Scanning cavity microscopy of a single-crystal diamond membrane Jonathan Körber1Maximilian Pallmann1Julia Heupel2Rainer Stöhr3Evgenij Vasilenko1 4Thomas Hümmer5Larissa Kohler1Cyril Popov2and David Hunger1 4

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Scanning cavity microscopy of a single-crystal diamond membrane

Jonathan Körber,1Maximilian Pallmann,1Julia Heupel,2Rainer Stöhr,3Evgenij

Vasilenko,1, 4 Thomas Hümmer,5Larissa Kohler,1Cyril Popov,2and David Hunger1, 4

1Physikalisches Institut, Karlsruhe Institute of Technology (KIT),

Wolfgang-Gaede Str. 1, 76131 Karlsruhe, Germany

2Institute of Nanostructure Technologies and Analytics (INA),

Center for Interdisciplinary Nanostructure Science and Technology (CINSaT),

University of Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany

33rd Institute of Physics, University of Stuttgart, Pfaﬀenwaldring 57, 70569 Stuttgart, Germany

4Institute for Quantum Materials and Technologies (IQMT), Karlsruhe Institute of Technology (KIT),

Herrmann-von-Helmholtz Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

5Faculty of Physics, Ludwig-Maximilians-University (LMU), Schellingstr. 4, 80799 Munich, Germany

(Dated: March 30, 2023)

Eﬃcient optical interfacing of spin-bearing quantum emitters is a crucial ingredient for quantum

networks. A promising route therefore is to incorporate host materials as minimally processed

membranes into open-access microcavities: it enables signiﬁcant emission enhancement and eﬃcient

photon collection, minimizes deteriorating inﬂuence on the quantum emitter, and allows for full

spatial and spectral tunability. Here, we study the properties of a high-ﬁnesse ﬁber Fabry-Pérot

microcavity with integrated single-crystal diamond membranes by scanning cavity microscopy. We

observe spatially resolved the eﬀects of the diamond-air interface on the cavity mode structure: a

strong correlation of the cavity ﬁnesse and mode structure with the diamond thickness and surface

topography, prevalent transverse-mode mixing under diamond-like conditions, and mode-character-

dependent polarization-mode splitting. Our results reveal the inﬂuence of the diamond surface on

the achievable Purcell enhancement, which helps to clarify the route towards optimized spin-photon

interfaces.

INTRODUCTION

Quantum networks built from individual optically ad-

dressable spins in solids interfaced with single photons

[1, 2] promise a variety of emerging applications, rang-

ing from secure communication over large distances to

distributed quantum computing, which could become

the basis of a future quantum internet [3]. A key build-

ing block for this is an eﬃcient interface between the

spin and photons to enable deterministic transfer of

quantum states between stationary and ﬂying qubits

[4–7]. The most powerful approach in this respect is to

couple quantum emitters to optical microcavities and

harness the Purcell eﬀect to enhance the emission [8, 9].

This reshapes the emission pattern into a single, well

collectable mode, increases the emission fraction into

the coherent zero-phonon line (ZPL), and broadens the

transition due to the shortening of the excited state life-

time such that spectral ﬂuctuations can be masked to

improve photon indistinguishability.

Nitrogen-vacancy (NV) centers in diamond are a

prime candidate material system in this respect that

stands out due to its exceptional spin coherence proper-

ties, the availability of a nuclear spin quantum register

[10], and lifetime-limited optical transitions that per-

mit the generation of spin-photon entanglement [11].

Several cavity architectures have been investigated to

demonstrate the basic principle of Purcell enhancement

of NV center emission [12–18]. Due to the high sen-

sitivity of NV centers to ﬂuctuating electric ﬁelds, a

promising approach to achieve narrow optical transi-

tions inside a cavity is based on open-access Fabry-Pérot

micro-cavities with incorporated minimally processed

single-crystal membranes [19–24], see ﬁgure 1a). This

approach has led to ﬁrst successful experiments, both

with NV [21, 24], SiV [25, 26] and GeV centers [27] in di-

amond, as well as with rare earth ions in oxide crystals

[28]. However, to the best of our knowledge, the desired

net improvement of the collection of lifetime-limited NV

center ZPL photons has not been achieved to date. In

earlier work, either the collection eﬃciency was rather

low [24], or the NV emission linewidth was more than

two orders of magnitude above the lifetime limit [21].

