All-optical signal processing in photonic structures with shifting bands
We propose the principal scheme of all-optical adder based on the dependence of electromagnetic spectra in photonic bandgap materials containing optically nonlinear layers on the light signal intensity. The system consisting of periodical layered structure covered by optically nonlinear material is...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2004
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| Cite this: | All-optical signal processing in photonic structures with shifting bands / E.Ya. Glushko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 4. — С. 343-349. — Бібліогр.: 12 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1192122025-02-23T19:25:13Z All-optical signal processing in photonic structures with shifting bands Glushko, E.Ya. We propose the principal scheme of all-optical adder based on the dependence of electromagnetic spectra in photonic bandgap materials containing optically nonlinear layers on the light signal intensity. The system consisting of periodical layered structure covered by optically nonlinear material is investigated and photonic structure behavior with changing intensity is calculated. Theoretical estimations of adder parameters are made for different nonlinear materials and frequencies of laser source. The work was partially supported by the grant STCU-2444. 2004 Article All-optical signal processing in photonic structures with shifting bands / E.Ya. Glushko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 4. — С. 343-349. — Бібліогр.: 12 назв. — англ. 1560-8034 PACS: 42.65.-k, 42.65.Pc, 42.70.Qs, 78.20.-e https://nasplib.isofts.kiev.ua/handle/123456789/119212 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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We propose the principal scheme of all-optical adder based on the dependence of electromagnetic spectra in photonic bandgap materials containing optically nonlinear layers on the light signal intensity. The system consisting of periodical layered structure covered by optically nonlinear material is investigated and photonic structure behavior with changing intensity is calculated. Theoretical estimations of adder parameters are made for different nonlinear materials and frequencies of laser source. |
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Glushko, E.Ya. All-optical signal processing in photonic structures with shifting bands Semiconductor Physics Quantum Electronics & Optoelectronics |
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All-optical signal processing in photonic structures with shifting bands |
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All-optical signal processing in photonic structures with shifting bands |
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All-optical signal processing in photonic structures with shifting bands |
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All-optical signal processing in photonic structures with shifting bands |
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All-optical signal processing in photonic structures with shifting bands |
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all-optical signal processing in photonic structures with shifting bands |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2004 |
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All-optical signal processing in photonic structures with shifting bands / E.Ya. Glushko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 4. — С. 343-349. — Бібліогр.: 12 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 343-349.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
343
PACS: 42.65.-k, 42.65.Pc, 42.70.Qs, 78.20.-e
All-optical signal processing in photonic structures with shifting
bands
E.Ya. Glushko
V. Lashkaryov Institute of Semiconductor Physics, 45, prospect Nauky, 03028 Kyiv, Ukraine,
Kyiv Slavonic University, 9, Anry Barbusse str., 03150 Kyiv, Ukraine,
Phone: 525 98 15, Fax: 528 94 07,
E-mail: eugene.glushko@scientist.com
Abstract. We propose the principal scheme of all-optical adder based on the
dependence of electromagnetic spectra in photonic bandgap materials containing
optically nonlinear layers on the light signal intensity. The system consisting of
periodical layered structure covered by optically nonlinear material is investigated and
photonic structure behavior with changing intensity is calculated. Theoretical
estimations of adder parameters are made for different nonlinear materials and
frequencies of laser source.
Keywords: all-optical processing, nonlinear materials, photonic bandgap materials.
Manuscript received 30.06.04; accepted for publication 16.12.04.
1. Introduction
The awaited advantages of all-optical principles use in
logical devices for optical computing, optical
associative memories, and optical interconnections are
connected with their higher operation frequencies in
signal processing, small energy losses and practically
unlimited possibilities to organize parallel operating the
signals [1-5]. The all-optical ideology is used to mean
the absence of electronic transforming signals at any
stage of the process as well as spin or phonon
mechanisms in signal processing. The reason of all-
optical anticipated efficiency in obvious axiom that each
signal transformation from one physical form into
another decreases the common speed of signal passing
through the device. By evaluations, the all-optical way
in computing devices may have a great importance for
the development of the next computer generation [4, 5].
We will consider all-optical signal processing
based on the intensity depending photonic bandgap
materials (PBG) containing optically nonlinear layers.
Due to nonlinearity under illumination, both the bands
position and local nonlinear modes position are shifted,
which leads to a strong deviation in transmission and
reflection of the light signal depending on its intensity.
