Towards Visible Frequency Comb Generation Using a Hollow WGM Resonator

Abstract

Optical frequency combs are widely used for metrology, optical clocks, optical communications and sensors. In whispering gallery mode (WGM) microcavity resonators, geometrical features enable the four-wave mixing phase match condition to be satisfied. Hence, frequency comb generation is achievable. Geometrical dispersion of hollow structure WGM cavities can broaden the comb span to the visible range.

Full text

Towards Visible Frequency Comb Generation using a Hollow WGM Resonator
Sho Kasumie, Yong Yang, Jonathan M. Ward, and S´ıle Nic Chormaic
Light-Matter Interactions Unit, Okinawa Institute of Science and
Technology Graduate University, Onna, Okinawa 904-0495, Japan.
(Dated: February 27, 2018)
Optical frequency combs are widely used for metrology, optical clocks, optical communications
and sensors. In whispering gallery mode (WGM) microcavity resonators, geometrical features enable
the four-wave mixing phase match condition to be satisfied. Hence, frequency comb generation is
achievable. Geometrical dispersion of hollow structure WGM cavities can broaden the comb span
to the visible range.
Keywords: Frequency comb, Four-wave mixing, Microbubble optical resonator
I. Introduction
The ability to confine light in microscopic circular or-
bits by a process of continuous total internal reflection
has pushed optical resonators towards the extremes of
optical quality [1], finesse [2] and mode volume [3]. These
so-called whispering gallery resonators (WGRs) [4, 5] and
their morphological dependent resonances have found ap-
plications from ultralow threshold nonlinear optics [6, 7]
and lasing [8] to bio/chemical sensing [9, 10], telecommu-
nications [11, 12], quantum optics [13] and optomechanics
[14, 15]. Apart from technical applications, these devices
have proven to be a test bed for fundamental physics
such as chaos theory [16] and quantum mechanics [17].
Frequency comb generation is arguably one of the most
important applications of WGRs. Frequency combs gen-
erated by phase-locked pulsed lasers produce equidistant
optical lines (or teeth) that can span from the UV to the
IR [18, 19]. The teeth act as an optical ruler and have
greatly advanced the field of optical metrology [20, 21].
Currently, optical combs require large lasers that con-
sume a lot of power, so significant effort is being made to
develop robust chip scale devices - WGRs are at the fore-
front of this development. In a silica WGR, a four-wave
mixing (FWM) process is employed to produce the fre-
quency comb [22, 23] where the signal and idler photons
are generated by the pump beam both of which are reso-
nant with WGMs of the cavity. This is particularly chal-
lenging because the free spectral range of a WGR is not
constant. In 2007, a pioneering approach for WGR comb
generation was proposed and experimentally confirmed
[23]. It was shown that a strong pump laser can intro-
duce phase modulations which shift resonance modes so
that the total dispersion of the cavity is in the anomalous
regime, thus making the FWM process possible [23].
Today it is possible to have on-chip WGRs, that use
continuous low power pump lasers to produce stable, oc-
tave spanning IR frequency combs [24]. However, ex-
tending these devices into the visible and UV regions is
technically challenging due to limitations in engineering
the dispersion in the resonator. While the material dis-
persion is fixed, geometrical dispersion can be modified
so that the total dispersion meets the required condition.
In such a context, WGRs with a hollow structure and
bottle shape were found to have additional degrees of
freedom in their design, namely the wall thickness and
curvature, which improves their geometrical dispersion
manipulability [25–28]. Here, we will discuss how this
dispersion engineering has been, to date, implemented in
hollow WGRs to create IR and visible combs.
II. Dispersion Management in Microbubble
Resonators
To achieve efficient FWM needed for generating a fre-
quency comb, a phase matching condition is required.
For WGMs, the mode structure is affected by both the
material and the geometric dispersion. In total, the dis-
persion of a WGR can be described as the variation of the
free-spectral-range (∆ωF SR ) and is categorized as normal
(∆ωF SR <0) or anomalous (∆ωF SR >0). The disper-
sion compensated regime is when the FSR is independent
of wavelength (i.e. ∆ωF S R < γ and γis the linewidth of
the cavity mode). In one-dimensional resonators, such as
a Fabry-P´erot cavity, the total dispersion is determined
by the material which usually has normal dispersion. By
introducing confinement, the total dispersion can be flat-
tened yet still remains in the normal dispersion regime
due to the overlap with air [29]. In WGRs, the con-
finement of the optical modes and the geometry of the
resonator can be modified in three-dimensions. Chang-
ing the geometry of the WGR, and therefore the physical
path of the WGMs, one can modify the effective refrac-
tive index of the modes (this is also true for different
mode orders) and this is the origin of the geometric dis-
persion. Therefore, by carefully controlling the size of
the WGR, the material dispersion can be controlled. For
a microsphere whose with a diameter larger than 150
µm, at a wavelength of 1.55 µm, the resonator is in the
anomalous dispersion regime. With introduction of the
Kerr effect, by pumping with an appropriate laser power,
the total dispersion can be compensated and degenerate
FWM can be achieved [29, 30]. For microtoriods, disper-
sion compensation is easier to control by varying the mi-
nor diameter of the toroid [23]. Changing the diameter of
the WGR only results in a slight change in the total dis-
persion. By altering the material [31] or choosing higher

