# Exceptional point proximity-driven mode-locking in coupled microresonators

Riku Imamura  Department of Electronics and Electrical Engineering, Faculty of
Science and Technology, Keio University, Yokohama, 223-8522, Japan  Shun Fujii
Department of Physics, Faculty of Science and Technology, Keio University,
Yokohama, 223-8522, Japan  Ayata Nakashima  Department of Electronics and
Electrical Engineering, Faculty of Science and Technology, Keio University,
Yokohama, 223-8522, Japan  Takasumi Tanabe<EMAIL_ADDRESS>Department of Electronics and Electrical Engineering, Faculty of Science and
Technology, Keio University, Yokohama, 223-8522, Japan

###### Abstract

We show theoretically and numerically that mode-locking is feasible with a
coupled-cavity system with gain and loss, notably, without any natural
saturable absorber. We highlight that in the vicinity of the exceptional
point, system $Q$ exhibits substantial modulation even with minor refractive
index changes and a minimal Kerr effect contribution. Leveraging this unique
behaviour, we propose an unprecedented approach wherein the lossy auxiliary
cavity functions as an efficient artificial saturable absorber, thus
facilitating mode-locking. This approach is not only novel, but also presents
considerable advantages over conventional systems where both gain and
saturable absorption are contained within a single microcavity. These benefits
include reduced operational power and ease of post-adjustment, achievable
through the manipulation of the coupling strength between the two
microcavities.

##  I Introduction

Passively mode-locked pulsed lasers have emerged as essential tools in a
variety of applications, including ultrafast laser spectroscopy and coherent
control [1, 2], femtosecond laser processing [3, 4], attosecond physics [5,
6], time and frequency standards [7], and telecommunications [8]. Shortly
after the invention of the laser, research into short-pulse generation was
conducted [9], and mode-locking using saturable absorption (SA) was developed.
Early laser systems employed laser dyes [10] and semiconductor saturable-
absorber mirrors (SESAMs) [11], both of which rely on natural SA. For a long
time, Kerr-lens mode-locking [12], a technique utilizing the self-focusing
effect to create artificial SA, has been used for mode-locking in solid-state
lasers. In recent years, the emergence of fibre lasers, which capitalize on
both natural and artificial SA effects achieved through carbon nanotubes
(CNTs) [13], graphene [14], nonlinear polarization rotation [15], and
nonlinear loop mirrors [16], has made ultrashort pulse lasers more accessible.

In recent times, the demand for high-repetition pulsed lasers has surged [17,
18, 19, 20] as they enable more effective data acquisition and faster material
processing speed. Consequently, researchers have developed harmonic mode-
locking techniques in fibre lasers [21], short-cavity solid-state lasers [22],
mode locked integrated external-cavity surface-emitting lasers [23], and
$\mathrm{Er^{3+}}$ doped fibre-ferrule cavities [24]. Among these,
nanophotonic devices fabricated from erbium-ion ($\mathrm{Er^{3+}}$) doped
glass [25, 26] stand out as potential cost-effective solutions, given the
maturity and robustness of the material. These devices are particularly
promising if a small mode-locked cavity can be fabricated. Therefore, a mode-
locked laser using a whispering-gallery-mode (WGM) microresonator [27], could
provide a cost-effective on-chip solution for demonstrating ultra-high
repetition rate optical pulses. However, the realization of SA in such a
system, without sacrificing essential parameters such as the cavity quality
factor ($Q$), poses a challenge if we choose to utilize CNTs or graphene.
Hence, it is essential to develop an entirely new approach for achieving
artificial SA and enabling passive mode-locking, especially if we aim to
realize femtosecond pulse laser sources in nanophotonic devices.

At the same time, systems consisting of coupled resonators with gain and loss
have been garnering interest and are being investigated for their ability to
break parity-time (PT) symmetry in structures such as waveguides [28],
photonic crystals [29], and microrings[30, 31, 32]. It has been proven that a
coupled cavity resonator can achieve low-threshold lasing when operated beyond
exceptional points (EPs), where eigenfrequencies coalesce [33]. This is due to
a significant reduction in system loss. Notably, the system loss in such
configurations exhibits considerable modulation near an EP.

In this work, we theoretically propose and numerically demonstrate passive
mode-locking in a coupled-cavity system with gain and loss. This system
uniquely leverages properties that emerge near the EPs. By exploiting the
extensive system loss modulation that occurs close to the EP, we achieve
efficient artificial SA, leading to ultrahigh-repetition mode-locking in a
small cavity system. We also anticipate that the required quality factor ($Q$)
of the system will be substantially relaxed thanks to the separation of gain
and loss in two distinct cavities. Moreover, we introduce a new parameter: the
coupling rate between the two microcavities. This additional control point
should facilitate easier experimental demonstration.

##  II Coupled cavities for mode-locking

###  II.1 Concept and operational mechanism

Our model system, as depicted in Fig. 1(a), is a pair of coupled
microresonators . The first resonator, cavity A, provides gain, while the
second one, cavity B, is a passive microresonator with the same diameter as
cavity A but with a higher loss (low $Q$). The difference between the $Q$
values of the two resonators should be noted because the distinction is
crucial as regards the mode-locking mechanism explored in this study.

With gain provided by cavity A, single and multi-mode lasing can be achieved
when a pump is applied. However, continuous wave (CW) lasing is only obtained
in the absence of an SA effect. Figures 1(a) and 1b show how our system can
exhibit an artificial SA that contributes to pulsing. Given the coupled nature
of cavities A and B, and the lossy attribute of cavity B, the light from
cavity A couples into cavity B, leading to its elimination due to the low-$Q$;
an observation suggesting that we can reduce system loss if we can manage the
decoupling of the two cavities.

The influence of the Kerr effect, characterized by an intensity-dependent,
instantaneous refractive index change, such as,

$n=n_{0}+n_{2}I,$ (1)

where $n_{2}$ is the nonlinear refractive index, and $I$ the intensity, is
evident when examining a pulse circulating within the cavity. With gain in
cavity A and $Q_{\mathrm{A}}>Q_{\mathrm{B}}$, the pulse peak shows pronounced
nonlinear refractive index modulation in cavity A, causing disparate resonant
frequency modulations in the two cavities, as explained in Fig. 1(b). This
results in an instantaneous decoupling of the cavities at the pulse peak; this
is an intuitive explanation despite the challenge of defining an instantaneous
resonant frequency within a round trip. Rigorously, this decoupling can also
be viewed as a phase velocity mismatch caused by the Kerr effect. With
initially identical resonant frequencies, cavities A and B experience
modulation and decoupling only at the pulse peak. As a consequence, the light
within cavity A undergoes decreased loss at the pulse peak, thereby
replicating the operation of SA behaviour.

The primary challenge is to secure a substantial degree of coupling/decoupling
modulation under conditions of minor refractive index modulation, given that
$n_{2}$ is typically small. To surmount this challenge, we propose exploiting
the potent modulation commonly observed near an EP in a coupled microresonator
system.

###  II.2 Numerical model

To investigate the new mode-locking technique that forgoes the use of any
natural SAs, we have constructed a model utilizing the approach described
below with nonlinear Schrödinger equations with gain [27] and mode coupling
terms [34], such as,

$\begin{split}T_{\mathrm{r}}\frac{\partial A\left(t,T\right)}{\partial
T}=iL\left(-\frac{\beta_{2}}{2}\cdot\frac{\partial^{2}}{\partial
t^{2}}+\gamma_{\mathrm{nl}}\left|A\left(t,T\right)\right|^{2}\right)A\left(t,T\right)+\frac{{g_{T}}_{\mathrm{r}}\left(T\right)-l_{\mathrm{A}}}{2}A\left(t,T\right)+i\frac{\kappa}{2}B\left(t,T\right),\end{split}$
(2)

$\begin{split}T_{\mathrm{r}}\frac{\partial B\left(t,T\right)}{\partial
T}=iL\left(-\frac{\beta_{2}}{2}\cdot\frac{\partial^{2}}{\partial
t^{2}}+\gamma_{\mathrm{nl}}\left|B\left(t,T\right)\right|^{2}\right)B\left(t,T\right)-\frac{l_{\mathrm{B}}}{2}A\left(t,T\right)+i\frac{\kappa}{2}A\left(t,T\right),\end{split}$
(3)

where $A(t,T)$ and $B(t,T)$ are the complex electrical field amplitudes (in a
slowly-varying envelope approximation) in cavities A and B. Here, $t$ and $T$
are the fast time and the slow time, respectively. Equations (2) and (3) are
interconnected through the last term, with $\kappa=\omega_{0}/Q_{\mathrm{c}}$
representing the coupling rate, where $Q_{\mathrm{c}}$ is the coupling $Q$.
$\gamma_{\mathrm{nl}}(=n_{2}\omega_{0}(cA_{\mathrm{eff}})^{-1})$ is the
nonlinear coefficient. ${g_{T}}_{\mathrm{r}}(T)$, and $l_{\mathrm{A,B}}$ are
the gain per roundtrip in cavity A, and losses per roundtrip in cavities A or
B, as below [27],

