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Input-output transmission characteristics
in heterogeneous photonic crystals

(based on JOSA B papers with E.Sargent and M.Sc. thesis of D. Agueev)

Optical limiters and switchers can be manufactured from
alternating bulk layers of photonic crystals with different
linear refractive indices and different Kerr nonlinearities.
Transmission of light through the periodic material is
simultaneously wavelength- and intensity-dependent. A typical
heterogeneous nonlinear photonic crystals is shown below:

The stationary transmission of light signals through heterogeneous
photonic crystals can be modelled with the coupled-mode nonlinear equations,
derived near the first Bragg resonance in photonic band-gap spectrum:

i A_{x} + n_{0k} B + n_{nl} (|A|^{2} + 2 |B|^{2}) A +
n_{2k} ((2|A|^{2} + |B|^{2}) B + A^{2} B*) = 0,

-i B_{x} + n_{0k} A + n_{nl} (2|A|^{2} + |B|^{2}) B +
n_{2k} ((|A|^{2} + 2|B|^{2}) A + A* B^{2}) = 0,
where A(x) is the amplitude of right-propagating wave,
B(x) is the amplitude of left-propagating wave,
n_{0k} is the standard deviation of the linear refractive
index, n_{nl} is the average Kerr nonlinearity coefficient,
and n_{2k} is the standard deviation of the Kerr nonlinearity.
The transmission problem of the coupled waves A(x) and
B(x) is defined on the finite interval 0 < x < L,
subject to the boundary conditions:

|A|^{2}(0) = I_{in}, B(L) = 0.
The transmitted intensity is defined as I_{out} = |A|^{2}(L),
while the reflected intensity is I_{ref} = |B|^{2}(0) = I_{in} -
I_{out}. The curve I_{out} versus
I_{in} is called the input-output transmission characteristics.
There are two typical input-output characteristics for heterogeneous photonic crystals, shown on the figure:

In the interactive software, the input-output transmission characteristics are computed versus the three parameters of
the coupled-mode equations n_{0k}, n_{nl},
and n_{2k}, the length of the heterogeneous photonic crystal L,
and the range of the interval for transmitted intensity
I_{start} < I_{out} < I_{fin}.
The results are displayed in a single graph.