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QED Induced Light-Matter Interaction in Nanowires
Luminescence from nanowires depending on wire geometry explained by exciton-polariton coupling with light is superseded by excitons formed from photoionization by QED photons created from the TIR confinement of absorbed excitation power
By: Thomas Prevenslik
Nanowires (NWs) have numerous applications including switching in electronic circuits, lasers, and optical information transfer. Emphasis here is light-matter interactions in ZnO wires as optical waveguides. The physics of exciton-polariton interaction with light is given in the seminal Paper: http://os.tnw.utwente.nl/
The question in light-matter interactions in NWs is whether free excitons comprising pairs of electrons and holes are created by direct photoexcitation from energetic photons, or by hypothetical exciton-polaritons resulting from the coupling of light with an exciton. However, if the exciton-polariton picture is valid, the notion of photons in NWs is insufficient, although photons in solids certainly exist. The exciton-polariton forms as the photon emitted by an electron-hole pair within a cavity reabsorbs back into the same electron-hole pair before interacting with anything else. Hence, it impossible to discriminate between the photon and the electron-hole pair because of the rapid cycling of energy back and forth between them Ibid
But the notion of the exciton-polariton is irrelevant if there is a source of energetic photons created inside NWs upon the absorption of laser energy. Photoexcitation by energetic photons is then likely to only produce free excitons that are lost to the continuum, thereby precluding any electron-hole pair to exist from which the energetic photon may subsequently be reabsorbed by the same electron-hole pair. If so,
What is the source of the energetic photons in NWs?
Source of Energetic Photons
QED induced radiation is the proposed source of energetic photons in NW’s. Indeed, NWs like quantum dots, carbon nanotubes, and other nanostructures show very high absorption spectra beyond the ultraviolet (UV) suggesting energetic photons are available to be created by photoexcitation. QED stands for quantum electrodynamics. QED radiation is the consequence of QM that requires the heat capacity of NWs to vanish under TIR confinement. QM stands for quantum mechanics and TIR for total internal reflection. See http://www.prlog.org/
Unlike classical physics that allows the atom to have thermal kT energy at the nanoscale, QM requires the heat capacity to vanish. Lacking heat capacity, absorbed energy cannot be conserved by an increase in temperature, and instead conservation proceeds by the QED induced creation of photons inside the NW. TIR confinement constrains the absorbed energy tangential to NW surfaces rather than throughout the volume because of their high surface to volume ratios. To obtain absorption spectra, lasers irradiate many NWs in a transparent liquid, but QED radiation is induced any time energy of any form is absorbed at the nanoscale, including Joule heating of individual NWs. See http://www.nanoqed.org/
Radial Emission Radial emission from a typical ZnO nanowire (4.9 micron length and 200 nm diameter) at laser energies of 3.17, 3.21, and 3.26 eV is illustrated above. See [Fig. 1 of Paper. Photons with 3.26 eV energy at the ZnO bandgap are detected with a uniform intensity over the entire wire; whereas, below 3.22 eV light is predominantly emitted at the wire ends. By QED radiation, the radial TIR confinement is a standing wave having wavelength w = 2nD, where n is the refractive index and D the wire diameter. For ZnO, having 1.9 < n < 2, w = 760 nm for n = 1.9. The QED photons created have Planck energy E = hc / w = 1.63 eV that act to confine all radiation having wavelengths longer than 760 nm. Shorter wavelength radiation tends to leak from the wire. The brightness at E = 3.26 eV occurs because the ZnO bandgap wavelength of 380 nm is an integer of 2 from the TIR confinement wavelength of 760 nm.
Longitudinal Emission Similar to radial emission, TIR confinement requires standing waves in the longitudinal emission to be a multiple of the length L of the wire, i.e., w = hc / L. Alternatively, the mode spacing is approximately linearly dependent on the inverse NW length.
Intensity and Excitation Power By QED radiation, the luminescence intensity increases with the excitation power because the absorbed power is conserved by creating QED photons within the TIR confinement wavelength. See [Fig. 3 of Paper]. Lower-energy modes are therefore pronounced with increasing excitation power as more energy accumulates in the TIR confinement than at higher-energy modes
Photon Dispersion The dispersion of photons confined in NWs of ZnO given in [Fig. 4 of Paper] assumes the lateral confinement of photons is by standing waves given by the Fabry-Perot modes, i.e., w / 2 = D. Hence, the wave vector k for photons (and polaritons) is, k = 2Pi / w = Pi / D. However, the Planck energy of photons is about 2X higher than experimental data for a range of D diameters. Because of this, the emission spectrum was thought determined by strong exciton-polariton coupling to light. However, Fabry-Perot modes assume the ZnO cavity has a unity refractive index. By QED radiation, the TIR confinement half-wavelength is, w / 2 = nD. What this means is the Planck energy of the QED photons are lower by a factor of n = 1.9 from that given by Fabry-Perot theory, and therefore approaches the ZnO bandgap energy of E = 3.26 eV. Hence, QED radiation provides a reasonable fit to the experimental NW luminescence spectrum.
Response Time Estimates of 10 fs lifetime based on FWHM measurements suggest QED radiation is the source of luminescence rather than exciton-polaritons. QED radiation is created by the TIR confinement of photons at the speed of light c / n in ZnO, e.g., for D = 200 nm, the QED photons respond at times of order Dn / c ~ 1 fs. In contrast, exciton rise time in luminescence of bulk ZnO at ambient temperature is about 400 ps. Hence, excitons by photoionization from QED photons are the favored path to NW luminescence compared to the far slower exciton-polariton interactions with light.
Wave Guiding QED radiation relies on the TIR confinement across the wire diameter for wave guiding of photons. For D = 200 nm, the TIR confinement has Planck energy E = 1.63 eV and wavelength w = 730 nm. Higher energy photons at the ZnO bandgap around 3.26 eV lack the radial confinement and emit over the wire length - not guided to the wire ends
1. Light-matter interaction in NWs is by free excitons created by direct photoexcitation from highly energetic QED induced radiation. Hypothetical exciton-polaritons resulting from the coupling of light cannot respond fast enough to be of any consequence in NW luminecsence.
2. QED radiation depending only on the size of NWs explains their significant absorption spectrum beyond the UV. Hypothetical polaritons may be dismissed as the source of absorption because excitons, like phonons can only respond at acoustic frequencies and not at the optical frequencies of QED radiation. Exciton-polaritons are therefore unlikely to form because the QED photon emitted from the electron-hole pair is more likely lost to the continuum before the exciton-polariton pair can respond by reabsorbing the QED photon.
3. Unlike exciton-polaritons, QED radiation in NWs relies on the TIR confinement of absorbed energy to create QED photons inside the NW. However, TIR confinement of photons is only momentary upon the absorption of energy and vanishes as the energy leaks to the surroundings, or is no longer supplied, i.e., if the NWs do not absorb energy, there is no TIR confinement.
4. NWs of ZnO having a band gap of 3.26 eV and diameters of 200 nm lack radial confinement and allow a large fraction of QED photons to escape the NW body. By selecting the NW diameter less than 100 nm, QED photons at the ZnO band gap are emitted at the NW ends.
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About QED Induced EM Radiation: Classically, absorbed EM energy is conserved by an increase in temperature. However, at the nanoscale, temperature increases are forbidden by quantum mechanics. QED radiation explains how absorbed EM energy is conserved at the nanoscale by the emission of nonthermal EM radiation.
Page Updated Last on: Apr 02, 2011