Vol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29032

Integrated silicon photonic device design byattractor selection mechanism based on
artificial neural networks: optical coupler andasymmetric light transmitter
EMRE BOR,1,2 ONUR ALPARSLAN,3 MIRBEK TURDUEV,2,* Y. SINAN HANAY,4
HAMZA KURT,1 SHIN’ICHI ARAKAWA,3 AND MASAYUKI MURATA3
1Department of Electrical and Electronics Engineering, TOBB University of Economics andTechnology, Ankara 06560, Turkey
2Department of Electrical and Electronics Engineering, TED University, Ankara 06420, Turkey
3Graduate School of Information Science and Technology, Osaka University, Osaka 565-0871, Japan
4Department of Computer Engineering, Erzurum Technical University, Erzurum 25700, Turkey*mirbek.turduev@tedu.edu.tr

Abstract: Recently, different nanophotonic computational design methods based on
optimization algorithms have been proposed which revolutionized the conventional design
techniques of photonic integrated devices. The intelligently designed photonic devices havesmall footprints and high operating performance along with their fabrication feasibility. In
this study, we introduce a new approach based on attractor selection algorithm to design
photonic integrated devices. In order to demonstrate the potential of the proposed approach,
we designed two structures: an optical coupler and an asymmetric light transmitter. The
designed photonic devices operate at telecom wavelengths and have compact dimensions. The
designed optical coupler has a footprint of only 4 × 2 μm2 and coupling efficiency of 87.5% at
a design wavelength of 1550 nm with spatial beam width compression ratio of 10:1.
Moreover, the designed optical coupler operates at a wide bandwidth of 6.45% where thetransmission efficiency is above 80%. In addition, the designed asymmetric light transmitterwith a size of 2 × 2 μm2 has the forward and backward transmission efficiencies of 88.1% and8.6%, respectively. The bandwidth of 3.47% was calculated for the designed asymmetric lighttransmitter where the forward transmission efficiency is higher than 80% and the backward
efficiency transmission is under 10%. In order to evaluate the operating performance of thedesigned photonic devices, coupling losses are analyzed. The presented results show that theattractor selection algorithm, which is based on artificial neural networks, can bring a
conceptual breakthrough for the design of efficient integrated nanophotonic devices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction
Photonic integrated circuits (PICs) have many advantages over integrated electronic circuits
such as having a large bandwidth, resistance to interference and nonexistence of Joule effect[1,2]. On the other hand, PICs have a considerable disadvantage in terms of lower integration
density comparing with conventional integrated electronic circuits. In order to overcome thedensity problem, the silicon-on-insulator (SOI) platforms are introduced, which enable thefabrication of higher integration density for PICs with low power consumption and highefficiency [1,3–5]. Moreover, SOI technology is compatible with complementary metaloxide-semiconductor (CMOS) fabrication process. Due to high refractive index contrast
between silicon (Si) and silicon dioxide (SiO2), SOI materials are suitable for designingphotonic integrated devices (PIDs). In general, design of PIDs depends on theoreticalknowledge and educated guess where the design parameters are subjected to brute-force
adjustments. However, brute-force tuning approach is not sufficient in the cases where the#340762
Journal © 2018https://doi.org/10.1364/OE.26.029032
Received 27 Jul 2018; revised 21 Sep 2018; accepted 16 Oct 2018; published 24 Oct 2018