The all-optical adder task is transformation of a physical
sequence of added signals to the logical sequence with
corresponding shift of digital units. The idea of angular
processing discussed in [6] for linear PBG materials is
continued here as regard to nonlinear materials. It is
important for our consideration that, when the intensity
is changed, the nonlinearity causes the changes in the
light signal angular distribution even at the steady input
beam angles.
We will take into account also the fact that, in the
logical adding process, there arise for some
configurations of PBG system controlled by nonlinear
insertions into the frequency-angular area sensitive to
the signal transformation depending on its intensity.
One more feature is that the adding process must be
accompanied by necessary utilization of superfluous
energy. For instance, let the physical sequence of two
added signals has the form (0,2,2,2,…,2) where
numbers show the intensity magnitude. If the adder
have transformed this sequence into the logical
sequence (1,1,1,1,…,0), then almost the half of the
input energy have to be drawn aside. There exists also
the problem of adder range precip by the rejected part
of light beams. In this work, we discuss the way to
solve the problem through the use of special precip
appendix joining the each adder cell output and
adsorbing the rejected energy.
The field structure for optically linear
semiconductor, dielectric and mixed type 1D and 2D
photonic crystals was investigated in previous works [6,
7]. It was shown that, for infrared optoelectronics of
wavelengths in the interval (1…10) μm, the investigated
structures GaAs/AlGaAs and GaAs/glass 1D layers had
the characteristic frequency ω0 in the interval
(2…20)⋅1014 s–1 and layer width ranging from 0.01 to
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 343-349.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
344
Fig. 1. Geometry of all-optical adder cell. The indexes a, 1, and
2 mark covering optically nonlinear layer and PhCr layers
respectively, na, n1, n2 are refraction indexes, ϕa, ϕ1a, ϕ2a are
total intrinsic reflection angles, ϕ0L, ϕ0R are left and right
incidence angles, parallelogram areas show the corresponding
total transmission cones.
0.20 μm. In this case, there exists a possibility to
operate by the mode population at a given frequency
using special input fibres delivering external signals to
each mode at separated angles ϕ(i), i = 1, 2,…, 16.
Calculated in [6] 32- and 16-periodic GaAs-SiO2
layered systems may serve as light reservoirs where two
binary sequences experience the physical mixing. As to
the signal adding, the problem was formulated there for
a transformer having non-linear input-output
characteristics of special view. Here, we will consider
the all-optical device that transforms physically mixed
sequence of signals into the logical sequence.
2. Trapped modes inside the photonic crystal that
contains nonlinear layers. The intrinsic problem.
One-dimensional periodic layered structures exhibit
bands and gaps in the spectrum of electromagnetic
waves. Originally proposed by Yablonovitch [8] the
PBG materials or the so-called photonic crystals (PhCr)
are attracting close attention due to a lot of possible
applications. Layered hierarchical structures and the
interferential nature of gap formation were investigated
in [9] using the angular-frequency diagram method.
Regular well controlled photonic spectrum
hierarchy produced by PhCr is the property perspective
in optical computing, transforming and storing devices.
Here, we will consider the physical principles and
parameters of an optical chip operating due to the
closed irradiation that is to say standing electromagnetic
waves trapped inside the crystal by the total intrinsic
reflection. In contrary to trapped irradiation, the
transmitted one transfers the energy and momentum
through the sample. Physically both types of waves may
be differed in their properties, especially if one uses the
analogy between quantum mechanical electronic states
and the photonic ones [6]. Just kind of gaps
corresponding to trapped waves has all grounds to be
named as photonic gaps. In the case when the field
source is located inside the PhCr, the field spectrum for
1D layered structure is described by the system of
interface boundary conditions [7, 9] presented in Table,
where ksz is the mode wavevector projection onto z-
direction in s-material, ds is an appropriate layer width.
