Machine learning based compact photonic structure design for strong light confinement

1 MB·

by  Mirbek Turduev

Machine learning based compact photonic structure design for
7 strong light confinement
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MIRBEK TURDUEV1,5,*, CAGRI LATIFOGLU2,5, IBRAHIM HALIL GIDEN3,6, and Y.

n
SINAN HANAY4,5
a
J
1 1Department of Electrical and Electronics Engineering, TED University, Ankara 06420,
3 Turkey

2Department of Industrial Engineering, TED University, Ankara 06420, Turkey
]
s 3Department of Electrical and Electronics Engineering, TOBB University of Economics
c
i and Technology, Ankara 06560, Turkey
t
p 4Department of Computer Engineering, TED University, Ankara 06420, Turkey
o
5Photonic Networks Research Group, TED University, Ankara 06420, Turkey
.
s
c 6Nanophotonics Research Group, TOBB University of Economics and Technology, Ankara
i 06560, Turkey
s
y *Corresponding author: [email protected]
h
p
[
Compiled February 2, 2017

1
v
0 Abstract
6 terparts, the optimized lens and coupler designs are
2 easy-to-fabricate via optical lithography techniques,
0 quitecompact,andcanoperateattelecommunication
0 Wepresentanovelapproachbasedonmachinelearn-
wavelengths. The outcomes of the presented study
. ing for designing photonic structures. In particular,
2 show that machine learning can be beneficial for ef-
0 we focus on strong light confinement that allows the ficient photonic designs in various potential applica-
7 designof an efficient free-space-to-waveguidecoupler
tions such as polarization-division, beam manipula-
1 which is made of Si- slab overlying on the top of
tion and optical interconnects.
:
v silica substrate. The learning algorithm is imple-
i mented using bitwise square Si- cells and the whole Studies on subwavelength light focusing phe-
X
optimized device has a footprint of 2µm×1µm, nomenon are increasing over time due to immense
r
a which is the smallest size ever achieved numerically. needs of light energy enhancement via confining it
To find the effect of Si- slab thickness on the sub- to a narrow region [1, 2, 3]. Light focusing into
wavelength focusing and strong coupling character- a tight spot smaller than the wavelength of light
istics of optimized photonic structure, we carried may findplace invariousopticalapplicationsinclud-
out three-dimensional time-domain numerical calcu- ingnanolithography,opticalmicroscopy,opticalmea-
lations. Corresponding optimum values of full width surementsandopticaldatastorage. Especially,high-
at half maximum and coupling efficiency were cal- resolution imaging and strong beam coupling can be
culated as 0.158λ and −1.87dB with slab thick- achievedbyusingthelightfocusingeffectbeyondthe
nessof280nm. Comparedtotheconventionalcoun- diffraction limit [4, 5]. Various subwavelength focus-
1
ing lenses have already been developed using meta- phase to come up with a final layout.
surfaces[6],plasmonics[7],metamaterials[8]andall- The details of ARLA can be found in [21], which
dielectric materials [9] as well as exploiting super- combines the additive updates feature of the percep-
oscillation [10] and hypergrating techniques [11]. tron algorithm [22] and the reward for state idea of
Conventionaltheoreticalapproachesmay not fully reinforcement learning [23]. However, we briefly ex-
provide analytical solutions for complex photonic plainthestepsinARLAasshowninFigure1. Inthe
structures. Furthermore, theoretically designed sys- upper diagram of the figure, operations in a single
tems may not satisfy the feasibility and performance round are depicted. The training phase starts with
requirements such as compactness, efficiency, band- creating a random photonic structure that needs to
width and energy loss drawbacks. For this reason, be mirror-symmetricalong x-axis to obtain the focal
different types of optimization algorithms such as point at the optical axis. That half of the structure
evolutionary algorithm [9], inverse optimization [12], is represented with a 10x10 binary matrix, where a
topology optimization [13], nonlinear search algo- 1 corresponds to Si- and 0 corresponds to air cells of
rithm [14], and the direct binary search algorithm 100nmx100nm. Thus,the sizeofcompletephotonic
[15] have been implemented to design efficient pho- structure equals 2µm×1µm. Next, finite-different
tonic integrated structures. However, to the best of time-domain (FDTD) method is used to calculate
authorsknowledge,thisisthefirsttimethatmachine full-widthathalfmaximums(FWHM)andmaximum
