arXiv (Cornell University),
Год журнала:
2023,
Номер
unknown
Опубликована: Янв. 1, 2023
Vortexed
photons
with
finite
orbital
angular
momentum
have
a
distinct
mode
profile
topological
charge
at
the
centre
of
mode,
while
propagating
in
certain
direction.
Each
different
$m$
is
orthogonal,
sense
that
overlap
integral
vanishes
among
modes
values
$m$.
Here,
we
theoretically
consider
superposition
state
3
left-
and
right-vorticies
Gaussian
without
vortex.
These
states
are
considered
to
be
assigned
quantum
states,
thus,
employed
$\mathfrak{su}(3)$
Lie
algebra
associated
SU(3)
group
classify
photonic
states.
We
calculated
expectation
8
generators
algebra,
which
should
observable,
since
Hermite.
proposed
call
these
parameters
as
Gell-Mann
parameters,
named
after
theoretical
physicist,
Murray
Gell-Mann,
who
established
Quantum
Chromo-Dynamics
(QCD)
for
quarks.
The
represented
on
8-dimensional
hypersphere
its
radius
fixed
due
conservation
law
Casimir
operator.
discussed
possibility
explore
QCD
experiments
classified
embed
SO(6)
SO(5).
Stokes
parameters
(
S
)
on
the
Poincaré
sphere
are
very
useful
values
to
describe
polarisation
state
of
photons.
However,
fundamental
principle
nature
is
not
completely
understood,
yet,
because
we
have
no
concrete
consensus
how
spin
photons,
quantum-mechanically.
Here,
considered
a
monochromatic
coherent
ray
described
by
many-body
state,
and
established
basis
in
connection
with
classical
description
based
parameters.
We
show
that
spinor
equivalent
Jones
vector
for
states,
obtain
operators
(Ŝ)
all
components
rotators
an
SU(2)
group
theory.
Polarisation
controllers
such
as
phase-shifters
also
obtained
quantum-mechanical
field
change
phase
wavefunction
states.
average
operators,
id="m2">S=⟨⟩
.
Lie
algebra
is
a
hidden
mathematical
structure
behind
various
quantum
systems
realised
in
nature.
Here,
we
consider
$SU(2)$
wavefunctions
for
polarisation
states
of
coherent
photons
emitted
from
laser
source,
and
discuss
the
relationship
to
spin
expectation
values
with
SO(3)
symmetry
based
on
isomorphism
theorems.
In
particular,
found
rotated
half-wave-plates
correspond
mirror
reflections
Poincar\'e
sphere,
which
do
not
form
subgroup
projected
O(2)
plane
due
anti-hermitian
property.
This
could
be
overcome
experimentally
by
preparing
another
half-wave-plate
realise
pristine
rotator
$SU(2)$,
allows
arbitrary
rotation
angles
determined
physical
rotation.
By
combining
2
quarter-wave-plates,
also
construct
genuine
phase-shifter,
thus,
realising
passive
control
over
full
sphere.
Journal of the Optical Society of America B,
Год журнала:
2024,
Номер
41(3), С. 589 - 589
Опубликована: Янв. 16, 2024
We
explored
an
equivalent
Mueller
matrix
method
for
analyzing
3-D
axial
errors
in
2-D
polarization
state
measurements
the
first
time,
to
best
of
our
knowledge.
The
treats
devices
with
as
a
closed
system,
within
which
transformation
field
is
described
using
3×3
coherency
and
generalized
Jones
(GJM).
4×4
component
numerically
evaluated
from
information
at
input
output
ports.
Furthermore,
research
has
identified
that
any
error
analyzer
(PSA)
can
be
classified
into
two
categories:
alignment
(AAE)
wave-vector
(WAE).
For
latter
case,
we
have
introduced
concept
equal
weight
variance
alternative
spiral
sampling
estimate
upper-bound
relative
(SoP)
error.
A
simulation
result
shows
ideal
bi-plate
PSA,
remains
below
3%
when
deviation
value
less
than
17.7
deg.
applied
analyze
arbitrary
sort
description
this
paper
simpler
9×9
nine-element
Stokes
vector,
potential
vector
beam
generation.