This emphasizes the further need to understand limita-

tions and improve the experimental realization of such

systems.

In this work, we perform a systematic study of the

cavity performance in the presence of diamond mem-

branes at room temperature. We use scanning cavity

microscopy [29–31] at a high ﬁnesse of up to 20000

to probe extended areas of a membrane. We observe

a spatial variation of the cavity mode character and

identify spatially localized mode mixing [32, 33], mostly

present in diamond-like regions. We model the observed

losses based on surface scattering, absorption, and mir-

ror transmission, and ﬁnd that we need to assume a

arXiv:2210.05514v2 [physics.optics] 29 Mar 2023

larger surface roughness than measured. Additionally,

we include bulk absorption in our model and ﬁnd good

agreement with the expected absorption for the used

diamond. Furthermore, we observe an increase of the

cavity loss for air-like modes with increasing diamond

thickness. We suggest that the mismatch between the

mode’s curved phase front and the planar diamond-air

interface can be the origin. Finally, we study the po-

larization modes of the cavity and observe an increased

polarization mode splitting with a dependence on the

mode character. This reveals birefringence of the mem-

brane, which we interpret as a signature of the local

strain distribution in the material.

Our results show that mode mixing, wavefront curva-

ture, and polarization mode splitting are important con-

tributions to the performance of cavities with integrated

membranes. We analyze how these eﬀects depend on

geometrical properties of the membrane and the cavity,

providing guidance to achieve optimized spin-photon in-

terfaces.

METHODS AND MATERIALS

Our experiments are performed using a ﬁber-based

Fabry-Pérot cavity which is schematically illustrated in

ﬁgure 1 (a). It consists of a macroscopic plane mirror

and a concave mirror that is processed at the end facet

of an optical ﬁber by CO2-laser machining [34]. We

use two diﬀerent ﬁber tips FA(FB) that show concave

proﬁles with small ellipticity, characterized by radii of

curvatures (ROCs) of 33.1 (55.2) µmalong one half axis

and 30.5 (48.7) µmalong the orthogonal one. The ﬁber

end facets are coated by ion beam sputtering with a

distributed Bragg reﬂector (DBR) (Laseroptik GmbH,

Garbsen, Germany), designed for a center wavelength

at 637 nm. Numerical simulations using a transfer ma-

trix model along with the measured layer thicknesses

of the DBR stacks yield transmissions of 52 (57) ppm

for the ﬁber mirrors at a wavelength of λ= 639.7 nm

that is used for the experiment. The plane mirror

(MA) consists of a superpolished fused silica substrate

(σrms <0.2 nm), coated for a transmission of 57 ppm

(see the Supplementary Material [35] for details on the

cavity mirrors as well as the expected and measured ﬁ-

nesse of the assembled cavities without the presence of

a diamond sample.

We study two CVD-grown single-crystal diamond

samples of general grade (Cornes Technologies, San

Jose, CA, USA) and electronic grade (element 6 ) qual-

ity. While most approaches propose the use of ul-

tra pure, electronic grade diamond samples, also sam-

ples with a higher natural abundance of nitrogen have

(a) (b)

(f) (g)

(d) (e)

(c)

250 μm

Figure 1. (a) Schematic drawing of the cavity setup: A

planar mirror (blue) carrying a diamond membrane can be

moved laterally to select a region of interest. A cavity

is formed together with a ﬁber mirror that can be nano-

positioned along three axes to record raster-scanning images.