The 1D layered system under consideration (Fig. 1)
consists of N binary periods of alternating layers 1-2
and besides it includes one covering layer a with the
refraction index sensitive to the intensity of the incident
light beam. The light transition through the system is
determined by the Maxwell boundary conditions that
form the system of 2N+4 equations. The matrix
structure of the system is presented in Table where L
and R columns mark the left and right media, the stroke
means the returning wave running in opposite to z
direction, I(ω) is the light signal intensity. The intrinsic
problem represents a situation when the source of the
light is located inside the PhCr, wave angles θs in each
s-material belong to the total reflection range of the
whole system: θa > φa and light energy don’t leave the
system. The electromagnetic field existing in the area
are field eigenmodes satisfying the dispersion equation
that describes the system determinant zeros. The
generalized matrix-production form of the dispersion
equation [7, 9] looks like:
( ) ,0
,
,
,
,
,
,
22
22
11
11 =⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
μλ
νμ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
μλ
νμ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
μλ
νμ
−
r
r
N
aa
aa
ll Z
Y
YZ (10)
where each matrix represents a layer of the proper width
ds. Adding a new layer causes arising of its transfer
matrix in the respective position. We will analyze one
more geometry besides that shown in Fig. 1 with two
ending nonlinear a-layers at both sides of the PhCr. The
production of binary structure layer matrixes under the
power sign gives the transfer matrix of the PhCr period
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
μλ
νμ
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
μλ
νμ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
μλ
νμ
,
,
,
,
,
,
22
22
11
11 , (2)
).sin()cos(2
),sin()cos(2
),cos(2
2
2
sszsss
sszsss
sszsss
dkiY
dkiZ
dkZY
θ=ν
θ=λ
=μ
s = a, 1, 2 (3)
The nonlinear a-material should meet the demand
of strong nonlinearity conjugated with small switching
times in the picosecond area. As to the PhCr its
nonlinearity must be insufficient and optical contrast
between neighboring layers must be well expressed.
Represented in Fig. 2 is the diagram of nonlinear
materials made in spirit of that published in [10]. The
most attractive for optical signal processing area that
unites the strong nonlinearity with small switching
times lies in the left upper corner apart from the main
sequence dots that occupy a direction from upper right
corner to lower left one. We suppose that materials with
lower refraction indexes are more preferred for the best
exhibition of the nonlinear blooming properties. To
demonstrate the general features of the effect, we will
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 343-349.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
345
Fig. 2. The diagram of optically nonlinear materials. The χ(3) –τ
diagram for nonlinear materials by [10]. 1 corresponds to quartz
glass, 2 is doped glasses area, 3 shows area of super-nonlinear
materials perspective for optical signal processing, 4 is area of
electron nonlinearity in semiconductors, 5 shows dyes area, 6
marks liquid crystals area. Repeating materials are presented at
the temperatures 10, 77, and 300 K from up to below (for
instance, GaAS).
Fig. 3. Band angular-frequency diagram for glass-silicon/glass
system. High-frequency range. Shaded areas are bands,
ω0 = 1.2415 eV, da =10 μm, d1 = 30 μm, d2 = 20 μm, I(ω) = 0.
Fig. 4. Bandgap intensity dependence. Shaded areas are bands,
ω0 = 1.2415 eV; 1 – R-scheme processing frequency
ωa1 = 6.356; 2 – T-scheme processing frequency ωa2 = 6.360ω0,
mode angle inside a-layer θa = 0.915, beam “one” intensity
I0 = 9.7·104 kW/cm2, q2 = 3·10–7 cm2 /kW.
consider here the copper chlorine nonlinear layer
controlling the optical properties of the structure. For
cubic crystals, the approximate refractive index
dependence vs external signal intensity looks like
)( ),()()( )3(
220 ωχ∼ω+ω=ω qIqnn aa . (4)
Here, na0(ω) is the refractive index without illumination,
I(ω) is the intensity of light signal, q2 is the nonlinearity
coefficient taken from Fig. 2. The frequency
dependence of refractive index was evaluated by the
expression
)()( 0100 aaaa nnn ω−ω+=ω , (5)
where na0 = 1.706, na1 = 0.1463, ωa0 = 1.606 eV for
CuCl layer.
The diagram gives q2 = 10–7 cm2/kW that produces
the needed 0.1…1 % modulation of the refraction index
at beam intensities I(ω) = 105 kW/cm2 having the order
of the optical breakdown intensity.
More suitable materials based on silicon glasses
doped by semiconductor impurities (Fig. 2, number 2)
have more preferred nonlinearity coefficient q2 ≈ 10–
6 cm2/kW, but corresponding switching times are worse.
The requirements to materials forming the PhCr are
described in the diagram by the area that lies lower than
the main sequence diagonal or by the area characterized
by large switching times. For optical signal processing
purposes, it is convenient for the processes inside PhCr
to be no more than q2 < 10–8 cm2/kW or if the switching
time τ > 10–6 s. In both cases, the PhCr nonlinearity will
be not essential in adopted area of signal intensities and
signal processing frequencies.
