M. P. van Exter

Plasmon-assisted transmission of entangled photons

The state of a two-particle system is said to be entangled when its quantum-mechanical wavefunction cannot be factorized into two single-particle wavefunctions. This leads to one of the strongest counter-intuitive features of quantum mechanics, namely non-locality. Experimental realization of quantum entanglement is relatively easy for photons; a starting photon can spontaneously split into a pair of entangled photons inside a nonlinear crystal. Here we investigate the effects of nanostructured metal optical elements on the properties of entangled photons. To this end, we place optically thick metal films perforated with a periodic array of subwavelength holes in the paths of the two entangled photons. Such arrays convert photons into surface-plasmon waves—optically excited compressive charge density waves—which tunnel through the holes before reradiating as photons at the far side. We address the question of whether the entanglement survives such a conversion process. Our coincidence counting measurements show that it does, so demonstrating that the surface plasmons have a true quantum nature. Focusing one of the photon beams on its array reduces the quality of the entanglement. The propagation of the surface plasmons makes the array effectively act as a ‘which way’ detector.We investigate whether entanglement is conserved when polarization entangled photons are converted to surface plasmons, propagating along subwavelength metal hole arrays. We find that entanglement survives, but is limited by spatial dispersion of the hole arrays.

Fano-type interpretation of red shifts and red tails in hole array transmission spectra

We present a unifying point of view which allows to understand spectral features reported in recent experiments with two-dimensional arrays of subwavelength holes in metal films. We develop a Fano analysis of the related scattering problem by distinguishing two interfering contributions to the transmission process, namely a non-resonant contribution (direct scattering) and a resonant contribution (surface plasmon excitation). The introduction of a coupling strength between these two contributions naturally induces resonance shifts and asymmetry of profiles which satisfy simple scaling relations. We also report an experiment to confirm this analysis.

Observation of Goos-Hänchen shifts in metallic reflection

We report the first observation of the Goos-Hänchen shift of a light beam incident on a bare metal surface. This phenomenon is particularly interesting because the Goos-Hänchen shift for p polarized light in metals is negative and much bigger than the positive shift for s polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface when this is excited by a p polarized beam of light.

Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers

We report a new technique to apply strain to a vertical‐cavity surface‐emitting semiconductor laser. This has allowed us to study the relation between strain and birefringence. We have found that the corresponding tensor is anisotropic, with a measured anisotropy 2p44/(p11−p12)=4.7±0.6. This anisotropy explains the natural preference of the polarization for the [110]/[110] axes.

Shannon dimensionality of quantum channels and its application to photon entanglement.

We introduce the concept of Shannon dimensionality D as a new way to quantify bipartite entanglement as measured in an experiment. This is applied to orbital-angular-momentum entanglement of two photons, using two state analyzers composed of a rotatable angular-sector phase plate that is lens coupled to a single-mode fiber. We can deduce the value of D directly from the observed two-photon coincidence fringe. In our experiment, D varies between 2 and 6, depending on the experimental conditions. We predict how the Shannon dimensionality evolves when the number of angular sectors imprinted in the phase plate is increased and anticipate that D approximately 50 is experimentally within reach.

Spectral signature of relaxation oscillations in semiconductor lasers

A novel and relatively simple expression is given for the optical spectrum of a single-mode semiconductor laser which, due to the presence of relaxation oscillations, consists of a strong central line with a broad weak sideband at each side. The coupling between phase and amplitude fluctuations is included in this derivation and is shown to result in an asymmetry between the relaxation oscillation sidebands. This asymmetry can be used to determine the linewidth enhancement factor. Using optical heterodyne detection, the spectrum of a Fabry-Perot-type AlGaAs laser has been measured as a function of output power. Information on the dynamics of the relaxation oscillations was thus obtained. The power dependence of the frequency and damping of the relaxation oscillations allowed the spontaneous lifetime and the dependence of the gain on both carrier density (differential gain) and intensity (gain saturation) to be separately determined. >

Strain-induced birefringence in vertical-cavity semiconductor lasers

We describe a new technique to study and control the polarization properties of planar vertical-cavity semiconductor lasers. The technique consists of the application of a controllable amount of strain by means of the thermal expansion that results from local heating in the vicinity of the device. Analytical expressions are derived for the strain and birefringence induced with this hot-spot technique. Experimentally, the relation between strain and birefringence is found to be highly anisotropic; this allows a natural interpretation of the distribution of the native polarization angles.

Tailoring the birefringence in a vertical‐cavity semiconductor laser

We demonstrate a technique to modify the strain in a planar vertical‐cavity semiconductor laser. The technique consists of locally melting a hole in the wafer next to the device by means of a focused laser beam. This allows manipulating both the magnitude and the orientation of the native birefringence in a permanent way.

Excess phase noise in self-heterodyne detection

The interpretation of self-heterodyne spectra is difficult if, apart from spontaneous emission, additional noise sources are presented. Measurements on an external-cavity semiconductor laser show how, for a relatively long delay, the high-frequency (Lorentzian) wings of the self-heterodyne spectrum are a sensitive measure for the quantum-limited (Schawlow-Townes) laser linewidth. The quantum-limited laser linewidth is shown to be inversely proportional to the output power. Values below 5 kHz are routinely measured. The full width at half maximum (FWHM) laser linewidth is larger than this due to excess low-frequency fluctuations, which are shown to result from the presence of side modes. >

Transverse mode formation in microlasers by combined gain- and index-guiding

The formation of transverse modes in end-pumped microlasers with combined index- and gain-guiding is investigated theoretically, We study the case of a planoconcave cavity pumped by means of a Gaussian optical field in the frame of the effective index method and the mean-field limit. We find crossings of the modal gains as the cavity losses are varied. Ring patterns are observed in both the near- and far-field profiles in qualitative agreement with the experiments. We study the bad-cavity region and observe one compact trapped gain-guided mode with large modal gain, and many other deformed index-guided modes with much less gain.