# Harnessing Brillouin Interaction in Rare-earth Aluminosilicate Glass
Microwires for Optoelectromechanic Quantum Transduction

Mrittunjoy Guha Majumdar<EMAIL_ADDRESS>Quantum Optics &
Quantum Information, Department of Instrumentation and Applied Physics, Indian
Institute of Science, Bengaluru 560012, India  C. M. Chandrashekar
<EMAIL_ADDRESS>Quantum Optics & Quantum Information, Department of
Instrumentation and Applied Physics, Indian Institute of Science, Bengaluru
560012, India  The Institute of Mathematical Sciences, C. I. T. Campus,
Taramani, Chennai 600113, India  Homi Bhabha National Institute, Training
School Complex, Anushakti Nagar, Mumbai 400094, India

###### Abstract

Quantum transduction, the process of converting quantum signals from one form
of energy to another is a key step in harnessing different physical platforms
and the associated qubits for quantum information processing.
Optoelectromechanics has been one of the effective approaches to undertake
transduction from optical-to-microwave signals, among others such as those
using atomic ensembles, collective magnetostatic spin excitations,
piezoelectricity and electro-optomechanical resonator using Silicon nitride
membrane. One of the key areas of loss of photon conversion rate in
optoelectromechanical method using Silicon nitride nanomembranes has been
those in the electro-optic conversion. To address this, we propose the use of
Brillouin interactions in a fiber mode that is allowed to be passed through a
fiber taper in rare-earth Aluminium glass microwires. It suggests that we can
efficiently convert a $195.57$ THz optical signal to a $325.08$ MHz microwave
signal with the help of Brillouin interactions, with a whispering stimulated
Brillouin scattering mode yielding a conversion efficiency of $\sim 45$%.

##  I Introduction

Integrated quantum information processing with localised quantum computing
systems and distributed quantum communication architecture requires the
ability to transduce efficiently between the relevant platforms Lauk et al.
(2020); Rakher et al. (2010); VanDevender and Kwiat (2007); Zhang et al.
(2018). Functionally, that often means a parametric conversion between
distinct regimes in which the systems are operating. For instance, if we
utilise superconducting qubits for quantum computing and undertake quantum
communication using light, we would need optical-to-microwave quantum
transduction capability Witmer et al. (2020); Forsch et al. (2020). Such
transduction usually involves the faithful transfer of quantum information
encoded in a set of bosonic operators ($\\{\hat{a}_{j}^{\dagger}\\}$) to
another set of bosonic operators ($\\{\hat{b}_{j}^{\dagger}\\}$). This could
be possible with distinct bosons, such as photons and phonons, or the same
kind of boson but with dissimilarity in the values within atleast one degree-
of-freedom, such as electromagnetic field modes at non-identical frequencies
Lau and Clerk (2019); Imade et al. (2021); Jiang et al. (2020).

When it comes to optical-to-microwave transduction, the primary problem is the
large difference between the mode-frequencies that lead to off-resonant
interactions Peairs et al. (2020); Lauk et al. (2020). Intermediate systems,
such as atomic ensembles Imamoğlu (2009); Hafezi et al. (2012); Verdú et al.
(2009); O’Brien et al. (2014); Fernandez-Gonzalvo et al. (2015); Williamson et
al. (2014) and magnons Everts et al. (2019); Hisatomi et al. (2016) that
couple to both modes - optical and microwave signals, can facilitate the
bridging of the energy-gap Holzgrafe et al. (2020). Optoelectromechanical
approaches can provide an efficient interface for undertaking quantum
transduction, with optomechanics using elements such as photoelasticity Aben
and Guillemet (1993); Mueller (1938); Aspelmeyer et al. (2014); Bowen and
Milburn (2015) and electromechanics using an interfacing capacitive element
Teufel et al. (2011); Haghighi et al. (2018); Jones and Nenadic (2013); Li and
Gröblacher (2020); Wu et al. (2020). Double-cavity optomechanical systems are
the centrepoint of a standard method for realisation of optical-to-microwave
transduction. Such a system couples a microwave resonator mode $C_{1}$ with
resonance frequency $\omega_{C,1}$ to the vibrational mode of a mechanical
resonator with frequency $\omega_{m}$, that is, simultaneously coupled to an
optical cavity mode $C_{2}$ with resonance frequency $\omega_{C,2}$.

The mediating phononic mode in the optoelectromechanical realisation of
quantum transduction is usually generated in a Silicon nitride (SiN)
nanomembrane. It has been experimentally demonstrated by Andrews et al.
Andrews et al. (2014) wherein SiN nanomembrane is used as one of the mirrors
in a Fabry-Perot cavity while constituting the capacitive coupling to a
superconductor microwave resonator. In the experiment, bidirectional
transduction was performed with 10% net efficiency, albeit with about 1700
noise quanta generated at cryogenic temperatures. The efficiency of conversion
was limited by microwave resonator losses and imperfect mode-matching,
although the two main sources of noise were the thermal vibrational noise and
spurious mechanical modes in the membrane. In another experiment, mechanically
mediated electro-optic conversion in an alternative feed- forward framework
was used to demonstrate microwave to optical conversion with 47% conversion
efficiency Higginbotham et al. (2018).

For efficient transduction, we must remove these spurious mechanical modes,
have low-loss optical transmission platform as well as large opto- and
electromechanical coupling rates. The use of photonic fibers optimises
transmission of optical quantum signals, and thereby the use of the same in
any transduction framework can help achieve high efficiency in the process. In
this paper, we propose the use of traveling-wave optomechanical interactions
known as Brillouin interactions using rare-earth aluminosilicate glass
microwires. A pressure or force density on the material results from
electrostriction or radiation pressure when optical modes of a waveguide
interfere with one another. In the event that there is conservation of
momentum and energy during the interaction, this pressure then stimulates an
acoustic wave. As a result of the acoustic field’s stresses altering the
medium’s dielectric characteristics and perturbing its boundaries, light is
essentially scattered across distinct optical modes. The new proposed scheme
using rare-earth aluminosilicate glass microwires also offers a conversion
rate of $\approx 45\%$, far higher than any other scheme using silicon based
membrane as transduction medium.

##  II Physical Interactions at Coupling Interfaces

Our scheme for undertaking optical-to-microwave transduction involves two
distinct physical interactions at the coupling interfaces: opto-acoustic
interactions using Brillouin scattering and dielectric-modulated magnetic
response at the acousto-electric interface Damzen et al. (2003); Sipe and
Steel (2016); Sturmberg et al. (2019).

###  II.1 Opto-acoustic Interaction with Brillouin Scattering

Certain underlying processes in optically isotropic material substrates result
in opto-acoustic interactions Sturmberg et al. (2019). The electromagnetic
field can produce mechanical strains in the waveguide through electrostriction
Sundar and Newnham (1992). The converse, in the phenomenon of photoelasticity,
is observed when stresses cause localized variations in the dielectric
permittivity Mueller (1938). Waveguide boundaries may physically shift as a
result of radiation pressure caused by the electromagnetic waves reflecting
off of the boundaries of the structure, which in turn drives acoustic waves. A
localised variation in the electromagnetic characteristics is caused by the
mobility of structural boundaries brought about by mechanical vibrations.
Stimulated Brillouin Scattering (SBS) is the nonlinear phenomenon whereby an
injected pump wave is scattered by an acoustic vibration into the Stoke and
anti-Stoke wave components Damzen et al. (2003); Pant et al. (2011); Garmire
(2017); Bai et al. (2018). In 1972, Ippen et al. achieved low-threshold
stimulated Brillouin scattering with input powers as low as 1 W Ippen and
Stolen (1972).

