# Versatile tuning of Kerr soliton microcombs in crystalline microresonators

Shun Fujii<EMAIL_ADDRESS>Department of Physics, Faculty of
Science and Technology, Keio University, Yokohama, 223-8522, Japan  Quantum
Optoelectronics Research Team, RIKEN Center for Advanced Photonics, Saitama
351-0198, Japan  Department of Electronics and Electrical Engineering, Faculty
of Science and Technology, Keio University, Yokohama, 223-8522, Japan  Koshiro
Wada  Department of Electronics and Electrical Engineering, Faculty of Science
and Technology, Keio University, Yokohama, 223-8522, Japan  Ryo Sugano
Department of Electronics and Electrical Engineering, Faculty of Science and
Technology, Keio University, Yokohama, 223-8522, Japan  Hajime Kumazaki
Department of Electronics and Electrical Engineering, Faculty of Science and
Technology, Keio University, Yokohama, 223-8522, Japan  Soma Kogure
Department of Electronics and Electrical Engineering, Faculty of Science and
Technology, Keio University, Yokohama, 223-8522, Japan  Yuichiro K. Kato
Quantum Optoelectronics Research Team, RIKEN Center for Advanced Photonics,
Saitama 351-0198, Japan  Nanoscale Quantum Photonics Laboratory, RIKEN Cluster
for Pioneering Research, Saitama 351-0198, Japan  Takasumi Tanabe
<EMAIL_ADDRESS>Department of Electronics and Electrical Engineering,
Faculty of Science and Technology, Keio University, Yokohama, 223-8522, Japan

###### Abstract

Microresonator-based optical frequency combs emitted from high-quality-factor
microresonators, also known as microcombs, have opened up new horizons to
areas of optical frequency comb technology including frequency metrology,
precision sensing, and optical communication. To extend the capability of
microcombs for such applications, large and reliable tunability is of critical
importance. Here, we show broad spectral tuning of Kerr soliton microcombs in
a thermally controlled crystalline microresonator with pump-detuning
stabilization. The fundamental elements composing frequency combs, namely the
center frequency, repetition frequency, and carrier-envelope offset frequency,
are spectrally tuned by up to $-48.8$ GHz, $-5.85$ MHz, and $-386$ MHz,
respectively, leveraging thermal effects in ultrahigh-Q crystalline magnesium
fluoride resonators. We further demonstrate a 3.4-fold enhancement of soliton
comb power resulting from thermal expansion with a temperature change of only
28 K by employing quantitative analyses of the fiber-to-resonator coupling
efficiency.

## Introduction

High-repetition rate microresonator-based frequency combs offer powerful and
compact optical frequency comb (OFC) sources that are of great importance to
various applications including a phase-coherent link for the optical to
microwave domain [1, 2], optical communication [3, 4], spectroscopy [5, 6],
and low-noise photonic microwave generation [7, 8, 9, 10]. In particular, the
soliton mode-locked states of microresonator frequency combs provide high
coherence and smooth spectral profiles [11], thereby making them highly
desirable for most applications [1, 3, 5, 7, 12, 13, 6, 2, 4, 8, 9]. One
significant difference between the microcombs and conventional OFC sources is
their resonator configuration [14, 15]. Most mode-locked lasers are based on
composite systems with a gain medium, bulky free-space optics, active and
passive optical fibers [15]; moreover, laser-cavity actuators such as
temperature control systems, piezoelectric transducer devices, or high
bandwidth modulators can be easily combined to fully exploit the performance
of lasers [16]. As a result, oscillation frequencies and repetition rates are
controlled by using such actuator elements or by regulating the cavity length
by moving end mirrors or cutting/fusion-splicing optical fibers. In contrast,
optical microresonators are usually made of a single dielectric material so
that their waveguides can strongly confine light in a tiny mode space [17]. In
return, this ultimately elemental configuration makes it a challenge to freely
tune the OFC properties.

Mechanical [18, 19] and electrical tuning [20, 21] can allow for dynamically
control and stabilize the microcombs, and they can readily act as fast
actuators for the comb frequencies in return for the limited spectral tuning
bandwidth. Similarly, resonance control via thermal effects has also been
implemented with an auxiliary laser coupled to a different resonance mode [22,
23], pump power control using an intensity modulator [24, 8, 2], or a Peltier
element installed in a cavity-packaged module [25]. Although these techniques
are suitable for narrow range of resonance tuning and compensation for
environmental perturbation, i.e., soliton initiation [24, 23] or long-term
stabilization [8, 25, 2], these studies have paid little attention to the
capability of the spectral tuning bandwidth. In this regard, temperature
control of the entire resonator system using integrated microheaters has been
adopted as the most effective and useful method of frequency tuning and
resonance control for on-chip resonators operating mainly with a comb mode
spacing exceeding 200 GHz [26, 27, 28, 29, 30, 31]. Despite the rapid progress
made on larger mode spacing combs, broadband tunability and flexibility of
soliton microcomb sources with a repetition rate in the microwave X- and
K-bands (8-27 GHz) have not been demonstrated. These frequency bands are
important because they constitute the mainstream method for ultralow-noise
photonic microwave generation with a direct optical-to-electric conversion
process, and the microwave synthesis of the lowest-level phase noise signals
has been achieved in millimeter-scale whispering-gallery-mode (WGM)
microresonators [2, 9, 7, 10]. Thus, widely tunable microcombs yielding the
microwaves at these bands require a better understanding of the dynamics of
soliton combs generated in WGM microresonators under thermal activation over a
wide dynamic range.

Here, we demonstrate and extend the spectral flexibility of a soliton
microcomb with a 23 GHz repetition rate by exploiting temperature control and
a detuning stabilization system. The center frequency, repetition frequency,
and offset frequency of a soliton comb with a radio-frequency (rf) repetition
rate are simultaneously tuned by thermal effects and stabilized by a feedback
loop. We further show that the output power of a soliton comb is distinctly
enhanced via thermally-induced coupling variation owing to the thermal
expansion of a resonator coupled to a tapered fiber that ensures coupling
flexibility. A qualitative analysis allows us to explain this interesting
result. Moreover, we address the complex dynamics underlying soliton tuning
arising from birefringence of crystalline magnesium fluoride
($\mathrm{MgF_{2}}$) resonators that gives rise to the difference in the
thermal sensitivity of optical resonances belonging to different polarization
modes. This feature leads to polarization-dependent tunability and has a
unique effect on the soliton self-frequency shift (SSFS) via mode-coupling-
induced dispersive wave (DW) emission.

## Results and Discussion

### System overview

The frequency tuning of cavity resonances in optical microresonators can be
driven by two thermal effects, namely the thermo-optic and thermal expansion
effects. The former originates from the change in refractive index and the
latter corresponds to the volume change of the material in response to
temperature variation, thus altering the optical length of the resonator. In
general, both effects alter the resonance frequencies following a simple
relation, $df/dT=-(\alpha_{n}+\alpha_{l})f$, where $\alpha_{n}=(1/n)(dn/dT)$
and $\alpha_{l}=(1/l)(dl/dT)$ are the thermo-refractive and thermal expansion
coefficients, respectively. The thermal coefficients in most resonator
materials including crystalline $\mathrm{MgF_{2}}$ are positive, whereas some
of the fluoride crystals (e.g., calcium fluoride, barium fluoride) or
polydimethylsiloxane (PDMS) possess negative thermo-refractive coefficients.
Although recent studies have demonstrated a potential advantage of the
negative thermo-optic effect for microcomb generation [32, 33], it often
results in resonance instability induced by thermo-optical oscillations [34].
As a result, a crystalline $\mathrm{MgF_{2}}$ resonator is widely used to
obtain a stable soliton state in thermal equilibrium [11, 7, 6, 2, 4].

