508
19 Dielectric Structures
(a)
(b)
(c)
Fig. 19.28 a SEM image of a microcavity disc laser diode with a disc radius of 50 µm. The p-contact ring electrode
defines the areas through which carriers are injected into the microdisc and where stimulated emission can take place. b
Radial distribution of the light output from the spiral-shaped microdisc laser diode measured below and above threshold.
The radius of the spiral microdisc was r 0 = 250 µm and the deformation parameters were = 0.05 (grey) and = 0.10
(black). An emission beam at an angle of α = 0 ◦ corresponds to a direction normal to the notch surface as shown in
the inset. Below the laser threshold, the emission pattern is essentially isotropic and independent of the deformation
parameter. Above the threshold, directional emission is clearly observed with the emission direction at a tilt angle
α ≈ 25 ◦ . The measured divergence angle of the far-field pattern is ∼ 75 ◦ for = 0.10 and ∼ 60 ◦ for = 0.05.
Reprinted with permission from [1656], ©2004 AIP. c Simulated near-field intensity pattern of an emission mode with
nk R ≈ 200 for deformation = 0.10. Reprinted with permission from [1654], ©2003 AIP
19.2.4 Hexagonal Cavities
Hexagonal cavities develop, e.g., in microcrystals of wurtzite semiconductors (with the c-axis along
the longitudinal axis of the pillar). In Fig. 19.29a, a ZnO tapered hexagonal resonator (needle) is shown.
Whispering gallery modes modulate the intensity of the green ZnO luminescence [1657].
4 In a simple
plane-wave model, the resonance condition is given by
6R i =
h c
n E
N +
6
π
arctan
β
3n 2 − 4
,
(19.59)
where R i is the radius of the inner circle (Fig. 19.29d), n is the index of refraction, N is the mode
number and β is given by β TM = 1/n (β TE = n) for TM (TE) polarization, respectively. Due to
birefringence, n (n ⊥ ) has to be used as the index of refraction for TM (TE) polarization.
4 We note that besides the green luminescence as in Fig. 10.20, an unstructured green band also occurs that is observed
here. Its origin may be linked to the oxygen vacancy [1658].
19 Dielectric Structures
(a)
(b)
(c)
Fig. 19.28 a SEM image of a microcavity disc laser diode with a disc radius of 50 µm. The p-contact ring electrode
defines the areas through which carriers are injected into the microdisc and where stimulated emission can take place. b
Radial distribution of the light output from the spiral-shaped microdisc laser diode measured below and above threshold.
The radius of the spiral microdisc was r 0 = 250 µm and the deformation parameters were = 0.05 (grey) and = 0.10
(black). An emission beam at an angle of α = 0 ◦ corresponds to a direction normal to the notch surface as shown in
the inset. Below the laser threshold, the emission pattern is essentially isotropic and independent of the deformation
parameter. Above the threshold, directional emission is clearly observed with the emission direction at a tilt angle
α ≈ 25 ◦ . The measured divergence angle of the far-field pattern is ∼ 75 ◦ for = 0.10 and ∼ 60 ◦ for = 0.05.
Reprinted with permission from [1656], ©2004 AIP. c Simulated near-field intensity pattern of an emission mode with
nk R ≈ 200 for deformation = 0.10. Reprinted with permission from [1654], ©2003 AIP
19.2.4 Hexagonal Cavities
Hexagonal cavities develop, e.g., in microcrystals of wurtzite semiconductors (with the c-axis along
the longitudinal axis of the pillar). In Fig. 19.29a, a ZnO tapered hexagonal resonator (needle) is shown.
Whispering gallery modes modulate the intensity of the green ZnO luminescence [1657].
4 In a simple
plane-wave model, the resonance condition is given by
6R i =
h c
n E
N +
6
π
arctan
β
3n 2 − 4
,
(19.59)
where R i is the radius of the inner circle (Fig. 19.29d), n is the index of refraction, N is the mode
number and β is given by β TM = 1/n (β TE = n) for TM (TE) polarization, respectively. Due to
birefringence, n (n ⊥ ) has to be used as the index of refraction for TM (TE) polarization.
4 We note that besides the green luminescence as in Fig. 10.20, an unstructured green band also occurs that is observed
here. Its origin may be linked to the oxygen vacancy [1658].