When we couple and guide a coherent laser beam into an optical microwire, the
light gives rise to as well as experiences various kinds of elastic waves that
have similar frequencies. While light is sensitive only to longitudinal and
shear bulk acoustic waves in standard optical fibers, the light and the
evanescent field access the outer-surface as well, in the case of a sub-
wavelength optical fiber, thereby causing the shaking of the wire due to
electrostriction which leads to surface acoustic waves (SAWs) being generated.
The effective refractive index along the microwire varies periodically due to
these ripples, leading to Bragg scattering of the light in the backward
direction as per phasematching condition. The velocity of the bulk and surface
acoustic waves differ significantly, with the surface wave travelling at a
velocity of around 0.9 that of a shear wave and giving rise to other optical
sidebands. Beugnot et al. found the surface acoustic wave mode to travel at a
velocity of 3400 m/s and a frequency of 6 GHz, having studied the generation
of SAWs in an 8 cm. long silica optical microwire that was drawn from a
single-mode fiber using the heat-brush method Beugnot et al. (2014).

Photon silica microwires, fabricated by tapering optical fibers, have been
seen to support stimulated Brillouin scattering Beugnot et al. (2014). It is
found that rare-earth materials like Lanthana and Ytterbia have a finite
effect on the Brillouin characteristics of silica-based oxide glass optical
fibers, with emergent attributes such as a wide Brillouin spectral width, low
acoustic velocity and a negative photoelastic constant Dragic et al. (2014).
Brillouin processes can alternatively be visualised as the formation and
destruction of quasi-particles, in this case photons and phonons Eggleton et
al. (2019). It is typically advantageous to differentiate interactions based
on whether there is an absorption or emission of the phonon. A phonon is
produced when a high-frequency photon undergoes the Stokes Brillouin
transition and changes into a lower-frequency Stokes photon Tang (1966); Hill
et al. (1976). This transition may happen naturally or may be stimulated.
Anti-Stokes transitions, wherein a phonon is absorbed while a lower-frequency
photon is changed to a higher-frequency photon, are also conceivable Enzian et
al. (2022). Brillouin processes can be triggered by either an optical seed
from an auxiliary optical field at the Stokes frequency or by thermal phonons
in the waveguide, which scatter the pump photons Bergman and Tur (2018).

In almost every system of practical importance, it is infeasible to compute
Brillouin scattering from first principles, for example by considering
Maxwell’s equations nonlinearly linked to the Christoffel equation. This is
caused by a division of scales. To start, the optical and acoustic problems’
temporal scales often differ by five orders of magnitude. Second, interaction
lengths on the millimetre scale are necessary for integrated waveguides that
have nonpareil and superlative gain coefficients to give a noticeable overall
response - the system scale is four orders of magnitude larger than the
acoustic wave length. A coupled mode description is especially appropriate to
Brillouin problems due to this scaling divergence Behunin et al. (2018). We
can express the acoustic and optical fields as eigenmodes of the waveguide,
which are weighted by envelop functions - $a_{n}(z,t)$ for each optical mode
and $b(z,t)$ for the acoustic field, thereby giving us the states Wolff et al.
(2015),

$|\psi(x,y,z,t)\rangle=\sum_{n}a_{n}(z,t)|\Psi_{n}(x,y)\rangle
e^{ik_{n}z-i\omega_{n}t}+c.c,\\\ |\phi(x,y,z,t)\rangle=b(z,t)|\Phi(x,y)\rangle
e^{iqz-i\Omega_{n}t}+c.c,$ (1)

where $c.c$ represents complex conjugation. The index $n$ are to characterise
the distinct optical modes, $q$ and $k_{n}$ are the acoustic and optical
wavenumbers, $\Omega$ and $\omega_{n}$ are the acoustic and optical
frequencies. Usually, the scope of applying such modal expansion depends on
whether the amplitudes (envelop functions) have a slower variation than their
respective carrier propagation terms. The basis functions
$|\Psi_{n}(x,y)\rangle$ are bound solutions to the eigenproblem
$(\nabla_{\perp}+i\beta\hat{z})\times(\nabla_{\perp}+i\beta\hat{z})\times|\Psi_{n}(x,y)\rangle=\varepsilon\mu_{0}\omega^{2}|\Psi_{n}(x,y)\rangle$
while $|\Phi(x,y)\rangle$ satisfy
$\rho\Omega^{2}|\Phi\rangle_{i}+\sum_{jkl}(\nabla_{\perp}+iq\hat{z})_{j}c_{ijkl}(\nabla_{\perp}+iq\hat{z})_{k}|\Phi\rangle_{l}=0.$
The first eigen-formulation arises from the manner in which optical fields
evolve by the electromagnetic wave equations in terms of the electric field
(E) and electric induction field (D):
$\nabla\times\nabla\times\textbf{E}=-\mu_{0}\partial_{t}^{2}\textbf{D}$,
$\textbf{D}=\varepsilon E$ and $\varepsilon=\varepsilon_{r}\varepsilon_{0}$,
with $\varepsilon$ being the dielectric constant. In Fig. 1 effective optical
mode in a 2D waveguide is show when the effective refractive index
$n_{\mathrm{eff}}=2.841$ of a rectangular waveguide. The second equation
arises from the acoustic wave equation for a mechanical displacement field
Auld (1973).

Figure 1: Illustration of effective optical mode in a 2D waveguide for
effective refractive index of microwire, $n_{\mathrm{eff}}=2.841$, with (a)
being $\mathrm{Re}(E_{x})$ and (b) being $\mathrm{Re}(E_{y})$.

The optical field satisfies the Maxwell’s equations: $\nabla\times
E=-\delta_{t}B$, $\nabla\times H=-\delta_{t}D+J$, where $B$ and $D$ are the
magnetic and electric induction fields, while $H$ and $E$ are the magnetic and
electric fields, respectively. $J$ denotes the dissipative current that arises
because of Ohmic losses. The optical side of the composite system is
characterised by,
$(\delta_{t}+v_{n}\delta_{z}+\Gamma_{n})a_{n}=\frac{1}{E_{n}}i\sum_{n^{\prime}}e^{i(\phi_{n}-\phi_{n^{\prime}})}[e^{i(qz-\Omega
t)}\omega_{n^{\prime}}Q_{nn^{\prime}}b+c.c.]a_{n^{\prime}}$ per optical mode
that takes part in the Brillouin scattering process, when we consider
variations in $\mathbb{E}$ due to an acoustic field, with $v_{n}$ being the
group velocity of the mode, $\Gamma_{n}$ being the amplitude damping
parameter, $\phi_{n}=k_{n}z-\omega_{n}t$ and $Q_{nn^{\prime}}$ denotes the
opto-mechanical perturbation overlap that characterises the interaction
between distinct optical states mediated by the acoustic field. The equations
of linear elasticity, which connect strain and mechanical displacement,
underlie the dynamics on the acoustic front : $S=\nabla_{s}U$,
$\rho\delta_{t}^{2}U=\nabla.T+f$, where $S$ is the linear strain tensor, $f$
is the body force density, $\nabla_{s}$ denotes the symmetric gradient
operator, $U$ stands for the infinitesimal mechanical displacement vector,
$\rho$ is the mass density and $T$ denotes the Cauchy stress. The equation for
the acoustic mode is then given by:
$(\delta_{t}+v_{b}\delta_{z}+\Gamma_{b})b=\frac{1}{E_{b}}e^{-i(qz-\Omega
t)}\Big{[}\sum_{nn^{\prime}}e^{i(\phi_{n}-\phi_{n^{\prime}})}a_{n}a_{n^{\prime}}^{*}\langle\Phi|F_{nn^{\prime}}\rangle+e^{-i(\phi_{n}-\phi_{n^{\prime}})}a_{n}^{*}a_{n^{\prime}}\langle\Phi|F_{n^{\prime}n}\rangle\Big{]}$,
where $|F\rangle=[0,f]^{T}$ is the driving term due to optical forces
(fluctuations of optical intensity).