Vol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29033

problem is to design compact and efficient PIDs. In recent years, diverse approaches areproposed to reduce the footprints and increase the performance of PIDs in the applications of
nanophotonics. Recently, the use of optimization algorithms enabled the design of compact
and high efficiency PIDs. For this purpose, the inverse design method was developed todesign several nanophotonic devices such as mode converters, fiber couplers, and wavelength
demultiplexers [6–8]. Also, nonlinear search algorithm was applied to design a polarization
beam splitter and optical diodes [9,10]. Recently, a machine learning algorithm wasintroduced to design a subwavelength focusing lens and an optical coupler [11]. Moreover, atandem of deep neural networks was utilized to predict the geometry of a structure for adesired response which still suffers from requiring a large data set [12]. These studies indicatethat the future of PICs/PIDs will heavily depend on automated intelligent design approaches[13].
In general, the efficient transmission of light between PIDs is an essential characteristic
for the performance of PICs. Here, it is important to provide a sufficient amount of injected
optical power to the PICs from the free-space because the injected light that circulates within
the PICs effects the proper operation of PIDs. However, coupling of light from free-space to
PIDs through the optical waveguides is a challenging issue in SOI platforms due to highrefractive index contrast and difference of mode orders between optical fibers andwaveguides. For this reason, design of an optical coupler that confines the incident light into awaveguide is important for applications of PICs. In this regard, various methods have been
introduced to couple incident light into a waveguide with high coupling efficiency and large
bandwidth, and to reduce the dimensions of optical couplers [11,14,15].
Another important issue for PICs is the unidirectional transmission of light, which is
required for the optical interconnections and optical isolation [16–19]. It is possible to obtain
optical isolation by violating the reciprocity condition. In order to design non-reciprocal
devices, metamaterials, magneto-optical materials, and indirect interband photonic transitions
are introduced [17–19]. However, these structures are not compatible with CMOS technology
and demand high input power and large integration area. Besides these proposed techniques,unidirectional light transmission can be partially achieved by designing all-dielectric passive
photonic devices by only restricting their operation to the certain input modes [20–22]. It is
important to note that the linear and time-independent devices do not break the Lorentz
condition. Also, an asymmetric light transmission device cannot be considered as an opticalisolator since it does not necessarily require an asymmetric scattering matrix [23]. Even
though some controversial studies are proposed on this issue, optical diodes, which are notconsidered as optical isolators, are introduced by limiting their functionality to finite numberof input modes [24].
In the proposed study, the application of attractor selection algorithm [25,26] based on
artificial neural networks (ANNs) is introduced to design two different compact efficientphotonic devices of an optical coupler and an asymmetric light transmitter (ALT). The
designed optical coupler provides the strong confinement of incident light propagating infree-space into Si- waveguide. The designed ALT allows transmission of light in one
direction but blocks it in the opposite direction. Both optical coupler and ALT devices are
numerically designed by using SOI materials. To the best of authors’ knowledge, it is the firsttime to demonstrate the successful utilization of an approach based on ANNs in order todesign PIDs.
2. Problem statement and artificial neural networks based photonic device
designIn nanophotonic applications, design of PIDs with high performance as well as their highfabrication densities is a challenging task due to the trade-off between those desired
properties. Conventional design methods based on analytic knowledge and intuitions are notsufficient to find a possible solution to balance that trade-off. In this regard, a demand of an

Vol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29034

approach that may balance the mentioned trade-off is aroused for designing efficient andcompact PIDs. Hence, in this study, we propose the application of attractor selection
algorithm to overcome that problem.
ANNs are a subclass of machine learning techniques, which are proven to be highly
capable in characterizing nonlinear relationships from pattern recognition to autonomousvehicle control systems. The deep learning paradigm is getting popular and embraced by all
fields in science, which is basically a multi-layer neural network. Although its origin dates
back to 1980s, the advances in recent years in storage technology and processing capabilities
proved feasibility of neural networks on solving problems. For instance, a deep neuralnetwork beat all the human crafter methods in the famous ImageNET image recognitioncompetition in 2012 [27]. Also, a computer beat the human champion of game Go for the firsttime in 2016 by using neural networks [28]. Recently, the effectiveness of machine learningin designing efficient nanophotonic devices is introduced [11,29].
In this study, we applied attractor selection algorithm, which can be considered asreinforcement learning and is based on neural networks, to design photonic devices.
Applications of attractor selection algorithm include optimizing optical network topologies[26,30] and routing of vehicular ad hoc networks [31]. The numerical analyses of thedesigned photonic devices are performed by using three-dimensional (3D) finite-differencetime-domain (FDTD) method [32], which is integrated into attractor selection algorithm.
Here, the designed photonic devices are intended to be compatible with SOI technology forpossible fabrication process in the future. Thus, Si is selected as the underlying main material
for the design process. During a design process, an intended photonic device is considered asa matrix of individual cells where high refractive index Si- scatterers are stated as “+1” andair cells are stated as “-1” in the matrix due to the operation of attractor selection algorithm.
The sizes of corresponding individual cells are fixed to be 100 nm × 100 nm where thematerial refractive indices of Si and air are fixed to nSi = 3.46 and nair = 1.0, respectively. We
should note that the fixed sizes of individual cells are chosen in accordance with the recent
fabrication technology based on SOI platforms [9,10]. The applied attractor selector
algorithm determines the state of each individual cell whether it will be Si or air. As a result, aphotonic device can be expressed as a matrix with defined elements of “plus ones” and“minus ones” only.
In order to design a photonic device, its desired optical characteristics should bedetermined as an objective function for the attractor selection algorithm. For this reason, we
defined distinct objective functions for modelling of an optical coupler and an ALT. The
mentioned objective function is actually the error value between the performance of currently
designed photonic device during the operation of algorithm and the initially predefineddesired performance. The algorithm iteratively updates the state of individual cells in aphotonic device to minimize that error value.
In the case of an optical coupler, the attractor selection algorithm managed to increase thetransmission efficiency for a predefined operating bandwidth in the telecom wavelengths. We
set the objective as finding a suitable photonic structure with maximum coupling efficiency
for a selected wavelength interval. Here, the corresponding error value is the summation ofdifferences between the transmission efficiency of instant designed photonic device andpredefined target value for all wavelengths of the operating bandwidth. In order to design an
optical coupler, the error values can be calculated as follows
Ecoupler
=