learning algorithm is utilized to design photonic de- sidelobelevels(MSLL)ofthefocusedlightbeamus-
vices with desired optical properties. ing MEEP [24]. Here, FWHM and MSLL values are
Machine learning has attracted much attention arranged as inputs for the reward function, which is
from both academia and industry recently. Re- defined as:
searchers leveraged machine learning successfully in
developing a self-learningrobotwhichcanwithstand R=Rmax−(w1×FWHM +w2×MSLL). (1)
failures [16], predicting hepatitis B positive patients
[17], improving components’ performances in opti- In this expression, w1 and w2 represent weights
cal communication systems [18], detecting malicious thatcontrolthetrade-offbetweenFWHMandMSLL
software automatically [19] and understanding eco- values. The objective of the design problem is to
logical phenomena [20]. Well-known applications in find a photonic layout that minimizes both FWHM
industry include driverlesscars,languagetranslation andMSLL;whenbothFWHMandMSLLvaluesap-
services (e.g. Google translate), credit decision sys- proaches to zero, reward approaches to Rmax, which
tems and anti-virus software. In all those diverse ex- isanarbitrarilychosenconstantthatsatisfiesthefol-
amples,thepowerofmachinelearningliesinaccurate lowing condition:
modeling and characterization of complex relation-
ships within the systems.
In this study, we propose using a machine learn- Rmax >(w1×FWHM +w2×MSLL). (2)
ing algorithm to construct highly efficient and com-
pactfocusinglensesthatareabletosurpassthelight In the second phase, the inference phase, ARLA
diffraction limit. The algorithm we use is called Ad- calculates a cumulative reward matrix from the re-
ditive Reinforcement Learning Algorithm (ARLA) sults obtainedinthe training phase. Aroundmatrix
[21] and like all the machine learning algorithms, is multiplication of the binary matrix evaluated and
ARLA consists of two phases: training and infer- its reward. ThenARLAnormalizesthis matrixAby
ence. In the training phase, which consists of a subtractingtheminimumvaluefromalltheelements.
numberofrounds,ARLAgeneratesrandomphotonic Next, ARLAapplies astepfunction, whichis shifted
′
structures, and records the optical performance of by the mean of A, to convertthe normalized matrix
′
each random structure. Later in the inference phase A to a binary matrix. Finally, the binary matrix is
ARLA uses the information collected in the training convertedbacktoaphotonicstructure,andthisfinal
2
Figure 1: Flowchart of ARLA optimization algorithm for subwavelengthlight focusing purpose.
structure is the final output of the algorithm, as can ing structure can be related to constructive interfer-
be seen from the inset in the figure. ence of propagating waves [25]: The optimized tur-
bid structure is perturbed in bitwise-scale so that
The number of training rounds N depends on the
desiredfocusingperformanceandthesizeofthepho- nanoscalelocalmodificationsexistinthecorrespond-
ing refractive index distribution. The incident wave,
tonicstructure. Inourstudythatnumberwaschosen
then,encountersmultiplelightscatteringwhileprop-
empirically. Due to independent nature of the train-
ing rounds, ARLA can be fully parallelizable. We agatingthroughthestructure. Suchscatteringmech-
anism enhances the constructive interferences at the
distributedthetrainingroundsto12differentvirtual
output so that a strong light focusing may emerge
machineseachhavingtwovirtualCPUsand3.75GB
[26].
RAM. ARLA can work with larger matrices as well,
at the cost of increased training times.
The optimized lens design is constructed on a
The output of ARLA givesan optimized structure silicon-on-insulator(SOI) substrateandcomposedof
withthehighestrewardprovidingthesubwavelength Si- slab having the refractive index of nSi = 3.47,
focusingeffect, whichis schematicallydrawnasinset see Fig. 2(a). Corresponding geometrical parame-
in Fig. 1. The dielectric medium is optimized in bit- ters of the lens structure are represented as an inset
wisescaleviathemachinelearningARLAmethodin inthesamefigure. Thewidthandheightofphotonics
order to control the near-field strong focusing effect, lens are equal to {W,L}={2µm,1µm}. 3D FDTD
see the corresponding steady-state electric field Ez calculations are carried out for the optimized struc-
distribution in the same figure. Obtained subwave- ture in order to analyze the effect of Si- slab thick-
length focusing effect through the optimized scatter- nessonthesubwavelengthfocusingperformance[27].