${g_{T}}_{\mathrm{r}}=g_{0}\left(\frac{1}{1+\frac{\overline{\left|A(t,T)\right|}^{2}}{P^{g}_{\mathrm{sat}}}}\right)\left(1+\frac{1}{\Delta
f_{g}^{2}}\frac{\partial^{2}}{\partial t^{2}}\right),$ (4)

$l_{\mathrm{A,B}}=T_{\mathrm{r}}\gamma_{\mathrm{A,B}}=T_{\mathrm{r}}\cdot\frac{\omega_{0}}{Q_{\mathrm{A,B}}},$
(5)

where the parameters are described in Tab. 1. When $A$ is nonzero, the last
term on the right-hand side of Eq. (2) can be rewritten as follows,

$i\frac{\kappa}{2}B=\left[\mathrm{Real}\left(i\frac{\kappa}{2}\frac{B}{A}\right)+i\cdot\mathrm{Imag}\left(i\frac{\kappa}{2}\frac{B}{A}\right)\right]A,$
(6)

where the real part (the first term) corresponds to gain and loss, whereas the
imaginary part (the second term) pertains to the phase modulation, both
arising due to the coupling. Given that $A$ and $B$ are functions of time $t$,
Eq. (6) shows that the effective gain and loss emerging as a result of the
coupling constitute a time-dependent function and may act as an artificial SA.

Equations (2) and (3) are solved using the split-step Fourier method, which is
a technique widely adopted for calculations involving microresonator frequency
combs [34]. As laid out in Tab. 1, we adopt a silica toroid microresonator
with a diameter of $D=300$ µm for our model. We only doped cavity A with
$\mathrm{Er^{3+}}$ ions to produce gain, setting the $Q_{\mathrm{A}}$ and
$Q_{\mathrm{B}}$ values at $1\times 10^{8}$ and $5\times 10^{6}$,
respectively. Cavities A and B are coupled with a coupling Q of
$Q_{\mathrm{c}}=8\times 10^{6}$. Parameters for dispersion and mode area are
obtained from the given structure, with the minor diameter of the toroid
specified as 30 µm. We note that both cavity exhibit the identical anomalous
dispersion value ($\beta_{2}=-12.24~{}\mathrm{ps^{2}/km}$).

##  III Results and Discussion

###  III.1 Demonstration of the mode-locking

The results of our computation are shown in Fig. 2(a), where we chart the
average power within each cavity ($P_{\mathrm{aveA}}$ and $P_{\mathrm{aveB}}$)
as a function of the number of roundtrips after starting the cavity pump. As
multimode lasing begins, the longitudinal modes remain unlocked, and the
temporal waveform undergoes a random modulation (Fig. 2(b). Following several
thousand round trips, we begin to observe the formation of a pulse, albeit an
unstable one (Figs. 2(c)). It takes approximately $7\times 10^{4}$ round trips
for the cavity to reach a state of complete stability. The temporal waveforms
for cavities A and B are shown in Figs. 3(a) and 3(b), respectively. At this
juncture, we witness clear mode-locking behaviour. The pulse shape has a
$\mathrm{sech^{2}}$ profile with a full-width at half maximum (FWHM) of 30 fs.
The phase of the pulse reveals it to be Fourier transform-limited, providing
direct evidence of mode-locking, with a corresponding spectral width of 84 nm
(FWHM).

Here, we confirm that the Kerr effect instigates instantaneous decoupling, and
thus serves as an artificial SA. Figures 3(c) and 3(d) show the associated
resonant wavelength shifts for the waveforms shown in Figs. 3(a) and 3(b),
calculated via instantaneous nonlinear refractive index modulation as given in
Eq. (1). The outcome indicates that the resonance of cavity A effectively
undergoes a frequency shift of up to 1.5 GHz. This shift surpasses the
linewidth of cavity B (with $Q_{\mathrm{B}}=5\times 10^{6}$). Given that the
shift in cavity B is negligible (Fig. 3(d)), we can instantaneously decouple
cavity A from cavity B only at the pulse peak. This process results in minimal
loss and allows the presence of the auxiliary cavity B to function as an
artificial SA.

Figure 3(e) offers greater clarity by depicting the effective gain and loss
experienced by cavity A due to its coupling with cavity B within a roundtrip.
The loss is clearly negligible at the pulse peak and subsequently increases at
the pulse tail. This finding reinforces our previous conclusion that the
coupled cavity system indeed realizes an artificial SA. However, a lingering
question persists: why does the SA occur so effectively with this parameter
set? Generally, the $n_{2}$ value is small, implying that the modulation would
only occur to a limited extent. To answer this question, it becomes crucial to
exploit the impact of the EP within this system.

###  III.2 The impact of the exceptional point

Upon a closer examination of the temporal phase in Fig. 3(b), a unique
structure is observable where the phase bifurcates before consolidating into
one as the intensity ascends. In an attempt to comprehend this behaviour, we
undertake a steady-state analysis of our coupled cavity system.

To simplify the picture, we consider two cavities; one with low loss (cavity
A, with $Q_{\mathrm{A}}=10^{8}$) and the other with high loss (cavity B, with
$Q_{\mathrm{B}}=5\times 10^{6}$). A coupled-mode analysis is then performed
based on the following expressions [33]:

$\frac{dA}{dt}=i\omega_{\mathrm{A}}A-\frac{\gamma_{\mathrm{A}}}{2}A+i\frac{\kappa}{2}B,$
(7)

$\frac{dB}{dt}=i\omega_{\mathrm{B}}B-\frac{\gamma_{\mathrm{B}}}{2}B+i\frac{\kappa}{2}A.$
(8)

At a steady state, the complex eigenfrequencies are given as

$\omega_{\pm}=\frac{\omega_{\mathrm{A}}+\omega_{\mathrm{B}}}{2}+i\frac{\chi}{2}\pm\beta,$
(9)

where, $\chi$ is the average decay rate given by
$\chi=\frac{1}{2}\left(\gamma_{\mathrm{A}}+\gamma_{\mathrm{B}}\right)$. Here,
we introduce $\beta(=\frac{1}{2}\sqrt{\kappa^{2}-\Gamma^{2}})$ to represent
the effect of the coupling rate $\kappa$ and of the difference in the decay
rates of the two cavities, given by
$\Gamma=\frac{1}{2}\left(-\gamma_{\mathrm{A}}+\gamma_{\mathrm{B}}\right)$. It
is worth noting that the real part of Eq. (9) corresponds to the resonant
frequencies, whereas the imaginary part signifies the system loss (i.e., $Q$).

Figures 4(a) and 4(b) present the imaginary and real components of the
eigenfrequencies stipulated in Eq. (9), plotted as functions of
$Q_{\mathrm{c}}$, which is the coupling $Q$ between the two cavities. The
plots vary with different $Q_{\mathrm{B}}$ values. Figure 4(a) shows that the
eigenfrequency (expressed in wavelength) moves beyond the EP as
$Q_{\mathrm{c}}$ increases. Here we consider the unique phase bifurcations
observed in Fig. 3(a), which we calculated using a $Q_{\mathrm{B}}$ value of
$5\times 10^{6}$. The system is linear at the tail of the pulse and resides
below the EP because $Q_{\mathrm{c}}$ is at $8\times 10^{6}$, as indicated by
the orange dotted line in Fig. 4(a). Owing to the bifurcation of the real part
of the eigenfrequency, a phase split becomes observable. As the pulse
intensity increases, $Q_{\mathrm{c}}$, quite intuitively, also effectively
grows thanks to the increased decoupling, leading to a collision of the
eigenfrequencies. Consequently, their phases merge into a single phase.

In Fig. 4(b), we witness substantial modulation of the system $Q$ in proximity
to the EP in all instances, a feature that substantially contributes to the
efficient SA behaviour. This outcome implies that if we can modulate
$Q_{\mathrm{c}}$, we might be able to adjust the system $Q$ significantly and
consequently realize an effective SA.