###  II.2 Magnetic Flux as Mediator of Acousto-electric Coupling

Inductance is the tendency of an electrical conductor to resist a change in
the electric current that flows through it Jones (2013). A magnetic field is
produced around a conductor by an electric current flowing through it. The
magnitude of the current determines the field strength, which follows any
variations in current. Electromagnetic induction is the process by which a
change in the magnetic field flowing through a circuit leads to the induction
of an electromotive force in the conductors. The cylindrical coil is an
idealized form of inductor having, on a cylindrical surface, a single-layer
winding of constant axial pitch Wheeler (1958). If we have a core of a rare-
earth aluminosilicate glass, we see a diamagnetic magnetic response at the
centre, which is altered based on geometric variations due to the acoustic
mode So et al. (2019); Majerová et al. (2022). In a rare-earth aluminosilicate
glass, the bonding characteristics of the $[\mathrm{SiO}_{4}]$ can be studied
using NMR and IR spectroscopy Kohli et al. (1992, 1993). In systems like
$\mathrm{CeO}_{2}-\mathrm{Al}_{2}\mathrm{O}_{3}-\mathrm{SiO}_{2}$ glasses, the
aluminium is seen to have Al(4) and Al(6) coordination, using NMR studies Lin
and Hwang (1996). In NMR studies, the Al(IV) lines show up as peaks at 54.7
ppm and 54.5 ppm for lanthanum and ytterbium glasses respectively Marchi et
al. (2005). The lanthanum-glasses possess a mixed silica-alumina network with
dispersed silicate groups, while other rare-earth aluminosilicate glasses, the
network is constituted primarily of silicate groups, with $\mathrm{Al}^{3+}$
as modifiers. A decrease in magnetic permeability was found in polycrystalline
Ni-Zn ferrites (NZFOs) upon increasing $\mathrm{Al}^{3+}$ substitution in
$\mathrm{Al}^{3+}$ substituted
$\mathrm{Ni}_{0.7}\mathrm{Zn}_{0.3}\mathrm{Fe}_{2}\mathrm{O}_{4}$
nanoparticles Birajdar et al. (2012). The silica in the system has a near-
unity permeability which may be reduced by the presence of the
$\mathrm{Al}^{3+}$.

Figure 2: The scheme for quantum transduction using optoelectromechanical
coupling of light in an optical fiber with a microwave signal through the
acoustic mode generated in Brillouin scattering in a rare-earth
aluminosilicate glass microwire. In this setup, the tapering of an optical
fiber carrying the optical signal comprises of the microwire, which is taken
as the core of a coil-inductor that is part of microwave resonator RLC
circuit. The variation of the cross-sectional area temporally, due to the
acoustic mode, leads to variations of magnetic flux and, as a result, the
electrical response in the microwave resonator.

##  III Results and Discussion

The primary element in our scheme involves a coil-inductor with a sub-
wavelength rare-earth aluminosilicate glass microwire core that facilitates
generation of surface acoustic waves using Brillouin scattering. Rare-earth
aluminosilicate glasses have high glass transformation temperatures and
moderate thermal coefficients of expansion Shelby and Kohli (1990). With high
concentrations of rare-earth ions, these glasses have excellent weathering
tendency. Interestingly, the glass properties like refractive index,
dilatometric softening, and glass transformation, temperatures have a linear
variation with respect to the rare-earth ionic radius. It has been
hypothesized that the field strength of these ions is the underlying basis for
such variations. Since the field strength is related to the ionic radius via
an inverse relation, we cannot separate the significance of the two.

The schematic illustration of our scheme is presented in Fig. 2 where rare-
earth aluminosilicate glass microwire is used as core. This coil is part of
the RLC microwave resonator circuit. The surface acoustic waves in the sub-
wavelength optical fiber can be effective tools to mediate inductively between
the incoming optical signals and a microwave resonator. If we assume that the
acoustic wave is phase-matched with the beat between the first two optical
modes such that $\Omega=\omega_{2}-\omega_{1}$ and $q=k_{2}-k_{1}$, we can
assume the driving force density F to be of the form

$\textbf{F}(\textbf{r},t)=\textbf{f}(\textbf{r},t)a_{1}^{*}a_{2}+c.c.$ (2)

If we were to consider the acoustic damping due to viscous forces $\eta$, we
can write the acoustic mode equation as

$(\partial_{z}+\frac{1}{v_{b}}\partial_{t}+\alpha)b=-\frac{i\Omega
a_{1}^{*}a_{2}}{\mathcal{P}_{b}}\mathcal{Q}_{b}$ (3)

where

$\alpha=\frac{\Omega^{2}}{\mathcal{P}_{b}}\Big{[}\int
d^{2}r\sum_{jkl}|\Phi\rangle_{i}^{*}\partial_{j}\eta_{ijkl}\partial_{k}|\Phi\rangle_{l}\Big{]},$
(4) $\mathcal{Q}_{b}=\int d^{2}r(|\Phi(x,y)\rangle
e^{iqz-i\Omega_{n}t})^{*}.\textbf{f}(r,t),$ (5)

with $\mathcal{Q}_{b}$ being the coupling parameter that is a work linear
density, $\mathcal{P}_{b}$ being the mode’s energy transport velocity and
$\alpha^{-1}$ is an effective dissipation length for the acoustic mode. We can
similarly write the equations for the optical envelope functions as

$\partial_{z}a_{1}+\frac{1}{v_{1}}\partial_{t}a_{1}=-\frac{i\omega_{1}a_{2}b^{*}}{\mathcal{P}_{1}}\mathcal{Q}_{1},$
(6)
$\partial_{z}a_{2}+\frac{1}{v_{2}}\partial_{t}a_{2}=-\frac{i\omega_{2}a_{1}b^{*}}{\mathcal{P}_{2}}\mathcal{Q}_{2}$
(7)

with

$\mathcal{Q}_{i}=\int d^{2}r\Big{[}(|\Psi_{i}(x,y)\rangle
e^{ik_{i}z-i\omega_{i}t})^{*}.\triangle\textbf{d}_{i}\\\
-\textbf{d}_{i}^{*}.\triangle\textbf{e}_{i}-\mu_{0}\textbf{h}_{i}^{*}.\triangle\textbf{h}_{i}\Big{]}$
(8)