3
(a) (b) (c)
100 nm 300 1.5 1
0.40
H 1
250 0.8
Si 0.45
W Slab Thickness (nm)112050000 0000....23345050FWHM ( λ) y-axis (μm)-00-..5105 000...246Field intensity (a.u.)
z L 0.20
y SiO 50 -1.5 0
x 2 1 .30 1.35 1.40 1.45 1.50 1.55 1.60 1 .30 1.35 1.40 1.45 1.50 1.55 1.60
Wavelength (μm) Wavelength (μm)
Figure 2: (a) Optimized bitwise photonic structure design as a near field sub-wavelength lens. (b) FWHM
map depending on the slab thickness and incident wavelength variations. (c) The cross-sections of field
intensities are taken at the output and plotted as a map depending on the incident wavelengths.
FWHM values are calculated at the output face of the Fig. 2(c) and Fig. 3 (see inset plot) that inci-
theoptimizeddesignwithrespecttothevariationsof dent beam is concentrated into a narrowerspot with
slabthicknessesHandthe incidentwavelengthswith almost negligible levels of additional undesired side
transversemagnetic-like(TM-like)polarization. This lobes.
relationshipisplottedasaFWHMmapinFig. 2(b). Toquantifythebroadbandsubwavelengthfocusing
The calculated map shows that the excited light fo- effect of the optimized lens structure, the slab thick-
cuses with FWHM values below 0.20λwhile the slab
thickness to be in the range of 250nm-300nm. Fur-
thermore,theminimumFWHMvaluewascalculated 0.20
1
as 0.155λ, which implies that the diffraction limit of
0.8
lotiefgchthhtnecoolooupgltdyimbainezdeddeofdpeetasitciegadnl.cinoTmothmbeuennceiocamart-pfiioaentldibsyblesytwetmihtehs,hSteOhlpeI 0.19 Intensity (a.u.)000...624 F0W.15H8Mλ =
sHla=b28th0icnkmn.ess of the optimized structure is fixed to M (λ) 0.18 0-1.5 -1 -0.5y-axi0s (μm0).5 1 1.5
λ=1.51 μm
H
In order to show the broadband subwavelength W
0.17
focusing effect of the designed photonic lens, cor- F
responding transverse cross-sections of output elec-
tric field intensities were calculated for varying in-
0.16
cident wavelengths ranging between 1.3µm−1.6µm
and superimposed in Fig. 2(c) as a transverse cross-
sectional intensity map. It should be noted that, 0.15
while dealing with the strong light focusing effect, 1 .30 1.35 1.40 1.45 1.50 1.55 1.60
it is crucial to consider the emergence of side lobes. Wavelength (μm)
Excessive side lobe radiations cause the reduction of
Figure 3: Calculated FWHM values depending on
the main lobe, which is undesirable for strong light
incident light wavelengths of the photonic slab lens
focusing. Therefore, a main purpose of using ma-
having H = 280nm thickness. Steady state electric
chine learning is to suppress the intensity levels of
field profile with its transverse cross-sectional inten-
the MSLLs besides of minimizing the FWHM val-
sity profile at λ=1.51µm are given as insets.
ues at the focal point. It can be clearly observed in
4
(a) 200 nm (b)300 (c)1.5 1
H 0.6 λ =1.35 μm λ =1.55 μm
z WSi L SiO Slab Thickness (nm)112205050000 00000.....12345Normalized transmission y-axis (μm)-00-..01155 0000....2468Field intensity (a.u.)
2
y x 501 . 30 1.35 1W.40ave1le.4n5gth1 (.μ5m0)1.55 1.60 -1.5-2 -1.5 -1 -0.5x-axi0s (μm0).5 1 1.5 2-2 -1.5 -1 -0.5x-ax0is (μm0).5 1 1.5 2 0
Figure 4: (a) Optimized photonic structure design for air-to-waveguide coupling application. (b) Corre-
sponding transmission efficiency map depending on the slab thickness and incident wavelength variations.