(b) Microscope image of a bonded membrane. A thinned-

down part for subsequent characterization lies within the

region framed by the semicircle shadow. (c) AFM mea-

surement of the membrane showing an rms-roughness of

σrms = 0.4 nm. Simulation of the electric ﬁeld inside the

cavity for a diamond-like (d) and an air-like (e) mode. The

refractive index proﬁle (orange dashed line) highlights the

air-diamond (AD) interface. (f ) and (g): Simulated cav-

ity resonance frequency as a function of the mirror separa-

tion for a diamond thickness of 6035 nm (diamond-like) and

6103 nm (air-like), respectively. The probe wavelength of

subsequent measurements λ= 639.7 nm is indicated by a

dashed blue line.

yielded NV centers with very promising optical coher-

ence properties recently [36]. Also, we choose here to

study one of the two samples being non-optimal in order

to clearly identify and quantify limiting factors. Such

factors can still aﬀect optimized samples, but would be

diﬃcult to diﬀerentiate without this comparison. The

main sample of this study (general grade quality) is

structured using an inductively-coupled plasma reactive

ion etching (ICP-RIE) procedure, resulting in a mem-

brane with a minimal thickness of approximately 5µm,

as described in [23]. Characterization on 4×4µm2sub-

regions of the membrane with an atomic force micro-

scope (AFM) - as an example shown in ﬁgure 1 (c) -

reveals a surface roughness of σrms = 0.4−0.5 nm af-

ter the ﬁnal etching steps. We bond the membranes

onto plane mirrors via van der Waals forces. Initial

interference fringes observed under a light microscope,

indicating an air gap between the membrane and the

mirror, broaden during the bonding procedure, and the

ﬁnal result for the general grade sample depicted in ﬁg-

ure 1 (b) shows almost no fringes (see [23] for details on

the bonding procedure).

We use a custom-developed nanopositioning stage to

control the cavity. It can be built cryo-compatible and

achieves very high passive stability and fast scanning

speed [37, 38]. In order to select a position on the a

sample, the plane mirror can be moved laterally, while

the ﬁber can be scanned additionally along all three di-

mensions using piezo-electric actuators to perform the

scanning cavity measurements. To probe the cavity,

we couple light of a tuneable diode laser (TDL) (Top-

tica DL pro 637 ) at a wavelength of λ= 639.7 nm into

the cavity ﬁber and measure the transmission behind

the plane mirror using an avalanche photodiode (APD)

(Thorlabs APD130A2/M ) connected to a 12-bit digital

storage oscilloscope. To obtain spatially resolved maps,

we raster-scan the ﬁber laterally on an area of about

60 ×60 µm2over the sample and modulate the cavity

length at each position over multiple free spectral ranges

(FSR) at a rate of 200 Hz. The maximum transmission

is recorded at each position, leading to a 2D-image that

shows relative changes of the cavity transmission as a

function of the position on the membrane, which we

refer to as a cavity transmission scan. To obtain the

cavity ﬁnesse, we modulate the cavity length at a re-

duced rate of typically 20 Hz and probe two consecutive

fundamental resonances, which we ﬁt with Lorentzian

lines. From this we calculate the ﬁnesse from the ra-

tio of the resonance distance and the average full width

at half maximum (FWHM). Due to piezo nonlinearity

and hysteresis, such measurements have an uncertainty

of ≈10% unless calibrated with care. For these mea-

surements, we align the polarization of the input light

with one of the two cavity polarization modes to probe

an isolated resonance.

The presence of the diamond-air interface leads to a

hybridized mode structure [6, 19, 23, 39]. Depending on

the diamond thickness, the cavity standing wave light

ﬁeld can either fulﬁll the boundary condition for the

air gap part where a ﬁeld node should form at the in-

terface, called an air-like mode, or match for the mode

in the diamond part where a ﬁeld maximum at the in-

terface is present, a so-called diamond-like mode, see

Fig. 1 (d) and (e). Since both conditions cannot be

met simultaneously, hybridized modes form, whose dis-

persion, ﬁnesse and loss strongly depend on the mode

character [19, 39]. For such a hybridized diamond-air

cavity, the mode dispersion, i.e. the frequency depen-

dent shift of the cavity resonances, deviates from the

linear behavior known from a bare Fabry-Pérot cavity

and shows a varying slope for diﬀerent diamond thick-

(a) (b)