where $\textbf{d}_{i}$ is the induction-mode, $\triangle\textbf{d}_{i}$ is the
perturbation of the same, $\textbf{h}_{i}$ is the magnetic field-mode with the
$\triangle\textbf{h}_{i}$ being the perturbation thereof, and
$\triangle\textbf{e}_{i}$ being the perturbation in the $i^{\mathrm{th}}$
electric field mode. The photoelastic effect, field perturbations due to
varying continuity conditions and effective dynamic magnetic couplign leads to
perturbations $\triangle\textbf{e}_{i}$, $\triangle\textbf{d}_{i}$ and
$\triangle\textbf{h}_{i}$ respectively. Here, $\mathcal{P}_{i}$ gives the
energy transport velocity of the $i^{\mathrm{th}}$ electromagnetic mode. Let
us take the steady-state case and solve the equation for the acoustic mode by
means of its Green’s function
$b(z)=-\frac{i\Omega\mathcal{Q}_{b}}{\mathcal{P}_{b}}\int_{0}^{\infty}dz^{\prime}a_{1}(z-z^{\prime})^{*}\times
a_{2}(z-z^{\prime})\exp(-\alpha z^{\prime})$. Assuming that the optical powers
change on a length scale that is much larger than $1/\alpha$, we can obtain
the stimulated Brillouin scattering gain
$G=\frac{\omega\Omega\mathcal{Q}_{1}\mathcal{Q}_{b}}{\mathcal{P}_{1}\mathcal{P}_{2}\mathcal{P}_{b}(\alpha-i\kappa)}$
with detuning parameter $\kappa$. The generated acoustic modes lead to the
cross-sectional area varying, leading to a change in the area of the inductor-
core within the magnetic flux. In our system, we will be using a segment of
the fiber taper as the dielectric core of a coil-inductor. The manner in which
the geometric perturbations in the core can influence the flux can be seen by
observing the changes in the electromotive force due to flux-variations:
$\varepsilon=-\frac{d\Phi_{B}}{dt}=-\frac{d(\textbf{B}.\textbf{S})}{dt}$. For
the finite coil in our system, we must consider the magnetic field in terms of
the vector potential: $\textbf{B}=\nabla\times\textbf{A}$. Given the geometry,
only the $\textbf{A}_{\theta}$ can be non-zero and $B_{r}=-\frac{\partial
A_{\theta}}{\partial z}$,
$B_{z}=\frac{1}{r}\frac{\partial(rA_{\theta})}{\partial r}$, while for a
solenoid made up of $n$ filaments per unit length, we have Callaghan and
Maslen (1960)

$A_{\theta}=\frac{a\mu
ni}{2\pi}\int_{\xi_{-}}^{\xi_{+}}d\xi\int_{0}^{\pi}\frac{\cos{\theta}d\theta}{\sqrt{\xi^{2}+r^{2}+a^{2}-2ar\cos{\theta}}}$
(9)

where $a$ is the radius of the coil, $\xi=y-l$ with $y$ is the axial
coordinate while $l$ is the distance of the filament from the origin,
$\xi_{\pm}=y\pm\frac{L}{2}$, $\mu$ is the permeability and $i$ is the current
in each filament. We can now find the magnetic-field components

$B_{r}=-\frac{a\mu
ni}{2\pi}\int_{0}^{\pi}\Big{[}\frac{\cos{\theta}d\theta}{\sqrt{\xi^{2}+r^{2}+a^{2}-2ar\cos{\theta}}}\Big{]}_{\xi_{-}}^{\xi_{+}}$
(10) $B_{z}=\frac{a\mu
ni}{2\pi}\int_{0}^{\pi}\Big{[}\frac{\xi}{r^{2}+a^{2}-2ar\cos{\theta}}\times\\\
\frac{(a-r\cos{\theta})d\theta}{\sqrt{\xi^{2}+r^{2}+a^{2}-2ar\cos{\theta}}}\Big{]}_{\xi_{-}}^{\xi_{+}}$
(11)

For a surface acoustic wave travelling in the core such that the radius is a
function of the axial distance $x(y,t)=A\sin{(2\pi y/\lambda-\omega t)}+r_{i}$
(where $A$, $\omega$ and $\lambda$ denote the amplitude, frequency and
wavelength of the acoustic mode while $r_{i}$ denotes the undisturbed radius),
we can write the area elements at the surface of the core as

$da_{z}=\frac{da_{r}}{\cos{(\zeta)}}=\frac{r_{i}+A\sin(\zeta)}{\sqrt{1+\cos^{2}{\zeta}}}\lambda
d\zeta$ (12)

where $\zeta=2\pi y/\lambda-\omega t$. Inductance is defined as
$L=n\Phi_{B}/i$, and in this case, for $r_{i}\rightarrow 0$,

$L=-\frac{\mu
n^{2}}{4}\Big{[}\frac{a^{2}r}{(\xi^{2}+a^{2})^{3/2}}\Big{]}_{\xi_{-}}^{\xi_{+}}\int\frac{r_{i}+A\sin(\zeta)}{\sqrt{1+\cos^{2}{\zeta}}}\lambda\cos{(\zeta)}d\zeta\\\
+\frac{\mu
n^{2}}{2}\Big{[}\frac{\xi}{\sqrt{\xi^{2}+a^{2}}}\Big{]}_{\xi_{-}}^{\xi_{+}}\int\frac{r_{i}+A\sin(\zeta)}{\sqrt{1+\cos^{2}{\zeta}}}\lambda
d\zeta$ (13)

If we consider $\xi>>a$ and $p^{2}=2-\sin^{2}{\zeta}$, with the integration
over $p$ with limits $1\rightarrow\sqrt{2}$, along with considering
$r_{i}=1\,\mu$m and $A=0.05\,\mu$m, we have $L=5.1\ times10^{-9}\mu$ for
velocity of acoustic mode $v=5727\,m/s$ and frequency
$f=11.476\,\mathrm{GHz}$, as is seen to be the case for a microwire
($r_{i}=1\,\mu$m, $l=8\,$cm) at incident light with wavelength 1534 nm (195.57
THz) in the case of lanthano-aluminosilicate Dragic et al. (2014), while
$n=250$. For a resonator circuit with $C=47\,pF$ and standard inductive
element $L=1\,$mH, we then have the frequency of

$f_{r}=\frac{1}{2\pi\sqrt{LC}}=325.08\,\mathrm{MHz}$ (14)

The primary hurdle when it comes to efficiency is the emergence of disparate
acoustic waves besides the surface acoustic waves we require. The primary
factors that lead to losses include the photon-to-acoustic mode conversion
efficiency and the losses in the microwave resonator circuit. Beginning with
the theory of Brillouin scattering, the Brillouin gain $g_{B}$ can be
expressed as Ippen and Stolen (1972)

$g_{B}=\frac{2\pi
n_{\mathrm{eff}}^{7}P_{12}^{2}}{c\rho\lambda^{2}v_{s}\triangle\nu_{B}}$ (15)

where $P_{12}$ is the elasto-optic constant, $\rho$ is the mean density of the
material, $n_{\mathrm{eff}}$ is the effective refractive index of the
microwire, $v_{s}$ is the sound velocity, $c$ is the speed of light in vacuum,
$\nu_{B}$ and $\triangle\nu_{B}$ are the frequency shift of the surface
acoustic wave and FWHM width of the spectrum respectively, while $\lambda$ is
the optical wavelength. Rare-earth aluminosilicates have an effective
refractive index of $n_{\mathrm{eff}}=1.65$ Shelby and Kohli (1990). The
Pockel’s constant is found to be $P_{12}=-0.027\pm 0.012$ Dragic et al.
(2013a). Aluminosilicate glass has a mean density of $\rho=3.48–4.19\pm
0.02\,\mathrm{g\,cm}^{-3}$ Marchi et al. (2005). For Yb-doped aluminosilicate
glass, we have $\nu_{B}=11$ GHz and $\triangle\nu_{B}=287-1550$ MhZ Dragic et
al. (2013b).

