductor Laser
⇒ Advantages of Semiconductor Lasers
Semiconductor lasers, also known as diode lasers, have transformed many technological fields due to their unique properties:
1. Small Size and Compactness:
⇒ Miniaturization:
Semiconductor lasers are typically very small (often just a few millimeters in length), making them easy to integrate into compact electronic devices.
⇒ Integration:
They can be directly integrated into semiconductor circuits, allowing for the creation of compact optoelectronic systems.
2. Low Cost:
Mass Production:
– Using well-established semiconductor fabrication techniques, these lasers can be produced in large volumes at low cost.
Economy:
– Their affordability makes them ideal for consumer electronics.
3. High Efficiency:
Electrical-to-Optical Conversion:
– Semiconductor lasers convert a significant fraction of electrical energy into light, often with efficiencies much higher than other laser types.
Low Power Consumption:
– They require relatively low operating currents and voltages, making them energy-efficient.
4. Direct Electrical Pumping:
Simplicity of Operation:
– Diode lasers are electrically pumped, meaning they do not require complex external pumping sources such as flashlamps or separate laser systems.
Ease of Modulation:
– They can be modulated directly by varying the electrical current, which is useful in communication systems.
5. Wavelength Versatility:
Tunable Emission:
– The emission wavelength of semiconductor lasers can be engineered by adjusting the semiconductor material composition and the structure of the active region.
Wide Range:
– They cover a wide range of wavelengths, from the infrared (IR) to the visible spectrum, which is useful for various applications.
Figure 7 Construction of Semiconductor laser
⇒ Uses of Semiconductor Lasers
1. Data Storage:
CDs, DVDs, and Blu-ray Discs:
– Semiconductor lasers are used as the light source in optical drives. Their small size and precise wavelength control allow for high-density data reading and writing.
2. Telecommunications:
Fiber-Optic Communication:
– They serve as the transmitters in fiber-optic networks. The high efficiency, low power consumption, and ability to operate at wavelengths compatible with optical fibers (e.g., 1.3 µm and 1.55 µm) make them ideal for long-distance communication.
High-Speed Data Transmission:
Semiconductor lasers can be modulated at very high frequencies, enabling high data transfer rates.
3. Consumer Electronics:
Laser Pointers and Barcode Scanners:
– Their small size, low cost, and ease of operation make semiconductor lasers common in everyday devices.
Display Technologies:
– Used in projectors and some emerging display technologies.
4. Sensing and Measurement:
Lidar (Light Detection and Ranging):
– Semiconductor lasers are used in distance measurement and 3D mapping.
Spectroscopy and Environmental Monitoring:
– Their precise wavelengths are useful for detecting and analyzing chemical compositions.
5. Medical Applications:
Surgery and Diagnostics:
– Diode lasers are used in various medical procedures (e.g., laser surgery, dermatology treatments, and optical coherence tomography).