Polarisation
states
are
described
by
spin
expectation
values,
known
as
Stokes
parameters,
the
trajectories
of
which
in
a
rotationally
symmetric
system
form
sphere
named
after
Poincaré.
Here,
we
show
that
broken
rotational
systems
can
exhibit
distinct
topological
structures
polarisation
states.
We
use
phase-shifter
to
circle
(S1)
,
interferes
with
original
input
due
phase
change
output
state
upon
rotation.
By
rotating
using
rotator,
become
torus
id="m2">S1×
arXiv (Cornell University),
Год журнала:
2023,
Номер
unknown
Опубликована: Янв. 1, 2023
Polarisation
is
described
by
an
$SU(2)$
wavefunction
due
to
macroscopic
coherence
of
photons
emitted
from
a
ubiquitous
laser
source,
and
thus,
pulse
expected
behave
as
quantum
bit
(qubit),
i.e.,
qubit
realised
number
photons.
Here,
we
show
that
arbitrary
single-qubit
operation
can
be
carried
out
for
such
employing
optical
modulators,
together
with
standard
plates,
in
computer-controlled
fibre-optic
configuration.
We
named
the
device
Poincaré
rotator,
which
allows
dynamic
control
over
polarisation
state
executing
amount
rotations
on
sphere.
The
rotator
works
operator
Lie
group,
combining
$U(1)$
change
phase
another
amplitude
wavefunction.
have
various
states,
$4
\times
4=16$,
$8
8=64$,
$10
10=100$
distinguishable
states
As
locus
sphere,
successfully
drawn
molecular
structure
Buckminsterfullerene
(C$_{60}$)
coastline
earth.
Twisted
photons
with
finite
orbital
angular
momentum
have
a
distinct
mode
profile
topological
charge
at
the
center
of
while
propagating
in
certain
direction.
Each
different
charges
m
is
orthogonal,
sense
that
overlap
integral
vanishes
among
modes
values
.
Here,
we
theoretically
consider
superposition
state
three
left
and
right
vortices
Gaussian
without
vortex.
These
states
are
considered
to
be
assigned
quantum
states;
thus,
employed
su(3)
Lie
algebra
associated
SU(3)
group
classify
photonic
states.
We
calculated
expectation
eight
generators
id="m2">
Advanced Materials,
Год журнала:
2024,
Номер
unknown
Опубликована: Дек. 1, 2024
Abstract
Topology,
the
study
of
properties
that
are
invariant
under
continuous
transformations,
in
which
number
pores
(genus)
is
a
profound
concept
determines
have
been
verified
many
microscopic
systems,
but
not
studied
macroscopic
materials.
Microgels
widely
used
materials,
and
based
on
microfluidics,
regular,
stable,
reproducible
microgels
can
be
prepared,
studies
from
perspective
topological
principles
reported.
In
this
paper,
system
boric
acid
ester
rapid
cross‐linking
strategy
rapidly
capture
changes
during
transient
process
droplet‐to‐ring
transition
proposed.
The
electrical
dissipation
associated
with
different
topologies
also
investigated,
demonstrating
change
structures
materials
affected
their
properties,
laying
foundation
for
design
modulated
micro
structured
topology
theory.
arXiv (Cornell University),
Год журнала:
2023,
Номер
unknown
Опубликована: Янв. 1, 2023
A
ray
of
photons,
emitted
from
a
laser
source,
is
in
coherent
state,
where
macroscopic
number
photons
are
degenerate
the
same
quantum
state.
The
state
has
degrees
freedom
for
spin
and
orbital
angular
momentum,
which
allow
an
arbitrary
superposition
among
orthogonal
states
with
varying
their
amplitudes
phases,
described
by
representation
theory
Lie
algebra
group.
Here,
we
experimentally
demonstrate
that
can
construct
generators
rotations
simply
combining
widely
available
optical
components,
such
as
half-
quarter-wave
plates
vortex
lenses.
We
have
found
between
vortexed
no-vortex
characterised
motion
topological
charge
upon
rotation
SU(3)
states.
also
realised
singlet
triplet
rays
polarisation
This
corresponds
to
realise
effective
SU(4)
confirmed
projection
SU(2)$\times$SU(2)
passing
through
polariser.