2
order radial and azimuthal modes in the WGR, the dis-
persion can also be slightly managed. This method was
used for achieving mid-IR comb generation in fluoride
WGRs [32].
In order to expand comb generation, the dispersion
should be more freely controlled, i.e. both the zero dis-
persion wavelength (ZDW) and the flatness of the dis-
persion curve need to be managed. According to the
principle mentioned above, a synthetic dimension needs
to be introduced to the 3D WGR. To-date there are three
ways reported: (i) Change the lateral profile of the WGR
and excite 3D confined bottle-like modes. The earliest
experimental demonstration was by Savchenkov et al.,
who observed 790 nm comb generation by exciting the
lateral modes in a CaF2cylinder [33]; (ii) Use a wedged
silica microdisk [34]. Microdisks with multiple wedges
were fabricated, so that the shorter wavelength modes
and longer wavelength modes occupied different space
at the wedges, thus experiencing different effective re-
fractive indices; (iii) Make a hollow structure such as a
microbubble. Microbubbles can be fabricated using sev-
eral techniques [27, 35, 36]. For example, in our earlier
work [37], two counter-propagating CO2laser beams were
used. The main point is to heat a small section of silica
capillary while pressurizing the air inside the capillary.
When the glass becomes soft, the air pressure pushes
out the wall of the capillary to form a bubble shape. In
order to get ultrathin walls and the intended bubble di-
ameter/shape, the capillary is first tapered using a CO2
laser and mechanical pulling stages.
It was first proposed in 2013 [26] that microbubbles
could be used for comb generation. The authors pointed
out that the dispersion can be altered not only by chang-
ing the diameter of the microbubble, but also by varying
the wall thickness or filling the core of the microbubble
with different materials. In this way, the ZDW of the
WGR can be shifted towards the ZDW of silica. They
designed and fabricated a microbubble with diameter of
134 µm and wall thickness of 3-4 µm.
FIG. 1. Degenerate FWM in a dispersion compensated mi-
crobubble resonator. Reproduced with permission from[26].
FIG. 2. Hyperparametric oscillation and IR comb genera-
tion in a microbubble resonator. Reproduced with permission
from [38].
With a pumping power of 3 mW, degenerated FWM
occurred at 1.55 µm, see Fig. 1. In comparison, degen-
erated FWM could not be excited in a microsphere of
the same diameter, which proved their claim. This work
showed that the wall thickness of the microbubble pro-
vides a way to control the dispersion. Later, in 2015,
Farnesi et al. fabricated a silica microbubble with diam-
eter of 475 µm and wall thickness of 3-4 µm [38]. By
increasing the pumping power up to 80 mW, they suc-
ceeded to obtain Type I and Type II frequency combs at
a wavelength of 1.56 µm [38], see Fig. 2. Hyperparamet-
ric oscillation incorporating FWM, a Raman process and
other nonlinear effects provided a much broader band-
width comb than the previous work [26]. These two works
show the capability of silica microbubbles for IR comb
generation. For comb generation in the visible spectrum,
the wall thickness needs to be reduced further so that the
ZDW of the microbubble can be shifted to even shorter
wavelengths, as will be discussed in Section IV.
III. Comb Generation in Bottle-Like
Microresonators
While the modes in conventional WGRs are gener-
ally confined to the equator, bottle-like microresonators
(BLMRs) are unique as the optical modes expand in two
dimensions along the surface and have been termed whis-
pering gallery etalons or bottle resonators (Fig. 3). The
two dimensional distribution of the optical mode also cre-
ates an equally spaced FSR. Consider a BLMR with a
parabolic curvature profile along the z-axis of its cylindri-
cal coordinate. The diameter is R(z) = R0[1 −(ζz)2/2],
where R0is the maximum radius at z= 0 and ζis the
curvature. The eigenfrequency of the bottle modes is