Figure 4(c) shows the system $Q$ as a function of the frequency detuning
$\Delta f$ between cavities A and B (i.e., $\Delta
f=f_{\mathrm{A}}-f_{\mathrm{B}}$) while maintaining $Q_{\mathrm{B}}$ at
$5\times 10^{6}$. It shows results for various $Q_{\mathrm{c}}$ values. If
$Q_{\mathrm{c}}$ is set at $2\times 10^{7}$, the system is beyond the EP,
which signifies that the two modes diverge into high and low $Q$s from the
outset (as depicted by the green dotted line in Fig. 4(b)). Consequently, the
system $Q$s have two values from the beginning, and the modulation remains
shallow, even when we alter the refractive index of the cavity. Conversely, if
$Q_{\mathrm{c}}$ is too small at $Q_{\mathrm{c}}=1\times 10^{6}$, the starting
point is significantly below the EP, as portrayed by the purple dotted line in
Fig. 4(b). To obtain efficient modulation, we must initialize close to the EP,
specifically at $Q_{\mathrm{c}}=8\times 10^{6}$, which is just below the EP.
As a result, with minor modulation of the detuning between the cavities, we
can obtain significant modulation of the system $Q$.

While our operation is set just below the EP, it is equally possible to
initialize the system just above the EP. However, it is critical to remain
close to the EP to ensure effective modulation of the system $Q$. The resonant
shift that we achieve is approximately 1.5 GHz (as shown in Fig. 3(c)),
leading to a modulation of the system $Q$ from $\sim 1\times 10^{7}$ to $\sim
4\times 10^{8}$, according to Fig. 4(c).

###  III.3 Mode-locking range

Lastly, we undertake a search for the optimal parameters. Figure 5(a) presents
our findings, visually encapsulated by using a colour map depicting the number
of peaks in the waveform generated after 70,000 roundtrips. Furthermore, we
evaluated the stability of the resulting waveform in an attempt to distinguish
between stable mode-locking, breather dynamics, and chaotic behaviour. The
region of stability is denoted by a white-dotted contour. The white solid line
indicates the condition of the EP.

To understand the result, we begin by pointing out that two conditions are
needed to achieve mode-locking. The first condition is a high system $Q$
because a low loss is needed to achieve lasing in the first place. It also
helps facilitate efficient optical nonlinear effects. The second condition is
to achieve efficient SA behaviour, which is essential for mode-locking. We
employ Figs. 5(b) and 5(c) to investigate these two properties.

Figure 5(b) is the system $Q$ as a function of $Q_{\mathrm{B}}$ when
$Q_{\mathrm{A}}=10^{8}$ and $Q_{\mathrm{c}}=8\times 10^{6}$. The system $Q$ is
high when $Q_{\mathrm{B}}$ is high since most of the light exhibits loss
through cavity B. But the system $Q$ recovers even when $Q_{\mathrm{B}}$
exhibits a reduction in its value due to the presence of the EP. Figure 5(c)
presents the maximum slope value of the system loss rate $\Delta\gamma_{\tau}$
across varying $Q_{\mathrm{B}}$ values. The system $Q$ ($Q_{\mathrm{sys}}$) as
a function of the cavity detuning $\Delta f$ was previously outlined in Fig.
4(c). The system loss rate, $\gamma_{\tau}$ is represented by
$\gamma_{\tau}=\omega_{0}/Q_{\mathrm{sys}}$, which also varies as a function
of detuning $\Delta f$. Thus, we define $\Delta\gamma_{\tau}$ as,

$\Delta\gamma_{\tau}=max\left|\frac{d\gamma_{\tau}(\Delta f)}{d(\Delta
f)}\right|.$ (10)

Here, $max$ indicates that we extract the peak value of the function.
Computing $\Delta\gamma_{\tau}$ for different $Q_{\mathrm{B}}$ values provides
the plot illustrated in Fig. 5(c). Intuitively, a larger value of
$\Delta\gamma_{\tau}$ indicates that even small detuning, arising from the
Kerr effect, can lead to significant modulation in the system’s loss rate. In
essence, a substantial $\Delta\gamma_{\tau}$ is indicative of an efficient
artificial SA.

To gain a comprehensive understanding of the results presented in Fig. 5(a),
let us consider a fixed $Q_{\mathrm{c}}$ at $8\times 10^{6}$. Initiating our
discussion at high $Q_{\mathrm{B}}$ values, where $Q_{\mathrm{B}}$ is $\sim
10^{8}$, the system $Q$ is at its zenith. However, as suggested by Fig. 5(c),
the potency of the artificial SA effect is minimal, rendering the system
unstable. As $Q_{\mathrm{B}}$ falls to roughly $5\times 10^{7}$, the increase
in $\Delta\gamma_{\tau}$ facilitates mode-locking in the system. The further
descent of $Q_{\mathrm{B}}$ to around $\sim 10^{7}$ situates the system on the
fringes of stable mode-locking, as depicted in Fig. 5(a). Even as
$\Delta\gamma_{\tau}$ increases, the system $Q$ diminishes substantially. It
is important to note that $Q$ values degenerate beyond the EP (to the right of
the solid white line in Fig. 5(a)). This infers that the intensities in
cavities A and B are nearly identical, implying that the nonlinear refractive
index modulations are virtually equivalent. Consequently, efficient detuning
between cavities A and B becomes unattainable, and therefore the recovered $Q$
hinders the stable mode-locked operation (i.e., breathing behaviour). Yet, as
$Q_{\mathrm{B}}$ nears the EP, $\Delta\gamma_{\tau}$ experiences a notable
surge, peaking at approximately 34.2 at the EP. Owing to the pinnacle slope
that occurs at $\Delta f=0$ , significant artificial SA arises close to EP,
facilitating mode-locking even with diminished system $Q$ values.

A region warranting particular attention lies to the left of the EP condition
($Q_{\mathrm{B}}<4\times 10^{6}$). Here, while $\Delta\gamma_{\tau}$ undergoes
a decline, the system Q exhibits a considerable resurgence, facilitating mode-
locking courtesy of the pronounced Kerr effect. In contrast to the region to
the right of the EP, the system $Q$ between modes A and B shows a marked
disparity that augments efficient system decoupling. This stability in mode-
locking persists until $Q_{\mathrm{B}}$ falls to $6\times 10^{5}$. Beyond
this, the diminished $\Delta\gamma_{\tau}$ restricts the attainment of mode-
locking (for $Q_{\mathrm{B}}<6\times 10^{5}$).

The insights gleaned from Figs. 5(b) and 5(c) shed light on the restoration of
mode-locking as $Q_{\mathrm{B}}$ decreases, a process that can be attributed
to the unique behaviour of the EP in a coupled cavity system. This
demonstrates the role of the EP as an enabler of mode-locking even under
low-$Q_{\mathrm{B}}$ conditions, revealing novel avenues for the manipulation
and control of lasing dynamics. Significantly, the optimal region for mode-
locking is relatively broad, thus offering promising prospects for
experimental implementation.

##  IV Conclusion

In conclusion, our study provides a comprehensive examination of a novel mode-
locking strategy that forgoes the utilization of natural SAs, instead
leveraging the Kerr effect and a coupled microresonator system in close
proximity to an EP. The results reveal the occurrence of mode-locking after
approximately $7\times 10^{4}$ round trips. The formed pulse adopts a
$\mathrm{sech^{2}}$ shape, with its Fourier transform-limited phase. The
resonant shift associated with the light intensity modulation underscores the
role of instantaneous decoupling as an artificial SA, contributing to
efficient mode-locking. Our exploration of the parameter space further
clarifies the conditions under which mode-locking is achieved. Notably, mode-
locking consistently occurs close to the EP, where substantial modulation of
the system $Q$ is possible.

Our research opens new avenues for exploring coupled microresonator systems as
platforms for efficient mode-locking, moving beyond the traditional use of
saturable absorbers. The broad sweet spot for achieving mode-locking,
identified through our investigations, offers exciting possibilities for the
experimental validation and application of this technique.

## Figures

### Figure 1

Figure 1: Model and principle. a. Schematic representation of our model.
Cavity A is a cavity with gain; Cavity B is a lossy cavity. Light is generated
in Cavity A and undergoes loss in Cavity B. b. Explanation of the principle of
artificial SA in a coupled cavity system. The left graph shows the temporal
waveform in Cavity A (blue line) and Cavity B (red line). The pulse intensity
in Cavity A is consistently higher due to its gain properties. At the pulse’s
peak, Cavity A exhibits strong nonlinearity, leading to modulation in the
refractive index. In contrast, the tail (or background) remains linear. The
right graphs show the resonant spectra for both cavities at the peak and tail
of the pulse. Initially, at the tail of the pulse, Cavities A and B couple
with each other since they share the same resonant wavelengths. However, as
the peak of the pulse in Cavity A demonstrates significant optical
nonlinearity, it causes a shift in resonant wavelengths between the two
cavities, resulting in their decoupling. Consequently, the light in Cavity A
experiences reduced loss.