We have calculated the eigenmodes of TH-
polarized plane waves trapped inside the PhCr by the
total intrinsic reflection in the dependence on the
incident angle, number of periods and layer widths. The
activation of such states may be performed through the
special input waveguides contacting with the nonlinear
layer covering the PhCr. The typical angular-frequency
diagram calculated for a nonlinear material taken from
the group 2 marked in Fig. 2 and silicon/glass layered
structure as the PhCr is shown in Fig. 3. Shaded areas
represent bands in the limit N → ∞. The angular
interval 0.914…1.00 rad corresponds to the total
intrinsic range of this structure where the standing
modes exist. Signal processing is performed at one of
the angles from this interval and close to one of the
band-gap-band zones. Presented figure gives a lot of
possibilities to choose the operation points. Moreover,
the undertaken calculations performed for different
structures have shown a very precise scale effect of the
band picture, especially in the lower part of the angular
interval. With the accuracy better than 10–4, the band
structure is not changed when transformations
tddt ss / , →ω→ω are made where t is constant and s
indicates materials. For the band structure shown in
Fig. 3, the same will be for ω0 = 0.12253 eV and
da = 100 μm, d1 = 300 μm, d2 = 200 μm. The reason is
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 343-349.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
346
in transfer matrix (3) arguments of sine and cosine ksds ,
where ks is proportional to ω. The scaling property
allows simply recalculate the photonic crystal
parameters needed for the given laser frequency of the
signals. For the laser signal wavelength 1.06 μm that
hits into Fig. 3 point ωl = 6.3ω0, the recalculation gives
the nonlinear layer and silicon/glass PhCr parameters
da = 1.51 μm, d1 = 3.02 μm, d2 = 4.53 μm. The order of
bandwidths of assumed values is about 600 cm–1 and
bandgaps 300 cm–1 (Fig. 3).
The intensity dependence of a selected spectral
fragment calculated by (4) for the frequency interval
(6.35…6.37)ω0 is shown in Fig. 4. Here, we assign the
light beam angle inside the a-layer θa = 0.915, the beam
“one” intensity equals to 9.7·104 kW/cm2, and
nonlinearity coefficient q2 = 3·107 cm2/kW. The left
arrow indicates R-scheme processing at the convenient
frequency ωa1 = 6.356ω0 corresponding to the chosen
laser wavelength. The convenient T-scheme processing
frequency ωa2 = 6.360ω0. In both cases, the arrow
position has to be chosen far enough from the band
edge inside for the transferred signal and outside for the
reflected one. The difference between R- and
T-schemes is in the signal intensity “one” or “two”
assigned for the reflected signal. The general demand
for the number of PhCr periods N > 15 is called to
supply absolute reflection and transmission for chosen
operation frequencies in the band edge vicinity. It is
also of importance to consider the angular properties of
the signal processing area. Taking into account the
finite number of modes inside the band, the angle of
processing θa should be corresponding to the possible
maximal density of states.
Using (6), one can recalculate the system structure
presented in Fig. 4 for energy unity ω0 = 1.2253 eV to
the proportion that provides both processing schemes at
the light signal wavelength 1.06 μm that gives for
R-scheme: da = 1.50 μm, d1 = 2.99 μm, d2 = 4.49 μm,
gap ΔR = 204.6 cm–1 and for T-scheme: da = 1.50 μm,
Fig. 5. Adder cell principal scheme. 1 – input waveguide; 2 –
input ledge; 3,4 – output waveguides (appendix lead isn’t
shown); 5 – nonlinear layer; 6,7 – two layers consisting the
structure period. Yellow (light) arrows show light signals, digits
show signal intensity for corresponding first, second or third
position.
d1 = 3.00 μm, d2 = 4.50 μm, gap ΔT = 188.6 cm–1. The
recalculation of Fig. 4 structure for GaN laser
wavelength 0.36 μm gives for R-scheme: da = 4.41 μm,
d1 = 8.82 μm, d2 = 13.23 μm, gap ΔR = 69.5 cm–1 and
for T-scheme: da = 4.41 μm, d1 = 8.82 μm,
d2 = 13.22 μm, gap ΔT = 64.0 cm–1.
In fact, in our case the nonlinear influence of the
active layer belongs to the kind of blooming effects.
