Lecture 1a Flashcards
What are examples of light behaving as a particle, a wave, or both?
- Light as just a particle:
- The Photoelectric Effect
- Compton Scattering - Light as just a wave:
- Young’s Double-Slit Experiment - Light as both:
- Quantum Interference with Single Photons
- Quantum Electrodynamics (QED): In QED, light is described in terms of photons that interact with charged particles, but calculations are done using wave functions that encompass probabilities and interference.
What is Compton Scattering?
Experiment: Compton scattering occurs when X-rays (high-energy photons) collide with electrons. it was observed that the scattered X-rays had a longer wavelength (lower energy) after the collision, demonstrating that photons transferred momentum to electrons.
Explanation: This scattering could only be explained by treating light as particles that carry momentum, as wave-based explanations could not account for the discrete energy and momentum changes observed in electrons.
What is Quantum Interference with Single Photons?
Experiment: In modern variations of the double-slit experiment, physicists shoot individual photons at the slits, one at a time. Astonishingly, even when photons pass through the slits one at a time, an interference pattern still gradually builds up on the detector screen. This implies that each photon interferes with itself, behaving as a wave. However, when detected, each photon lands at a single point on the screen, indicating particle-like behavior.
What is the classical description of light?
Light is an electromagnetic wave: Paired oscillation of E and B fields, solution of the Maxwell equations (more about Maxwell equations in the written notes).
An example of light is a plane wave.
What is the dielectric response?
The dielectric response refers to how a material (specifically a dielectric or insulating material) responds to an external electric field. When an electric field is applied to a dielectric material, it causes a shift in the positions of electric charges within atoms and molecules. This response creates an internal electric field within the material that partially opposes the applied field, reducing the effective field within the material.
if confused think about what would happen if a hydrogen atom was placed in the middle of the electric field. where would its electron density shift to? (positive terminal) and does this cause a reduction in the effect field?
What exactly is a plane wave?
A plane wave is a type of wave in which the wavefronts (surfaces of constant phase) are infinite, flat planes. In this type of wave, the wave oscillates in a uniform manner perpendicular to the direction of propagation (example in digital notes)
Such a wave has the following characteristics:
1. Uniform Amplitude and Phase Across Planes
2. Propagation in One Direction
3. Mathematical Representation: More in written notes
What is dephasing in a propagating wave?
In physical systems where multiple waves interact or interfere (e.g., in optics or quantum mechanics), dephasing describes how these waves gradually shift out of sync with each other due to differences in phase accumulation* along the z-axis. The rate of dephasing depends on the wavenumber—larger wavenumbers lead to faster phase accumulation per unit length, causing quicker dephasing over the same distance.
*Phase accumulation refers to the progressive increase in the phase of a wave as it travels through space or time
Y3ani how a point on a wave moves with time.
What is the difference between a real wave and a plane wave?
Perfect plane waves are idealized and theoretically extend infinitely in space. Real waves can approximate plane waves over short distances or small regions, but they will eventually diverge or dissipate
(this will be dived into more at the end, I just wanted to make a clear separation for now)
The Electromagnetic radiation spectrum.
It is shown in digital notes. You need to recognize what frequency intells about the type of EM (radio, x-ray, etc).
What is the solution of the magnetic field using Maxwell’s equation?
Found in written notes
Can B always be found from E using Maxwell’s equations?
This is tricky but generally no:
In electromagnetic waves, both E and B fields propagate together and are related by a fixed ratio in free space. In such cases, knowing E and the wave vector k often allows the determination of B. However, if E varies in a way that is not part of a propagating wave (such as in quasi-static fields or localized fields near sources), B cannot be found without additional information about currents or initial magnetic field conditions.
Why is the ratio in free space (E/B = c)?
This relationship arises because, in free space, Maxwell’s equations dictate that an oscillating electric field E induces a magnetic field B and vice versa, such that:
𝐵= (𝑘 × 𝐸) / 𝜔 = 𝐸×𝑐.
This fixed ratio tells us that in a vacuum, for any propagating electromagnetic wave, the magnitude of the magnetic field B is always
1/c times the magnitude of the electric field E. This relationship holds regardless of the wave’s frequency or wavelength, as long as it’s traveling through free space.
What are the two types of polarization mentioned?
- Linear polarization: E and B oscillate along a line (basically what we have been talking about)
- Circular polarization: a state of polarization where the electromagnetic wave rotates in a circular pattern as it propagates. In circularly polarized light, the tip of the electric field vector traces a helix along the direction of propagation. (This is shown in digital notes)
What are waveplates?
a device that can change the axis of
linear polarisation (or turn linear pol.
into circular, and vice-versa).
A depiction is shown in digital notes
What are polarizers?