### Figure 2

Figure 2: Calculation results obtained from coupled nonlinear Schrödinger
equations. a. The average optical power in Cavity A (blue) and Cavity B (red)
as a function of the roundtrips. b. Spectral intensity and phase, alongside
temporal intensity and phase, within a roundtrip at roundtrip 10,000. c. At
roundtrip 30,000.

### Figure 3

Figure 3: a. Mode-locked temporal waveform and spectrum (inset) in Cavity A at
roundtrip 70,000. The blue line represents intensity, while the grey lines
show the phase. b. As a., but for Cavity B. c. Calculated resonant shift for
Cavity A resulting from Kerr nonlinear refractive index modulation. A maximum
frequency shift of $\sim 1.5$ GHz is observed at the pulse peak. The black
dotted line indicates the frequency linewidth (FWHM) for a cavity with a $Q$
of $10^{6}$. d. As c. but for Cavity B. e. The nonlinear loss and gain profile
in Cavity A arising from the system’s coupling and decoupling within the
roundtrip. The black solid line depicts the net gain in Cavity A (i.e.,
$g_{0}$ minus the loss $Q_{\mathrm{A}}$). The green line shows the extra loss
in Cavity A due to its coupling with Cavity B. The blue curve portrays the
overall net gain/loss profile in Cavity A. The green and blue curves are
applicable only when the intensity within cavity A is nonzero.

### Figure 4

Figure 4: a. The real part of the eigenfrequency (resonant frequency) depicted
as a wavelength shift from the baseline resonance at 1550 nm, for various
$Q_{\mathrm{B}}$ values. $Q_{\mathrm{A}}$ is consistently set at $10^{8}$. The
orange line represents the condition where $Q_{\mathrm{c}}=8\times 10^{6}$,
the parameter set utilized for the computations in Figs. 2 and 3. b. Imaginary
part of the eigenfrequency (representing gain and loss) displayed as system
$Q$, across different $Q_{\mathrm{B}}$ values. $Q_{\mathrm{A}}$ remains
constant at $10^{8}$. c. System $Q$ plotted against the detuning between
Cavity A and Cavity B for a range of $Q_{\mathrm{c}}$ values. $Q_{\mathrm{A}}$
and $Q_{\mathrm{B}}$ are set at $10^{8}$ and $5\times 10^{6}$, respectively.
The condition $Q_{\mathrm{c}}=8\times 10^{6}$ is consistent with the
parameters employed in the analyses of Figs.2 and 3.

### Figure 5

Figure 5: a. Colour map illustrating the count of peaks in the temporal
waveform per roundtrip (indicating the number of pulses per roundtrip) after
70,000 roundtrips as a function of $Q_{\mathrm{B}}$ and $Q_{\mathrm{c}}$. The
region enclosed by a white dotted line represents the stable mode-locked
regime. The white solid line signifies the position of the EP. b. System $Q$,
as calculated from Eq. (9), plotted as a function of $Q_{\mathrm{B}}$ when
$Q_{\mathrm{A}}$ and $Q_{\mathrm{c}}$ are $10^{8}$ and $8\times 10^{6}$,
respectively. The system $Q$ decreases as $Q_{\mathrm{B}}$ reduces, but it
recovers due to the presence of the EP. A high $Q$ is essential to obtain
sufficient net gain and optical nonlinearity in cavity A, which are required
for lasing and mode-locking. c. $\Delta\gamma_{\tau}$ plotted as a function of
$Q_{\mathrm{B}}$ when $Q_{\mathrm{A}}$ and $Q_{\mathrm{c}}$ are $10^{8}$ and
$8\times 10^{6}$, respectively. $\Delta\gamma_{\tau}$ reaches its maximum
value of $\sim 34.2$ in an EP condition. The definition of
$\Delta\gamma_{\tau}$ is provided in the main text. A higher value corresponds
to substantial modulation of the system loss rate given a specific refractive
index modulation. This property is necessary for achieving efficient
artificial SA.

Table

Table 1: Parameters employed in the calculations unless otherwise specified in the text Parameter | Variable | Value of A | Unit
---|---|---|---
Intrinsic $Q$ of Cavity A | $Q_{\mathrm{A}}$ | $1\times 10^{8}$ | $-$
Intrinsic $Q$ of Cavity B | $Q_{\mathrm{B}}$ | $5\times 10^{6}$ | $-$
Coupling Q | $Q_{\mathrm{c}}$ | $8\times 10^{6}$ | $-$
Cavity diameter | $D(=L/\pi)$ | 300 | µm
Resonant wavelength | $\lambda_{0}(=2\pi c/\omega_{0})$ | 1.55 | µm
Roundtrip time | $T_{\mathrm{r}}$ | 4.52 | ps
Refractive index | $n_{0}$ | 1.44 | $-$
Nonlinear refractive index | $n_{2}$ | $2.2\times 10^{-20}$ | $\mathrm{m^{2}/W}$
Effective mode area | $A_{\mathrm{eff}}$ | $21.28$ | µ$\mathrm{m^{2}}$
Second order dispersion | $\beta_{2}$ | $-12.24$ | $\mathrm{ps^{2}/km}$
Saturated gain | $g_{0}$ | $5\times 10^{-2}$ | $/\mathrm{roundtrip}$
Saturation power | $P^{\mathrm{g}}_{\mathrm{sat}}$ | 144.8 | mW
Gain bandwidth | $\Delta f_{\mathrm{g}}$ | 2.50 | THz

Acknowledgments This work was supported by JSPS KAKENHI (JP19H00873,
JP22K14625), by MEXT Quantum Leap Flagship Program (MEXT Q-LEAP)
JPMXS0118067246 and by JST SPRING (JPMJSP2123).

Competing financial interests The authors declare that they have no competing
financial interests.

Correspondence and requests for material should be addressed to TT (email:
takasumi@elec.keio.ac.jp).

## References

  * [1] A. H. Zewail, “Laser femtochemistry,” Science 242, 1645–1653 (1988).
  * [2] R. Itakura, K. Yamanouchi, T. Tanabe, T. Okamoto, and F. Kannari, “Dissociative ionization of ethanol in chirped intense laser fields,” J. Chem. Phys. 119, 4179–4186 (2003).
  * [3] F. Korte, J. Serbin, J. Koch, A. Egbert, C. Fallnich, A. Ostendorf, and B. N. Chichkov, “Towards nanostructuring with femtosecond laser pulses,” Appl. Phys. A: Mater. Sci. Process. 77, 229–235 (2003).
  * [4] T. Tanabe, F. Kannari, F. Korte, J. Koch, and B. Chichkov, “Influence of spatiotemporal coupling induced by an ultrashort laser pulse shaper on a focused beam profile,” Appl. Opt. 44, 1092–1098 (2005).
  * [5] F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
  * [6] T. Gaumnitz, A. Jain, Y. Pertot, M. Huppert, I. Jordan, F. Ardana-Lamas, and H. J. Wörner, “Streaking of 43-attosecond soft-x-ray pulses generated by a passively CEP-stable mid-infrared driver,” Opt. Express 25, 27506–27518 (2017).
  * [7] T. Fortier and E. Baumann, “20 years of developments in optical frequency comb technology and applications,” Commun. Phys. 2, 1–16 (2019).
  * [8] A. Hasegawa and Y. Kodama, _Solitons in Optical Communications_ (Clarendon Press, 1995).
  * [9] A. J. DeMaria, D. A. Stetser, and H. Heynau, “Self mode‐locking of lasers with saturable absorbers,” Appl. Phys. Lett. 8, 174–176 (1966).
  * [10] E. P. Ippen, C. V. Shank, and A. Dienes, “Passive mode locking of the cw dye laser,” Appl. Phys. Lett. 21, 348–350 (1972).
  * [11] U. Keller, W. H. Knox, and H. Roskos, “Coupled-cavity resonant passive mode-locked Ti:sapphire laser,” Opt. Lett. 15, 1377–1379 (1990).
  * [12] D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked ti:sapphire laser,” Opt. Lett. 16, 42–44 (1991).
  * [13] S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol. 22, 51–56 (2004).
  * [14] Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
  * [15] M. E. Fermann, “Passive mode locking by using nonlinear polarization evolution in a polarization-maintaining erbium-doped fiber,” Opt. Lett. 18, 894 (1993).
  * [16] I. N. Duling, “Subpicosecond all-fibre erbium laser,” Electron. Lett. 6, 544–545 (1991).
  * [17] T. Tanabe, S. Fujii, and R. Suzuki, “Review on microresonator frequency combs,” Jpn. J. Appl. Phys. 58, SJ0801 (2019).
  * [18] T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative Kerr solitons in optical microresonators,” Science 361 (2018).
  * [19] C.-Z. Ning, “Semiconductor nanolasers and the size-energy-efficiency challenge: a review,” Adv. Photonics 1, 014002 (2019).
  * [20] H. Pfeifer, L. Ratschbacher, J. Gallego, C. Saavedra, A. Faßbender, A. von Haaren, W. Alt, S. Hofferberth, M. Köhl, S. Linden, and D. Meschede, “Achievements and perspectives of optical fiber Fabry–Perot cavities,” Appl. Phys. B 128, 29 (2022).
  * [21] B. C. Collings, K. Bergman, and W. H. Knox, “Stable multigigahertz pulse-train formation in a short-cavity passively harmonic mode-locked erbium/ytterbium fiber laser,” Opt. Lett. 23, 123–125 (1998).
  * [22] S. Kimura, S. Tani, and Y. Kobayashi, “Kerr-lens mode locking above a 20 GHz repetition rate,” Optica 6, 532 (2019).
  * [23] U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429, 67–120 (2006).
  * [24] A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively modelocked fiber lasers using carbon nanotubes,” Opt. Express 19, 6155–6163 (2011).
  * [25] L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very High-Q Whispering-Gallery mode resonances observed on fused silica microspheres,” EPL 23, 327–334 (1993).
  * [26] D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
  * [27] T. S. Prugger Suzuki, A. Nakashima, K. Nagashima, R. Ishida, R. Imamura, S. Fujii, S. Y. Set, S. Yamashita, and T. Tanabe, “Design of a passively mode-locking whispering-gallery-mode microlaser,” J. Opt. Soc. Am. B 38, 3172–3178 (2021).
  * [28] C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
  * [29] K. Takata, K. Nozaki, E. Kuramochi, S. Matsuo, K. Takeda, T. Fujii, S. Kita, A. Shinya, and M. Notomi, “Observing exceptional point degeneracy of radiation with electrically pumped photonic crystal coupled-nanocavity lasers,” Optica 8, 184 (2021).
  * [30] H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346, 975–978 (2014).
  * [31] B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity–time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
  * [32] K. Komagata, A. Tusnin, J. Riemensberger, M. Churaev, H. Guo, A. Tikan, and T. J. Kippenberg, “Dissipative Kerr solitons in a photonic dimer on both sides of exceptional point,” Commun. Phys. 4, 1–13 (2021).
  * [33] B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
  * [34] S. Fujii, A. Hori, T. Kato, R. Suzuki, Y. Okabe, W. Yoshiki, A.-C. Jinnai, and T. Tanabe, “Effect on Kerr comb generation in a clockwise and counter-clockwise mode coupled microcavity,” Opt. Express 25, 28969–28982 (2017).