There have been studies on the variation of compressional wave velocity and
shear wave velocity of four types of aluminosilicate glasses as a function of
pressure, and the velocity ranged from $\sim 5.5-8$ km/s for compressional
wave velocity, ranged $\sim 3.2-4.2$ km/s for shear wave velocity and ranged
$\sim 4-6.2$ km/s for bulk sound velocity for pressure varying over $0-8$ GPa
Aoki et al. (2020). Using these values, we obtain the Brillouin gain of
$g_{B}=1.0727\times 10^{-11}$ m/W. From literature, a Yb-doped aluminosilicate
fiber with 5 mol% of alumina and 0.2 mol% of Ytterbia has been seen to have a
Brillouin Gain coefficient of $1.1\times 10^{-11}$ m/W, while phosphosilicate
fiber having 20 mol% of $\mathrm{P}_{2}\mathrm{O}_{5}$ and 0.6 mol% of
Ytterbia, the BGC is seen to be around $0.7\times 10^{-11}$ m/W Dragic et al.
(2013b). The critical power is given by Pant et al. (2011):

$P_{\mathrm{cr}}=21\frac{A_{\mathrm{eff}}}{\kappa g_{B}L_{\mathrm{eff}}}$ (16)

where $\kappa$ is the parameter that accounts for variations in polarisation.
For our purposes, we take $\kappa$ to be unity. If we take a microwire with
$1\,\mu$m diameter over a length of 8 cm, $P_{\mathrm{cr}}=19.2194$ W. We can
describe the spontaneous emission noise by adding a spontaneous emission term
to the equations that describe how the pump and Stokes waves evolve Ferreira
(2011). The amplified spontaneous scattered power per unit frequency is given
by

$P(\nu,z)=\frac{\hbar\nu}{A_{e}}\frac{\Gamma^{2}}{\delta^{2}+\Gamma^{2}}g_{B}(N+1)G(\nu,z)\int_{z}^{L}\frac{P_{p}(z^{\prime})}{G(\nu,z^{\prime})}dz^{\prime}$
(17)
$G(\nu,z)=\exp{\Big{[}\int_{z}^{L}\Big{(}\frac{P_{p}(z)}{A_{e}}\frac{\Gamma^{2}}{\delta^{2}+\Gamma^{2}}g_{B}-\alpha\Big{)}dz]\Big{]}}$
(18)

where $A_{e}$ is the effective core area, $\Gamma^{-1}$ is the acoustic phonon
lifetime, $\delta$ parametrizes any detuning of the signal from the Stimulated
Brillouin Scattering gain line center, $P_{p}$ is the pump wave power and
$\alpha$ is the absorption coefficient. $N\approx\frac{kT}{h\nu_{B}}$ denotes
the number of acoustic phonons in thermal equilibrium, with $k$ being the
Boltzmann constant and $T$ being the absolute temperature. In our scheme, if
we take $\nu_{B}=11.476\,\mathrm{GHz}$ at $T=298$ K, $N\approx 565$ phonons.
Fiber-ring lasers can have pulse duration of 4-30 ps Yao et al. (2022).
Specific kinds of systems such as whispering-mode stimulated Brillouin
scattering has shown a field distribution for the photonic and phononic modes,
with a maximum photon-to-phonon conversion of $\sim 45$%. If the phonon-to-
microwave conversion is optimum, we can regard the overall efficiency to be
comparable to the existing schemes for quantum transduction. In this setup,
the noise-power significantly depends on the magnitude of the signal in the
gain-saturation regime. It is particularly high when the signal has low power.
This imposes certain constraints on such a Brillouin-scattering based system.

##  IV Conclusion

We have proposed a scheme for realisation of optoelectromechanic quantum
transduction using rare-earth aluminosilicate glass microwires as the
dielectric core of a coil-inductor. Our scheme makes use of Brillouin
interactions in a fiber mode that is allowed to be passed through a fiber
taper. We have shown how we can convert a light at 195.57 THz to a microwave
signal at 325.08 MHz. We see that the Brillouin gain coefficient obtained for
rare-earth aluminosolicates of $1.0727\times 10^{-11}\,$m/W can give a
critical power of $P_{cr}=19.2194$ W. Given the ease of access and
manoeuvrability of microwires in experimental setups, it can be a practically
relevant scheme for quantum transduction and can be further engineered for
desired transduction. For a whispering SBS mode, we can attain upto $45$%
conversion efficiency using optoelectromechanical transduction scheme
presented in this paper.

Acknowledgement : MGM and CMC acknowledge the support from the Office of
Principal Scientific Advisor to Government of India, Project No.
Prn.SA/QSim/2020

Data Availability Statement : Data sharing not applicable to this article as
no datasets were generated or analysed during the current study.

