Tero Setälä

Van Cittert–Zernike theorem with Stokes parameters

We formulate the van Cittert-Zernike theorem for spatially incoherent partially polarized sources in terms of the traditional polarization (one-point) Stokes parameters and the coherence (two-point) Stokes parameters. This leads to a physically insightful connection between the source polarization and the field coherence. We show that the far-zone coherence is given by a Fourier relation of the source-plane polarization and apply the results to investigate the far-zone properties of a field emitted by an incoherent source limited by an annular aperture.

Exact surface-plasmon polariton solutions at a lossy interface

Making use of a rigorous electromagnetic treatment, we demonstrate that the approximate results that are customarily employed for the analysis of a plasmon field at a metal/dielectric boundary are incorrect even in some situations in which they are supposed to hold. We show further that a new type of surface-plasmon solution exists that does not follow from the standard approximate analysis. Energy-flow considerations indicate that the new polariton is a backward-propagating surface wave, as encountered in manmade structures. Our results are likely to find applications in metal/semiconductor and metamaterial plasmonics.

Electromagnetic theory of optical coherence [Invited]

The coherence theory of random, vector-valued optical fields has been of great research interest in recent years. In this work we formulate the foundations of electromagnetic coherence theory both in the space-time and space-frequency domains, with particular emphasis on various types of optical interferometry. Analyzing statistically stationary, two-component (paraxial) electric fields in the classical and quantum-optical contexts we show fundamental connections between the conventional (polarization) Stokes parameters and the associated two-point (coherence) Stokes parameters. Measurement of the coherence and polarization properties of random vector beams by nanoparticle scattering and two-photon absorption is also addressed.

Partial polarization of optical beams and near fields probed with a nanoscatterer.

We consider theoretically the detection of the spectral polarization characteristics of random, partially polarized optical beams and near fields by probing them with a dipolar nanoparticle. We show that measuring the polarization state of the scattered far field with a conventional waveplate-polarizer setup, possibly in several directions, results in the full 3×3 polarization matrix at the probe site. This allows us to deduce the distributions of the degree of polarization of the field and the Stokes parameters of the polarized part of the field with a resolution limited by the probe size. Regarding random near fields we show that, in analogy with a known result on beam fields, a degree of polarization of three-component light fields put forward in recent literature can in some cases be interpreted as a ratio of the intensity in the polarized part of the light to that of the total field. We demonstrate the technique by considering the probing of a Gaussian-Schell model beam and a thermally excited near field. The method extends the current scanning-probe techniques to the detection of partial polarization of random light fields and can find applications in nanophotonics and polarization optics.

Coherent-mode representation of partially polarized pulsed electromagnetic beams

Coherent-mode representation provides physical insight and computational simplification into the analysis of random optical signals. In this work, we present the coherent-mode decomposition for pulsed electromagnetic beam fields. We show that the mode decomposition can be done for any valid space-frequency or space-time coherence matrix representing nonstationary pulsed electric field, and moreover, the spectral and temporal modes are connected via a Fourier transform relation. The analysis also yields the coherent modes of electromagnetic time-domain signals in temporal optics. We present the overall degree of coherence as a measure of the average temporal or spectral and spatial coherence of the beam. Several illustrative examples are discussed analytically and numerically.

Polarization time of unpolarized light

Light produced by most natural and artificial sources is unpolarized or partially polarized. At any instant of time, however, such random light can be regarded as fully polarized, but the polarization state may vary drastically within short time intervals. This rate of change is another attribute that separates one unpolarized beam from another. Here, we study such polarization dynamics and, for the first time to our knowledge, measure the characteristic time, called the polarization time, in which the instantaneous polarization state stays essentially unaltered. The technique employs a polarization-sensitive Michelson interferometer and two-photon absorption detection valid for electromagnetic light, yielding superior femtosecond time resolution. We analyze two unpolarized light sources: amplified spontaneous emission from a fiber amplifier and a dual-wavelength laser source. The characterization of polarization dynamics can have significant applications in optical sensing, polarimetry, telecommunication, and astronomy, as well as in quantum and atom optics.

Ultrashort coherence times in partially polarized stationary optical beams measured by two-photon absorption

We measure the recently introduced electromagnetic temporal degree of coherence of a stationary, partially polarized, classical optical beam. Instead of recording the visibility of intensity fringes, the spectrum, or the polarization characteristics, we introduce a novel technique based on two-photon absorption. Using a Michelson interferometer equipped with polarizers and a specific GaAs photocount tube, we obtain the two fundamental quantities pertaining to the fluctuations of light: the degree of coherence and the degree of polarization. We also show that the electromagnetic intensity-correlation measurements with two-photon absorption require that the polarization dynamics, i.e., the time evolution of the instantaneous polarization state, is properly taken into account. We apply the technique to unpolarized and polarized sources of amplified spontaneous emission (Gaussian statistics) and to a superposition of two independent, narrow-band laser beams of different mid frequencies (non-Gaussian statistics). For these two sources femtosecond-range coherence times are found that are in good agreement with the traditional spectral measurements. Although previously employed for laser pulses, two-photon absorption provides a new physical principle to study electromagnetic coherence phenomena in classical and quantum continuous-wave light at extremely short time scales.

Partial coherence and polarization of a two-mode surface-plasmon polariton field at a metallic nanoslab

Rigorous electromagnetic theory is utilized to characterize the partial spatial coherence and partial polarization of a two-mode field consisting of the long-range and the short-range surface-plasmon polariton at a metallic nanofilm. By employing appropriate formulations for the spectral degrees of coherence and polarization, we examine the fundamental limits for these quantities associated with such a superposition field and explore how the degrees are influenced when the media, frequency, and slab thickness are varied. It is in particular shown that coherence lengths extending from subwavelength scales up to thousands of wavelengths are possible and their physical origins are elucidated. In addition, we demonstrate that for ultra-thin films the generally highly polarized two-mode field can be partially polarized in close vicinity of the polariton excitation region. The results could benefit cross-disciplinary electro-optical applications in which near-field interactions between plasmons and nanoparticles are exploited.

Statistical similarity and complete coherence of electromagnetic fields in time and frequency domains

We investigate the statistical similarity of partially polarized, partially coherent electromagnetic fields in time and frequency domains, and the relationship between statistical similarity and complete coherence. We find that, both in time domain and frequency domain, the complete coherence of two fields is equivalent to the fields being both fully polarized and statistically similar. Unlike in scalar coherence theory, statistical similarity alone is found not to constitute a sufficient condition for complete coherence. We derive the conditions under which spectrally completely coherent fields are also temporally fully coherent, and we point out that temporally completely coherent fields are necessarily fully spectrally coherent at all frequencies. Complete temporal and spectral coherence of electromagnetic fields are found to be related to the recently introduced concept of strict cross-spectral purity, but in contrast to the scalar case, strict cross-spectral purity is not a necessary condition for complete temporal coherence if the fields have different spectral polarization states.

Surface-plasmon polariton solutions at a lossy slab in a symmetric surrounding

A rigorous theoretical formulation based on electromagnetic plane waves is utilized to construct a unified framework and identification of all possible surface-plasmon polariton solutions at an absorptive slab in a symmetric, lossless dielectric surrounding. In addition to the modes reported in literature, sets of entirely new mode solutions are presented. The corresponding fields are classified into different categories and examined in terms of bound and leaky modes, as well as forward-and backward-propagating modes, both outside and inside the slab. The results could benefit plasmon based applications in thin-film nanophotonics.