3
FIG. 3. Illustration of a bottle mode. Reproduced with per-
mission from [25].
[25]:
νj,m =c
2nπ sj2
R2
0
+2ζj
R0
(m+1
2) (1)
with jand mrepresenting its longitudinal and axial mode
numbers, cand nrepresent the speed of light in vacuum
and the refractive index in the material, respectively. In a
practical system, with very small curvature, the variation
of the FSR is:
∆νG
F SR ≈c[ζR0(m+ 1/2)]2
2πnR0j3(2)
The material dispersion is ∆ν0
F SR ≈c2λ2/4π2n3R2∗
GV D and GV D =−(λ/c)(∂2n/∂λ2) with λrepresenting
the wavelength.
FIG. 4. Total dispersion of a BLM in terms of the FSR varia-
tion for different working wavelengths. Reproduced with per-
mission from [28]
The dispersion curves for bottle modes and WGMs in
BLMRs of radii 51 µm and 75 µm are plotted in FIG. 4
which shows that the dispersion is always in the anoma-
lous regime around 1.55 µm regardless of the bottle’s
diameter [28]. It can also be seen that, for the bottle
modes, geometric dispersion does not shift the ZDW sig-
nificantly, while the dispersion for the WGM shifts the
ZDW depending on the radius of the BLMR. In a hollow
WGR, the geometric dispersion can be managed by de-
signing the diameter, curvature and wall thickness. The
implication for this is that for a conventional WGM at
1.55 µm it is not possible to create a comb in a resonator
with a diameter below 150 µm due to the normal dis-
persion at small diameters. However, for bottle modes,
anomalous dispersion can be maintained at smaller diam-
eters due to the additional geometric dispersion of these
modes.
To test this hypothesis in experiment, a BLMR with a
diameter of 102 µm and a stem diameter 90 µm was fab-
ricated. The wall thickness was estimated to be 3 −4µm
and did not play any role in this case. Light was coupled
to the BLMR via a tapered fibre that was mounted so
that its position along the z-axis could be finely adjusted.
Of course, not only the third nonlinearity FWM is ex-
cited, Raman scattering can also generate a frequency
comb [38]. To exclude the Raman process, the laser
power was kept above the FWM threshold but below the
Raman lasing threshold. Frequency comb generation by
FWM was confirmed by judicious selection of the fibre
position, i.e. when a WGM was pumped no FWM was
generated; however, when the tapered fiber position was
moved to pump a bottle mode then FWM was observed
(Fig. 5). Thus, it was shown that the dispersion can be
engineered in bottle modes to lift the restrictions imposed
by conventional WGMs. As stated, the wall thickness did
FIG. 5. FWM in a hollow BLMR when the taper is positioned
25 µmm away from the center (dashed line). Reproduced with
permission from [28]
not play a role in this experiment; however, combining
the effect of the parabolic curvature with a thin wall re-
mains to be explored as an additional means of dispersion
tuning.