## References

  * Lauk et al. (2020) N. Lauk, N. Sinclair, S. Barzanjeh, J. P. Covey, M. Saffman, M. Spiropulu, and C. Simon, Quantum Science and Technology 5, 020501 (2020).
  * Rakher et al. (2010) M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, Nature Photonics 4, 786 (2010).
  * VanDevender and Kwiat (2007) A. P. VanDevender and P. G. Kwiat, JOSA B 24, 295 (2007).
  * Zhang et al. (2018) M. Zhang, C.-L. Zou, and L. Jiang, Physical review letters 120, 020502 (2018).
  * Witmer et al. (2020) J. D. Witmer, T. P. McKenna, P. Arrangoiz-Arriola, R. Van Laer, E. A. Wollack, F. Lin, A. K. Jen, J. Luo, and A. H. Safavi-Naeini, Quantum Science and Technology 5, 034004 (2020).
  * Forsch et al. (2020) M. Forsch, R. Stockill, A. Wallucks, I. Marinković, C. Gärtner, R. A. Norte, F. van Otten, A. Fiore, K. Srinivasan, and S. Gröblacher, Nature Physics 16, 69 (2020).
  * Lau and Clerk (2019) H.-K. Lau and A. A. Clerk, npj Quantum Information 5, 1 (2019).
  * Imade et al. (2021) Y. Imade, V. E. Gusev, O. Matsuda, M. Tomoda, P. H. Otsuka, and O. B. Wright, Nano Letters (2021).
  * Jiang et al. (2020) W. Jiang, C. J. Sarabalis, Y. D. Dahmani, R. N. Patel, F. M. Mayor, T. P. McKenna, R. Van Laer, and A. H. Safavi-Naeini, Nature communications 11, 1 (2020).
  * Peairs et al. (2020) G. Peairs, M.-H. Chou, A. Bienfait, H.-S. Chang, C. Conner, É. Dumur, J. Grebel, R. Povey, E. Şahin, K. Satzinger, et al., Physical Review Applied 14, 061001 (2020).
  * Imamoğlu (2009) A. Imamoğlu, Physical review letters 102, 083602 (2009).
  * Hafezi et al. (2012) M. Hafezi, Z. Kim, S. L. Rolston, L. A. Orozco, B. Lev, and J. M. Taylor, Physical Review A 85, 020302 (2012).
  * Verdú et al. (2009) J. Verdú, H. Zoubi, C. Koller, J. Majer, H. Ritsch, and J. Schmiedmayer, Physical review letters 103, 043603 (2009).
  * O’Brien et al. (2014) C. O’Brien, N. Lauk, S. Blum, G. Morigi, and M. Fleischhauer, Physical review letters 113, 063603 (2014).
  * Fernandez-Gonzalvo et al. (2015) X. Fernandez-Gonzalvo, Y.-H. Chen, C. Yin, S. Rogge, and J. J. Longdell, Physical Review A 92, 062313 (2015).
  * Williamson et al. (2014) L. A. Williamson, Y.-H. Chen, and J. J. Longdell, Physical review letters 113, 203601 (2014).
  * Everts et al. (2019) J. R. Everts, M. C. Berrington, R. L. Ahlefeldt, and J. J. Longdell, Physical Review A 99, 063830 (2019).
  * Hisatomi et al. (2016) R. Hisatomi, A. Osada, Y. Tabuchi, T. Ishikawa, A. Noguchi, R. Yamazaki, K. Usami, and Y. Nakamura, Physical Review B 93, 174427 (2016).
  * Holzgrafe et al. (2020) J. Holzgrafe, N. Sinclair, D. Zhu, A. Shams-Ansari, M. Colangelo, Y. Hu, M. Zhang, K. K. Berggren, and M. Lončar, Optica 7, 1714 (2020).
  * Aben and Guillemet (1993) H. Aben and C. Guillemet, in _Photoelasticity of Glass_ (Springer, 1993), pp. 86–101.
  * Mueller (1938) H. Mueller, Journal of the American Ceramic Society 21, 27 (1938).
  * Aspelmeyer et al. (2014) M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Reviews of Modern Physics 86, 1391 (2014).
  * Bowen and Milburn (2015) W. P. Bowen and G. J. Milburn, _Quantum optomechanics_ (CRC press, 2015).
  * Teufel et al. (2011) J. D. Teufel, D. Li, M. Allman, K. Cicak, A. Sirois, J. Whittaker, and R. Simmonds, Nature 471, 204 (2011).
  * Haghighi et al. (2018) I. M. Haghighi, N. Malossi, R. Natali, G. Di Giuseppe, and D. Vitali, Physical Review Applied 9, 034031 (2018).
  * Jones and Nenadic (2013) T. B. Jones and N. G. Nenadic, _Electromechanics and MEMS_ (Cambridge University Press, 2013).
  * Li and Gröblacher (2020) J. Li and S. Gröblacher, New Journal of Physics 22, 063041 (2020).
  * Wu et al. (2020) M. Wu, E. Zeuthen, K. C. Balram, and K. Srinivasan, Physical Review Applied 13, 014027 (2020).
  * Andrews et al. (2014) R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, Nature physics 10, 321 (2014).
  * Higginbotham et al. (2018) A. P. Higginbotham, P. S. Burns, M. D. Urmey, R. W. Peterson, N. S. Kampel, B. M. Brubaker, G. Smith, K. W. Lehnert, and C. A. Regal, Nature physics 14, 1038 (2018).
  * Damzen et al. (2003) M. Damzen, V. Vlad, A. Mocofanescu, and V. Babin, _Stimulated Brillouin scattering: fundamentals and applications_ (CRC press, 2003).
  * Sipe and Steel (2016) J. Sipe and M. Steel, New Journal of Physics 18, 045004 (2016).
  * Sturmberg et al. (2019) B. C. Sturmberg, K. B. Dossou, M. J. Smith, B. Morrison, C. G. Poulton, and M. J. Steel, Journal of Lightwave Technology 37, 3791 (2019).
  * Sundar and Newnham (1992) V. Sundar and R. Newnham, Ferroelectrics 135, 431 (1992).
  * Pant et al. (2011) R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, Optics express 19, 8285 (2011).
  * Garmire (2017) E. Garmire, New Journal of Physics 19, 011003 (2017).
  * Bai et al. (2018) Z. Bai, H. Yuan, Z. Liu, P. Xu, Q. Gao, R. J. Williams, O. Kitzler, R. P. Mildren, Y. Wang, and Z. Lu, Optical Materials 75, 626 (2018).
  * Ippen and Stolen (1972) E. Ippen and R. Stolen, Applied Physics Letters 21, 539 (1972).
  * Beugnot et al. (2014) J.-C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, arXiv preprint arXiv:1401.2362 (2014).
  * Dragic et al. (2014) P. Dragic, C. Kucera, J. Ballato, D. Litzkendorf, J. Dellith, and K. Schuster, Applied Optics 53, 5660 (2014).
  * Eggleton et al. (2019) B. J. Eggleton, C. G. Poulton, P. T. Rakich, M. Steel, G. Bahl, et al., Nature Photonics 13, 664 (2019).
  * Tang (1966) C. Tang, Journal of Applied Physics 37, 2945 (1966).
  * Hill et al. (1976) K. Hill, D. Johnson, and B. Kawasaki, Applied Physics Letters 29, 185 (1976).
  * Enzian et al. (2022) G. Enzian, L. Freisem, J. J. Price, A. O. Svela, J. Clarke, M. Szczykulska, J. Nunn, I. A. Walmsley, J. Silver, L. Del Bino, et al., in _Optical and Quantum Sensing and Precision Metrology II_ (SPIE, 2022), vol. 12016, pp. 87–90.
  * Bergman and Tur (2018) A. Bergman and M. Tur, Sensors 18, 2863 (2018).
  * Behunin et al. (2018) R. O. Behunin, N. T. Otterstrom, P. T. Rakich, S. Gundavarapu, and D. J. Blumenthal, Physical Review A 98, 023832 (2018).
  * Wolff et al. (2015) C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, Physical Review A 92, 013836 (2015).
  * Auld (1973) B. A. Auld, _Acoustic fields and waves in solids_ (Krieger Publishing Company, 1973).
  * Jones (2013) D. S. Jones, _The theory of electromagnetism_ (Elsevier, 2013).
  * Wheeler (1958) H. A. Wheeler, Proceedings of the IRE 46, 1595 (1958).
  * So et al. (2019) B. So, J. She, Y. Ding, J. Miyake, T. Atsumi, K. Tanaka, and L. Wondraczek, Optical Materials Express 9, 4348 (2019).
  * Majerová et al. (2022) M. Majerová, M. Škrátek, B. Hruška, A. Dvurečenskij, P. Švančárek, A. Prnová, J. Kraxner, E. Bruneel, K. De Buysser, and D. Galusek, Pure and Applied Chemistry 94, 197 (2022).
  * Kohli et al. (1992) J. Kohli, J. Shelby, and J. Frye, Physics and chemistry of glasses 33, 73 (1992).
  * Kohli et al. (1993) J. Kohli, R. Condrate, and J. Shelby, Physics and chemistry of glasses 34, 81 (1993).
  * Lin and Hwang (1996) S.-L. Lin and C.-S. Hwang, Journal of non-crystalline solids 202, 61 (1996).
  * Marchi et al. (2005) J. Marchi, D. Morais, J. Schneider, J. Bressiani, and A. Bressiani, Journal of non-crystalline solids 351, 863 (2005).
  * Birajdar et al. (2012) A. Birajdar, S. E. Shirsath, R. Kadam, M. Mane, D. Mane, and A. Shitre, Journal of Applied Physics 112, 053908 (2012).
  * Shelby and Kohli (1990) J. E. Shelby and J. T. Kohli, Journal of the American Ceramic Society 73, 39 (1990).
  * Callaghan and Maslen (1960) E. E. Callaghan and S. H. Maslen, _The magnetic field of a finite solenoid_ , vol. 465 (National Aeronautics and Space Administration, 1960).
  * Dragic et al. (2013a) P. D. Dragic, J. Ballato, S. Morris, and T. Hawkins, JOSA B 30, 244 (2013a).
  * Dragic et al. (2013b) P. D. Dragic, J. Ballato, S. Morris, and T. Hawkins, Optical Materials 35, 1627 (2013b).
  * Aoki et al. (2020) K. Aoki, T. Sakamaki, T. Ohashi, O. Ikeda, and A. Suzuki, Physics and Chemistry of Minerals 47, 1 (2020).
  * Ferreira (2011) M. F. Ferreira, Encylopedia of Optical Engineering, Taylor & Francis, London (2011).
  * Yao et al. (2022) G. Yao, Z. Zhao, Z. Liu, X. Gao, and Z. Cong, Chinese Optics Letters 20, 071402 (2022).