λend

∑ (T

i = λstartdesired− Ti )(1)

where, Tdesired is the user defined broadband target transmission efficiency and Ti is thenormalized transmission efficiency for as ith selected wavelength of the operating bandwidth.
The limits of bandwidth are denoted by λstart and λend.

Vol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29035

Separately, we applied the attractor selection algorithm to obtain an asymmetric lighttransmission effect. For this purpose, the algorithm is utilized to increase the transmission
efficiency in the direction of forward propagation of light but decrease the transmission
efficiency in the direction of backward propagation of light. Thus, in the case of designing an
ALT, we defined two objectives for algorithm. The first objective is to maximize thetransmission efficiency in the forward direction for the selected design wavelength. The
second objective of algorithm is to minimize the transmission efficiency in the backward
direction for the same operating wavelength. For this reason, we need to calculate multiple
error values such as error value for higher forward transmission efficiency and error value forlower backward transmission efficiency. Since the attractor selection algorithm operates onlywith a single error value, we use the summation of two error values as a total error value tosimultaneously minimize the both calculated error values. We used the following formula forerror value to design an ALT
E=
ALT(TFdesired − TF ) + (TB − TBdesired )(2)

where, TF and TB denote the normalized transmission efficiencies of forward and backward
directions at the selected design wavelength, respectively. Also, TFdesired and TBdesired denotethe user defined target transmission efficiencies for forward and backward directions at adesign wavelength, respectively.
The intended designs of photonic devices are schematically represented in Figs. 1(a) and
1(b), respectively, for an optical coupler and an ALT. As can be seen from the schematics, thefinal designed photonic devices will consist of individual Si- cells and air holes that are
distributed on SiO2 substrate. In Fig. 1(a) we attempted to depict the compression of incident
light (wide yellow arrow in air) into Si- nano-waveguide (narrow yellow arrow). Besides, inFig. 1(b), the green arrow shows the enabled forward propagation of light, whereas the red
curved arrow represents the back reflection of blocked light. Here, the designed intermediate
region should provide an asymmetric light transmission effect.

Fig. 1. Schematic representations of the intended design of (a) an optical coupler and (b) an
ALT.

At this point, it is important to give detailed explanation for the principle of operation of
applied attractor selection mechanism. Since the attractor selection mechanism is a bioinspired model, it would be beneficial to further explain its biological counterparts. In
biological systems, the cell growth is controlled by the interaction of the metabolic reaction
network and gene regulatory network in the cell [25]. The gene reaction network produces theproteins that react with the nutrition in the environment. Each gene has an expression level
controlling the level of the protein production. In the metabolic reaction network, these
proteins convert the nutrition to the substances that are necessary for the cell growth. The
amount of the produced substances controls the activity level of the gene regulatory network
as a feedback mechanism. A high level of substances implies a favorable condition, so thecell accepts it as an attractor state and continues to run the gene reaction network with thesimilar expression levels. Otherwise, it means that the current expression levels are notfavorable for the current environment, so the expression levels start to deviate from the last
attractor as the noise becomes dominant.

