SUPPLEMENTARY MATERIAL:
Measurement techniques: The samples are mounted in a liquid He continuous flow
cryostat with a base temperature T = 4.2 K. Photoluminescence measurements are done using a
custom-built scanning confocal microscopy setup. The scanning system uses a 100X objective
and has an optical resolution of ~ 500 nm (diffraction limited). The static PL and hysteresis
studies use a CW laser tuned to 532 nm as the excitation source. The PL is collected through the
100 μm aperture of a fiber and dispersed through a 300 mm spectrometer onto a TE cooled CCD
camera with a spectral resolution of 0.14 nm. The angle of the linear polarization of the incident
excitation is controlled electronically using a liquid crystal variable wave plate (VWP). The
time-resolved measurements use a streak camera (resolution of 2 ps) with a mode-locked,
tunable Ti:Sapphire with a pulse width of 150 fs and a repetition rate of 76 MHz, tuned to 725
nm as the exciting laser.
The spatial mode profiles in Figs. 1c and 2b are taken by scanning the excitation laser
across the sample and taking a spectrum at each position. As we collect the PL through the same
objective, we are always exciting and probing the same part of the photonic molecule. The
bistability and hysteresis studies defocus the excitation spot to illuminate the entire coupled pair
while the collection spot is kept focused at the center of the photonic molecule. The excitation
spot is then positioned to provide uniform or non-uniform excitation as desired.
Polarization dependence: We calibrate the VWP at 532 nm using a standard setup
comprising a quartz linear polarizer, a zero order quarter wave plate and the VWP itself.
Variation of the VWP input voltage causes the linear polarization to continuously rotate between
0 and 180°. Our measurement of the beam after the final objective shows a 0.5% variation
between P = 0° and 90° polarized excitation. We then investigate the power dependence of the
1
emission off the disks on the sample at T = 10 K. The data (Fig. S3) show a linear increase in PL
intensity with excitation power over the same range as used in the coupled cavity studies, as well
as no disparity between the PL intensity as the incident polarization is switched between P = 0°
and 90°.
Sample statistics: All microdisks studied in this letter are fabricated following the method
in ref. [25]. For the geometries of the coupled systems studied, multiple sets of disks are
investigated and the data reported in the main text found to be reproducible. These include 10
pairs of coupled circular disks, 9 pairs of elliptical disks coupled along their major axes, and 9
pairs of elliptical disks coupled along their minor axes. Additional data from a subset of these
disks is shown in Figs. S4-S6 (elliptical disks coupled along major axes), Figs. S7-S9 (elliptical
disks coupled along minor axes) and Fig. S10 (circular disks). In Figs. S4-S6 optical hysteresis is
observed clearly for P = 90° in the anti-bonding mode emission along with the reduced threshold
on the power ramp down branch. These disk pairs also demonstrate modulation of the mode
intensity when P is switched, as seen in Fig. 4. The data in Figs. S7-S9 confirm the findings of
Fig. S1 where the polarization based hysteresis in the elliptical disks coupled along the minor
axes is less in magnitude and converse to those in the disks coupled along the major axes. Figure
S10 shows no hysteresis in the circular disks under any polarization condition.
2
PL (a.u.)
(a)
755
760
765
770
775
mode intensity (103)
Wavelength (nm)
20 (b)
10
0
0
100
200
300
mode intensity (103)
Pump power (W/cm2 )
20 (c)
10
0
0
100
200
300
2
Pump power (W/cm )
:
Figure S1 (a) PL Spectrum of elliptical microdisks coupled along the minor axes with the laser
positioned at the center of the PM, showing two distinct cavity modes; the bonding mode at
761.6 nm and the anti-bonding at 760.2 nm. (b) Non-uniform excitation with P = 0º and (c) P =
90º. Neither shows any thermal effects, but excitation with P = 0º demonstrates mild optical
hysteresis. This is the opposite effect to that observed in the elliptical cavities coupled along the
major axes.