Figure 2. (a) Surface topography of the etched diamond

membrane. The blue frame indicates the region where cavity

transmission scans are performed. Black contour lines with

a stepsize of 156 nm are used to highlight the height proﬁle

of the membrane. (b) Cavity transmission map of the blue

framed region in (a).

ness at a ﬁxed wavelength. As shown in a simulation of

cavity resonances in ﬁgure 1 (f), the dispersion exhibits

the smallest slope for a conﬁguration with predominant

diamond-like character, and the steepest slope for a pre-

dominant air-like conﬁguration as in ﬁgure 1 (g). To

maximize the coupling to color centers in the mem-

brane, diamond-like modes are beneﬁcial because they

show a larger electric ﬁeld inside the diamond [39] as it

can be seen by comparing ﬁgures 1 (d) and (e). How-

ever, for this conﬁguration, the scattering loss at the di-

amond surface becomes maximal, requiring a trade-oﬀ

depending on the surface roughness level. Furthermore,

a recent study observed additional loss associated with

diamond-like modes which could not be conclusively ex-

plained by surface scattering [40]. In general, a compre-

hensive investigation of the cavity performance and its

relation to the diamond surface topography would be

desirable, while experiments to date report only punc-

tual measurements of cavity performance on diamond

membranes, mostly under air-like conditions.

RESULTS AND DISCUSSION

Mode-character-dependent cavity loss

We study the spatially varying eﬀect of the diamond

membrane on cavity modes by performing laterally re-

solved cavity transmission measurements as described

above. To increase the imaged area, 16 of such scans

are performed at neighboring positions on the mem-

brane with slight overlaps at the edges and consecu-

tively stitched together.

The ﬁnal transmission scan obtained with ﬁber mir-

ror FAis shown in ﬁgure 2 along with a height map

of the membrane taken with a home-built white-light

interferometric microscope (WLI). Notably, the cavity

transmission in ﬁgure 2 (b) exhibits distinct bright and

dark fringes that match the shape of the height map

in ﬁgure 2 (a), evidencing the correlation between the

cavity transmission and the membrane thickness. Since

the composition of the cavity mode changes with the di-

amond thickness at a periodicity of λ/ (2nd)[39], with

nd= 2.41 the refractive index of diamond, our measure-

ments reveal the relative change of the cavity trans-

mission as a function of the hybridized mode compo-

sition. To compare the thickness change of the dia-

mond membrane obtained from the WLI measurement

to the structure observed in cavity transmission, we es-

timate the region covered by the cavity scans (see Sup-

plementary Material [35]). This region is indicated by

the blue frame in ﬁgure 2 (a). For a horizontal line

at the central y-position of this region, the WLI image

shows a thickness change of ∆WLI

h≈780 nm. Roughly

seven bright fringes along the x-axis in the central y

position of the cavity scan yield a thickness change of

∆cav

h= (7 −1) ·λ/ (2nd)≈800 nm, thus showing good

agreement with the WLI measurement.

To understand how the composition of the hybridized

cavity mode aﬀects the cavity losses in more detail, we

proceed with measuring the cavity ﬁnesse and the mode

composition for points along a horizontal line, covering

several bright and dark fringes in ﬁgure 3 (a). As shown

in ﬁgure 3 (b), the cavity ﬁnesse spans values between

200 and 5500 and follows closely the cavity transmis-

sion measurements. In order to link each measurement

position with the character of the hybridized mode, we

investigate the dispersion of the cavity mode. To this

end, we couple light from a white-light laser (Fianium

Whitelase SC450 ) into the cavity and measure trans-

mission spectra with a spectrometer (Andor Shamrock)

for diﬀerent cavity lengths. The mode character is de-

rived from the slope of the mode dispersion at the wave-

length λ= 639.7 nm of the probe laser used for the ﬁ-

nesse measurements. Here, a steep slope corresponds

to a mode with high air-like character and a ﬂat slope

to a mode with high diamond-like character [19]. We

deﬁne the mode character by assigning a value of 1 for

the steepest slope (air-like, A) and 0 for the lowest slope

(diamond-like, D) with corresponding values in between

(see Supplementary Material [35]).