Vol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29036

During the design process, the photonic device can be interpreted as the level of theprotein production, whose expression levels are represented as x = (x1, x2, …, xn). Here, theexpression level of xi, which is between [-1, 1], determines whether the ith individual cell in
the photonic device is Si or air. If xi < 0, then ith individual cell in the photonic device isdefined to be an air. Otherwise, it is defined to be a Si- individual cell. According to Ref. 26,
analytical expression for calculation of xi is as follows:
 


dxi
=α ⋅  f ⋅  ∑ Wij ⋅ x j − θ  − xi  + η


dt

  j


(3)

In Eq. (3), α is the growth rate, which is a function of the error value of the photonic
device showing whether the current photonic device is favorable in the current environment.
The η is the Gaussian noise term showing the strength of stochastic behavior. The noise
dominates the system in case the error value of the photonic device is low and the systemchanges randomly to find a new attractor state. The deterministic behavior is controlled by the
sigmoidal regulation functionf ( z ) = tan h ( µ z )(4)where, µ is the gain parameter. W is the regulatory matrix, which moves the photonic device
to an attractor state when the growth rate is high. θ is the threshold value for expression level.
The error value E is then converted to the growth rate α by

α=

1
1+ e

( δ ⋅( E − ζ ) )(5)

where δ is the gradient and the ζ is the threshold error rate. The regulatory matrix W is a
Hopfield neural network [33] containing a set of possible attractors calculated by using
orthogonal projection [34,35]. Let X be a matrix whose rows are the attractors coded
according to bipolar coding. First, we calculate the pseudo-inverse matrix X+. Then theregulatory matrix is calculated by simply(6)
W = X+X
The attractor selection algorithm parameters were empirically set to µ = 10 and δ = 0.20.
During the design process of an optical coupler, the threshold error rate is selected as ζ = 5,
whereas the threshold error rate is fixed to ζ = 1 in order to design an ALT. The variance ofthe noise η is selected 0.30. The iterative attractor selection algorithm can be summarized inthree phases. Firstly, FDTD method is performed to calculate the error value of the current
photonic device. Then, using the growth rate α calculated by the error value and the noiselevel, the new expression levels x = (x1, x2, …, xn) are calculated. Finally, the individual cellsof photonic device are updated according to the new expression levels. It should be noted thatthe algorithm is manually terminated when the calculated error value does not change for a
relatively long time. We want to note that the simulation time for the design of each proposed
devices took two months. The computational experiments are done by running threecomputers in parallel fashion to speed-up the numerical calculations. The hardware
specifications of the corresponding computers are as follows: Computer 1 (3.3GHz Intel i73960x CPU, 6 Cores, 32GB RAM); Computer 2 (2.9GHz Intel Xeon E5-2690 CPUx2, 2x8
Cores, 64 GB RAM); Computer 3 (2.26GHz Intel Xeon X7560 CPUx2, 2x8 Cores, 512 GB
RAM).
3. Results and discussion
In this study, we designed a compact optical coupler with a footprint of 4 × 2 μm2 by using
attractor selection algorithm. The designed optical coupler consists of Si- individual cells witha size of 100 nm × 100 nm and a thickness of 240 nm where the Si- nano-waveguide with aVol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29037

width of 400 nm is butt-coupled to the optical coupling region. Due to goal of obtaining
compact coupler, we fix the length of the coupler as 2 µm. In Fig. 2(a), 3D view and top viewof the photonic device are depicted with its structural dimensions. We should note that thedesigned optical coupler confines in-plane incident light injected from free-space into Sinano-waveguide. The direction of light propagation is denoted by yellow arrow as an inset in
Fig. 2(a). Throughout the 3D FDTD simulations, SiO2 material is selected as a substrate forthe optical coupler to ensure the possible realization of SOI platform. The proposed optical
coupler is designed to be symmetrical with respect to the x-axis (corresponding axes areshown as inset in Fig. 2(a)). In 3D FDTD simulations to calculate the coupling efficiency ofthe optical coupler, a broadband plane-wave light source of transverse-electric (TE)polarization covering 1300 nm – 1800 nm range is used to excite the photonic device where
the electric field components are along the xy-plane (Ex, Ey) and the magnetic field Hz isperpendicular to the xy-plane. Also, perfectly matched layers are employed in thecomputational domain to eliminate the undesired back reflections [36].

