19.2 Microscopic Resonators
507
(a)
(b)
(c)
Fig. 19.27 a SEM image of a quadrupolar cylinder laser with deformation parameter ≈ 0.16 on a sloped InP pedestal.
The light grey area in the top view is the electrical contact. b Simulated near-field intensity pattern of a chaotic whispering
gallery mode for = 0.06 and n = 3.3. c Simulated near-field intensity pattern of a bow-tie mode for = 0.15. The
length of the minor axis for (b) and (c) is 50µm. Reprinted with permission from [1653], ©1998 AAAS
One other possible deformation of the circular disc geometry is a ‘flattened quadrupole’ as shown
in Fig. 19.27a. This shape can be parameterized by a deformation parameter and the angle-dependent
radius r (φ) given by
r (φ) = R
1 + 2 cos
2
(2φ)
1/2 .
(19.57)
For small deformation, the whispering gallery modes become chaotic and exhibit preferred emission
along the long axis of the resonator (Fig. 19.27b). For larger deformations ( ≥ 0.14), a stronger and
qualitatively different directionality occurs in the shape of a bow-tie [1653] as shown in Fig. 19.27c.
The optical laser power extracted from deformed resonators was found to increase exponentially with
; for = 0.2 it was 50 times larger than for the circular resonator.
Another modification that can be applied to the microdisc in order to increase outcoupling of light,
is the spiral resonator [1654] as shown in Fig. 19.28a. The radius is parameterized by
r (φ) = R
1 +
2π
φ
.
(19.58)
The experimental emission pattern is displayed in Fig. 19.28b. It exhibits a maximum along the
direction of the tangent at the radius step. The simulated near-field intensity of such an emission mode
is shown in Fig. 19.28c. In a spiral laser, ray dynamics is also chaotic [1655].
507
(a)
(b)
(c)
Fig. 19.27 a SEM image of a quadrupolar cylinder laser with deformation parameter ≈ 0.16 on a sloped InP pedestal.
The light grey area in the top view is the electrical contact. b Simulated near-field intensity pattern of a chaotic whispering
gallery mode for = 0.06 and n = 3.3. c Simulated near-field intensity pattern of a bow-tie mode for = 0.15. The
length of the minor axis for (b) and (c) is 50µm. Reprinted with permission from [1653], ©1998 AAAS
One other possible deformation of the circular disc geometry is a ‘flattened quadrupole’ as shown
in Fig. 19.27a. This shape can be parameterized by a deformation parameter and the angle-dependent
radius r (φ) given by
r (φ) = R
1 + 2 cos
2
(2φ)
1/2 .
(19.57)
For small deformation, the whispering gallery modes become chaotic and exhibit preferred emission
along the long axis of the resonator (Fig. 19.27b). For larger deformations ( ≥ 0.14), a stronger and
qualitatively different directionality occurs in the shape of a bow-tie [1653] as shown in Fig. 19.27c.
The optical laser power extracted from deformed resonators was found to increase exponentially with
; for = 0.2 it was 50 times larger than for the circular resonator.
Another modification that can be applied to the microdisc in order to increase outcoupling of light,
is the spiral resonator [1654] as shown in Fig. 19.28a. The radius is parameterized by
r (φ) = R
1 +
2π
φ
.
(19.58)
The experimental emission pattern is displayed in Fig. 19.28b. It exhibits a maximum along the
direction of the tangent at the radius step. The simulated near-field intensity of such an emission mode
is shown in Fig. 19.28c. In a spiral laser, ray dynamics is also chaotic [1655].