<s>
Coupled	B-Algorithm
mode	I-Algorithm
theory	I-Algorithm
(	O
CMT	O
)	O
is	O
a	O
perturbational	O
approach	O
for	O
analyzing	O
the	O
coupling	O
of	O
vibrational	O
systems	O
(	O
mechanical	O
,	O
optical	O
,	O
electrical	O
,	O
etc	O
.	O
)	O
</s>
<s>
Coupled	B-Algorithm
mode	I-Algorithm
theory	I-Algorithm
allows	O
a	O
wide	O
range	O
of	O
devices	O
and	O
systems	O
to	O
be	O
modeled	O
as	O
one	O
or	O
more	O
coupled	O
resonators	O
.	O
</s>
<s>
Coupled	B-Algorithm
mode	I-Algorithm
theory	I-Algorithm
first	O
arose	O
in	O
the	O
1950s	O
in	O
the	O
works	O
of	O
Miller	O
on	O
microwave	O
transmission	O
lines	O
,	O
Pierce	O
on	O
electron	O
beams	O
,	O
and	O
Gould	O
on	O
backward	B-Algorithm
wave	I-Algorithm
oscillators	I-Algorithm
.	O
</s>
<s>
In	O
the	O
late	O
1990s	O
and	O
early	O
2000s	O
,	O
the	O
field	O
of	O
nanophotonics	B-Algorithm
has	O
revitalized	O
interest	O
in	O
coupled	B-Algorithm
mode	I-Algorithm
theory	I-Algorithm
.	O
</s>
<s>
Coupled	B-Algorithm
mode	I-Algorithm
theory	I-Algorithm
has	O
been	O
used	O
to	O
account	O
for	O
the	O
Fano	O
resonances	O
in	O
photonic	O
crystal	O
slabs	O
and	O
has	O
also	O
been	O
modified	O
to	O
account	O
for	O
optical	O
resonators	O
with	O
non-orthogonal	O
modes	O
.	O
</s>
<s>
Since	O
late	O
2000s	O
,	O
researchers	O
have	O
capitalized	O
on	O
coupled	B-Algorithm
mode	I-Algorithm
theory	I-Algorithm
to	O
explain	O
the	O
concept	O
of	O
magnetically	O
coupled	O
resonators	O
.	O
</s>
<s>
The	O
oscillatory	O
systems	O
to	O
which	O
coupled	B-Algorithm
mode	I-Algorithm
theory	I-Algorithm
applies	O
are	O
described	O
by	O
second	O
order	O
partial	O
differential	O
equations	O
.	O
</s>
<s>
The	O
formulation	O
of	O
the	O
coupled	B-Algorithm
mode	I-Algorithm
theory	I-Algorithm
is	O
based	O
on	O
the	O
development	O
of	O
the	O
solution	O
to	O
an	O
electromagnetic	O
problem	O
into	O
modes	O
.	O
</s>
<s>
some	O
of	O
the	O
coupled	B-Algorithm
mode	I-Algorithm
theories	I-Algorithm
are	O
derived	O
directly	O
from	O
the	O
Maxwell	O
differential	O
equations	O
although	O
others	O
use	O
simplifications	O
in	O
order	O
to	O
obtain	O
a	O
Helmholtz	O
equation	O
.	O
</s>