Fig. 2. (a) 3D and top view of designed optical coupler are shown with structural dimensions
where the yellow arrow represents the incident light. (b) Normalized transmission efficiency isplotted and shaded region indicates the operating bandwidth of proposed photonic device. (c)Steady state magnetic field and (d) intensity distributions at z = 0 plane of 3D FDTD region are
given for wavelength of λ = 1550 nm. Dashed lines indicate the boundaries of optical coupler
and direction of incident light is represented by arrows. (e) Lateral cross-sectional intensity
profiles at input region (Air) and nano-waveguide region (Wvg) of the device are represented.
(f) Field and (g) intensity distributions in yz-plane at nano-waveguide region of the photonic
device are given for wavelength of λ = 1550 nm where dashed lines denote the boundaries ofdielectric materials.

As aforementioned, the attractor selection algorithm is applied to design an optical
coupler that operates for a defined operating region of telecom wavelengths. In this regard, inFig. 2(b), we provided the coupling efficiency plot for the final generated optical coupler. In
this figure, the shaded region indicates the predefined operating regime of wavelengths
between 1500 nm and 1600 nm for design process where they correspond to the λstart and λend
in Eq. (1), respectively. As a result, attractor selection algorithm designed an optical couplerthat exhibits the coupling efficiency higher than 84% for a bandwidth of 6.45% centered at
the wavelength of 1550 nm as can be seen in Fig. 2(b). At the center wavelength of 1550 nm
the corresponding transmission efficiency is calculated as 87.5%. Cross-sectional views ofsteady state spatial magnetic field Hz and intensity |Hz|2 distributions at z = 0 plane of 3D
FDTD region are represented in Fig. 2(c) and (d), respectively, for the incident wavelength of
λ = 1550 nm. In these figures, the dashed lines indicate the boundaries of the proposed optical
coupler. As can be seen from Fig. 2(c), the designed photonic device couples incident lightinto a nano-waveguide. It should also be pointed out that the proposed optical coupler has ahigh conversion ratio of 10:1, i.e., the spatial width of the coupling region is 4 µm, whereas

Vol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29038

the Si- nano-waveguide has the spatial width of 0.40 µm. As can be seen from Figs. 2(c) and2(d), the designed coupling region minimizes the back reflections originated from theinterface between air and coupling region and squeezes down the injected light from freespace into output nano-waveguide with a high coupling efficiency of 87.5%. The compressionof the propagating wave is achieved by transforming the incident plane wavefronts to theconverging wavefronts, i.e., propagating light converges into the point at the interface
between coupler and nano-waveguide junction region. Therefore, converged light thatrevealed at the entrance of the butt-coupled nano-waveguide is easily confined and allowed topropagate with high transmission efficiency. In Fig. 2(e), the cross-sectional intensity profiles
along y-axis at the input (air) and the output (on nano-waveguide) of the designed device issuperimposed to show the spatial compression of incident light. In Figs. 2(f) and 2(g), thecross-sections of steady state magnetic field and intensity distributions at yz-plane on the
nano-waveguide are shown, respectively, where the boundaries of the device are denoted withthe dashed lines. It can be seen from these figures that the coupled light is strongly confinedin the nano-waveguide with negligible leakage to the SiO2 substrate.

Fig. 3. (a) Field, (b) intensity and (c) phase distributions at z = 0 plane of 3D FDTD region are
given for wavelength of λ = 1500 nm. (d) Field, (e) intensity and (f) phase distributions at z = 0
plane of FDTD region are given for wavelength of λ = 1600 nm. Dashed lines represent theboundaries of optical coupler and arrows indicate the direction of incident light.

In order to investigate the broadband operation of designed optical coupler, steady statemagnetic field, intensity and phase distributions at z = 0 cross-sectional plane of 3D FDTD
region are calculated and represented in Figs. 3(a)-3(c) for wavelength of 1500 nm and in
Figs. 3(d)-3(f) for wavelength of 1600 nm. These selected wavelengths are the edge
wavelengths of selected operating bandwidth. According to the transmission efficiency plot
given in Fig. 2(b), the coupling efficiencies of designed optical coupler at 1500 nm and 1600
nm are equal to 84% and 85%, respectively. In this regard, the propagating field distributions
shown in Fig. 3(a) and 3(d) indicate the strong coupling effect. Moreover, as seen from Fig.
2(b), the coupling efficiency plot is nearly linear (negligible fluctuations) within the defined
operating bandwidth. Therefore, one can expect the strong light confinement effect for theintermediate operating wavelengths that lie between wavelengths of 1500 nm and 1600 nm.
Similarly, for the same operating edge wavelengths, one can see the strong light confinementin nano-waveguide from spatial intensity distributions, which are given in Figs. 3(b) and 3(e).
In addition, we extracted and plotted the related phase distribution for the wavelength of 1500