# Exploring the Potential of AI-Generated Synthetic Datasets: A Case Study on
Telematics Data with ChatGPT

Ryan Lingo
Honda Research Institute, USA
<EMAIL_ADDRESS>

###### Abstract

This research delves into the construction and utilization of synthetic
datasets, specifically within the telematics sphere, leveraging OpenAI’s
powerful language model, ChatGPT. Synthetic datasets present an effective
solution to challenges pertaining to data privacy, scarcity, and control over
variables - characteristics that make them particularly valuable for research
pursuits. The utility of these datasets, however, largely depends on their
quality, measured through the lenses of diversity, relevance, and coherence.
To illustrate this data creation process, a hands-on case study is conducted,
focusing on the generation of a synthetic telematics dataset. The experiment
involved an iterative guidance of ChatGPT, progressively refining prompts and
culminating in the creation of a comprehensive dataset for a hypothetical
urban planning scenario in Columbus, Ohio. Upon generation, the synthetic
dataset was subjected to an evaluation, focusing on the previously identified
quality parameters and employing descriptive statistics and visualization
techniques for a thorough analysis. Despite synthetic datasets not serving as
perfect replacements for actual world data, their potential in specific use-
cases, when executed with precision, is significant. This research underscores
the potential of AI models like ChatGPT in enhancing data availability for
complex sectors like telematics, thus paving the way for a myriad of new
research opportunities.

_K_ eywords Sythetic Datasets $\cdot$ Telematics $\cdot$ ChatGPT $\cdot$
Prompt Engineering

##  1 Introduction

The advent of Artificial Intelligence (AI) and Machine Learning (ML) has
revolutionized numerous fields, expanding the realm of possibilities with vast
computational abilities and innovative techniques. A critical element fueling
this advancement is the accessibility of large-scale datasets. However, data
availability often confronts challenges such as privacy concerns, scarcity of
information, and constraints in manipulating variables for research. In
response, the creation of synthetic datasets has emerged as a promising
solution. Synthetic datasets, produced artificially, circumvent many of these
issues while preserving the statistical properties of the original data. This
allows for experimental control and confidentiality, making them particularly
beneficial in data-sensitive fields like healthcare, finance, and the
automotive industry.

While the potential of synthetic datasets is significant, their effectiveness
is fundamentally dependent on their quality, a characteristic primarily
defined by three aspects: diversity, relevance, and coherence. Ensuring high
standards in these aspects is of utmost importance for synthetic data to be a
reliable tool in research and applications.

This paper employs OpenAI’s language model, ChatGPT, as a tool for generating
synthetic data, with a focus on the telematics domain. The telematics sector,
encompassing telecommunications and vehicular technologies, stands to benefit
substantially from an increased availability of data for research, planning,
and technological advancement. This paper showcases the procedure of crafting
synthetic telematics data using ChatGPT through a case study, delving into the
complications and corresponding solutions tied to this process, and assessing
the quality of the resulting dataset. The intention lies in offering a glimpse
into the potential of AI-generated synthetic datasets, underscoring their
promise as a vital resource in the realm of data science.

##  2 Related Work

The emergent utility of synthetic data in recent years, owing to its potential
in enhancing privacy and representation, has sparked research interest in
various sectors. This section synthesizes the most significant studies in this
field, focusing particularly on the application of synthetic data and the role
of artificial intelligence.

Savage [2] pioneers the discourse in the paper "Synthetic data could be better
than real data", asserting that machine-generated data sets could potentially
augment both privacy and representation in artificial intelligence. However,
Savage cautions that the successful application of synthetic data hinges on
the delicate balance between achieving accurate representation and mitigating
privacy invasion.

Complementing Savage’s narrative, Stadler et al. [3] introduce an empirical
perspective in their paper "Synthetic Data – Anonymisation Groundhog Day." The
authors execute a quantitative evaluation of the privacy gain associated with
synthetic data publishing. In a stark comparison with preceding anonymisation
techniques, they assert that synthetic data either inadequately thwarts
inference attacks or it fails to retain data utility, indicating the need for
a balanced approach.

Simultaneously, the application of synthetic data in healthcare is aptly
highlighted by Gonzales et al. [1] in their paper "Synthetic data in health
care: A narrative review." They identify seven potential use cases of
synthetic data in healthcare, which encompass research, hypothesis testing,
public health research, health IT development, education, training, public
data release, and data linking.

Hassani and Silva [4] diversify this conversation by examining the
implications of artificial intelligence, particularly ChatGPT, in the realm of
data science. In their paper "The Role of ChatGPT in Data Science: How AI-
Assisted Conversational Interfaces Are Revolutionizing the Field", they
elucidate how ChatGPT can augment various aspects of the data science
workflow. They contend that it can aid in data cleaning, preprocessing, model
training, and result interpretation, and provide fresh insights to drive
decision-making.

Despite the research surrounding synthetic data and ChatGPT, there exists a
conspicuous knowledge gap regarding the use of ChatGPT in creating synthetic
telematics data. The current body of literature hence necessitates further
exploration into the prospective benefits and challenges of employing ChatGPT
for synthetic telematics data generation.

##  3 Theoretical Background and Potential of Synthetic Datasets

###  3.1 Introduction to Synthetic Data: A Paradigm Shift

The digital revolution and the rise of data-centric decision making has
catalyzed the emergence of a potent instrument—synthetic data. This data,
algorithmically crafted without real-world collection, has gained prominence
due to an escalating need for extensive, adaptable data that adheres to
privacy and accessibility constraints. This study investigates the concept of
synthetic data, exploring its creation, applications, potential shortcomings,
and its utility as a powerful resource for beginners in data analysis and data
science.

###  3.2 Exploring the Characteristics of Synthetic Datasets

In essence, a synthetic dataset is a conglomerate of artificially devised data
points that ideally retain the statistical properties of a corresponding real-
world dataset. This type of data emulates the features and behaviors of actual
data without encompassing any confidential or sensitive information. The
generation of synthetic data deploys intricate algorithms and techniques,
including a range of machine learning methodologies, to assure that the
generated data faithfully mirrors the attributes of the original dataset.