# Photon: A Cross Platform P2P Data Transfer Application

Abhilash Shreedhar Hegde Undergraduate Dept of Computer Science & Engineering
The National Institute of Engineering Mysuru, Karnataka, India
<EMAIL_ADDRESS>Amruta Narayana Hegde Undergraduate Dept of Computer
Science & Engineering The National Institute of Engineering Mysuru, Karnataka,
India<EMAIL_ADDRESS>Adeep Krishna Keelar Undergraduate Dept of
Computer Science & Engineering The National Institute of Engineering Mysuru,
Karnataka, India<EMAIL_ADDRESS>
Ananya Mathur Undergraduate Dept of Computer Science & Engineering The
National Institute of Engineering Mysuru, Karnataka, India
<EMAIL_ADDRESS>C. Vidya Raj Professor & Dean Dept of Computer Science
& Engineering The National Institute of Engineering Mysuru, Karnataka, India
<EMAIL_ADDRESS>
###### Abstract

Modern computing requires efficient and dependable data transport. Current
solutions like Bluetooth, SMS (Short Message Service), and Email have their
restrictions on efficiency, file size, compatibility, and cost. In order to
facilitate direct communication and resource sharing amongst linked devices,
this research study offers a cross-platform peer-to-peer (P2P) data
transmission solution that takes advantage of P2P networks’ features.

The system enables cost-effective and high-performance data transport by using
the compute, storage, and network resources of the participating devices.
Simple file sharing, adaptability, dependability, and high performance are
some of the important benefits. The examination of the suggested solution is
presented in this paper and includes discussion of the P2P architecture, data
transfer mechanisms, performance assessment, implementation issues, security
concerns, and the potential difficulties that needs to be addressed.

The research intends to validate the efficacy and potential of the suggested
cross-platform P2P data transfer solution, delivering better efficiency and
dependability for users across various platforms, through practical
investigations and comparisons with existing approaches.

###### Index Terms:

Peer-to-Peer Networks, Local Area Networks, Mobile Application, Cross-
Platform, Flutter.

##  I Introduction

Data transfer is the application of computing techniques to transmit
electronic or analog data from one device to another. The transferred data may
be of any type, size, context, and nature and it can be accomplished through
network-less modes, from copying data to an external device and then copying
from that device to another. However, this is a time-consuming task and ,even,
an irritating job, in case of multiple changes and transferring of the same
file is done. While some wireless and communication features enable data
transfer smoothly, these being Bluetooth, SMS (Short Message Service), and
Email, they all possess several flaws. Bluetooth does provide good efficiency
for very nearby devices and small files, however, takes a large amount of time
for larger files and is sometimes incompatible with devices that are of lower
quality or branding. Data transfer through SMS is impractical considering its
limitations in size and cost, while Emails, too, have similar flaws.

A peer-to-peer network is an information technology infrastructure that allows
two or more computer systems to connect and share resources without requiring
a separate server or server network. Unlike the client-server architecture,
there is no central server for processing requests and sending responses, for
the peers directly interact with one another. Each computer in a P2P network
provides resources to the network and consumes resources that the network
provides. Resources such as files, printers, storage, bandwidth, and
processing power can be shared between various computers in that network.
Advantages of a P2P Network, within the local area, include easy file sharing,
reduced costs, adaptability, reliability, high performance, and efficiency.

With the existing options with some flaws or with the application in need
having to face some of the flaws with either poor access to the internet and
or previous solutions being non-functional, our proposal aims to address the
above-mentioned with a solution that can tackle the issues on a wide variety
of platforms with ease. Our solution aims to be cross-platform, thus able to
run on any environment and provide the best performance.

##  II Literature Survey

Turbo Share – File sharing application developed by Suraj Bhul et al., [5],
was based on Peer-to-Peer data transfer technology. The app supports features
like multiple file transfer, viewing file sharing history, average data
transfer speed, etc. But it lacks cross-platform availability as it supports
only android devices.

A paper published by Paulo R. M. de Andrade, et al.,[2], describes how cross-
platform applications work and a comparison of the same with native
applications. It draws contrasting features between hybrid, native, and web
apps. It shows how operating systems have evolved, what are the needs for
cross-platform apps, and the richness offered by them when compared to native
apps. It also gives statistical insight into the usage of several types of
applications (native, cross-platform, and web apps).

A paper published by Yoonsik Cheon and team [3], describes their working
experience on converting their natively built Android application to cross-
platform by means of the Flutter framework. The paper describes their
application that was built on a Java platform and how it was to convert the
application using the Flutter framework to make it cross-platform.

A paper by Mr. D. S. Thosar and team, [4], reviews the aspects of file sharing
using a local area network in a peer-to-peer network. The paper speaks of the
various drawbacks that Bluetooth, SMS (Short Message Service) and Internet
based transfer of data ie files face and how a minimal set client to client-
based transfer technology can help to transfer files.

A paper by Wenhao Wu [1] describes cross-platform app development using React
Native and Flutter. React Native is a JavaScript framework that lets
developers build apps using JavaScript. It uses a design principle like React.
It uses declarative approach to design the User Interface (UI). React Native
uses the same fundamental user interface as the building blocks for native
android and iOS apps. The same paper also describes about the ’Flutter’
framework which unlike React Native, does not use JavaScript but rather uses a
newly developed language called ’Dart’. Dart was developed and is maintained
by Google. It provides features like cross- platform support, rich User
Interface features and hot-reload.

##  III Proposed Solution: Photon

Photon is a cross-platform file-transfer application built using the Flutter
framework. It uses HTTP to transfer files between devices. One can transfer
files between devices that run Photon. (No Wi-Fi router is required; one can
use hotspot). Some of the features of photon are,

  * •

Cross-platform support - For instance, one can transfer files between Android
and Windows, GNU/Linux based, Macintosh based systems and vice-versa.

  * •

Transfer multiple files - One can pick any number of files and transfer them
efficiently.

  * •

Smooth User Interface - In contrast to the strictly bound design paradigms
such as Model-View-View Model (MVVM), Model-View-Presenter (MVP), Clean
Architecture and such, the application uses the ”Material You” design
paradigm, an evolution of the Material Design language. Introduced by Google
in 2014, it focuses on customization, personalization, and expressing
individuality within the user interface.

  * •

Minimal internet usage - Transfer of data over the internet, while is
efficient and reliable given the factors being favourable, has the drawbacks
of being expensive, and in case of unfavourable conditions might suffer from
latency. However, in this application, data transfer is facilitated by using
Wireless Fidelity (Wi-Fi) Direct Technology or P2P (Peer to Peer), allowing
devices to connect directly with each other via Wi-Fi without an intermediate
access point. This type of method provides faster transfer speeds when
compared to other technologies such as Bluetooth.

  * •

Security - Uses a secure secret code generation for authentication
(internally). Even though the files are streamed at local area network, these
files cannot be downloaded/received without using the application. Thus, no
external client like a browser can get the transferred files using an URL as
the secret code is associated with the URL. It will be regenerated for every
session.