Vol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29039

nm and 1600 nm in Figs. 3(c) and 3(f), respectively. The phase distributions show that theincident light with plane phase fronts transformed to the convex shaped phase fronts inside
the optical coupler. As a result, the propagating light with the converged phase fronts is
confined into the nano-waveguide. It is important to note that the dashed lines indicate theboundaries of coupling region and butt-coupled nano-waveguide in Figs. 3(a)-3(f).

Fig. 4. (a) Locations of monitors in order to calculate transmission, reflection and out-of-planeloss are shown on 3D view of designed optical coupler. (b) Transmission, reflection and outof-plane loss efficiencies are plotted where shaded region indicates the operating bandwidth.

Further, we analyze the reflection and out-of-plane loss characteristics of the designed
optical coupler. For this reason, we placed an optical power monitor behind the incident lightsource to calculate reflection from the entrance surface of the designed photonic device. In
addition, we placed an optical power monitor above the coupling region to calculate the outoff-plane losses. In Fig. 4(a), locations of corresponding monitors are schematicallyillustrated as perspective 3D view. The calculated efficiencies are plotted in Fig. 4(b). As canbe seen, the reflected optical power is under 2.5% of total input optical power and out-offplane loss is calculated as less than 5% at the operating bandwidth. The designed optical
coupler has been examined not only in terms of the transmission efficiency but also in termsof the magnetic field dynamics and we demonstrate the successful application of attractor
selection mechanism based on artificial neural networks. Also, one can consider othercoupling scenarios such as fiber to waveguide coupler, waveguide to waveguide and freespace to waveguide. Such approaches can be targeted with the algorithm developed in thepresent work. We should note that there are various problems in the integrated photonics thatneed to be improved to obtain efficient, compact and broadband manipulation of photons.
In addition to the coupler design, here we considered the design of an ALT device via theattractor selection algorithm. The proposed photonic device has compact footprint size of 2 ×
2 μm2 with a thickness of 300 nm. Similarly, in the design of optical coupler device, Siindividual cells with dimensions of 100 nm × 100 nm are intelligently distributed on a SiO2
substrate to generate an ALT by the attractor selection algorithm. In 3D FDTD simulations of
the ALT design, TE polarized plane-wave source is employed and the design wavelength isfixed to 1550 nm. The asymmetric light transmission region (designed region) is sandwiched
between input and output Si- waveguides with the spatial widths of 2 μm and thicknesses of
300 nm as can be seen in Fig. 5(a). Also, in Fig. 5(b), the top view of the designed photonic
device is schematically represented where forward and backward directions are indicated byblue and red arrows, respectively. As expressed in Eq. (2) the purpose of implemented
attractor selection algorithm is to allow forward light transmission and block backward lightpropagation within the ALT device. It should be noted that, during the design process,incident light is coupled to the input waveguide and transmission efficiency is calculated in
the output waveguide. Another important point to be raised is that the definitions of the termsof “input” and “output” are depends on the direction of excitation of the designed ALT where“input” corresponds to the location of the light source and “output” defines the location of
optical power monitor. The placed monitors inside the input and output waveguides areVol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29040