3
30 (a)
20
P = 90°
P = 0°
mode intensity (103)
10
0
0
100
200
300
(b)
20
10
P = 90°
P = 0°
0
0
100
200
300
2
Pump power (W/cm )
Figure S2 (a) Mode emission from elliptical microdisks coupled along the major axes for P = 0º
(open triangles) and P = 90º (filled triangles), while excitation power is ramped up. Although the
latter leads to optical hysteresis when power is ramped down, the emission intensities are not
markedly different while ramping up (b) Similar data plotted for elliptical disks coupled along
the minor axes.
4
4
intensity (103)
P = 90º
P = 0º
2
0
0
100
200
Pump power (W/cm2 )
Figure S3 PL emission from the bare GaAs substrate, off of the microdisk cavities. Emission
intensity for the two linear polarizations, P = 0º (open triangles) and P = 90º (filled triangles)
show no disparity. PL is linear over the excitation power range shown at T = 10 K.
5
15 (a)
10
mode intensity (103)
5
0
15 (b)
10
5
0
15 (c)
10
5
0
0
100
200
Pump power (W/cm2 )
Figure S4 Optical hysteresis and switching effects observed in elliptical disk coupled along
major axes (Disk pair #2) (a) Non-uniform pumping (schematic) with P = 90° (double-headed
arrows denote polarization state). Hysteresis is observed as the excitation power is first increased
in steps (black) and then decreased (red). (b) Non-uniform pumping with P = 0° showing no
hysteresis. (c) Excitation signal power is stepped up with P = 90°. At the power corresponding
to the point on the ramp down curve highlighted by long solid arrow (172 W/cm2) the
polarization is switched to P = 0°.
6
15
(a)
10
5
0
mode intensity (103)
(b)
10
5
0
(c)
10
5
0
0
100
200
Pump power (W/cm2 )
Figure S5 Optical hysteresis and switching effects observed in elliptical disk coupled along
major axes (Disk pair #3) (a) Non-uniform pumping (schematic) with P = 90°. Hysteresis is
observed as the excitation power is first increased in steps (black) and then decreased (red). (b)
Non-uniform pumping with P = 0° showing no hysteresis. (c) Excitation signal power is stepped
up with P = 90°. At the power corresponding to the point on the ramp down curve highlighted
by long solid arrow (212 W/cm2) the polarization is switched to P = 0°.
7
15
(a)
10
5
0
mode intensity (103)
(b)
10
5
0
(c)
10
5
0
0
100
200
Pump power (W/cm2 )
Figure S6 Optical hysteresis and switching effects observed in elliptical disk coupled along
major axes (Disk pair #4) (a) Non-uniform pumping (schematic) with P = 90°. Hysteresis is
observed as the excitation power is first increased in steps (black) and then decreased (red). (b)
Non-uniform pumping with P = 0° showing no hysteresis. (c) Excitation is ramped up with P =
90°, ramped down with P = 0°, switched to P = 90° (solid arrow) at 200 W/cm2, switched back
to P = 0° at 185 W/cm2 (dotted arrow) and ramped down all the way.
8
(a)
20
mode intensity (103)
10
0
(b)
20
10
0
0
100
200
Pump power (W/cm2 )
Figures S7 Optical hysteresis observed in elliptical disk coupled along minor axes (Disk pair #2)
(a) Non-uniform excitation with P = 0º and (b) P = 90º. Neither shows any thermal effects, but
excitation with P = 0º demonstrates mild optical hysteresis. This is the opposite effect to that
observed in the elliptical cavities coupled along the major axes.
9
(a)
20
mode intensity (103)
10
0
(b)
20
10
0
0
100
200
Pump power (W/cm2 )
Figures S8 Optical hysteresis observed in elliptical disk coupled along minor axes (Disk pair #3)
(a) Non-uniform excitation with P = 0º and (b) P = 90º.
10
(a)
20
mode intensity (103)
10
0
(b)
20
10
0
0
300
200
100
Pump power (W/cm2 )
Figures S9 Optical hysteresis observed in elliptical disk coupled along minor axes (Disk pair #4)
(a) Non-uniform excitation with P = 0º and (b) P = 90º.
11
20
(a)
mode intensity (103)
10
0
(b)
10
0
0
100
200
Pump power (W/cm2 )
Figure S10 Non-uniform pumping in circular disk pairs do not show any marked hysteresis for
either (a) P = 90º or (b) P = 0º.
12