This document summarizes an experiment to efficiently couple light between a tapered optical fiber and a diamond nanobeam waveguide. The goals were to fabricate a diamond nanostructure capable of guiding visible and infrared light, taper an optical fiber for single-mode propagation, and characterize the power transfer between the waveguides using coupled mode theory. Simulations showed transmission varying with waveguide separation and wavelength due to changing coupling strength. Experiments demonstrated coupling dependence on separation and wavelength, but did not achieve phase matching due to equipment limitations.

1. Efficient broadband optical coupling between tapered optical fibre and
diamond nanobeam waveguide
Jakub Jadwiszczak
IQST/NINT Nanophotonics Lab, University of Calgary, Canada
Objectives
The goals of this project were to:
• Manufacture a diamond nanostructure with a
geometry capable of supporting guided modes
of a visible and infra-red laser beam.
• Taper an optical fibre to appropriate
single-mode propagation conditions, and
dimple it to allow access to nano-sized
features of the diamond structure.
• Employ coupled mode theory in simulations
and experiment to describe power transfer
between the two waveguides.
• Realise phase-matched coupling between the
nanobeam and fibre modes, and characterise
this as a function of wavelength and
waveguide separation.
Introduction and Theory
The motivation behind this project stems from
work done in the Barclay group on the optome-
chanical properties of diamond [1] and those of
nitrogen-vacancy (N-V) centres [2].
Figure 1: Nanobeam manufactured in diamond through reac-
tive ion etching.
Coupled mode theory is a restatement of Maxwell’s
equations and treats a compound waveguide struc-
ture as a sum of simpler waveguides [3], in this case
the optical fibre taper and the diamond nanobeam.
When the waveguides interact as light passes
through the fibre, it can be shown that the trans-
mission changes with their relative position, and is
given by:
T(h) = cos2
(sL) +


∆β
2


2
sin2
(sL)
s2
(1)
where s2
= κ2
+
∆β2
4
and ∆β is a function of L,
the waveguide interaction length.
The eigenmodes of the coupled system are referred
to as supermodes, possessing a propagation de-
pendence e−iβ±z
, with:
β± =
βf + βn
2
±


βf − βn
2


2
+ κ2 (2)
where κ(h) is the height-dependent coupling coef-
ficient. [1]
Figure 2: Effective index dispersion for the waveguide modes.
Supermodes derived from (2) are shown by the solid curves.
Experimental Methods
The diamond waveguides were fabricated using
inductively-coupled plasma reactive ion etching
(ICPRIE), as seen in Fig. 1. The optical fibre
was tapered by symmetrical pulling over a torch
flame. The signal through the fibre was monitored
until a condition of single-mode propagation was
reached.
Figure 3: Top left: pull spectrogram exhibiting characteris-
tic beats. Top right: evanescent light scatters off ceramic
blade used for dimpling. Bottom left: fibre situated on the
nanobeam. Bottom right: example of mode simulation.
The taper was dimpled and mounted on a piezo-
electric stage to bring it close to the nanobeam.
Laser beam transmission through the fibre was
monitored as the waveguide system was manipu-
lated.
Results
Figure 4: Idealised transmission through the fibre as a func-
tion of height (left) and wavelength (right). Minima in curves
correspond to phase-matching.
The simulated behaviour seen in Fig. 4 was partly
reproduced in physical experiments, with clear de-
pendence of mode coupling strength on waveguide
separation. The phase-matching condition was not
reached, however, due to laser failure.
Figure 5: Transmission change as the beam moves towards
the mounted fibre taper (two sets of data). Note the lack of
a minimum as phase-matching is not reached.
Conclusion
• Visible fibre mounting proved too difficult to
test coupling in the range desired for N-V centre
emission.
• Geometry-dependent coupling was
demonstrated between the two waveguides at IR
wavelengths, and characterised as a function of
λ and separation.
• Efficiency of coupling increased from 20% to
57% and finally 68% as phase-matching was
approached.
References
[1] B. Khanaliloo, H. Jayakumar, et al.,
arXiv:1502.01788.
[2] P. Barclay, et al., Phys. Rev. X, vol. 1, p. 011007,
2011.
[3] E. Peral, A. Yariv, Lightwave Technology, Journal
of, vol. 17, p. 942-947, 1999.