shown in the 3D view of designed ALT in Fig. 5(c). We should note that only thetransmission efficiencies in both directions are considered during the design process.
Moreover, reflection and out-off-plane loss characteristics of the designed ALT are also
investigated and the locations of the required optical power monitors are also depicted in Fig.
5(c). Corresponding transmission, reflection and out-of-plane loss efficiencies are plotted inFig. 5(d) for both forward and backward directions where the design wavelength of 1550 nm
is indicated. For the forward direction, transmission efficiency of incident light (TF) is
calculated as 88.1% by using whereas the backward transmission efficiency (TB) is
suppressed to be 8.6% at the design wavelength. The designed ALT has an operating
bandwidth of 3.47% (the bandwidth is shown by shaded region in Fig. 5(d)), i.e., between the
wavelengths of 1527 nm and 1581 nm, where the forward transmission efficiency is higher
than 80% and backward transmission is lower than 10%. Here, forward reflection efficiency(RF) and backward reflection efficiency (RB) are calculated as 1.7% and 58%, respectively,
which is expected for an ALT. In addition, out-of-plane losses are calculated as 4.1% and5.9% for forward and backward directions, respectively. It can be concluded that the design
region does not allow the incident light escaping to the outer-plane. However, especially forbackward direction, large amount of energy may leave the device from its sides and leak tothe substrate.

Fig. 5. (a) 3D view and (b) top view of the designed ALT are represented with structuraldimensions. Forward and backward directions of incident light are indicated with blue and red
arrows, respectively. (c) Positions of optical power monitors in order to calculate transmission,reflection and out-of-plane loss for both forward and backward directions are schematically
represented on 3D view of designed ALT. (d) Normalized efficiencies for forward
transmission (TF), backward transmission (TB), forward reflection (RF), backward reflection(RB), forward out-of-plane loss (LF) and backward out-of-plane loss (LB) are plotted where
yellow line indicates the operating wavelength of λ = 1550 nm. The bandwidth is shown by
shaded region in Fig. 5(d)).

In addition, we investigated the cross-sectional steady state magnetic fields and intensitiesof the designed asymmetric light transmitter operating for both forward and backward
directions at wavelength of 1550 nm. In Figs. 6(a) and 6(b), cross-sectional views at z = 0
plane in 3D FDTD computation domain for magnetic field and intensity distributions offorward direction are given, respectively. Also, in Figs. 6(c) and 6(d), cross-sectional views ofmagnetic field and intensity distributions at the yz-plane (x = 2 µm location) on output
waveguide for forward direction are given, respectively. Similarly, cross-sectional views ofmagnetic field and intensity distributions for backward excitation case are extracted at z = 0

Vol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29041

plane which are represented in Figs. 6(e) and 6(f), respectively. The cross-sectional views ofmagnetic field and intensity distributions at yz-plane (x = −2 µm location) on output
waveguide for backward direction are shown in Figs. 6(g) and 6(h), respectively. In thesefigures, dashed lines denote the boundaries of design region and waveguides. Also, forward
and backward directions of incident light are denoted by arrows left-to-right and right-to-left,
respectively. As can be seen from the Figs. 6(a) and 6(e), the coupled light at output
waveguides displays multi-mode characteristic even if the incident coupled light has singlemode characteristic at the input waveguides. Also, this effect can be clearly observed fromcross-sectional views of confined magnetic fields in Figs. 6(c) and 6(g), the transmitted light
exhibits multi-mode characteristic in output waveguides for both forward and backward
directions. One can conclude that the arising mode order conversion effect is the main
physical mechanism of asymmetric transmission of light. In other words, the intelligently
disordered modulation of refractive index introduces a distortion for input single-mode, which
results in a multi-mode guided light at output waveguide. Thus, the propagation of light isenabled in the forward direction but almost disabled in the backward direction since theobserved multi-mode in the backward direction is not supported by the design medium. Whileforward propagation of light is allowed through the designed medium, due to highly
scattering nature of the refractive index profile, phase distortion, and multi-mode generation
occur. However, in the reverse direction, strong back-reflection of light gives rise to almost
no light penetration to the other side.

Fig. 6. For forward direction, (a) magnetic field and (b) intensity distributions at z = 0 plane atwavelength of λ = 1550 nm. Cross-sectional views of (c) magnetic field and (d) intensity
distributions in yz-plane (x = 2 µm location) are shown for forward direction. For backward
direction, (e) magnetic field and (f) intensity distributions at z = 0 plane. Cross-sectional viewsof (g) magnetic field and (h) intensity distributions in yz-plane (x = −2 µm location) are shownfor backward direction. The dashed lines represent the boundaries of design medium andwaveguides. The arrows indicate the forward (left-to-right) and backward (right-to-left)
directions of incident light.

