Whispering Gallery Mode Resonators

As a first component for integrated photonic circuits, disc resonators with a disc diameter of 20µm and a disc thickness of approximately 1.2µm on a stem with di-ameter 10µm are fabricated using the photoresist functionalised with nanocrystals (see Section 7.3).

The mode structure of the whispering gallery modes (WGMs) in the disc res-onators is analysed by means of coupling in a tunable external-cavity diode laser at around 770 nm via the evanescent fields of a tapered optical fibre. A sketch of the measurement technique is shown in Figure 7.4 (a). By tuning the frequency of the laser over the distinct whispering gallery modes, light is coupled into the resonator (see Figure 7.4 (c)) and different modes can be observed as Lorentzian shaped dips in the transmitted power. The polarisation of the incoming light is chosen to maximise coupling depth. For normalisation of the data sets, at first a reference scan with the fibre taper not being coupled is performed. These data are then compared with the results when the same tapered fibre is coupled to the resonator. Corresponding quality factors (Q factors) are calculated from the dips by a Lorentzian fit function with an additional linear term to better match the local environment of the resonances. All measurements are performed with the tapered fibre in full contact. The observed free spectral range of 6.5 nm of the resonator shown in Figure 7.4 (d) fits well to the expected value of 6.4 nm for a disc with diameter 20µm derived from geometrical considerations assuming an index of re-fraction of 1.5. The highest Q factors are as large as 10⁴ at a wavelength of around 770 nm (see Figure 7.4 (e)).

Next, a homebuilt confocal microscope is used to raster scan the fabricated res-onator discs (see Figure 7.5 (a)) and to identify single NV centres by measuring the second-order autocorrelation functiong⁽²⁾(τ) in a Hanbury Brown and Twiss inter-ferometer (see Section 2.4.2). In parallel, a grating spectrometer is used to resolve the emission spectra of the individual emitters. Figure 7.5 (b) shows a confocal scan of a resonator where fluorescent defects can be identified as bright spots on the resonator. Encircled is a spot on the resonator’s outer rim where coupling to the disc’s whispering gallery modes is expected. Figure 7.5 (d) displays an autocorre-lation measurement of fluorescence collected from that spot. A clear antibunching dip is observed reaching a value of g⁽²⁾(0) = 0.31±0.04 as deduced from the fit shown as red curve. No background correction is applied to these data. This mea-surement shows that the bright spot indeed corresponds to a single NV centre in the disc resonator.

The fluorescence spectrum of a NV centre at room temperature is typically broad-ened over 200 nm from approx. 600 nm to 800 nm by phonon sidebands (see Chap-ter 3). This corresponds well to the measured emission spectrum shown in Fig-ure 7.5 (c). The peak at approximately 630 nm stems from fluorescence of the

0 -2 -4

-6 ^{6.5 nm}

a b c

d

relative trans- mission /dB FWHM = 62.0 pm

Q = 1.2 10· 4

e

relative trans- mission

765 770 775 780

wavelength /nm 777.5 wavelength /nm778.0 778.5 0

.5 1

i ii

iii iv

Figure 7.4.: Mode measurements of whispering gallery resonators produced using the DLW in the hybrid photoresist. In (a) a tunable laser is coupled to a disc res-onator via a tapered fibre. Upon sweeping the laser frequency, the transmitted light is modulated by the modes of the resonator. (b) shows the 20μm resonator being approached by a 1.5μm thick tapered fibre, while in (c) the scattered light when a tapered fibre is coupled to a resonator is shown. In panels i-iv the frequency of the light coupled to the resonator is changed from the off-resonant case to resonance.

(d) shows a scan of the laser wavelength over many modes with a free spectral range of 6.5 nm indicated by the red arrows. (e) is a scan of a single resonator mode with a quality factor Q of 1.2×10⁴. ((a,d,e) adapted from [177])

7.4. Diamond Doped Laser-Written Microstructures

excitation detection

time (ns) 0

g(2)(τ)

620 wavelength (nm)

intensity (norm.)

1

0

0 1

counts (arb. u.)

-100 -50 0 50 100

640 660 680

a b

c

1 2 d

Figure 7.5.:DLW resonator containing single NV centres. A diamond nanocrystal containing a single NV centre is coupled to whispering gallery modes of a DLW disc resonator. (a) shows the measurement scheme. Detection and excitation take place at the same point in a confocal configuration. (b) is a scanning confocal microscope image of the resonator disc. The circle indicates a bright spot identified as single NV centre. Its fluorescence is analysed in (c) and (d). Scalebar is 5µm. (c) shows the spectrum of the collected fluorescence. The resonator modes are seen as modulation on the broad NV centre phonon sidebands. The peak at 630 nm stems from the photoresist and can be bleached over time. The autocorrelation function of the fluorescence from the NV centre is shown in (d). A clear antibunching behaviour can be seen. The red curve is a fit to the data with g⁽²⁾(0) = 0.31±0.04. (Figure source: [177])

Figure 7.6.: Tuning of DLW written resonator by a 405 nm laser. Each spectrum is integrated for 30 second while the laser is focussed on the resonator’s rim inside a vacuum atmosphere. Vertical offsets are added for clarity and increase with increasing time. (Figure adapted from: [177])

photoresist and bleaches after long excitation. For confocal scans and correlation measurements this background light is suppressed by spectral filtering. In addi-tion, there is a fine modulation of the spectrum due to the cavity resonances. It is attributed to photons that are initially emitted into the resonator modes and afterwards scattered out by the diamond nanocrystal. Hence, these photons are detected in addition to the flat unmodulated spectrum emitted directly out of the disc.

Having now single NV centres coupled to the modes of a whispering gallery resonator, for efficient coupling two more requirements have to be met: Firstly, the system has to be compatible with the environment in a cryostat, because in order to get a sharper zero phonon line, the NV centres need to be cooled to liquid helium temperatures. Secondly, there need to be ways of tuning the resonance of the resonator, in order to match them to the zero phonon line. Both requirements are met by the resonator-emitter system. Cooling it down in a liquid helium flow cryostat does not destroy the structures. Also, its modes can be tuned by shining in a focussed 405 nm laser. This laser causes a permanent change in the resonator’s material and in this way changes the mode structure. Similar techniques are used in References [228, 248] and in Section 6.1, but with the difference, that in the cryostat there is vacuum. So, oxidation as process can be ruled out and the change is probably due to a heat-induced modification of the material composition. In Figure 7.6, subsequently acquired spectra are shown while of the resonator’s modes are tuned.