They are devices that can split two different polarizations (or suppress one and transmit the other) as shown in digital notes notes
The transmitted intensity is a function of the angle the incident light makes with the polarizer’s axis:
I(tr) ∝ E^2 ∝ cos^2(a)
Why do polarizers show this relation
I(tr) ∝ E^2 ∝ cos^2(a)?
When polarized light passes through a polarizer, only the component of the electric field E that is aligned with the polarizer’s transmission axis will pass through. If the incident electric field makes an angle α with the polarizer’s axis, the component of the electric field that aligns with the polarizer is:
𝐸(tr) = 𝐸 cos(𝛼)
Where E is the amplitude of the electric field of the incident light.
Now we can recognize that The intensity.
I of a light wave is proportional to the square of the amplitude of its electric field, given by 𝐼 ∝ 𝐸^2. Therefore, the intensity of the transmitted light will be:
𝐼(tr) ∝ (𝐸cos(𝛼))^2=𝐸^2cos^2(𝛼)
This cos^2(𝛼) dependence is key to the behaviour of polarizers. It shows that the transmitted intensity reaches a maximum when 𝛼=0 (when the electric field and transmission axis are aligned) and is zero when α=90 (when they are perpendicular).
What is energy density and its equations?
Written notes
What is intensity and power?
Written notes
What is the relation between intensity and energy density?
Written notes
What is the Poynting vector?
The Poynting vector S represents the direction and rate of energy flow per unit area in an electromagnetic field. It is given by:
S=E x H (x in this case shows a cross product)
where: E is the electric field, and H is the magnetic field.
The magnitude of the Poynting vector ∣S∣ corresponds to the power per unit area, and its direction indicates the direction of energy propagation. It is fundamental in describing how energy is transferred through electromagnetic waves.
What are optical cavities?
Structures defined to confine EM field with low loss. This allows for more interaction of light with matter.
An example of a cavity application is that they are used to build lasers and cavity QED!
What is the solution of the wave equation when we have a cavity with metal mirrors?
Written notes + verification of it
What do we learn from our verification of the solution?
Written notes
What is a mode?
Solution of the wave equation. When we start quantifying theories we will refer to it a lot ;0.
What is the solution of the wave equation when we have a cavity with 3 Dimensions?
Depiction is shown in digital notes.
The solution is:
E(x,y,z,t) = A(x,y,z)*cos(wt)
Where A(x,y,z) is a wave function representing the EM field at position (x,y,z).
From this equation we can make 3 takeaways:
- We can separate spatial and time dependence.
- Mode is stationary, not propagating.
- Energy is well-defined, making it easier to introduce energy quantization.
Do E and B oscillate synchronously?
Depends on the type of wave:
- If it is a plane wave then yes they do as the wave equations (shown in digital notes) depend on the cosine.
-if it is a cavity wave, then no as the wave equations for B and E (shown in digital notes) are determined by different functions (E is by sin and B is by cos) they cannot physically be in phase. We will then have E oscillating with a constant zero B field and vice versa. The Energy will then oscillate between E and B fields, in the following manner:
E = E(el) + E(magn) ∝ Cos^2(wt) + Sin^2(wt)
A question will be asked to the professor about this
How can we calculate intensity from Young’s interferometer?
Written notes
What are other examples of Interformeters
- Mach-Zehnder interferometer
- Michelson interferometer
- Speckle
What is the Mach-Zehnder interferometer?
It is depicted in the notes.
Important takeaways are:
- A “Beamsplitter”: is a semi-transparent mirror where due to it having a different refractive index it causes a light beam to be split. Some light is transmitted and some is reflected.
- We will have an interface between paths one and two at the second BS since path two travels a longer distance
- The relationship that is established here is that when one path is constructive the other is destructive since they approach each other on an orthogonal plane.
What is a Michelson interferometer?
It is depicted in the notes.
Important takeaways are:
Honestly, really nothing new was added.
What is a Speckle?
Depicted in the notes.
Basically, when light is illuminated on a diffuser (i.e. rough surfaces) light will be reflected in so many different ways. The Sum over the many different light paths gives rise to complex interference
pattern, called “speckle”
Do we always get interference?
This is a tricky question.
So as of yet, we have only investigated with «Ideal» classical EM fields. Such fields have a well-defined frequency and constant density (this is shown in the digital notes). An example of such a field is idealized plane waves (or cavity) - there is a fixed phase relation between different space or time points.
Now, in reality, almost no light source emits perfectly sinusoidal waves; real light sources often exhibit phase and amplitude fluctuations. These phase fluctuations may wash out interference if the source lacks coherence (this is shown in the digital notes). For example, since a standard LED light isn’t monochromatic, different wavelengths will create overlapping fringes in Young’s double-slit experiment, resulting in a washed-out interference pattern.
How is intensity calculated in the case of washed-out interference?
Written notes