  * •

Supports high-speed data transfer - Photon is capable of transferring files at
a remarkably high rate, depending upon the Wi-Fi bandwidth however, no
internet connection required.

###  III-A Architecture of Photon

Photon was built using the Flutter framework, designed to provide a fast,
efficient, and reactive application experience. It is widget-based approach
and reactive programming model, combined with the built-in navigation system
and rich set of tools, making it highly feasible for developing high-quality,
responsive and performance applications.

  * •

Widgets - Being the building blocks of Flutter UI (User Interface), from
buttons to layout elements, it describes its UI elements and behaviour. It
consists of two types - StatelessWidgets representing those widgets which
cannot change its state and StatefulWidgets that can be updated and rebuilt.

  * •

Composition - Flutter follows a composition model, complex UI elements are
built by combining multiple widgets which can be either nested or combined in
various methods to get the desired interface.

  * •

Reactive Framework - Changes to the user interface are triggered by the
changes in the application state, defining the reactive behaviour. This
approach helps to keep the user interface coordinated with the underlying
states.

  * •

Hot Reload - Flutter allows developers to make changes in the code and see the
changes immediately without restarting the application, speeding the
development process by providing a fast feedback loop facilitating iterative
development.

  * •

Rendering - Flutter bypasses the native UI components of the underlying
platform and uses its own rendering engine called Skia which renders its UI to
the native canvas, resulting in a highly customizable and performant UI
experience.

Photon was built using the Model-View-Controller (MVC) architecture pattern,
the Model being the data structures that provides necessary data, the View
being the interface that the user gets to see and the Controller being the
intermediate link between the View and the Model, responsible for handling
user input, updating the model and view appropriately. The separation between
the three layers makes it easy to debug and helps to build stable systems with
the clear separation between the application and the business logic. The
changes in the View will not affect the Model, making it easier to make
changes without breaking the application. In the case of Photon being built
with the Flutter framework, multiple screens and views using the same logic
reduces code duplicity, increasing code reusability.

###  III-B Working of Photon

Photon works between two interacting devices, one being a Sender of some data
and the other being the Receiver of the shared Data. The Sender object
initially upon starting the Photon application gets to pick two options (Send
and Receive) and upon choosing Send, the sender first picks the data (be
files/pictures/videos/apk files) that sender wishes to send from the device
(be mobile/desktop) and starts the server. Simultaneously, the other object
the Receiver upon choosing the Receive option first must discover the Sender
within the same network and upon discovery, sends a Permission request to the
Sender who can either deny or accept permission to start the session between
the two. A session is generated between the two objects where the Receiver
gets the file index from the sender who also transfers the files to the
Receiver. After receiving the file, the Receiver can terminate from the
session and end the session, while the Sender too ends the Session with the
Receiver by stopping the server.

Some of the functionalities are described.

  * •

Writing services enables end to end functionality of the application.

  * •

To facilitate the file picking mechanism, the application should be able to
pick files from the device which is provided by the file_picker package to
pick files from the local storage.

  * •

To implement the file transfer mechanism, the application uses Hyper Text
Transfer Protocol (HTTP). When Peer 1 sends the files to Peer2, it sets up a
HTTP-server locally which is received by Peer2 when it makes a HTTP-GET
request. To improve the efficiency, the application does not load the whole
file into the memory streams the file into bytes of data, hence the device
never runs out of memory.

  * •

Error Handling is an important feature that helps to handle a lot of unknown
scenarios that prevent the smooth functioning of the application, Photon is
coded with several try-catch cases.

Figure 1. Sequence diagram showing interaction between peers

###  III-C Performance Check of Photon

To check the performance of Photon, the application was tested against a
variety of devices ranging from Mobile-to-Mobile transfers, Mobile to Desktop
Transfers and Desktop to Desktop Transfers. Mobile environments include
Android and iOS while Desktop environments include Windows (Windows 10,
Windows 11), GNU/Linux (Ubuntu 18.10, Ubuntu 20.04) and Macintosh OS
(Operating System) (Ventura). The results are tabulated to various files of
sizes ranging from few megabytes to 5 gigabytes are displayed in the table I.

TABLE I: File size vs Time taken File size in MB | Time taken in seconds
---|---
1 | 0.039
10 | 0.4
20 | 1
50 | 2
100 | 5
1000 | 62
5000 | 314
aBetween macOS Ventura and Android 13.
TABLE II: Transferring data between different devices System Type | PDF File | Video File
---|---|---
Android Samsung | 5s | 17.20s
iOS iPhone | 4s | 16.80s
Dell Inspirion 3410 AMD Ryzen 5 Win 10 | 4.5s | 16.4s
Dell Inspirion 3000 Intel i5 5th Gen (Linux) | 8s | 24.4s
MacBook Air | 5s | 11.4s
aPDF size - 100MB and High Quality Video - 300MB |

###  III-D Testing

One key aspect of system testing for a Flutter app is testing for
compatibility across different platforms. This means testing the app on a
range of devices, such as smartphones and tablets, with different screen sizes
and resolutions, as well as testing the app on different operating systems
such as Android, GNU/Linux, Windows and macOS. This helps ensure that the app
functions correctly on all platforms and that users have a consistent
experience across devices. For testing software, various test strategies are
to be used such as unit testing, integration testing, system testing etc. The
project was put through intensive testing methods to ensure efficiency and
accuracy.

TABLE III: Test cases

###  III-E CONCLUSION AND FUTURE ENHANCEMENTS

A comprehensive solution to the problems with data transfer is provided by the
suggested Peer- to-Peer Data Transfer App Within Local Area Network, which
also delivers a quick, effective, and cross-platform experience. The programme
enables direct communication between devices within a local area network by
utilising a peer-to-peer network infrastructure, doing away with the
requirement for a separate server. This strategy guarantees quicker data
transfer speeds while simultaneously saving money. The programme optimises
bandwidth usage because it does not rely on the internet, making it the best
option for sending large files or sensitive data. Future updates can
concentrate on extending support to Android TV devices to further improve the
app. With this improvement, the app’s functionality would be expanded and
smooth data transfer between Android TV devices and other local network
devices made possible. Additionally, a user-friendly and visually beautiful
application will be made possible through ongoing improvements to the user
interface and overall user experience.

## Acknowledgments

We would like to thank our institution ”The National Institute of Engineering,
Mysuru” For all the support rendered. Also we wish to acknowledge all the
contributors of various technical papers and journals for their valuable
contribution.

## References

  1. 1.

Wenhao Wu, “React Native vs Flutter, cross-platform mobile application
frameworks”, Metropolia University of Applied Sciences Bachelor of Engineering
Information technology Thesis 01 March 2018.
https://www.theseus.fi/bitstream/handle/10024/146232/thesis.pdf?sequence=1

  2. 2.

Paulo Roberto Martins de Andrade et al., “Cross Platform App: A Comparative
Study”, University of Regina.
https://www.researchgate.net/publication/271965071_Cross_Platform_App_A_Comparative_Study

  3. 3.

Yoonsik Cheon et al., “Converting Android Native Apps to Flutter Cross-
Platform Apps”, Las Vegas, NV, USA,2022.
https://ieeexplore.ieee.org/document/9799091

  4. 4.

Mr. D. S. Thosar et al., “A review on file sharing using LAN in peer-to-peer
network”, S.V.I.T Chincholi, Nashik, 2021

  5. 5.

Suraj Bhul et al., “File Sharing Application: Turbo Share”, 2022.