19.2 Microscopic Resonators
509
(d)
(e)
Fig. 19.29 a–c SEM images of ZnO nanoneedle fabricated by pulsed laser deposition. d Schematic geometry of crosssectional plane. R i (R) is the radius of the incircle (circumscribing circle). The circumference of the inscribed white
hexagon, representing the path of a whispering gallery mode, has a length of 6R i . e Two-dimensional plot of spectra
recorded along a linescan along the needle’s longitudinal axis. The left vertical axis shows the linescan position x, the
right one refers to the respective needle diameter D. The spectral maxima, i.e. the measured WGM energies, appear
as bright belts going from the bottom left corner to the right upper one. With decreasing diameter, all resonances shift
systematically to higher energies. The white dots give theoretical TM-resonance energy positions obtained from (19.59),
white crosses give the same for TE-polarization. Reprinted with permission from [1657], ©2004 APS
A N = 26 whispering gallery mode of a hexagonal resonator is shown in Fig. 19.30c,d. The 6-fold
symmetric emission stems from the edges of the hexagon. While whispering gallery resonators have
typically mode numbers N 1, in such hexagonal resonators the whispering gallery modes could be
followed down to N = 1 [1657] as shown in Fig. 19.29a, b, e.
Under high optical pumping laser action occurs on the whispering gallery modes. The peak positions,
close to the band gap in the spectral region of the electron-hole plasma, follow (19.59) [1660], as
shown for various diameters in Fig. 19.31. Pumping threshold even at room temperature is below
100 kW/cm
−2 [1661].
509
(d)
(e)
Fig. 19.29 a–c SEM images of ZnO nanoneedle fabricated by pulsed laser deposition. d Schematic geometry of crosssectional plane. R i (R) is the radius of the incircle (circumscribing circle). The circumference of the inscribed white
hexagon, representing the path of a whispering gallery mode, has a length of 6R i . e Two-dimensional plot of spectra
recorded along a linescan along the needle’s longitudinal axis. The left vertical axis shows the linescan position x, the
right one refers to the respective needle diameter D. The spectral maxima, i.e. the measured WGM energies, appear
as bright belts going from the bottom left corner to the right upper one. With decreasing diameter, all resonances shift
systematically to higher energies. The white dots give theoretical TM-resonance energy positions obtained from (19.59),
white crosses give the same for TE-polarization. Reprinted with permission from [1657], ©2004 APS
A N = 26 whispering gallery mode of a hexagonal resonator is shown in Fig. 19.30c,d. The 6-fold
symmetric emission stems from the edges of the hexagon. While whispering gallery resonators have
typically mode numbers N 1, in such hexagonal resonators the whispering gallery modes could be
followed down to N = 1 [1657] as shown in Fig. 19.29a, b, e.
Under high optical pumping laser action occurs on the whispering gallery modes. The peak positions,
close to the band gap in the spectral region of the electron-hole plasma, follow (19.59) [1660], as
shown for various diameters in Fig. 19.31. Pumping threshold even at room temperature is below
100 kW/cm
−2 [1661].