Though the covered active layer is thin as compared
with the volume of PhCr, the change of the signal
intensity leads to the sufficient change in the incidence
angle of the wave incident from the nonlinear layer onto
the linear PhCr. On the other hand, the kind of
nonlinearity belongs to amplitude bistability effect.
3. Adder cell schemes
The system under consideration changes its reflectivity
in dependence on signal intensity and may transmit bits
to the neighbor major-order cell if the signal
corresponds to “2”. We solve the task of an optical bit
signal shift to the high-order digit position by using
these two outputs for each input signal. One of the
output signals intends for bit transport from junior
position to major one if the physically added signal “2”
arrives to the cell. Another one serves for both signals
“1” and “0” pass through the cell without changing.
There exist two ways to organize the shift of bit signal
from low-order digit position to the high-order digit. In
framework of R-scheme, the non-binary signal reflects
from the cell. In the T-scheme, the signals of double
intensity pass through the cell without changing. The
cell structure for T-scheme of signal processing is
plotted in Fig. 5. The input signals “0”, “1” or “2” pass
through the waveguide 1 directed relatively to the
surface at the processing angle. The reflected signal
arrives to output lead 3. The transferred signal passes
through the output waveguide 4. The input and output
waveguides communicate with the cell by means of
special ledges having the semi-spherical shape and
situated on the outer sample surface. They aimed to
supply the beam hitting inside the total reflection range.
In fact, the system considered above does not absorb
the light beam energy. The only system action is to direct
signals “1” and “2” through different outputs. The next
problem is to reduce the intensity of the signal “2” passed
through the cell to demanded “1”. It can be achieved by
the use of special beam splitters dividing doubled light
signal into two equal parts. The splitter in the form of an
appendix has to be joined to each adder cell output that
corresponds to signal “2”. Depending on chosen
processing scheme, it may be the reflection or
transmission output. Another function of the beam
appendix is in adsorbing of rejected energy. The maximal
amount of the rejected energy during the adding process
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 343-349.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
347
may reach a half of the input energy and the energy must
be drawn aside.
In considered above cases described by Figs 1, 3-5
the system nonlinearity was presented in one outer layer.
We have analyzed also the case with two nonlinear
covering layers at both sides of PhCr when both output
signal angles coincide. The calculated cell parameters
were the same, if the number of PhCr periods remained
big enough (N ≥ 20).
It is noteworthy that three-input adder cell design has
the principal character. The design differs the adder cell
from logical gates [12] where only two inputs are used.
The adder third wave-guide input meant for the bit
shifting into the side of the major digit. The analysis
performed shows that transformation of the described
adder cell into any of logical gates needs uniting the pair
of inputs or blanking-off one of them.
4. Signal processing inside the adder body
Below we propose an essential development of all-optical
adder presented in [6]. The perspective system for an
adder cell includes one or several nonlinear layers
covered the 1D photonic crystal. Due to sensitive areas in
the system’s angular-frequency diagram inside the whole
reflection range the nonlinearity effect may lead to
considerable change in light reflection and transmission.
Both solitary local modes and band modes may be used.
Due to the nonlinear shift depending on the input signal
intensity 0, 1 or 2 the cell proposed gives two output
signals: in reflection 0, 1, and 0 respectively, and in
transmission 0, 0, and 1 respectively. The combination of
neighboring output signals allows performing the
transformation of simple physical addition to logical one.
The binary summing scheme proposed before in [6]
for two binary complicate optical signals having the
structure of junior bits determined from characteristics of
optical threshold amplifier. Demanded input-output
characteristics of an amplifier that should transform a
simple fractional optical signal into the simple integer
signal of standard intensities include the existence of
special falling areas. The presence of falling areas inside
the input-output characteristics enabled to transform non-
binary signal (02) arising after the physical summation of
two equal signals (01) and (01) into the binary one (10).
The modified approach is based on cell properties
that allow differ signals “1” and “2”. There exist two
close ways to organize binary adding of complicated
signals built on the signal “2” reflection or transmission:
R-scheme and T-scheme.
To realize the adder R-scheme let us situate the cells
in columns and rows in such a way that unitary signals
bringing the logical “one” let to move along rows
without changing. Doubled signals due to the a-layer
nonlinearity, chosen PhCr structure and frequency range
are forced to reflect from the cell and redirect to the cell
corresponding to the next digit and situated in the next
column. The extra-intensity can be drawn aside by
special appendix waveguides shown by red curls in
Fig. 6.