For uniaxial crystals such as $\mathrm{MgF_{2}}$, optical anisotropy should be
considered [35, 36]. The use of a resonator made from $z$-cut
$\mathrm{MgF_{2}}$ crystal results in slightly different refractive indices
for the transverse-electric (TE) mode (extra-ordinary polarized,
$n_{e}=1.382$) and the transverse-magnetic (TM) mode (ordinary polarized,
$n_{o}=1.371$), and similarly the thermal coefficients exhibit anisotropy. In
this work, we adopted the following values: $\alpha_{n,e}=0.23\times
10^{-6}~{}\mathrm{K^{-1}}$, $\alpha_{n,o}=0.64\times
10^{-6}~{}\mathrm{K^{-1}}$, and $\alpha_{l}=8.9\times
10^{-6}~{}\mathrm{K^{-1}}$ at room temperature [35]. We also note that the
thermal expansion can mainly be attributed to the ordinary direction
$\alpha_{l,o}$, which corresponds to the expansion of the radial direction of
the resonator [37]. Strictly speaking, thermal expansion coefficients are
given as a function of temperature, but the impact is considered negligibly
small in this study.

Figures 1(a) and 1(b) show the experimental setup and concept of thermal
resonance tuning in an $\mathrm{MgF_{2}}$ microresonator. While the tuning
efficiency of resonance frequencies is independent of the resonator diameter,
that of the mode-spacing, i.e., the free-spectral range (FSR), depends on the
native mode spacing: $df_{\mathrm{FSR}}/dT=-c(\alpha_{n}+\alpha_{l})/(2\pi
n_{g}R)$, where $c$ is the speed of light in a vacuum, $n_{g}$ is the group
index, and $R$ is the effective radius of a resonator. Thus, the tuning
efficiency of the FSR corresponds $-213.2$ kHz/K for the TE mode and $-222.8$
kHz/K for the TM mode for the 23.35 GHz-FSR resonator that we used for soliton
generation as described in the following section. The tuning efficiency of the
resonant frequencies corresponds to $-1.765$ GHz/K for the TE mode and
$-1.845$ GHz/K for the TM mode in the 1550 nm band. Figure 1(c) and 1(d) show
the transmission spectra and resonance shifts with the resonator temperature
increasing from 300 K ($\Delta T=$ 0 K) to 325 K ($\Delta T=$ 25 K),
respectively. The fitted slopes yield an average efficiency of $-1.77$ GHz/K,
which indicates that these modes belong to the TE mode families. We also
clearly observe the polarization dependence of the resonance tuning efficiency
as shown in Figs. 1(e) and 1(f). By offsetting the frequency shift of one of
the TE modes, we can recognize the mode families exhibiting different tuning
efficiencies as the TM modes, and the difference is $\Delta
f_{\mathrm{TM}-\mathrm{TE}}\approx 80$ MHz/K. It is sometimes difficult to
assign the polarization for WGM resonators; however, a simple measurement of
the amount of thermal shift readily distinguishes between the polarizations in
$\mathrm{MgF_{2}}$ resonators. Interestingly, a few measured resonances show
intermediate efficiency between the TE and TM modes due to the degeneracy of
the effective indices, which forms a hybridized mode between orthogonal
polarization modes [38].

Figure 1:  Resonant frequency tuning efficiency for orthogonally polarized
modes in a crystalline $\mathrm{MgF_{2}}$ microresonator. (a) Schematic
experimental setup. Transmission spectra are recorded using a photodetector
(PD) and an oscilloscope (OSC). The polarization of a continuous-wave (CW)
laser is controlled by using a fiber polarization controller (FPC). The
frequency axis of the transmission spectrum is calibrated with the reference
signal of a Mach-Zehnder interferometer (MZI). AWG: Arbitrary waveform
generator, TEC: Thermoelectric cooler. (b) Orthogonally polarized modes
exhibit a different tuning efficiency with a temperature increase. Mode
families belonging to the transverse-magnetic (TM) modes show greater
efficiency than transverse-electric (TE) modes due to the difference in the
thermo-optic coefficient. (c) Transmission spectra at $\Delta T=$0 K (blue)
and $\Delta T=$25 K (red). (d) Extracted resonance shifts for 10 different
modes in TE-polarization, which yields an average efficiency of $-1.77$ GHz/K.
(e) The relative frequency shifts of TM mode families to the TE mode when the
temperature is increasing by 5.0 K. (f) Extracted relative resonance shifts to
one of the TE modes.

### Versatile tuning of soliton microcombs

We perform the spectral tuning of a soliton microcomb using a temperature-
controlled $\mathrm{MgF_{2}}$ microresonator with an FSR of 23.35 GHz. A
thermoelectric cooler (TEC) element is used to control the resonator
temperature with 0.01 K accuracy with the appropriate feedback control, which
enables active thermal tuning. First, we generate a soliton comb at 25 ∘C
($\Delta T=0$ K) and measure the soliton beat note, which directly yields the
soliton repetition rate. Here, the pump detuning is flexibly controlled by
applying a modulation frequency to a phase modulator. We obtain temperature-
dependent optical and electrical spectra as shown in Fig. 2, while pump
detuning dependence is presented in Fig. 3 (see Methods and Supplementary Note
1 for the details of our experimental setup). The pump detuning is an
essential parameter for determining both the fundamental properties of a
soliton comb such as the soliton pulse width and the soliton noise limit,
which involves the soliton spectral recoil induced by DWs and the Raman effect
[39, 40, 9].

Figure 2(a) shows the measured optical spectra of single-soliton states when
the temperature is increased up to 53 ∘C with a fixed detuning of 10.5 MHz.
The frequencies of each comb line are defined by the well-known relation,
$f_{m}=f_{\mathrm{ceo}}+m\times f_{\mathrm{rep}}$, where $f_{m}$ is the
frequency of each comb mode and the index $m$ is an integer. Since the
repetition rate $f_{\mathrm{rep}}$ is directly obtained as the beat frequency
as shown in Figs. 2(b) and 2(c), it is easily possible to extract the carrier-
envelope offset frequency $f_{\mathrm{ceo}}$ by subtracting the pump frequency
from an integer multiple of $f_{\mathrm{rep}}$ ($m=6365$). Figures 2(d)-2(f)
show the variation in the pump (center) frequency $f_{p}$, $f_{\mathrm{rep}}$,
and $f_{\mathrm{ceo}}$, where the fitting slope (solid line) yields the tuning
efficiency, $-1.74$ GHz/K, $-208$ kHz/K, and $-14.1$ MHz/K, respectively. The
total tuning ranges of $f_{p}$, $f_{\mathrm{rep}}$, and $f_{\mathrm{ceo}}$
reach $-48.8$ GHz, $-5.85$ MHz, and $-386$ MHz, respectively, with 28 K
temperature change. The measured tuning efficiencies agree well with the
theoretical predictions discussed in the previous section, and the results
confirm that the pump mode belongs to the TE modes. It should also be noted
that the total tuning range of the pump frequency exceeds 2-FSRs owing to the
narrow mode spacing of our millimeter-scale resonator. This feature makes it
possible to search for a desired resonance mode by using a thermal heating
method instead of broadband laser frequency control, whose tuning range
depends on the performance of the pump laser and may be insufficient to access
all resonance modes within 1-FSR.

Figure 2:  Active thermal tuning of a soliton frequency comb. (a) A sequence
of optical spectra of a single soliton state as a function of temperature with
a fixed detuning of 10.5 MHz. The fitted envelope (blue line) indicates that
the spectral center is shifted to the pump frequency (soliton recoil). (b, c)
Radio-frequency beat-note spectrum yielding a soliton repetition frequency at
311.8 K ($\Delta T=$13.7 K) and temperature-dependent beat signals (d-f)
Results of soliton tuning for the pump frequency, repetition frequency, and
extracted carrier-envelope offset frequency, which yield the efficiency of
each comb property. The solid red lines correspond to the results of linear
regression. (g) Dependence of the soliton recoil frequency on temperature
change. (h) Measured average soliton power (blue dots) and calculated coupling
efficiency $\eta$ (green symbols) versus temperature change.