(c) Spatial field intensity distributions of optimized structure calculated for the incident wavelengths of
λ=1.35µm (left) and λ=1.55µm (right). The dashed boxes represent the structure boundaries.
ness is fixed to H=280 nm and the FWHM values of to analyze the coupling efficiency depending on the
thefocusedbeamarecalculatedwithintelecomwave- slabthickness. Free-space-to-waveguidecouplingeffi-
lengths. Corresponding FWHM plot is represented ciencyoftheoptimizedstructureisplottedaccording
in Fig. 3. As can be seen from the figure, calculated tothevariationofincidentwavelengths’andgivenas
FWHMvalues werelessthan0.197λ,wherethe min- atransmissionmapinFig. 4(b). Ascanbeseenfrom
imum value of FWHM was calculated as 0.158λ at themap,thecouplingefficiencyofabove50%(−3dB)
operating wavelength λ = 1.51µm. The spatial elec- is obtained in the case of the slab thickness greater
tric field intensity profile with its transverse cross- than 250nm.
sectional plot is calculated at λ=1.51µm and given In the case of setting the coupler thickness to
as insets in the same figure. The FWHM plot shows 280nm,thecorrespondingcouplingefficiencywascal-
that the optimized structure provides a broadband culated to be around 65%(−1.87dB) within S (short
subwavelength focusing effect under λ/6 within the wavelengths) and C (erbium window) wavelengths.
telecom wavelengths. Such strong subwavelength fo- Fig. 4(c) demonstrates steady-state spatial inten-
cusing property as well as small footprint size imply sity profiles of the optimized coupler having 280
that the optimized photonic lens can also be consid- nm thickness for the incident wavelengths of λ =
eredasanalternativeandpromisingsolutionforfree- {1.35µm,1.55µm}. The optimized coupler and the
space-to-waveguide optical coupling applications. In output waveguide are shown as dashed boxes in the
addition, the optimized structure is all-dielectric so figure. It can be inferred from the field intensity cal-
thatsuchaphotonicdeviceisfreeofabsorptionlosses culations in Fig. 4(c) that the proposed coupler de-
and it may operate in a broadband regime compar- sign strongly confines the light to the output waveg-
ing to its metamaterial and plasmonic counterparts uide with ten times smaller width. In other words,
[28, 29]. The coupling effect is also investigated in the designedcouplertransferslightenergyfrom2µm
detail in the study using proposed machine learning width waveguide to 200nm waveguide (with beam
based photonic lens. compressing ratio of 10:1) with 65% coupling effi-
Theoptimizedphotoniclensdevicecanalsobeap- ciency.
plied for free-space-to-waveguide coupling problems. Inconclusion,all-dielectricsubwavelengthfocusing
For this reason, Si- bulk waveguide with the width lens and air-to-waveguide coupler were designed uti-
of 200nm is butt-coupled to the back face/output lizingmachinelearningforthefirsttime. Theperfor-
of the structure. 3D representation of the opti- mance of optimized photonic structure was analyzed
mized free-space-to-waveguidecoupler is represented employing 3D FDTD numerical calculations. The
in Fig. 4(a). The thicknesses of Si- slab and coupled footprint of whole optimized system is 2µm×1µm,
waveguide are scanned in the range of 50nm-300nm whichisthoughttobeverycompactcomparedtothe
5
other systems in the literature. A minimum FWHM [7] Fangwei Ye, Dumitru Mihalache, Bambi Hu,
valueof0.158λandamaximumcouplingefficiencyof and Nicolae C Panoiu. Subwavelength vorti-
−1.87dB were calculated for the optimized photonic cal plasmonic lattice solitons. Optics letters,
structure with the slab thickness of 280nm. The ob- 36(7):1179–81,2011.
tained sub-wavelengthlight focusing andstrongcou-
[8] Akash Kannegulla and LiJing Cheng. Sub-
pling effects can be can be useful in various appli-
wavelength focusing of terahertz waves in sili-
cation domains such as medicine, optical communi-
con hyperbolic metamaterials. Optics Letters,
cation, sensing structures and high precision optical
41(15):3539,2016.
device designs.
Funding. The authors acknowledge the partial
[9] E Bor, M Turduev, and H Kurt. Differential
financial support of NATO SPS research grant No:
evolutionalgorithmbasedphotonicstructurede-
985048.
sign: numerical and experimental verificationof
Acknowledgement. The authors would like to subwavelength λ/5 focusing of light. Scientific
thank Emre Borfor his helpful comments during the Reports, 6, 2016.
optimization process.
[10] Fu Min Huang and Nikolay I. Zheludev. Super-
resolution without evanescent waves. Nano Let-
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