The ideal synthetic dataset demands meticulous replication of inherent
patterns present in the original data. However, the dataset generated with
ChatGPT might not conform to such rigorous standards. Considering the data is
generated from randomized sources, there is an inevitable compromise in the
depth and breadth of information compared to a comprehensive synthetic
dataset. Critical to note is the primary objective - not to mirror reality
flawlessly, but rather to enhance research capabilities and nurture
educational ventures. The generated synthetic dataset in this paper, though
perhaps not as exhaustive, provides a controlled environment. This environment
allows researchers and learners to conduct experiments, explore, and derive
insights, all the while ensuring privacy and confidentiality. In the pursuit
of knowledge, such a dataset proves adept in facilitating understanding and
analysis of intricate data structures and patterns.

##  4 The Implications and Applications of Synthetic Datasets

###  4.1 A Panorama of Applications for Synthetic Datasets

Synthetic datasets permeate a multitude of disciplines, with the following
areas being notably dominant:

  * •

Machine Learning and Artificial Intelligence: Synthetic data can prove
instrumental in training machine learning models, particularly when the
procurement of real-world data is restricted or infeasible due to privacy
considerations.

  * •

Testing and Validation: Synthetic data is frequently employed in software
testing to assess system performance across varying scenarios, ensuring no
confidential data is disclosed during the process.

  * •

Research and Development: When accessing real-world data is challenging or
ethically dubious, researchers often depend on synthetic data for experimental
design and hypothesis testing.

  * •

Data Augmentation: Synthetic data can rectify dataset imbalance by generating
data for underrepresented classes, thereby enhancing machine learning model
performance.

  * •

Privacy-Preserving Data Sharing: In sectors dealing with sensitive data, such
as healthcare, finance, and automotive industries, synthetic datasets
facilitate secure data sharing while preserving privacy.

  * •

Education and Learning: Synthetic data can play a pivotal role in education,
particularly for experiential learning in data science and machine learning.
These datasets can be tailored to demonstrate specific concepts or techniques,
negating the need for exhaustive data collection or dealing with privacy
issues. This allows students, educators, and competition participants to
experiment, make mistakes, and learn, all without jeopardizing real-world
sensitive data.

Thus, synthetic datasets play a vital role in our progressively data-driven
world, striking a balance between utility, privacy, and accessibility. Given
the emphasis on the educational applications of synthetic data, it becomes
highly relevant for the objectives of this study.

###  4.2 The Role of Synthetic Data in Real-World Scenario Modelling

Synthetic data is invaluable when modeling various scenarios. For instance, in
telematics, which includes data collection about a vehicle’s usage, location,
and driver behavior, acquiring real-world data for every possible driving
scenario can be arduous, if not impossible. Synthetic data can simulate a
broad spectrum of conditions, from normal to extreme, enabling comprehensive
testing and training of telematics systems, contributing to the evolution of
safer, more efficient vehicle technologies.

###  4.3 Synthetic Data: An Ally for Data Privacy

In our digital era, data privacy is of paramount concern. Synthetic data
emerges as a privacy champion, allowing organizations to draw insights from
data without disclosing sensitive or confidential information. For instance,
in telematics, the data collected often includes sensitive data, such as
precise location data and potentially personally identifiable information
(PII). By generating synthetic datasets that maintain the statistical
properties of the original without including any actual PII, privacy can be
preserved during in-depth analyses, predictive model development, or data
sharing with third parties. It’s also worth noting that in scenarios where
achieving a synthetic dataset that is statistically identical to the original
proves unfeasible, a dataset that is statistically close enough can still
serve effectively for educational and experimental applications. This slightly
less precise alternative yet maintains essential characteristics for
exploration and understanding, offering a robust solution for privacy-
preserving data utilization.

###  4.4 Synthetic Data and its Impact on Scalability and Flexibility

Algorithmically generated synthetic data provides scalability and flexibility,
allowing organizations to produce as much (or as little) data as necessary for
their distinct applications. This aspect is crucial when stress-testing
systems or training intricate machine learning models. The versatility of
synthetic data enables its adaptation to represent specific scenarios,
populations, or conditions, thereby enabling more targeted and precise
analyses and predictions. It is noteworthy to add that the specific nature of
data and its level of congruence with the original source will vary from one
use case to another. This reflects the bespoke nature of synthetic data
generation, making it a vital tool for a wide range of scenarios. The
unprecedented ease in creating synthetic data today necessitates further
scholarly exploration of its various potential applications. Hence, the need
for continued research to decipher the maximum potential of synthetic data in
all possible use cases remains integral to advancing our knowledge in this
rapidly evolving field.

###  4.5 Addressing Data Imbalance with Synthetic Data

Imbalanced data poses a significant challenge in machine learning, often
leading to models biased towards overrepresented classes. Synthetic data
offers a resolution by generating additional data for the underrepresented
classes, thus creating a more balanced dataset that improves learning and
facilitates fairer predictions. For instance, in telematics, certain
infrequent driving behaviors can be artificially generated, producing a more
balanced dataset for model training and leading to advancements in driver
safety and vehicle performance. Building upon this notion, not just the
creation, but also the augmentation of synthetic data using large language
models (LLMs) could emerge as one of the most crucial use cases. When a sample
of original data is available, it is feasible to map its distributions onto
the synthetic data, which enhances the authenticity and richness of the
synthetic dataset. This specific application, which encompasses both creation
and augmentation of synthetic data with LLMs, represents a crucial frontier in
machine learning. Given its immense potential to reshape our approach to data
imbalances, it justifiably necessitates extensive, focused research.

##  5 The Inherent Challenges of Utilizing Synthetic Data

###  5.1 Limitations in the Complexity and Variability of Synthetic Data

While synthetic data provides a multitude of possible benefits, it is not
without its inherent challenges. A primary concern is the potential lack of
full complexity and variability that characterizes real-world data. Being
algorithmically generated, synthetic data might fail to fully encapsulate the
intricate details, correlations, and unpredictability found in its real-world
counterparts. This shortfall may result in models that perform well with
synthetic data but do not generalize effectively to real-world scenarios.

To illustrate this point, consider telematics. A synthetic dataset might
simulate a range of driving conditions, but it might not account for subtle,
influential factors such as driver fatigue, distractions, or even the nuanced
effects of billboard advertisements along a route. These omissions could
significantly impact the performance of predictive models when applied to
real-world data.

###  5.2 The Risk of Inherited Biases in Synthetic Data

Another inherent challenge of synthetic data is its potential to propagate the
biases embedded in the model used for its generation. If the model creating
the synthetic data contains biases, whether from the original training data or
algorithmic bias, these biases can be transferred to the synthetic data,
leading to skewed results and potentially biased conclusions.

For instance, suppose a model generating synthetic telematics data was
primarily trained on urban driving conditions. In that case, it might
inadvertently over-represent these conditions in the synthetic data, leading
to an under-representation of rural or off-road driving scenarios. Such biases
could potentially skew the conclusions drawn from the analysis or predictions
based on this data, thereby affecting the validity of decisions made using
these insights.

###  5.3 Overfitting Risk Associated with Synthetic Data

The exclusive use of synthetic data for model training can lead to
overfitting—a situation where a model exhibits high performance on the
training data but struggles to generalize to new, unseen data. This issue can
arise if the synthetic data does not adequately represent the variability
inherent in real-world scenarios.

In the domain of telematics, consider a model trained on synthetic data to
predict engine failure based on various parameters, such as driving style,
vehicle load, and environmental conditions. If the synthetic data does not
capture the full spectrum of real-world variations and complexities, the model
might become excessively specialized to the synthetic dataset, leading to
overfitting. Consequently, the model’s predictive performance may decline when
applied to real-world data

###  5.4 Addressing the Challenges of Synthetic Data

The objections raised towards synthetic data, although reasonable, are not
insurmountable. With strategic advancements and diligent application, these
concerns can be reduced.

The challenge of fully capturing the complexity and variability of real-world
data can be approached by refining the data generation algorithms and
including a wider set of influencing factors and conditions. In the context of
telematics, this could mean extending the generation process to factor in
additional elements such as driver fatigue or distractions. While this
introduces an added layer of complexity, it holds the potential for enhancing
the practicality and precision of synthetic data.

The potential risk of inherited biases in synthetic data can be mitigated
through balanced and careful training of the generative models. This involves
incorporating diverse and representative datasets during the training phase to
prevent over- or under-representation of specific conditions or classes.
Continuous monitoring and correction of any observable bias in the generated
synthetic data through iterative improvements in the data generation process
is also essential.