To investigate the effect of thermal tuning on soliton properties in detail,
we then plot the recoil frequency and average soliton power as a function of
temperature (Fig. 2(g) and 2(h)). We draw attention to the fact that
temperature change leads to a variation in the soliton recoil frequencies even
with the same detuning values (Fig. 2(g) and Fig. 3(b)). Since the Raman
effect can be neglected in $\mathrm{MgF_{2}}$ crystals because of the very
narrow gain bandwidth, DW emission, which results from higher-order dispersion
and mode couplings, must critically affect the degree of soliton recoil [9,
40, 31]. Even though the spectral positions of the DWs are inherent features
in a single microresonator with fixed detuning, we find that the intensity and
positions of strong peaks vary irregularly with temperature, and this
indicates that changes in resonator temperature have a strong influence on
resonator mode structure, i.e., thermally-induced resonance shift.
Specifically, birefringent properties, which affect the tuning efficiency for
orthogonal polarization, induce considerable mode hybridization rather than
linear frequency shifts of all the resonant modes via strong cross-
polarization mode coupling [38]. The design and prediction of the spectral
position of the DWs are still challenges [41]; nevertheless, we believe that
thermal activation could be utilized for the active tuning of the DWs in a WGM
resonator supporting many different transverse modes.

More surprisingly, the soliton power is significantly increased with the
temperature change even though a tapered fiber is in contact with the
resonator and the position is not adjusted during the series of measurements.
This result is not intuitively anticipated because the changes in the pump
frequency and repetition frequency have little impact on the average soliton
power given by $P_{\mathrm{sol}}=\frac{2\eta
A_{\mathrm{eff}}}{n_{2}Q}\sqrt{-2nc\beta_{2}\delta\omega}$ [42, 40, 4], where
$\eta$ is the coupling efficiency, $A_{\mathrm{eff}}$ is the effective mode
area, $n$ is the refractive index, $n_{2}$ is the nonlinear index, and $Q$ is
the total decay rate. Although the pump detuning
$\delta\omega=(\omega_{0}-\omega_{p})$ and resonator group-velocity dispersion
$\beta_{2}$ contribute to the soliton power, we can decouple them because the
measured pulse widths $\tau=\sqrt{-{c\beta_{2}}/{2n\delta\omega}}$ are almost
constant ($\tau\approx 178$ fs) under a fixed detuning of 10.5 MHz, which is
direct evidence that the overall dispersion is unchanged. In fact, the pulse
widths follow the theoretical prediction even for different temperatures at
the same detuning value (Fig. 3(c)). When we neglect the changes in the mode
area, refractive index and nonlinear refractive index for a temperature
increase of 28 K, another possibility is that the significant change in the
soliton power is caused by the variation in the coupling rate
$\eta/Q~{}(={n_{2}P_{\mathrm{sol}}}/{2A_{\mathrm{eff}}\sqrt{-2nc\beta_{2}\delta\omega}})$.
The green symbol in Fig. 2(h) represents the extracted coupling efficiency
$\eta=\kappa_{\mathrm{ext}}/(\kappa_{\mathrm{int}}+\kappa_{\mathrm{ext}}$) as
a function of temperature change at a constant intrinsic cavity decay rate
($\kappa_{\mathrm{int}}/2\pi=0.43$ MHz). This result indicates that the
coupling strength, namely $\kappa_{\mathrm{ext}}/2\pi$, is eventually
increased 3.4 times (0.38 MHz to 1.3 MHz) by heating the resonator despite the
fact that neither the position nor the diameter of the fiber, which could
alter the coupling strength, is adjusted during the measurement. It should be
noted that the accessible soliton step varies due to the change in the fiber-
to-resonator coupling condition as the cavity temperature increases. We
emphasize that the coupling strength is known to be determined by the mode
overlap integral and phase mismatch between a resonant mode and a fiber mode.
In this respect, we theoretically detail the mechanism of the thermally-
induced coupling variation.

Figure 3:  Observed soliton properties with different effective detuning and
temperature. (a) Optical spectra of a single soliton state with different
detuning at 34 ∘C ($\Delta T=9.0$ K). The effective detuning is scanned from 8
MHz (blue) to 20.5 MHz (red) in 2.5 MHz steps. (b,c) Measured recoil frequency
and soliton pulse width derived from a $\mathrm{sech^{2}}$-fit versus the
effective detuning. The positive (negative) value of the recoil frequency
corresponds to the blue (red) shift with regard to the pump frequency. A
dashed black line for the pulse width represents a theoretical curve.

### Analysis of dynamic change in coupling strength

In light of the experimental results, we numerically analyze the effect of the
thermal activation on the coupling strength between a WGM resonator and a
silica tapered fiber coupler (The calculations are detailed in Methods and
Supplementary Note 2-4). Figure 4(a) shows a schematic model of our simulation
for the coupling strength in a millimeter-scale $\mathrm{MgF_{2}}$ resonator.
On the assumption of a weak coupling approximation (i.e., the coupling
coefficient is sufficiently small compared with the propagation constant), the
coupling coefficient can be expressed as [43],

$\begin{split}\tilde{\kappa}=&\frac{\omega\epsilon_{0}}{4}(n_{\mathrm{r}}^{2}-n_{0}^{2})N_{f}N_{r}\\\
&\times\iiint\left(\bm{E}_{\mathrm{f}}\cdot\bm{E}_{\mathrm{r}}^{*}\right)e^{i\Delta\beta
z}dxdydz\end{split}$ (1)

where $\bm{E}_{\mathrm{f(r)}}$ corresponds to the complex electric field
amplitudes of the fiber (resonator), $N_{\mathrm{f(r)}}$ is the normalization
constant for the fiber (resonator), and $n_{\mathrm{r}}$ and $n_{0}$ are the
refractive indices of the resonator and air. The difference between the
propagation constants $\Delta\beta=\beta_{\mathrm{f}}-\beta_{\mathrm{r}}$
contributes to the phase mismatch between the fiber and resonator modes. The
integration is performed over a volume of the resonator in a three-dimensional
Cartesian coordinate system, where the $z$-axis represents the length
direction of a tapered fiber. The coupling strength is then obtained from the
relation $\kappa_{\mathrm{ext}}\approx|\tilde{\kappa}|^{2}(c/2\pi
n_{\mathrm{r}}R)$, which accordingly corresponds to $\omega/Q_{\mathrm{ext}}$.
Importantly, Eq. (1) indicates that both the overlap integral between the
fiber and resonator modes and the phase-matching condition are central to the
coupling strength. As a hypothesis, the thermal expansion effect can modify
the coupling strength as a result of the variation in the mode overlap, which
is determined by the degree of contact between the fiber and resonator, and
the thermo-optic effect changes the effective refractive indices, thus
altering the phase-matching condition.

To investigate the dynamics of coupling variation, we first begin with
numerical simulation of the coupling strength with respect to fiber diameter
for different transverse modes when the fiber and resonator are placed in
contact at one point. Figures 4(b) and 4(c) present the mode field
distribution for featured five transverse modes and the calculation results.
As mentioned earlier, $\mathrm{MgF_{2}}$ resonators exhibit different
refractive indices for orthogonal polarized modes, and therefore the fiber
diameter which minimizes the phase mismatch also differs for the TE and TM
mode families. In addition, higher-order polar and radial modes exhibit
different coupling strengths due to the difference of the propagation constant
and mode profiles. The two modes (2nd and 4th) of the five WG modes are not
shown in Fig. 4(c) because the coupling strengths are several orders of
magnitude smaller, and coupling does not occur. This is because the fiber is
positioned at $y=0$ in this simulation, thus significantly reducing the mode
overlap. The coupling strength for varying the fiber position, defined as
polar angle $\varphi$, is presented in Fig. 4(d), where the fiber position is
moved along a resonator curvature. This result confirms that higher-order WG
modes can also be efficiently excited by changing the contact position of the
fiber. Indeed, the coupling strength can be controlled by carefully adjusting
the contact position, fiber thickness, and effective coupling length, namely
the degree of contact with a resonator, in practical experiments.