Fig. 6. R-scheme of physical signal transformation into logical
sequence. The arrows show light signals, digits show signal
intensity. (0, 1, 2) (0, 1, 0) and (001) in both outputs. The curl
appendixes at reflection outputs reduce reflected 2 units twice.
Extended matrix of the boundary conditions system. Matrix elements: ssZ θ= cos ; sssY θε−= sin ; ))(( ωε=ε Iaa ;
)exp( sszss dikZV = ; )exp( sszss dikYW −= , s = a, 1, 2, l, r.
L L' a a' 1 1' 2 2' … N–2' N–1 N–1' N N' r
Zl Zl –Za –Za 0 0 0 0
–Yl Yl Ya
–Ya 0 0 0 0
0 0 Va Va* –Z1 –Z1 0 0
0 0 Wa Wa* Y1 –Y1 0 0
0 0 0 0 V1 V1* –Z2 –Z2
0 0 0 0 W1 W1* Y2 –Y2
0 0 0 0 0 0 V2 V2*
…
… V–2* –Z–1 –Z–1
W–2* Y–1 –Y–1
V–1 V–1* –ZN –ZN 0
W–1 W–1* YN
–YN 0
VN VN* –Zr
WN WN* Yr
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 4. P. 343-349.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
348
The adder T-scheme is characterized by another way
of digit shifting. In T-scheme, doubled signals pass
through the cell without decreasing, whereas the physical
“one” reflects from the cell body and is taken into
account in this row digit. The transferred physical signal
“two” must be detached into two signals “one” and one
of them continues its way. In this case, the extra-intensity
is also drawn aside by special appendix waveguides.
For both schemes, the number of cells in a column
equals to the whole number of optical adder digit
capacity. The digit hierarchy from junior to major is
reflected in the adder in sequence directed from the top to
down. Then the number of cells in a row depends on the
row position in hierarchy. To process all three possible
types of input physically added binary sequences
containing “0”, “1” or “2” graded intensities the every
next row should be one cell longer.
If s is the adder’s digit capacity, then for total cell
number S we have:
2
)1( ssS +
= (6)
For example, the 256-digit capacity adder should be
consisted of 32896 cells connecting by optical channels
in one of two possible schemes.
5. Summary and discussion
We have considered the features of all-optical signal
processing based on mechanisms of nonlinear refraction
index dependence on signal intensity. The details of
adder cell design need more detail investigation of
processes accompanied the signal transformation:
heating, energy losses and energy redistribution
between different channels. Important ones are
geometry factors that determine the scale of system
energy gaps from tens to thousands of inversed
centimeters and mode energetic width. The width
depends on both signal source and PhCr properties. The
system imperfectness like deviating layer widths and
refraction indexes ratio, interface boundaries roughness,
light absorption and others cause nonzero eigenstate
width. The mode width must be much less than the
operation frequency distance from the nearest band
edge. So, under similar conditions the more preferred
are more thick layers ensured a higher accuracy in the
widths ratio. A special contribution into the nonzero
eigenstate width arises due to finite light beam section.
This kind of state width restricts the cell miniaturization
by the condition the beam section should be large in
comparison with the light wavelength. The rough
evaluation of a 256-digit device gives the order of
10 cm for its lateral sizes and 5 cm for the width if the
operation wavelength is about a micrometer. The
calculations performed here for materials taken from
Fig. 2 give a lot of angular-frequency ranges suitable
for R- or T-signal processing schemes. The most
effective area of parameters is the problem of further
investigations. The suitable nonlinear materials for the
controlling covering layer must be chosen in the left
upper side of the diagram presented in Fig. 2. Other
characteristics being equal to those of materials with
smaller refraction indexes are more preferred.
The heat nonlinearity may be important in the
acting adder due to the divergence of neighbouring
material optical constants in the process of thermal
expansion. To make the heating influence negligible,
the difference between the thermal expansion
coefficients of materials should be controlled. The due-
to-heat relative divergence of refractive indexes for all
material pairs have to be much less than that due to
nonlinearity. In our case, it is easy to evaluate that the
heating processes are weak for chosen materials. The
heating problem could be solved by efficient
organization of the adder topology when possible extra-
intensity may be leaded away from adder cells through
the special appendix waveguides with following
returning to the laser resonator for additional pumping.
Acknowledgements
The work was partially supported by the grant STCU-
2444.
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