The proper optical isolation is the perfect prevention of light propagation in backward
direction for any order of coupled modes and can only be achieved by breaking the Lorentz
symmetry condition [23]. Selection of different guided-modes at input and output for
unidirectional light transmission is not sufficient to obtain optical isolation. However, if we
restrict the operation of our designed photonic device to certain guided-modes, we canconsider it as a kind of optical diode. It should be noted that the proposed ALT does not
function as an optical isolator. In order to fully examine the optical isolation effect, allVol. 26, No. 22 | 29 Oct 2018 | OPTICS EXPRESS 29042

possible guided modes for backward direction should be investigated. Because the totalenergy is irregularly divided on different modes, some selected modes can exhibit
unidirectional light transmission characteristic. In other words, one particular mode can have
low backward transmission efficiency whereas another mode can have relatively highbackward transmission efficiency. If one selects the particular guided-mode with low
backward transmission efficiency, it cannot be considered as an optical isolation since “anasymmetric scattering matrix” is required for all possible guided modes to obtain opticalisolation. Furthermore, if one chooses linear and time-independent materials to design aphotonic device, it will have a symmetric scattering matrix and thus, it will be impossible toachieve an optical isolation. In the light of these given explanations, we can conclude that our
proposed ALT device is not an optical isolator because the photonic device is designed madeof all-dielectric materials. On the other hand, designed compact photonic device exhibits
asymmetric light transmission behavior due to the difference between the mode orders of
oppositely propagating waves.
In addition, we performed FDTD simulations to present the robustness of the proposed
optical coupler and ALT devices for possible fabrication imperfections. For this purpose, we
introduced random noise of 5%, i.e., random modulation, to 2D-code-like structures in order
to simulate the possible fabrication errors of missing air and Si- cells. At the wavelength of1550 nm, the original device has transmission efficiency of 87.5% whereas the imperfectdevice shows a transmission efficiency of %83.2. Hence, one can consider that the difference
between calculated transmission efficiencies of original and imperfect is at a reasonable level.
Similarly, we introduce a random noise of 5% to the designed ALT device to analyze its
performance variation due to fabrication imperfections of missing Air/Si- cells. The proposed
original ALT device has the transmission efficiencies of 88.1% and 8.6%, respectively, forforward and backward excitation at wavelength of 1550 nm. On the other hand, the forward
and backward transmission efficiencies are calculated as 81.4% and 13.8%, respectively, forimperfect ALT device operating at 1550 nm. Moreover, we considered additional fabrication
error which can appear due to variations in cell spatial sizes. Hence, we randomly varied thecell sizes of proposed coupling and ALT devices between 95 nm and 105 nm. Here, thetransmission efficiency of coupling device was decreased to 80.6% at the operating
wavelength of 1550 nm. Furthermore, the forward transmission efficiency of imperfect ALT
device is calculated as 78.9% whereas its backward transmission efficiency is equal to 12.2%.
As a result, the designed devices can be considered as robust to the small imperfections in cell
sizes.
4. Conclusion
In summary, we propose a new design approach in nanophotonics, which is based on attractor
selection algorithm and demonstrate its applications by designing an optical coupler and an
ALT. The performed 3D FDTD analyses show that the designed photonic integrated devices
have compact sizes, high efficiencies, and compatibility with CMOS fabrication technology.
The proposed optical coupler with footprint of 4 × 2 μm2 has the coupling efficiency of 87.5%
and conversion ratio of 10:1 at optical telecom wavelength of 1550 nm. Also, it has broad
operating bandwidth of 6.45% for coupling efficiency over 80%. The proposed ALT exhibits
unidirectional light transmission characteristic for certain guided-modes with forward
transmission efficiency of 88.1% and backward transmission efficiency of 8.6% atwavelength of 1550 nm. The bandwidth of 3.47% is calculated for the designed ALT where
the forward transmission efficiency is higher than 80% and backward transmission efficiency
is under 10%. The designed ALT has footprint of only 2 × 2 μm2 which is the smallest alldielectric ALT reported to date. In addition, designed photonic devices are feasible forpossible fabrication process. To conclude, attractor selection algorithm based on ANNs canbe considered as a powerful design tool for the future of photonic integrated devices.

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Funding
Scientific and Technological Research Council of Turkey (TUBITAK) under Project
116F182.
Acknowledgement
H. Kurt acknowledges partial support from the Turkish Academy of Sciences.
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