Figure 4:  Analysis of the coupling strength in a crystalline
$\mathrm{MgF_{2}}$ microresonator coupled to a silica tapered fiber. (a)
Schematics of the fiber-resonator coupling model in $x$-$y$-$z$ coordinates,
where $R$ and $r$ correspond to a resonator radius and curvature,
respectively. The fiber position along the curvature is given by the polar
angle $\varphi$. (b) Mode profiles of several whispering-gallery (WG) modes.
The fundamental mode is designated as 1st and the higher-order modes are named
sequentially. The color bar shows the electric field intensity. (c) Simulated
coupling strength versus fiber radius for three WG modes. The fiber radius
showing the maximum coupling strength modes is shifted literally due to the
difference between refractive indices of the transverse-electric (TE) and
transverse-magnetic (TM) modes. (d) Coupling strength as a function of fiber
position $\varphi$ for the TE modes. (e) Contour map of coupling strength
showing the dependence on fiber radius and effective coupling length $\Delta
l$ for the TE 1st mode. The color bar shows the coupling strength
$\kappa_{\mathrm{ext}}/2\pi$ in units of MHz. (f, g) Coupling strength as a
function of temperature for the 1st, 3rd, and 5th TE modes at different fiber
radii, (f) for $r_{\mathrm{taper}}=$1 µm and (g) for $r_{\mathrm{taper}}=$1.65
µm. The temperature-dependent refractive index change modifies the phase-
matching condition, resulting in increased or reduced coupling strength.

To consider the effect of the effective coupling length $\Delta l$ instead of
single point coupling at $z=0$, we modified Eq. (1) by including an additional
coupling term $\tilde{\kappa}_{\Delta l}$ supposing that the mode overlap is
maximized at $z=0$ and remains constant in the finite coupling regime $\Delta
l$. Then, the additional coupling term is given by $\tilde{\kappa}_{\Delta
l}=\tilde{\kappa}_{z=0}\sin({\Delta\beta\Delta l/2})/(\Delta\beta/2)$ [44].
Such an approach is referred to as a pulley-style configuration and widely
employed with integrated resonators to precisely engineer the coupling
strength [44, 45, 46]. The significant difference is that the tapered fiber
used in our system provides a considerable degree of coupling flexibility in
contrast to integrated resonators with a fixed waveguide as mentioned earlier.
The dependence of the coupling strength on effective coupling length and fiber
diameter is shown in Fig. 4(e) as a contour map. The coupling strength
exhibits a periodic dependence on the effective coupling length, which
originates from a relative phase shift between the fiber and resonator modes
as seen in a directional coupler [47]. When the fiber diameter is 3.3 µm
(typical diameter of a tapered fiber is 2–4 µm in our experiments), the
coupling strength for the fundamental (1st) TE mode is gradually increased
from $\kappa_{\mathrm{ext}}/2\pi\approx$ 0.56 to 2.7 MHz with $\sim$10 µm
coupling length change. The results in the fundamental TM mode are also
presented in Supplementary Note 5.

Our interest here is whether or not the thermal effects indeed modify the
coupling strength. Since the temperature-dependent resonator expansion is
given by $\Delta R(\Delta T)=\alpha_{l}R\Delta T$, the radius of the resonator
($R=1400$ µm) is increased by $\sim$0.5 µm with 30 K heating. It should be
noted that the change in the effective coupling length is a difficult
parameter to assess experimentally because it relies on the tensile strength
of the tapered fiber and the actual tapered length. Nevertheless, we emphasize
that the effective coupling length is likely to increase by several microns or
several tens of microns in practical experiments (See Supplementary Note 3),
and therefore, the thermal expansion effect (i.e., the change in the effective
coupling length) could cause a dynamic, wide range coupling enhancement as
seen in our experimental results in Fig. 2. We further mention that the
thermo-optic effect also contributes to the coupling strength via the phase-
mismatch condition $\Delta\beta$ due to the considerable difference in the
thermo-optic coefficients of silica and $\mathrm{MgF_{2}}$ crystal. In thermal
equilibrium, the temperature of a silica tapered fiber is considered to be the
comparable to that of the resonator in the region where the fiber is in
contact with the resonator. However, we find that the phase-mismatch induced
by the thermo-optic effect only alters the coupling strength of up to
$\sim$20% with a 50 K temperature change (Fig. 4(f,g)) and is thus less
effective than the expansion effect.

## Conclusions

In summary, we have experimentally demonstrated the versatile tuning of rf
repetition-rate soliton combs in a crystalline $\mathrm{MgF_{2}}$
microresonator. The main properties of frequency combs, namely, the center
frequency, repetition frequency, and carrier-envelope offset frequency are
tuned by $-48.8$ GHz, $-5.85$ MHz, and $-386$ MHz, respectively, by using the
temperature control of a fiber-coupled resonator system. Additionally, we show
the possibility of spectrally tuning the DWs accompanied by soliton recoil via
the dynamic modification of cavity mode structures due to the birefringence of
crystalline microresonators. Thermally-induced coupling variation that leads
to pronounced soliton power enhancement has also been demonstrated and studied
theoretically to validate this effect. So far, optimization of a coupling
position and a fiber thickness has been performed based on practical
experiences and patient adjustment rather than a theoretical method. The
quantitative analyses also provide helpful guideline for the rational
optimization of this “rule of thumb” fiber-resonator coupling to multi-mode
WGM resonators.

Previous studies have not reported such a significant coupling change induced
by thermal effects [26, 29, 30, 4, 31]. In our case, the flexibility of the
tapered fiber coupler and the relatively large thermal expansion coefficient
of the crystalline material (e.g. $\mathrm{MgF_{2}}:8.9\times
10^{-6}~{}\mathrm{K^{-1}}$. fused $\mathrm{SiO_{2}}:0.6\times
10^{-6}~{}\mathrm{K^{-1}}$, $\mathrm{Si}:2.6\times 10^{-6}~{}\mathrm{K^{-1}}$
[35]) allow modification of the coupling strength, and resulting in the
enhancement of the soliton comb power. Although the implementation of
thermally-induced dynamic coupling control is a challenge, it would be
possible if the resonator and the waveguide have very different thermo-optic
coefficients. For future practical applications, broad and reliable soliton
tuning could be employed in microcomb systems. In particular, photonic rf
oscillators exploit the intrinsic low phase-noise properties of soliton combs
in ultrahigh-Q crystalline resonators [2], whereas the thermal drift of
optical resonances leads to the degradation of the phase-noise performance in
the low Fourier frequency regime. Thus, temperature control and subsequent
high-level stabilization [48, 49] are essential for mitigating the thermal
drift and pursuing the fundamental noise limit of soliton microcombs [50].
This study provides a greater understanding regarding wide-range tunability of
the comb frequency and output power towards the implementation of both a high-
purity photonic oscillator and a high-coherence laser source for optical
communications and dual-comb spectroscopy that requires precise control of the
difference between repetition frequencies.

## Methods

### Experimental setup

An $\mathrm{MgF_{2}}$ microresonator is fabricated from a $z$-cut crystalline
disk by shaping and hand polishing with diamond slurry. The FSR of 23.35 GHz
corresponds to a major radius of 1.49 mm and typical loaded Q-factors are
$10^{8}$–$10^{9}$ in the 1550 nm band. The curvature radius is approximately
$50$ µm. The group-velocity dispersion of the pumped mode in our work is
$\beta_{2}=d^{2}\beta/d\omega^{2}\approx-6.3~{}\mathrm{ps^{2}/km}$, yielding
anomalous dispersion. The group-velocity dispersion is defined as the
derivative of the inverse group velocity with respect to the angular frequency
[51]. The crystalline resonator is fixed with adhesive to a metal rod a few
centimeters long, so that the temperature of the resonator is controlled
through the metal parts with a temperature transducer. For soliton generation,
a continuous-wave fiber laser (linewidth$<$0.1 kHz) is amplified by an erbium-
doped fiber amplifier (EDFA), and an optical power of $\sim$400 mW is coupled
via a silica tapered fiber. The length of the tapered region is $\sim$40 mm,
and the diameter of the tapered fiber and the contact position with the
resonator is optimized to make it possible to observe distinct soliton steps.
Typically, we employed fiber diameters of 2–4 µm, and brought the fiber into
contact with the resonator to realize stable light coupling. A single soliton
is generated via a forward laser frequency sweep with an adequate scan speed
(0.1–10 MHz/ms), and then the soliton is captured by activating a servo
controller to lock the effective detuning via a phase-modulation technique [8,
52, 4]. The feedback control of the pump laser frequency enables us to
stabilize the soliton state against the thermal drift of the cavity resonance
and the long-term frequency fluctuation of the pump laser [52]. The absolute
frequency of the pump laser is monitored by using a wavelength meter, whose
spectral resolution (0.1 pm) limits the absolute accuracy of $f_{p}$ and
$f_{\mathrm{ceo}}$.

### Numerical analysis of resonator and fiber modes

Mode profiles of the WGM resonator and tapered fiber are calculated by
conducting a finite element simulation and a theoretical analysis,
respectively. We perform a finite element method (FEM) simulation by using FEM
software (COMSOL Multiphysics) to calculate the resonator modes. For the
simulation, we model an axisymmetric WGM resonator with a resonator radius of
1400 µm and a curvature of 25 µm, respectively, with a calculation area of 55
µm by 55 µm. The refractive indices of $\mathrm{MgF_{2}}$ for the TE and TM
modes are set independently for the simulation.

To calculate the mode overlap integral between the fiber and resonator modes,
the three-dimensional electrical components are mapped on Cartesian-coordinate
grids and then normalized by a factor, given as,

$1=\frac{1}{2}N_{\mathrm{f(r)}}^{2}\sqrt{\frac{\epsilon_{0}}{\mu_{0}}}\iint
n_{\mathrm{f(r)}}(x,y)|\bm{E}|_{\mathrm{f(r)}}^{2}dxdy.$ (2)

The $y$\- and $x$-axes correspond to the dominant directions of the electrical
field of the TE, and TM modes, respectively. The mode field of a tapered fiber
can be analytically obtained by solving the wave equation in the cylindrical
coordinates, where the propagation direction is taken to be the $z$-direction
and the center of the contact position is defined as $z=0$. A detailed
derivation is presented in Supplementary Note 2. The equation gives several
fiber modes with different propagation constants, whereas we only focus on the
fundamental fiber mode, i.e., $\mathrm{HE}_{11}$ mode, which is linearly
polarized single-maximum mode for the simulation. The refractive indices for a
fiber and surrounding air are set at $n_{\mathrm{f}}=1.444$ and $n_{0}=1.000$
at 25∘C.

### Calculation of coupling coefficient

The coupling coefficient is obtained by performing a three-dimensional
integration of Eq. (1). The integration for the $x$–$y$ plane, which is
transverse to the propagation direction, is performed over the cross-sectional
area of an $\mathrm{MgF_{2}}$ microresonator at each $z$-point. Because of the
resonator curvature $r$, the overlap integral gradually decreases in
accordance with the light propagation in the $z$-direction. Then, the overlap
integral is further integrated along the $z$-axis to take the phase-matching
condition into account. A sufficiently large integral interval is chosen so
that the coupling coefficient converges to a constant value. When we calculate
the additional coupling introduced by the effective coupling length, the
section is considered to be a straight waveguide for simplicity, which can be
justified because the resonator radius ($R=1400$ µm) is much larger than the
diameter of a tapered fiber ($\sim$2–4 µm). The effective refractive index for
a resonator mode is calculated from the electric field distribution and
temperature-dependent refractive indices for extraordinary and ordinary rays
(See Supplementary Note 3 for details).

## Acknowledgments

This work is supported in part by JSPS KAKENHI (JP19H00873, JP22K14625). S.F.
acknowledges support from RIKEN Special Postdoctoral Researcher Program. The
authors thank Dr. W. Yoshiki for supporting numerical simulation.

## Author contributions

S.F and K.W. performed the experimental measurements. S.F. and R. S. conducted
the numerical simulations. K. W. fabricated the crystalline microresonators,
and S. F., K. W., H. K. and S. K. developed the experimental setups. S. F. and
K. W. analyzed the data. S. F wrote the manuscript with input from Y. K. and
T. T.. All authors had constructive discussions. S. F. and T. T. supervised
the project.

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# Annotating and normalizing biomedical nes with limited knowledge††thanks:
This paper should have been published in the Proceedings of the 5th Workshop
on BioNLP Shared Tasks. Unfortunately, due to their complete lack of funding,
the authors could not afford the registration fees, a mandatory expense for a
contribution to be published in the aforementioned proceedings.

Fernando Sánchez León
unaffiliated
<EMAIL_ADDRESS>
Ana González Ledesma
unaffiliated
<EMAIL_ADDRESS>
###### Abstract

Named entity recognition (ner) is the very first step in the linguistic
processing of any new domain. It is currently a common process in BioNLP on
English clinical text. However, it is still in its infancy in other major
languages, as it is the case for Spanish. Presented under the umbrella of the
PharmaCoNER shared task, this paper describes a very simple method for the
annotation and normalization of pharmacological, chemical and, ultimately,
biomedical named entities in clinical cases. The system developed for the
shared task is based on limited knowledge, collected, structured and munged in
a way that clearly outperforms scores obtained by similar dictionary-based
systems for English in the past. Along with this recovering of the knowledge-
based methods for ner in subdomains, the paper also highlights the key
contribution of resource-based systems in the validation and consolidation of
both the annotation guidelines and the human annotation practices. In this
sense, some of the authors discoverings on the overall quality of human
annotated datasets question the above-mentioned ‘official’ results obtained by
this system, that ranked second (0.91 F1-score) and first (0.916 F1-score),
respectively, in the two PharmaCoNER subtasks.

##  1 Introduction

Named Entity Recognition (ner) is considered a necessary first step in the
linguistic processing of any new domain, as it facilitates the development of
applications showing co-occurrences of domain entities, cause-effect relations
among them, and, eventually, it opens the (still to be reached) possibility of
understanding full text content. On the other hand, Biomedical literature and,
more specifically, clinical texts, show a number of features as regards ner
that pose a challenge to NLP researchers Cohen and Demner-Fushman (2014): (1)
the clinical discourse is characterized by being conceptually very dense; (2)
the number of different classes for nes is greater than traditional classes
used with, for instance, newswire text; (3) they show a high formal
variability for nes (actually, it is rare to find entities in their “canonical
form”); and, (4) this text type contains a great number of ortho-typographic
errors, due mainly to time constraints when drafted.

Many ways to approach ner for biomedical literature have been proposed, but
they roughly fall into three main categories: rule-based, dictionary-based
(sometimes called knowledge-based) and machine-learning based solutions.
Traditionally, the first two approaches have been the choice before the
availability of Human Annotated Datasets (had), albeit rule-based approaches
require (usually hand-crafted) rules to identify terms in the text, while
dictionary-based approaches tend to miss medical terms not mentioned in the
system dictionary Rebholz-Schumann et al. (2011). Nonetheless, with the
creation and distribution of had as well as the development and success of
supervised machine learning methods, a plethora of data-driven approaches have
emerged —from Hidden Markov Models (HMMs) Ephraim (2002), Support Vector
Machines (SVMs) Habib and Kalita (2010) and Conditional Random Fields (CRFs)
He and Kayaalp (2008), to, more recently, those founded on neural networks
Armengol-Estapé et al. (2019). This fact has had an impact on knowledge-based
methods, demoting them to a second plane. Besides, this situation has been
favoured by claims on the uselessness of gazetteers for ner in, for example,
Genomic Medicine (GM), as it was suggested by Cohen and Demner-Fushman (Cohen
and Demner-Fushman, 2014, p. 26):

> One of the findings of the first BioCreative shared task was the
> demonstration of the long-suspected fact that gazetteers are typically of
> little use in GM.

Although one might think that this view could strictly refer to the subdomain
of GM and to the past —BioCreative I was a shared task held back in 2004—, we
can still find similar claims today, not only referred to rule-based and
dictionary-based methods, but also to stochastic ones Armengol-Estapé et al.
(2019).

In this paper, in spite of previous statements, we present a system that uses
rule-based and dictionary-based methods combined (in a way we prefer to call
resource-based). Our final goals in the paper are two-fold: on the one hand,
to describe our system, developed for the PharmaCoNER shared
task111http://temu.bsc.es/pharmaconer/, dealing with the annotation of some of
the nes in health records (namely, pharmacological, chemical and biomedical
entities) using a revisited version of rule- and dictionary-based approaches;
and, on the other hand, to give pause for thought about the quality of
datasets (and, thus, the fairness) with which systems of this type are
evaluated, and to highlight the key role of resource-based systems in the
validation and consolidation of both the annotation guidelines and the human
annotation practices.

In section 2, we describe our initial resources and explain how they were
built, and try to address the issues posed by features (1) and (2) above.
Section 3 depicts the core of our system and the methods we have devised to
deal with text features (3) and (4). Results obtained in PharmaCoNER by our
system are presented in section 4. Section 5 details some of our errors, but,
most importantly, focusses on the errors and inconsistencies found in the
evaluation dataset, given that they may shed doubts on the scores obtained by
any system in the competition. Finally, we present some concluding remarks in
section 6.

##  2 Resource building

As it is common in resource-based system development, special effort has been
devoted to the creation of the set of resources used by the system. These are
mainly two —a flat subset of the snomed ct medical ontology222From
https://browser.ihtsdotools.org/., and the library and a part of the
contextual regexp grammars developed by Sánchez-León Sánchez-León (2018) for a
previous competition on abbreviation resolution in clinical texts written in
Spanish. The process of creation and/or adaptation of these resources is
described in this section.

###  2.1 SNOMED CT

Although the competition proposes two different scenarios, in fact, both are
guided by the snomed ct ontology —for subtask 1, entities must be identified
with offsets and mapped to a predefined set of four classes (PROTEINAS,
NORMALIZABLES, NO_NORMALIZABLES and UNCLEAR); for subtask 2, a list of all
snomed ct ids (sctid) for entities occurring in the text must be given, which
has been called concept indexing by the shared task organizers333In the
train+dev datasets, only 17 of the PROTEINAS (‘proteins’) and NORMALIZABLES
(‘standardizable’) entities have an id not in the snomed ct ontology. Besides,
just 40 out of 5,615 annotations —not taking into account the class UNCLEAR,
which is not considered for the system evaluation— are tagged as
NO_NORMALIZABLES (‘non standardizable’), many of them due to the fact that
they include elliptical constructions.. Moreover, PharmaCoNER organizers
decided to promote snomed ct substance ids over product, procedure or other
possible interpretations also available in this medical ontology for a given
entity. This selection must be done even if the context clearly refers to a
different concept, according to the annotation
guidelines444https://bit.ly/2qxofgd, p. 4. (henceforth, AnnotGuide) and the
praxis. Finally, PROTEINAS is ranked as the first choice for substances in
this category.

These previous decisions alone on the part of the organizers greatly simplify
the task at hand, making it possible to build (carefully compiled) subsets of
the entities to be annotated. This is a great advantage over open domain ner,
where (like in GM) the texts may contain an infinite (and very creative
indeed) number of nes. For clinical cases, although the ne density is greater,
there exist highly structured terminological resources for the domain.
Moreover, the set of classes to use in the annotation exercise for subtask 1
has been dramatically cut down by the organizers.

With the above-mentioned initial constraints in mind, we have painstakingly
collected, from the whole set of snomed ct terms, instances of entities as
classified by the human annotators in the datasets released by the organizers
and, when browsing the snomed ct web version, we have tried to use the
ontological hierarchical relations to pull a complete class down from snomed
ct. This way, we have gathered 80 classes —from lipids to proteins to peptides
or peptide hormones, from plasminogen activators to dyes to drugs or
medicaments—, that have been arranged in a ranked way so as to mimic human
annotators choices555Note that we have gathered the complete set of medical
terms included in snomed ct, but, for the purpose of this shared task, we only
use a subset of it.. The number of entities so collected (henceforth, ‘primary
entities’) is 51,309.

###  2.2 Contextual regexp grammars

Some of the entities to be annotated, specially those in abbreviated form, are
ambiguous without a context. This is the case, for instance, of PCR, whose
expanded forms are (among other meanings; we use only English expanded forms)
‘reactive protein c’, ‘polymerase chain reaction’, ‘cardiorespiratory arrest’.
In order to deal with these cases, we use a contextual regexp rule system with
a lean and simple rule formalism previously developed Sánchez-León (2018). As
an exemplification, we include one rule to deal with one of the cases of the
preceeding ambiguity:

    b:[il::bioqumica|en sangre|hemoglobina|
       hemograma|leucocit|parsito|plaqueta|
       prote.na|recuento|urea] - [PCR] - >
    [m=protena]

A rule has a left hand side (LHS) and a right hand side (RHS). There is a
focus in the LHS (PCR, within dashes) and a left and right context (that may
be empty). When the left context includes a b: (like in this case), it
indicates either left or right context. The words in the context can take
other qualifiers —in this case, the matching will be case insensitive (i to
the left of bioquímica) and local (l), which means the disjunction of words
and/or stems can be found in a distance of 40 characters (this can be
modifified by the user). Hence, the rule applies, selecting the proteína
expansion (in RHS) of PCR if any of the words/stems specified as local context
(40 chars maximum) is matched either to the left or right of the focus term
(which is usually an abbreviation).

With no tweaking at all for the datasets in PharmaCoNER competition, the
system annotates correctly 18 out of 20 occurrences of PCR in the test dataset
(a precision of 0.9)666Note that 2 of the PCR occurrences in the train+dev
datasets have been incorrectly mapped to the protein interpretation (file
S1130-63432014000100012-1, 2 times)..

This component of the system is important because, only when the previous
abbreviation is expanded as the first string (that of a protein name), it must
be annotated, according to the AnnotGuide. The same ambiguity happens with Cr,
which may mean ‘creatinine’ or ‘chrome’777Again, one of the occurrences of Cr
has been incorrectly mapped to the former extended form (file
S0212-16112012000500042-1).. These expansions are both NORMALIZABLES, but,
obviously, their sctid is different.

The system currently uses 104 context rules, only for abbreviations and
acronyms in the clinical cases. These rules, contrary to what is commonly
referred in the biomedical processing literature Armengol-Estapé et al.
(2019), do not require a special domain knowledge (none of the authors do have
it) and can be written, most of the times, in a very straightforward way in
the formalism briefly described above.

##  3 Development

In general, dictionary-based methods rely on strict string matching over a
fixed set of lexical entries from the domain. This is clearly insufficient to
deal with non-canonical linguistic forms of nes as used in clinical texts. For
this reason, we have devised two different solutions to this shortcoming.

In the first place, we have munged a great number of our primary entities, in
a way similar to that described in Sánchez-León Sánchez-León (2019) for
gazetteers used for protected information anonymization in clinical texts. We
basically transform canonical forms in other possible textual forms observed
when working with biomedical texts. With such transformations, a system module
converts a salt compound like clorhidrato de ciclopentolato into
ciclopentolato clorhidrato, or simply the PP de potasio into its corresponding
adjective potásico. Other, more complex conversions include the treatment of
antibodies —for instance anticuerpo contra especie de Leishmania becomes ac.
Leishmania, among other variants—, or pairs of antibiotics normally prescribed
together —which have a unique sctid and whose order we handle just as the
‘glueing’ characters. Note, incidentally, that, while the input to this pre-
processing step is always a string, the output can be a regular expression,
that is linked to a sctid. Plural forms are also generated through this
module, that uses 45 transformations (not all equally productive). Using these
transformation rules, we produce 139,150 ‘secondary entities’, many of them
regexps. As a final (simple) example of this, consider the entity antígeno
CD13: after applying one of the previous string-to-regexp transformations, it
is converted to:

    (?:antgeno )?CD[- ]?13

With the previous regexp, the system is able to identify (and string-
normalize) six different textual realizations of the same unique snomed ct
term. There are more complex rules that, thus, produce many more potential
strings. The important thing with this strategy is that through the generative
power of these predictably-created regexps from snomed ct entities the system
is able to improve its recall and overcome the limitations of traditional
dictionary-based approaches.