4
IV. Visible Comb Generation in Microbubble
Resonators
To-date, most visible comb generation in WGRs is
done indirectly. An IR comb is first generated through
FWM and then is mapped to the visible range through
second [39] and third harmonic generation [40]. This was
demonstrated in a Si3N4microring by exploiting the high
nonlinearity of the material. The low efficiency of the
higher order harmonic generation process results in lower
quality combs, compared to direct IR Kerr combs. Thus,
combs generated directly by visible frequency FWM is
still being studied. As discussed in the introduction, and
the previous section, direct Kerr frequency comb genera-
tion in the visible range from silica microspheres, toroids
or disks is almost impossible due to the material disper-
sion limit. Better dispersion engineering is required to
go beyond this limitation.
A route to visible combs in hollow microcavities was
recently detailed theoretically [41] for a spherical bub-
ble WGR. The inner diameter, wall thickness and outer
diameter are ρ0,tand ρ1=ρ0+t, respetively. For a
general case, the inner medium, the bubble wall and sur-
rounding medium can all have different refractive indices,
n1,n2and n3, respectively. Then the eigenfrequency is
determined by the characteristic equation:
np
3
χ0
l(z31)
χl(z31)=np
2
Nlψ0
l(z21) + χ0
l(z21)
Nlψl(z21) + χl(z21 )(3)
where zij =kniρj,kis the complex wavenumber and
lis the azimuthal mode number. For simplicity, kis
real k= 2π/λ and only the first order radial mode is
considered. p=±1 is the polarization coefficient where
p= 1 for TE modes and p=−1 for TM modes and the
coefficient Nlis:
Nl=np
1ψ0
l(z10)χl(z20 )−np
2ψl(z10)χ0
l(z20)
np
1ψl(z10)ψ0
l(z20)−np
2ψ0
l(z10)ψl(z20 )(4)
Also, ψl(z) = zJl(z) and χl(z) = zYl(z), where Jland
Ylare the spherical Bessel functions of first and second
kind. The characteristic equation can be used to identify
eigen frequencies. The geometric dispersion is the differ-
ence in resonance frequencies where νl=ckl/2πn2
and ∆νl=νl+1 −νl. On the other hand material disper-
sion is related to the Sellmeier equations [42]:
n2−1 = B1λ2
λ2−C2
1
+B2λ2
λ2−C2
2
+B3λ2
λ2−C2
3
(5)
where nis the refractive index of the material. The
constants are determined by experiments and, for sil-
ica, B1= 0.6961663, B2= 0.4079426, B3= 0.8974794,
C1= 0.0684043, C2= 0.1162414 and C3= 9.896161 [42].
The total dispersion is obtained by summing the geomet-
ric and material dispersion (Fig. 6).The plot shows how
the ZDW can be pushed into the visible range by using
thinner wall and larger bubble diameters. Theoretical
FIG. 6. Dispersion for TM modes in MBR. Reproduced with
permission from [41].
calculations for materials other than silica are available
in [43].
Recently, experimental work confirmed these theoret-
ical predictions by demonstrating, for the first time, a
direct Kerr comb in the visible range [44]. 14 comb
lines were observed around a pump wavelength of 765
nm (Fig.7). The result suggests that comb lines could be
pushed further into the visible range by simply decreasing
the wall thickness and increasing the pump power. The
table summarizes the current state-of-the-art for comb
generation in hollow microresonators.
FIG. 7. Frequency comb generation in a MBR at a center
wavelength of 765 nm. Up to 14 comb lines are excited. Re-
produced with permission from [44].
V. Conclusion
In this brief review, we have discussed recent progress
in the generation of optical frequency combs using
WGMs. The geometrical properties of these devices
enables the required FWM phase matching condition
to be satisfied, leading to frequency comb generation.
To-date, the geometrical dispersion of hollow structure
WGRs has been studied in order to broaden the comb

5
Team Lei Soria Nic Chormaic
Diameter (µm) 136 475 120
Wall Thickness (µm) 3 −4 3 −4<1.5
Pump Wavelength (nm)∼1545 1552.4∼765
Laser Pow (mW ) 3 −4∼80 ∼6
Q factor 5 ×107− −
# of comb lines 5 many 14
TABLE I. The current state-of-the-art of frequency comb gen-
eration in MBRs.
span to the visible range. Visible combs from microres-
onators could have applications in ground, and satellite
based, astrophysical and LIDAR measurements as well
as miniaturisation of rubidium and cesium atomic clocks.
Further work on this topic is ongoing worldwide, in
order to increase the functionality of WGRs in frequency
comb applications.
Acknowledgments
This work was supported by Okinawa Institute of Sci-
ence and Technology Graduate University.
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