As for the risk of overfitting associated with synthetic data, a mixed
approach utilizing both real and synthetic data for model training could be
adopted. This hybrid strategy could leverage the benefits of synthetic data
while preserving the capacity to generalize to real-world conditions.
Techniques such as regularization, cross-validation, and ensemble methods can
also be deployed to counter overfitting. For instance, in the telematics
example, a blend of real-world data and synthetic data encompassing various
driving conditions could lead to a more robust and generalizable model.

To summarize, while synthetic data indeed presents challenges, these are not
insurmountable barriers. It’s essential to underscore that while all these
concerns are valid and warrant attention, the scope of this paper is primarily
to initiate the conversation around generating a telematics dataset using
ChatGPT. With careful application, continuous improvement, and strategic
advancements, synthetic data can prove an invaluable tool in data science,
particularly in data-sensitive fields, and further research in this area is
merited

##  6 An Examination of ChatGPT’s Role in Synthetic Dataset Generation

###  6.1 Leveraging ChatGPT in Language Modelling for Synthetic Data
Generation

ChatGPT, a product of OpenAI, represents an advanced language model utilizing
machine learning to generate text reminiscent of human discourse. Its
potential extends beyond mere text generation, enabling the creation of
structured data in response to specific prompts.

Leveraging the capabilities of ChatGPT, this paper proposes a practical
demonstration involving the generation of a synthetic dataset. The focus will
be on crafting a rudimentary telematics dataset. This dataset, while
simplified, is intended to serve as an educational resource, encapsulating key
data points inherent in telematics analytics.

This study emphasizes the creation of a synthetic dataset with composition
limited to randomly generated values. While this approach may not replicate
the direct correspondence found in real-world data, it serves as a highly
conducive environment for exploratory research, analytical processing, and in-
depth learning. In fact, the apparent simplicity of this randomly generated
data allows for clearer understanding and manipulation, providing an ideal
introductory tool in the realm of telematics data.

Throughout the process of generating and exploring this synthetic dataset, it
is critical to bear in mind the primary objective is not an exact emulation of
real-world telematics data. Instead, the focus lies in providing an accessible
gateway for individuals aiming to develop a foundational understanding of such
complex data. Thus, the value of this synthetic dataset lies not in its
replication of real-world data, but in its ability to facilitate learning,
discovery, and comprehension of telematics data structure and interpretation.

###  6.2 Methodological Considerations: Utilizing ChatGPT for Synthetic
Dataset Creation

In the generation of synthetic datasets using ChatGPT, the initial stage
involves the delineation of the data’s anticipated format and structure. When
contemplating a scenario involving tabular traffic pattern data, for instance,
the structure might comprise elements such as date, time, location, traffic
volume, and weather conditions.

Following this, the process segues into the formulation of a sequence of
prompts which serve to guide ChatGPT about the character of the data intended
for generation. Armed with these well-structured prompts, ChatGPT stands
primed to assist effectively in the orchestration of a synthetic telematics
dataset.

###  6.3 Extending Synthetic Data Applications Beyond Demonstrative Purposes

Engaging with the process of synthetic data creation entails acknowledging its
extensive potential that extends beyond mere research and demonstration. In
scenarios where synthetic data are expected to integrate into production or
operational environments, the process is not restricted to the act of data
generation alone.

A vital part of the process is the incorporation of a robust validation and
testing phase, essential for validating the quality of the synthetic data and
evaluating its suitability for its intended function. This crucial phase could
involve statistical comparisons with real data and the employment of synthetic
data within various models.

Though this paper primarily concentrates on delving into potential
applications, rather than preparing for real-world operational use, the
importance of a comprehensive validation process should not be diminished for
those intending to broaden their exploration of synthetic data. This pivotal
step facilitates the unlocking of a synthetic dataset’s full potential, thus
charting the path towards robust, privacy-conscious, and holistic data
solutions.

##  7 An Exploration of Synthetic Telematics Data Generation using ChatGPT

###  7.1 Introduction to Telematics

Telematics, the synergistic blend of telecommunications and informatics, plays
a pivotal role in today’s data-driven era, specifically within the realms of
vehicular operation and urban mobility. At its core, telematics is concerned
with the collection, processing, and transmission of information pertaining to
remote entities, predominantly vehicles, facilitated by telecommunication
devices.

Consequently, the breadth of telematics data encapsulates numerous
informational parameters, including a vehicle’s precise location, speed, idle
time, instances of harsh acceleration or abrupt braking, fuel consumption,
along with other intricate diagnostic data. This wealth of information is
typically harvested via a combination of GPS technology, onboard diagnostics,
and sensory devices. The richness and scope of telematics data make it a
compelling field for the application of synthetic data generation.

###  7.2 The Influence of Telematics Data

Telematics data holds the power to deliver transformative insights across
diverse sectors, with particular prominence in urban planning and traffic
management. A comprehensive understanding of traffic patterns, derived from
this data, is an indispensable asset for managing road infrastructure planning
and traffic congestion. This knowledge facilitates the pinpointing of peak
congestion times and zones, the formulation of strategies for optimizing
traffic flow, the planning of enhanced public transportation routes, and the
overall improvement of the commuter experience.

With the growing ubiquity of Internet of Things (IoT) devices and the
enhancement of connectivity, telematics data has emerged as a critical
component in smart city initiatives. Real-time traffic data can be harnessed
to steer emergency services towards quicker response times, or to inform eco-
routing strategies aimed at curtailing carbon emissions. Therefore, the
potential and impact of telematics data extend far beyond its conventional
applications, leading the charge towards a smarter and more sustainable urban
environment.

###  7.3 Telematics Data in Research and Innovation

Beyond immediate operational applications, telematics data also has immense
potential for research and innovation. Researchers can leverage this data to
predict future traffic trends, improve urban planning, and facilitate the
development of autonomous vehicles. Given the growing concern for privacy and
data security, synthetic telematics data, mirroring real-world data without
compromising privacy, has become a significant research area. Synthetic
datasets can aid researchers in bypassing privacy-related obstacles and
uncovering new insights in urban mobility.

###  7.4 Generation of Synthetic Telematics Data using ChatGPT

The process of synthesizing a telematics dataset with ChatGPT involves prompt
experimentation and iterative refinement, with gradual increases in prompt
complexity. The initial step starts with a simple open-ended prompt such as,
“Can you create a telematics dataset for me?” This step provides an insight
into ChatGPT’s interpretation and structuring of telematics data.

Figure 1: Initial output from ChatGPT in response to the open-ended prompt:
’Can you create a telematics dataset for me?’ - illustrating the AI’s
interpretation and structuring of telematics data.

This initial, basic prompt serves as our first insight into how ChatGPT
understands and structures telematics data. It forms the foundation upon which
we build, enhancing our prompts iteratively for better and more specific
outputs.

The beauty of this approach lies in its progressive nature, reminiscent of a
teaching or training process where we start with the basics and gradually
introduce more complex elements.

From our first prompt, "Can you create a telematics dataset for me?", we glean
several key observations. Firstly, ChatGPT demonstrates an understanding of
what telematics data is, signifying that it is capable of generating data
relevant to our use case.

However, the output is quite short, consisting of only five rows, which
indicates that we may need to provide clearer instructions about the size of
the dataset we desire.

Moreover, while the model generates telematics data, the output format is not
readily usable. The data is not in a format, such as a CSV or Pandas’
DataFrame, that is amenable to further analysis or processing.

These crucial insights inform us that while ChatGPT understands the concept of
a ’telematics dataset’, it requires more specific instructions to generate the
type and format of data we’re targeting. Consequently, these revelations guide
us as we craft more complex prompts in our subsequent iterations.

Moving forward in our data generation journey, our second prompt brings more
specificity to the table, directly addressing some limitations we noticed with
our initial, more open-ended prompt. Our refined prompt reads, "Can you create
a telematics dataset for me that has 100,000 rows and is exportable into CSV
format or a Pandas DataFrame?"

Figure 2: ChatGPT’s response to the refined prompt: ’Can you create a
telematics dataset for me that has 100,000 rows and is exportable into CSV
format or a Pandas DataFrame?’ - showcasing the impact of increased
specificity on synthetic data generation.

This expanded prompt offers a few key enhancements:

  1. 1.

Dataset Size: Explicitly requesting 100,000 rows sets a clear expectation for
the scale of the dataset, influencing potential data generation methods and
potential optimizations for handling larger datasets.

  2. 2.

Format: The prompt’s specification for an exportable CSV format or a Pandas’
DataFrame offers clear guidance on the dataset’s structure.