Secondly, to tackle with careless drafting of clinical reports, a Levenshtein
edit distance library888We use Text::Levensthtein::Flexible library, from Perl
ecosystem. One of the anonymous reviewers has shed doubts about the use of
Perl as a language for “NLP and text-mining nowadays”. In this respect, we are
not committed with a given programming language more than we are with our
native language —and we have submitted our paper in English, a foreign
language for us. The system could have been implemented in any other
programming language more popular “nowadays”, provided that we were as
proficient in it as we are in Perl and the language used were as efficient in
string and regexp handling and in I/O operations as Perl is. In this regard,
the most popular language nowadays —Python— is 2 to 10 times slower for these
particular features. Perl is even faster for regexp processing than Python
PyPy —see, for instance, https://github.com/mariomka/regex-benchmark.
Idiomatic Perl is even faster. Finally, Perl has a long tradition in biology
and medicine text processing. is used on the whole background dataset. The
process is run once, using our secondary entities as lexicon999With
enumeration of strings from non-infinite-loop regexps. and a general
vocabulary lexicon to rule out common words in the candidate search process.
We have used distances in the range 1-3 (depending on string length) for
sequences up to 3 words long101010These words are not isolated from the byte
stream, and the process uses textual anchors to delimit them as word
candidates. Consequently, no proper tokenization is performed.. The output of
this process, which links forms with spelling errors with canonical ones and,
thus, to sctids, can be inspected prior to its inclusion in the system
lexicon, if so desired.

###  3.1 Annotation process

As such, the annotation process is very simple. The program reads the input
byte stream trying to identify known entities by means of a huge regexp built
through the pre-processing of the available resources. If the candidate entity
is ambiguous and (at least) one contextual rule exists for it, it is applied.
For the rest of the nes, the system assigns them the class and sctid found in
our ranked in-memory lexicon. As already mentioned in passing, the system does
not tokenize text prior to ner, a processing order that we consider the right
choice for highly entity-dense texts. The data structures built during pre-
processing are efficiently stored on disk for subsequent runs, so the pre-
processing is redone only when resources are edited.

##  4 Results

According to the organizers, and taking into account the ha of the tiny subset
from the background dataset released to the participants111111When compared
with the rest of the tasks in BioNLP-OST 2019, the time given to PharmaCoNER
participants to submit their system runs is 4 times longer than the mean
—longer time that is unnecessary if system is mature enough. On the other
hand, the dataset released for evaluation purposes is more than 4 times larger
than the mean. As a consequence, participating groups have to annotate full
domain corpora rather than just test dataset(s). A shorter submission period
and a smaller test dataset would be preferable, and besides fairer, in future
calls., the system obtained the scores presented in table 1, ranking as second
best system for subtask1 and best system for subtask2 Gonzalez-Agirre et al.
(2019).121212The authors have been unable to obtain these results with the
official script, downloaded from https://github.com/PlanTL-
SANIDAD/PharmaCoNER-CODALAB-Evaluation-Script. In their execution of the
evaluation script, system results are better (?)..

| Precision | Recall | F1-score
---|---|---|---
Subtask 1 | 0.90625 | 0.91314 | 0.90968
Subtask 2 | 0.91108 | 0.92083 | 0.91593
Table 1: Results for PharmaCoNER test dataset (both subtasks)

Our results are consistent with our poor understanding of the classes for
subtask 1. Having a null knowledge of Pharmacology, Biomedicine or even
Chemistry, assigning classes (as requested for subtask 1) to entities is very
hard, while providing a sctid (subtask 2) seems an easier goal. We will
explain the point with an example entity —ácido hialurónico (‘hyaluronic
acid’). Using the ontological structure of snomed ct, one can find the
following parent relations (just in English):

hyaluronic acid is-a mucopolysaccharide is-a protein

The authors have, in this case, promoted the PROTEINAS annotation for this
entity, disregarding its interpretation as a replacement agent and overlooking
a recommendation on polysaccharides in the AnnotGuide. Fortunately, all its
interpretations share a unique sctid. The same may be true for

haemosiderin is-a protein

which is considered NORMALIZABLE in the test dataset. Similar cases are
responsible for the lower performance on subtask 1 with respect to the more
complex subtask 2.

In spite of these human classification errors, our system scores outperform
those obtained by PharmacoNER Tagger131313The tagger authors, some of them
also organizers of shared task, have changed the casing of the name for the
program. Armengol-Estapé et al. (2019), a simpler system using a binary
classification and a very different organization of the dataset with a smaller
fragment for test (10% of the data as opposed to 25% for the official
competition). In fact, our system improves their F1-score (89.06) by 1.3
points when compared with our results for the more complex PharmaCoNER subtask
1.

##  5 Discussion

In this section, we perform error analysis for our system run on the test
dataset. We will address both recall and precision errors, but mainly
concentrate on the latter type, and on a thorough revision of mismatches
between system and human annotations.

In general, error analysis is favoured by knowledge-based methods, since it is
through the understanding of the underlying reasons for an error that the
system could be improved. Moreover, and differently to what happens with the
current wave of artificial neural network methods, the whole annotation
process —its guidelines for human annotators, the collection and appropriate
structuring of resources, the adequate means to assign tags to certain
entities but not to other, similar or even pertaining to the same class— must
be clearly understood by the designer/developer/data architect of such
systems. As a natural consequence of this attempt to mimick a task defined by
humans to be performed, in the first place, also by humans, some
inconsistencies, asystematic or missing assignments can be discovered, and
this information is a valuable treasure not only for system developers but
also for task organizers, guideline editors and future annotation campaigns,
not to mention for the exactness of program evaluation results.

Most of the error types made by the system (i.e., by the authors) in class
assignment for subtask 1 have already been discussed. In the same vein, as
regards subtask 2, a great number of errors come from the selection of the
‘product containing substance’ reading from snomed ct rather to the
‘substance’ itself. This is due to inexperience of the authors on the domain
and the wrong consideration of context when tagging entities —the latter being
clearly obviated in the AnnotGuide.

In the following paragraphs, some of the most relevant inconsistencies found
when performing error analysis of our system are highlighted. The list is
necessarily incomplete due to space constraints, and it is geared towards the
explanation of our possible errors.

###  5.1 Inconsistency in the ag

Among some of the paradoxical examples in the AnnotGuide it stands out the
double explicit consideration of gen (‘gene’), when occurs alone in context,
as both an entity to be tagged (positive rule P2 of the AnnotGuide) and a noun
not to be tagged (negative rule N2). This inconsistency (and a bit of bad
luck) has produced that none of the 6 occurrences as an independent noun —not
introducing an entity— is tagged in the train+dev (henceforth, t+d) while the
only 2 in the same context in the test dataset have been tagged. This amounts
for 2 true negatives (tns) for the evaluation script.

###  5.2 Inconsistency in ha as regards ag

The AnnotGuide proposal for the treatment of elliptical elements is somewhat
confusing. For these cases, a longest match annotation is proposed, which is
difficult to replicate automatically and not easy to remember for the human
annotator. In many contexts, the annotator has made the right choice —for
instance, in receptores de estrógeno y de progesterona— whereas in others do
not —$|$anticuerpos anticardiolipina$|$ $|$IgG$|$ e $|$IgM$|$, with ‘$|$’
marking the edges of the annotations. The last example occurs twice in the
test dataset. Hence, the disagreement counts as 6 tns and 2 false positives
(fps)141414When we indicate this kind of information, mostly using only fps,
it must be understood that the system made the choice(s) that the authors
judge as correct, although disagreeing with ha and/or AnnotGuide..

On the other hand, there is a clear reference to food materials and nutrition
in the AnnotGuide, where they are included in the class of substances.
However, none of the following entities is tagged in the test dataset: azúcar
(which is mandatory according to AnnotGuide and was tagged in t+d; 1 fp);
almidón de maíz (also mandatory in AnnotGuide; 1 fp); and Loprofín, Aglutella,
Aproten (hypoproteic nutrition products, 3 fps in total)151515On nutrition
replacements, see also section 5.3..

There is an explicit indication in the AnnotGuide to annotate salts, with the
example iron salts. However, in the context sales de litio (‘lithium salts’),
only the chemical element has been tagged (1 fp161616Note, in passing, that
these span errors account for 1 tn also for the evaluation scripts.).

