https://physicstoday.scitation.org/doi/pdf/10.1063/1.3047693

Introduction to the Theory of Coherence and Polarization of Light

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation, photonic crystal fiber

We demonstrate a broadband, thin-film, polarizing beam splitter based on an anisotropic diffraction grating composed of reactive mesogens (polymerizable liquid crystals). This achromatic polarization grating (PG) manifests high diffraction efficiency (~100%) and high extinction ratio (⩾1000:1) in both theory and experiment. We show an operational bandwidth Δλ/λ0~56% (roughly spanning visible wavelength range) that represents more than a fourfold increase of bandwidth over conventional PGs (and significantly larger than any other grating). The diffraction angle and operational region (visible, near-infrared, midwave infrared, and ultraviolet wavelengths) may be easily tailored during fabrication. The essence of the achromatic design is a stack of two chiral PGs with an opposite twist sense and employs the principle of retardation compensation. We fully characterize its optical properties and derive the theoretical diffraction behavior.

Achromatic diffraction from polarization gratings with high efficiency.

Throughout optics and photonics, phase is normally controlled via an optical path difference. Although much less common, an alternative means for phase control exists: a geometric phase (GP) shift occurring when a light wave is transformed through one parameter space, e.g., polarization, in such a way as to create a change in a second parameter, e.g., phase. In thin films and surfaces where only the GP varies spatially—which may be called GP holograms (GPHs)—the phase profile of nearly any (physical or virtual) object can in principle be embodied as an inhomogeneous anisotropy manifesting exceptional diffraction and polarization behavior. Pure GP elements have had poor efficiency and utility up to now, except in isolated cases, due to the lack of fabrication techniques producing elements with an arbitrary spatially varying GP shift at visible and near-infrared wavelengths. Here, we describe two methods to create high-fidelity GPHs, one interferometric and another direct-write, capable of recording the wavefront of nearly any physical or virtual object. We employ photoaligned liquid crystals to record the patterns as an inhomogeneous optical axis profile in thin films with a few μm thickness. We report on eight representative examples, including a GP lens with F/2.3 (at 633 nm) and 99% diffraction efficiency across visible wavelengths, and several GP vortex phase plates with excellent modal purity and remarkably small central defect size (e.g., 0.7 and 7 μm for topological charges of 1 and 8, respectively). We also report on a GP Fourier hologram, a fan-out grid with dozens of far-field spots, and an elaborate phase profile, which showed excellent fidelity and very low leakage wave transmittance and haze. Together, these techniques are the first practical bases for arbitrary GPHs with essentially no loss, high phase gradients (∼rad/μm), novel polarization functionality, and broadband behavior.

Fabrication of ideal geometric-phase holograms with arbitrary wavefronts

The Talbot effect, also referred to as self-imaging or lensless imaging, is of the phenomena manifested by a periodic repetition of planar field distributions in certain types of wave fields. This phenomenon is finding applications not only in optics, but also in a variety of research fields, such as acoustics, electron microscopy, plasmonics, x ray, and Bose–Einstein condensates. In optics, self-imaging is being explored particularly in image processing, in the production of spatial-frequency filters, and in optical metrology. In this article, we give an overview of recent advances on the effect from classical optics to nonlinear optics and quantum optics. Throughout this review article there is an effort to clearly present the physical aspects of the self-imaging phenomenon. Mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of Talbot self-imaging are still expected in the future.

The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics

We introduce a class of partially coherent beams with spatially varying correlation properties. It is shown that mathematically simple modifications in the coherence function of conventional Gaussian Schell-model beams lead to partially coherent fields with extraordinary free-space propagation characteristics, such as locally sharpened and laterally shifted intensity maxima. We study the properties of such fields based on an elementary-mode interpretation and by numerical simulations. The results demonstrate the potential of coherence modulation for beam shaping applications.

Propagation characteristics of partially coherent beams with spatially varying correlations

A coherent-mode representation for spatially and spectrally partially coherent pulses is derived both in the space–frequency domain and in the space–time domain. It is shown that both the cross-spectral density and the mutual coherence function of partially coherent pulses can be expressed as a sum of spatially and spectrally and temporally completely coherent modes. The concept of the effective degree of coherence for nonstationary fields is introduced. As an application of the theory, the propagation of Gaussian Schell-model pulsed beams in the space–frequency domain is considered and their coherent-mode representation is presented.

Theory of spatially and spectrally partially coherent pulses.

It is shown that partially spectrally coherent pulses of light with controlled spectral coherence properties can be generated by temporal modulation of beams emitted by stationary light sources. A method for generation of spectrally Gaussian Schell-model-type pulses is presented.

Spectral coherence properties of temporally modulated stationary light sources

We consider partially coherent plane-wave pulses with non-uniform correlation distributions and study their propagation in linear second-order dispersive media. Particular models for coherence functions are introduced both in time and frequency domains. It is shown that the maximum peak of the pulse energy can be accelerating or decelerating and also self-focusing effects are possible due to coherence-induced propagation effects.

Non-uniformly correlated partially coherent pulses

The modal theory for spectrally partially coherent nonstationary plane waves is introduced. The theory is first developed in the space-frequency domain and then extended to the space-time domain. Propagation properties of the coherent modes are analyzed. The concept of the overall degree of coherence is extended to the domain of nonstationary fields, and it is shown that the overall degree of coherence of partially coherent plane-wave pulses is the same in the space-frequency and space-time domains. The theory is applied to the recently introduced concept of spectrally Gaussian Schell-model plane-wave pulses.

Hanna Lajunen

Papers

Propagation characteristics of partially coherent beams with spatially varying correlations

Theory of spatially and spectrally partially coherent pulses.

Spectral coherence properties of temporally modulated stationary light sources

Non-uniformly correlated partially coherent pulses

Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses.