The nature of light, extending from the optical to the x-ray regime, is reviewed from a diffraction point of view by comparing field-based statistical optics and photon-based quantum optics approaches. The topic is introduced by comparing historical diffraction concepts based on wave interference, Dirac’s notion of photon self-interference, Feynman’s interference of space–time photon probability amplitudes, and Glauber’s formulation of coherence functions based on photon detection. The concepts are elucidated by a review of how the semiclassical combination of the disparate photon and wave concepts have been used to describe light creation, diffraction, and detection. The origin of the fundamental diffraction limit is then discussed in both wave and photon pictures. By use of Feynman’s concept of probability amplitudes associated with independent photons, we show that quantum electrodynamics, the complete theory of light, reduces in lowest order to the conventional wave formalism of diffraction. As an introduction to multi-photon effects, we then review fundamental one- and two-photon experiments and detection schemes, in particular the seminal Hanbury Brown–Twiss experiment. The formal discourse of the paper starts with a treatment of first-order coherence theory. In first order, the statistical optics and quantum optics formulations of coherence are shown to be equivalent. This is elucidated by a discussion of Zernike’s powerful theorem of partial coherence propagation, a cornerstone of statistical optics, followed by its quantum derivation based on the interference of single-photon probability amplitudes. The treatment is then extended to second-order coherence theory, where the equivalence of wave and particle descriptions is shown to break down. This is illustrated by considering two photons whose space–time probability amplitudes are correlated through nonlinear birth processes, resulting in entanglement or cloning. In both cases, the two-photon diffraction patterns are shown to exhibit resolution below the conventional diffraction limit, defined by the one-photon diffraction patterns. The origin of the reduction is shown to arise from the interference of two-photon probability amplitudes. By comparing first- and second-order diffraction, it is shown that the conventional first-order concept of partial coherence with its limits of chaoticity and first-order coherence has the second-order analogue of partial entanglement, with its limits corresponding to two entangled photons (“entangled biphotons”) and two cloned photons (“cloned biphotons”), the latter being second-order coherent. The concept of cloned biphotons is extended to the case of
n cloned photons, resulting in a
1/n reduction of the diffraction limit. In the limit of
nth-order collective state are shown to propagate on particle like trajectories, reproducing the 0th-order ray-optics picture. These results are discussed in terms of the linearity of quantum mechanics and Heisenberg’s space–momentum uncertainty principle. Finally, a general concept of coherence based on photon density is developed that in first order is equivalent to the conventional wave-based picture.
Although we tend to think of optical interference as a classical wave phenomenon, recent experiments have revealed a number of effects that are not describable in classical terms. This is particularly true of interference effects involving the detection of a photon pair. We shall refer to them as fourth order interference, on the grounds that the joint probability density for the detection of one photon at r sub 1 at time t and another r sub 2 at time t is proportional to the fourth order correlation function of the field. This probability is readily measured when two photodetectors are positioned at r sub 1 and r sub 2 and the signals from the two detectors are fed to a coincidence counter that registers 'simultaneous' detections by the two detectors in coincidence. The topics covered include: fourth order interference measurements; the Franson experiment; and experimental test of the de Broglie guided wave theory.
Interference experiments like the light and electron double-slit are crucially important to quantum mechanics since they illustrate the core principle of wave-particle duality, by demonstrating the wave-like aspect of particle phenomena. In such experiments, a device is typically required to manipulate the particle-wave dual phenomenon, producing controllable interference. Metasurfaces, with their highly flexible configurability, can serve as more versatile versions of such devices. They are powerful tools capable of modulating a broader category of effects beyond classical interference, such as the quantum Hong-Ou-Mandel (HOM) effect. The HOM effect is caused by interference taking place not between coherent waves from distinct sources which intersect in real space, but rather between parallel processes indistinguishable to the measurement apparatus. Existing research has highlighted the outsized importance of measurement in HOM interferometry, by showing that the occurrence of process interference depends only on indistinguishability at the detectors and nowhere else. We are therefore interested in how quantum measurement occurs in HOM, and how metasurfaces can be used to enhance the HOM effect. In this thesis, we extend a formulation of quantum trajectory theory in two-eigenstate systems to 𝑁-state systems, producing a three-state formalism which serves as a possible description of coincidence pair detection in HOM experiments. We then develop an analytic model of polarisation HOM interferometry capturing both the width and the 𝑔2 ratio of the HOM dip; finally, we design and fabricate a metasurface that exhibits polarisation filtering with respect to two-photon coincidence, whereupon HOM photon bunching occurs only at select metasurface orientations relative to photon polarisation. Our three-state quantum state collapse model offers a promising explanation for how state measurement takes place in an HOM interferometer, where the interferometer output is a superimposition of three two-photon eigenstates. Meanwhile, our interferometer model and experiments provide evidence of successful polarisation filtering in HOM interferometry.