There exist other differing-span mismatches between human and automatic
annotation. These include anticuerpos anticitoplasma de neutrófilo, where the
ha considers the first two words only (in one of the occurrences, 1 fp); in
the text fragment b2 microglobulina, CEA y CA 19,9 normales, CA 19,9 is the
correct span for the last entity (and not CA, 1 fp); A.S.T is the span
selected (for A.S.T., 1 fp); finally, in the context lgM anticore only lgM has
been tagged (1 fp).

Other prominent mismatch between had and AnnotGuide is that of DNA, which is
explicitly included in the AnnotGuide (sects. P2 and O1). It accounts for 2
fps.

But perhaps one of the most common discrepancies between human and automatic
annotation has to do with medicaments normally prescribed together, which have
a unique sctid. Examples include amiloride/hidroclorotiazida (1 fp); and
betametasona + calcipotriol (1 fp) in the test set. This situation was also
observed in the t+d corpus fragment (tenofovir + emtricitabina, carbonato
cálcico /colecalciferol, lopinavir/ritonavir).

###  5.3 Inconsistency in ha on the test set as regards t+d sets

Some inconsistencies between dataset annotations have turned the authors
crazy: NPT (acronym for ‘total parenteral nutrition, TPN’) is tagged in the
train+dev dataset 15 out of 21 times it occurs171717However, at least one
expanded variant of it —nutrición parenteral, ‘parenteral nutrition’— is never
tagged.. The common sense of frequency in the ha of texts has led us to tag it
in the background set. Unluckily, neither NPT nor its expansion have been
tagged in the test dataset. This has also been the behaviour in ha for
‘parenteral nutrition’ and ‘enteral nutrition’ (and their corresponding
acronyms) in test dataset, since these entities have not been tagged. We asked
the organizers about this and other entities for which we had doubts, either
because the AnnotGuide didn’t cover their cases or because the ha didn’t match
the recommendations in the AnnotGuide. Woefully, communication with the
organizers has not been very fluent on this respect. All in all, this bad
decision on the part of the authors amounts for 6 fps (more than 7.5% of our
fps according to evaluation script).

For other cases, decisions that may be clearly induced from the tagging of
train+dev datasets, have not been applied in the test corpus fragment. These
include cadenas ligeras (5 times in t+d, 1 fp in test); enzimas hepáticas
(tagged systematically in t+d, 1 fp); p53 (also tagged in t+d, 1 fp).

Another entity that stands out is hidratos de carbono (‘carbohydrates’). It is
tagged twice in the t+d dataset, occurring 4 times in the set (once as HC).
However, although the form carbohidratos has been annotated twice in the test
set, hidratos de carbono has been not (1 fp).

Moreover, suero (‘Sodium chloride solution’ or ‘serum’) deserves its own
comment. Both entity references are tagged in the train+dev datasets (although
with the latter meaning it is tagged only 4 out of 12 occurrences). We decided
to tag it due to its relevance. In the test dataset, it occurs 5 times with
the blood material meaning, but it has only been tagged twice as such (one of
them being an error, since it refers to the former meaning). Our system tagged
all occurrences, but tagged also one of the instances with the former meaning
as serum (3 fps).

Finally, there are some inconsistencies within the same dataset. For example,
nutricional agent Kabiven is tagged as both NORMALIZABLES (with sctid) and
NO_NORMALIZABLES in the very same text. The same happens with another
nutritional complement, Cernebit, this time in two different files. The
perfusion solution Isoplasmal G (with a typo in the datasets —Isoplasmar G) is
tagged as NORMALIZABLES and UNCLEAR. These examples reveal a vague
understanding (or definition) of criteria as regards fluids and nutrition, as
we pointed out at the beginning of this section.

###  5.4 Asystematic/incomplete annotation

Some of the entities occurring in the test dataset have not always been
tagged. This is the case for celulosa (annotated only once but used twice, 1
fp); vimentina (same situation as previous, 1 fp); LDH (tagged 20 times in t+d
but not in one of the files, 1 fp); cimetidina (1 fp); reactantes de fase
aguda (2 fps; 2 other occurrences were tagged); anticuerpos antinucleares
(human annotators missed 1, considered fp).

###  5.5 Incorrect sctids

On our refinement work with the system, some incorrect sctids have emerged.
These errors impact on subtask 2 (some also on subtask 1). A large sample of
them is enumerated below.

ARP (‘actividad de renina plasmática’, ‘plasma renin activity’, PRA) cannot be
linked to sctid for renina, which happens twice. In the context ‘perfil de
antigenos [sic] extraíbles del núcleo (ENA)’, ENA has been tagged with sctid
of the antibody (1 fp). In one of the files, tioflavina is linked to sctid of
tioflavina T, but it could be tioflavina S. Thus, it should be
NO_NORMALIZABLE. Harvoni is ChEBI:85082 and not <null> (1 fp). AcIgM contra
CMV has a wrong sctid (1 fp). HBsAg has no sctid in the test set; it should be
22290004 (‘Hepatitis B surface antigen’) (1 fp).

There are other incorrect annotations, due to inadvertent human errors, like
biotina tagged as PROTEINAS or VEB (‘Epstein-Barr virus’) being annotated when
it is not a substance. Among these mismatches between ha and system
annotation, the most remarkable is the case of synonyms in active principles.
For instance, the brand name drug Dekapine has been linked to ‘ácido
valproico’ in the former case and to ‘valproato sódico’ in the latter. These
terms are synonymous181818Although, ‘valproato sódico’ is the name used in the
leaflet, as it can be seen in the Spanish Medicament Agency, AEMPS, web page
(https://cima.aemps.es/cima/dochtml/p/48828/P_48828.html: last consulted on
16.07.2019)., but sadly they don’t share sctid. Hence, this case also counts
as a fp.

A gold standard dataset for any task is very hard to develop, so a continuous
editing of it is a must191919Besides, when the dataset is being used in a
shared task, this refinement process should be available to participants while
the task is open.. In this discussion, we have focused on false positives
(fps) according to the script used for system evaluation, with the main
purpose of understanding the domain knowledge encoded in the linguistic
conventions (lexical/terminological items and constructions) used by health
professionals, but also the decisions underlying both the AnnotGuide and the
ha practice.

In this journey to system improvement and authors enlightenment, some
inconsistencies, errors, omissions have come up, as it has been reflected in
this section, so both the guidelines for and the practice of annotation can
also be improved in future use scenarios of the clinical case corpus built and
maintained by the shared task organizers.

Our conclusion on this state of affairs is that some of the inconsistencies
spotted in this section show that there were not a rational approach to the
annotation of certain entities contained in the datasets (apart from other
errors and/or oversights), and, hence, the upper bound of any tagging system
is far below the ideal 1.0 F1-score. To this respect, in very many cases, the
authors have made the wrong choice, but in others they were guided by analogy
or common sense. Maybe a selection founded on probability measures estimated
on training material could have obtained better results with this specific
test dataset. However, in the end, this cannot be considered as an indication
of a better system performance, since, as it has been shown, the test dataset
used still needs more refinement work to be used as the right dataset for
automatic annotation evaluation.

##  6 Conclusions

With this resource-based system developed for the PharmaCoNER shared task on
ner of pharmacological, chemical and biomedical entities, we have demonstrated
that, having a very limited knowledge of the domain, and, thus, making wrong
choices many times in the creation of resources for the tasks at hand, but
being more flexible with the matching mechanisms, a simple-design system can
outperform a ner tagger for biomedical entities based on state-of-the-art
artificial neural network technology. Thus, knowledge-based methods stand on
their own merits in task resolution.

But, perhaps most importantly, the other key point brought to light in this
contribution is that a resource-based approach also favours a more critical
stance on the dataset(s) used to evaluate system performance. With these
methods, system development can go hand in hand with dataset refinement in a
virtuous circle that let us think that maybe next time we are planning to add
a new gazetteer or word embedding to our system in order to try to improve
system performance, we should first look at our data and, like King Midas,
turn our Human Annotated Dataset into a true Gold Standard Dataset.

## Acknowledgements

We thank three anonymous reviewers of our manuscript for their careful reading
and their many insightful comments and suggestions. We have made our best in
providing a revised version of the manuscript that reflects their suggestions.
Any remaining errors are our own responsability.

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