# Contents

How Can We Interpret Polarisation and Frequency When Dealing With One Photon?

*I explain how one photon relates to Maxwell’s equations and the classical theories of light.*

Are Coherent States of Light Classical or Quantum?

*More on how classical optics is embedded in the larger whole of modern quantum theory.*

Is Light a Wave or a Particle?

*It seems they’re still teaching the outdated idea that light is sometimes a wave and sometimes a particle but never both at once. Here’s how the second-quantised electromagnetic field gets rid of this outdated idea.*

Mixed Quantum States, Wigner’s Friend and the Mueller and Density Matrices

*A mixed quantum state is more complicated than a pure state. Here I illustrate this concept with the Wigner’s Friend thought experiment and show how its analysis is deftly handled by the density matrix approach and relate it the the Jones and Mueller calculusses of classical optics.*

Can Planck’s Constant Be Derived fro Maxwell’s Equations?

*Of course not! But Maxwell’s equations and the Lorentz transformation do indeed constrain the Planck Law’s form.*

Why do Lasers Need Mirrors at Their Ends?

*Some detail on how the laser cavity shapes and influences the basic physical processes inside the device.*

Wavefront Aberration Wrought by Stochastic Surface Roughness and Mahajan’s Strehl Ratio Formula

*How does high spatial frequency surface roughness or texture of lens elements affect wavefront aberration. Mahajan’s Strehl ratio formula has a theoretically exact interpretation in the case of surface roughness with suitable egodicity assumptions.*

Microscopy Kinds, Techniques and Relative Performances

*Here I give an overview of the performances, in signal to noise terms, of different microscopy techniques. I show why slides must be prepared rather than imaging living tissue for some techniques and also show how other techniques overcome this requirement and allow direct imaging of living tissue.*

Holograms, Diffraction and the Helmholtz Equation

*A summary of the ideas behind a hologram.*

Just How Much Data Can We Stuff Through an Optical Fibre?

*I explore roughly how far can we go with optical fibre communications*

Two Unwonted Proofs of the Thin Lens Formula

*The thin lens formula is readily proven, but not in ways that are particularly near to the deeper nature of light. Here are two different proofs I’ve come up with and refined over the years.*

What is the Difference between a Plane Wave and Collimated Field?

*This difference can be subtle and confusing, and the language often used is sloppy and imprecise. I try to clarify these words.*

Tunnelling in Total Internal Reflexion and Evanescent Fields

*A detailed look at optical tunnelling, or what goes on in detail in total internal reflexion; I look at the Goos-Hänchen effect.*

*I look at the meaning of this most basic word in optics and wave physics.*

Circular Polarisation Eigenstates, The Riemann-Silberstein Vector and Angular Momentum of Light

*Circular polarisation eigenstates are the most natural entities for thinking about light with. The Riemann-Silberstein notation, whereby one can work with diagonalised Maxwell equations, brings these states into sharp focus.*

Fluorophores and Old Aged Particles

*Fluorophores often show exponential lifetime probability distributions. But this is not always so and indeed, if we look carefully at their very short term behaviour, this statement is never exactly true. Here’s why, and what the special meaning of the exponential distribution is.*

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