Classical and Physical Optics

Classical and physical optics encompass the study of light both as rays and as waves. In the geometric regime, light is treated as straight-line propagation subject to reflection and refraction at interfaces, governed by Snell’s law and the law of reflection. Lenses, mirrors and prisms are analysed by paraxial approximations, yielding simple formulas for image formation and magnification. Beyond the paraxial domain, deviations from ideal imaging—such as spherical aberration, coma, astigmatism, field curvature and distortion—require full three-dimensional treatments and ray-tracing techniques. Physical optics restores the wave nature of light, introducing concepts of interference, diffraction and coherence. Interference underlies phenomena from thin-film coatings to optical coherence tomography, while diffraction sets fundamental limits on resolution via the Rayleigh and Abbe criteria. Coherence—spatial and temporal—controls the visibility of interference fringes and is central to modern metrology and imaging methods. Polarisation describes the orientation of the electric field in transverse electromagnetic waves and finds applications in stress analysis, ophthalmic diagnostics and polarimetric sensing. Together, these frameworks explain how structured materials, graded-index media and engineered surfaces can mould wavefronts to achieve sub-wavelength focusing, beam shaping and high-contrast imaging. The interplay of geometric and wave optics supports global technologies in microscopy, communications, laser processing and environmental sensing, illustrating optics’ enduring importance across science and engineering.

Research from Nature Portfolio

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Research from all publishers

Analytical continuation of two-dimensional wave fields on branched surfaces has been shown to admit a finite multi-valued basis, each term expressed as a Green’s integral along specialised contours. This work illuminates the branch-set geometry arising from canonical scatterers—such as edges and segments—and underpins efficient coordinate-equation approaches for planar diffraction problems.

A study of diffraction by a right-angled, no-contrast penetrable wedge employed a two-complex-variable Wiener–Hopf formulation to derive integral representations of the underlying spectral functions. The authors identified the novel concept of additive crossing of branch lines, reformulating the physical diffraction challenge as a functional equation that offers new paths to semi-analytical solutions for penetrable geometries.

In the quarter-plane diffraction problem, researchers applied the stationary phase method to double Fourier integrals of unknown spectral functions. By leveraging prior analytical-continuation results, they obtained closed-form far-field asymptotic expansions, recovering classical patterns and deriving new expressions for secondary diffracted waves in the plane of the scatterer.

Classical and Physical Optics publication trend

The graph below shows the total number of articles in classical and physical optics across all publications each year (not limited to Nature Index journals).

Technical terms

Helmholtz equation: A partial differential equation governing time-harmonic wave propagation in homogeneous media.

Wiener–Hopf technique: An analytical method for solving boundary-value problems by factorising integral kernels in the complex plane.

Stationary phase method: An asymptotic technique for approximating oscillatory integrals by locating points where the phase is stationary.

Analytical continuation: Extension of a multi-valued complex function beyond its original domain to reveal branch points and cuts.

Far-field asymptotics: Approximate expressions for wave amplitudes at large distances from scatterers, capturing angular radiation patterns.

References

1. Analytical continuation of two-dimensional wave fields. Proceedings of the Royal Society A (2021).
2. Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions. The Quarterly Journal of Mechanics and Applied Mathematics (2023).
3. A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem. The Quarterly Journal of Mechanics and Applied Mathematics (2024).
4. Physical Optics and Advanced Optical Principles.