The second attempt underscores the value of providing explicit instructions in
the prompts. Precise requirements can minimize the likelihood of needing
multiple iterations and can enhance the chances of producing a synthetic
dataset aligned with research needs from the outset.

Although the second prompt exhibits marked improvement over the initial
attempt, the refinement process is iterative, offering continual opportunities
for enhancement. The objective is not to produce a flawless synthetic
telematics dataset at the first instance, but to understand the capabilities
and limitations of the ChatGPT model more deeply, and to learn how to steer it
towards producing the needed data.

With this insight, the focus shifts to the creation of the third prompt.
Building upon the improvements achieved so far, the objective becomes to
strike an optimal balance between specificity and data diversity. This
approach aims to more effectively guide ChatGPT in the generation of a
synthetic dataset that is both usable and better aligned with the
requirements.

Venturing further into the exploration of synthetic dataset creation, the
third prompt incorporates an additional layer of complexity: context. This
step involves asking ChatGPT to envision a real-life scenario, providing a
more tangible backdrop for the data generation process.

The updated prompt is: "Imagine you are a city planner in Columbus, Ohio. You
have been tasked with studying the traffic patterns around the city. The goal
is to help people who have never worked with telematics data have a synthetic
dataset they could practice on. Can you create a telematics dataset that has
100,000 rows and is exportable into CSV format or a Pandas DataFrame? I would
like it to have the following columns: [’driver id’, ’timestamp of trip start
time’, ’timestamp of trip end time’, ’longitude of trip start’, ’latitude of
trip start’, ’longitude of the trip end’, ’latitude of the trip end’, ’average
speed’, ’day of the week’, ’vehicle type’, ’heading’, ’road type’, ’weather
conditions’], as well as any other columns you think would be useful."

Introducing not only a contextual backdrop to guide data generation, but also
explicitly requesting specific columns previously unmentioned, adds further
depth to the synthetic data generation. This third prompt places ChatGPT in
the shoes of a city planner in Columbus, Ohio, intending to generate a
synthetic telematics dataset. Simultaneously, it encourages the model to draw
from its vast training data and suggest additional variables that might
enhance analysis, by inviting it to introduce any other columns it deems
useful.

This example underscores the iterative nature of refining AI requests. By
providing a context, explicitly defining the size and format of the dataset,
and leaving room for the model’s creativity, it edges closer to a synthetic
dataset that meets research and learning requirements. The outcome and
insights from this third endeavor provide the next topic of exploration.

###  7.5 Dealing with Challenges and Debugging

Diving deeper into the complexity of prompts naturally results in more
elaborate outputs, and consequently, the likelihood of encountering issues
elevates. Nonetheless, it’s essential to view these problems not as setbacks
but integral parts of the process. They present opportunities to better
understand the workings of ChatGPT and, importantly, how to leverage its
abilities to address the issues that surface.

During the third iteration, the first coding issue emerged. The code produced
by ChatGPT did not execute as anticipated and returned an error. This
occurrence is not uncommon when working with AI models such as ChatGPT. By
escalating the complexity of the task, the likelihood of encountering an issue
proportionately increases. However, this is precisely where the advantage of
using AI becomes apparent.

Instead of manually debugging the issue, ChatGPT was utilized to identify the
problem and generate a solution. Simply pasting the error back into ChatGPT
elucidated the nature of the error and yielded rectified code that executed
without glitches.

This real-world scenario illustrates the adaptability and power of ChatGPT.
Its capability to understand and correct its own errors further emphasizes its
potential in generating increasingly complex synthetic datasets.

Figure 3: Snapshot of the synthetic telematics dataset as viewed in a Pandas
DataFrame.

##  8 A Methodical Approach to Evaluating the Quality of a Synthetic Dataset

Evaluating the quality of a synthetic dataset calls for a meticulous,
systematic approach, especially when no real-world comparison dataset is
available. Using the created synthetic telematics dataset as an example, the
following stages are suggested to effectively assess its quality.

###  8.1 Diversity Examination

The dataset should exhibit a reasonable range across all variables. For
example, a dataset in which all trips are of the same length, or where a
single type of weather condition prevails, may not provide insightful results.
A prompt for generating Python code to examine the data distribution might be
as follows: “Show how to generate summary statistics for each column in a
Pandas DataFrame for understanding the data distributions within a telematics
dataset.” Keep in mind that the name of the CSV may require modification to
align with the one used during dataset creation.

###  8.2 Relevance Evaluation

Data should align with the real-world context it is intended to reflect.
Therefore, it becomes necessary to ensure that vehicle speeds fall within
city-appropriate limits and that weather conditions are congruent with the
climate typical to Columbus, Ohio. A Python code prompt for checking such
relevance could be: “Provide a method to visualize the distribution of average
speeds in a synthetic telematics dataset. Could you generate a code snippet
for a histogram?” The output following this relevance examination is provided
in the subsequent section.

Figure 4: Output of ChatGPT when queried for generating a Python code snippet
to visualize the distribution of average speeds in the synthetic telematics
dataset.

Figure 5: Histogram of average vehicle speeds obtained from the synthetic
telematics dataset. This visualization is the result of running the Python
code provided by ChatGPT, demonstrating the application of ChatGPT’s generated
code in analyzing synthetic data.

###  8.3 Coherence Verification

Synthetic data should adhere to certain logical principles. For instance,
start times for trips must invariably precede the corresponding end times, and
vehicular headings should remain plausible within the urban framework. A
prompt to generate Python code for verifying this consistency could be phrased
as follows: “What is the procedure to scrutinize timestamp data within a
synthetic telematics dataset? Could a Python code snippet be crafted to
ascertain if trip initiation and termination times align logically?”

###  8.4 Optimizing Synthetic Dataset Assessment

These meticulous steps facilitate a thorough assessment of the synthetic
dataset’s applicability and credibility, even when a real-world comparative
dataset is not available. It’s crucial to emphasize that the process of
generating a synthetic dataset is iterative. Each evaluation serves to enhance
understanding of the dataset’s strong points and areas requiring improvement,
thereby fostering the generation of progressively superior synthetic datasets.

##  9 Conclusion

The process of synthetic dataset creation, as outlined in this paper, involves
multiple iterations and is heavily reliant on providing precise and
comprehensive prompts to guide the AI model, in this instance, ChatGPT. The
capacity to generate synthetic data presents transformative opportunities
across various sectors, including telematics, where privacy concerns and data
scarcity can obstruct progress and innovation.

This exploratory procedure highlighted the advantages of synthetic dataset
creation, with emphasis on their potential to preserve data privacy, augment
real-world data, and provide controlled environments for experimental
purposes. Simultaneously, light was shed on potential difficulties, such as
ensuring the quality and representativeness of synthetic data and the
necessity for meticulous, iterative prompt development.

A practical demonstration navigated the generation of a synthetic telematics
dataset for Columbus, Ohio. Beginning with a basic prompt, the complexity was
gradually increased, with each stage providing learning opportunities for
refining the prompts to achieve the desired output. This step-by-step approach
led to the creation of a dataset with 100,000 rows, demonstrating ChatGPT’s
capability to handle complex tasks.

An assessment of the synthetic dataset’s quality was also conducted, focusing
on the uniqueness, diversity, and relevance of the data points. Descriptive
statistics and visualizations were utilized to explore data characteristics
and the interrelations among variables. Without a real-world comparative
dataset, the importance of applying multiple testing techniques and verifying
the logical coherence and relevance of the synthetic data was acknowledged.

In conclusion, synthetic datasets generated by models like ChatGPT indeed hold
significant potential. However, it is important to remain objective,
acknowledging that they are not perfect replacements for real-world data and
have inherent limitations. Nonetheless, their potential applications in
sectors such as telematics are wide-ranging, providing new avenues for
research and experimentation. With careful crafting of prompts and stringent
evaluation of outputs, AI-generated synthetic data can become a powerful
instrument in a data scientist’s toolkit.

## References

  * [1] Aldren Gonzales, Guruprabha Guruswamy, and Scott R Smith.  Synthetic data in health care: A narrative review.  In PLOS Digital Health, no. 1, p. e0000082, 2023.
  * [2] Neil Savage.  Synthetic data could be better than real data.  In Nature, Apr. 27, 2023.
  * [3] Theresa Stadler, Bristena Oprisanu, and Carmela Troncoso.  Synthetic Data – Anonymisation Groundhog Day.  In arXiv.org, Jan. 24, 2022.
  * [4] Hossein Hassani and Emmanuel S. Silva.  The Role of ChatGPT in Data Science: How AI-Assisted Conversational Interfaces Are Revolutionizing the Field.  In Big Data and Cognitive Computing, no. 2, p. 62, Mar. 2023.