The results are shown together with a corresponding

measurement of the ﬁnesse in ﬁgure 3 (c). The mode

character follows closely the ﬁnesse and the transmis-

sion of the cavity, proving that the losses of the cavity

are dominated by eﬀects associated with the character

of the hybridized mode. To evidence the strong corre-

lation between the cavity losses and the mode compo-

sition again over a larger region of the membrane, we

scan the ﬁber similar to the lateral transmission mea-

surements across the membrane and measure the ﬁnesse

of the cavity at each position. The resulting ﬁnesse scan

in ﬁgure 3 (d) conﬁrms the correlation between cavity

ﬁnesse and mode composition obtained along the single

line described above.

We repeat the measurement with a second ﬁber mir-

ror FBsince we observed high losses for the ﬁrst ﬁber

mirror already without diamond membrane. Taken at

a slightly diﬀerent position, the measurement shown in

ﬁgure 3 (e) again reﬂects the shape of the membrane.

The ﬁnesse spans values between ∼3000 and slightly

above 20,000, which remains lower than the value ob-

served for the cavity without membrane Fbare

max = 32,400

(see Supplementary Material [35]). To understand the

contribution of diﬀerent sources of loss, we analyze a

line cut through the data shown in ﬁgure 3 (e) and ﬁt it

with a model containing mode-dependent mirror trans-

mission, scattering losses at the diamond-air interface,

and absorption from the diamond [39], see ﬁgure 3 (f).

Therefore, we describe the ﬁnesse F= 2π/Leﬀ with the

eﬀective losses [39]

Leﬀ =E2

max,a

ndE2

max,d

Lf+Lm+Lscat(σrms) + Labs(αd)(1)

Here, Lm(Lf) are the losses due to transmission at the

planar (ﬁber) mirror that we extract by a transfer ma-

trix model using the measured DBR-layer thicknesses

from the manufacturer. The scattering loss [39]

Lscat = sin22πndtd

λ0·(1 + nd)(1 −nd)2

·4πσrms

λ02

(2)

originates from the diamond surface roughness σrms.

Scattering can also occur on the diamond-mirror inter-

face, depending on the termination of the mirror coat-

ing. Here, the mirror is terminated with a layer of high

refractive index, leading to a ﬁeld node at the surface

such that scattering can be omitted. In addition, we

include absorption loss Labs = 2αdtddescribed by the

absorption coeﬃcient αdof the diamond sample. For

the general grade diamond sample, which contains an

increased nitrogen concentration >100 ppb, a broad-

band absorption with αd∼0.1−0.5cm−1is expected

[41].

For all loss contributions, knowledge of the diamond

thickness and the local mode character are important.

Therefore, we evaluate a measurement of the cavity

mode dispersion at one location, i.e., the mode fre-

quency shift as a function of the mirror separation, and

ﬁt a simulation to the measured dispersion to obtain the

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Scanningcavitymicroscopyofasingle-crystaldiamondmembraneJonathanKörber,1MaximilianPallmann,1JuliaHeupel,2RainerStöhr,3EvgenijVasilenko,1,4ThomasHümmer,5LarissaKohler,1CyrilPopov,2andDavidHunger1,41PhysikalischesInstitut,KarlsruheInstituteofTechnology(KIT),Wolfgang-GaedeStr.1,76131Karlsruhe,Germany2I...

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Scanning cavity microscopy of a single-crystal diamond membrane Jonathan Körber1Maximilian Pallmann1Julia Heupel2Rainer Stöhr3Evgenij Vasilenko1 4Thomas Hümmer5Larissa Kohler1Cyril Popov2and David Hunger1 4.pdf

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Scanning cavity microscopy of a single-crystal diamond membrane Jonathan Körber1Maximilian Pallmann1Julia Heupel2Rainer Stöhr3Evgenij Vasilenko1 4Thomas Hümmer5Larissa Kohler1Cyril Popov2and David Hunger1 4

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