Realization of a multichannel drop filter using an ISO-centric all-circular photonic crystal ring resonator

Accepted Manuscript Title: Realization of a multichannel drop filter using an ISO-centric all-circular photonic crystal ring resonator Authors: Alireza Tavousi, Hamid Heidarzadeh PII: DOI: Reference:

S1569-4410(18)30055-5 https://doi.org/10.1016/j.photonics.2018.05.010 PNFA 658

To appear in:

Photonics and Nanostructures – Fundamentals and Applications

Received date: Revised date: Accepted date:

15-2-2018 28-4-2018 21-5-2018

Please cite this article as: Tavousi A, Heidarzadeh H, Realization of a multichannel drop filter using an ISO-centric all-circular photonic crystal ring resonator, Photonics and Nanostructures - Fundamentals and Applications (2018), https://doi.org/10.1016/j.photonics.2018.05.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Realization of a multichannel drop filter using an ISO-centric all-circular photonic crystal ring resonator

1Department

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Alireza Tavousia, Hamid Heidarzadehb* of Electrical Engineering, Velayat University, 99111-31311, Iranshahr, Iran Email: [email protected] 2Department

of Electrical Engineering, University of Bonab, 55517-61167, Bonab, Iran Corresponding author e-mail: [email protected]

Highlights

A high efficiency of in-plane multi-channel drop filter (MCDF) is demonstrated.

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Five-channel filters with reasonable drop efficiencies from at least 76%, up to 100%,

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The crosstalk across all the channels was varied from -10 db as the worst case down to -

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

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were obtained.

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50 db as the best case.

Abstract: Here, by using a square-lattice-type photonic crystal (PhC) and an ISO-centric all-

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circular ring resonator (RR), a high efficiency in-plane multichannel drop filter (MCDF) is realized. By conducting full-spectrum transmission studies on available tuning parameters such as

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RR radius, RR refractive index, PhC lattice high and low refractive indices, and PhC lattice constant, the transmission behavior of each parameter is found in terms of blue or red shift wavelength dependencies. The single unit of the PhC-based filter is optimized to work at a desired

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optical wavelength (e.g., λ0=1550nm). The MCDF is formed by cascading a desired number of the basic unit (e.g., five units), whereas using the knowledge learned from full-spectrum transmission behavior, each unit is proportionally tuned to operate at a desired different wavelength with an appropriately engineered channel spacing and crosstalk. The high efficiency dropping task of MCDF was successfully acquired with reasonable drop efficiencies as low as

76%, up to 100%. The crosstalk across all channels varied from -10 db as the worst case down to -50 db as the best case; this ensures a hopeful application of the MCDF.

Keywords: Photonic crystal; ring resonator; multichannel drop filter; all-circular hub; ISO-centric

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hub

1. Introduction:

In recent years, artificially made plasmonic and photonic crystal devices have been considerably studied for numerous applications in variety of subject fields. For example, in inplane wave-guiding-type applications such as switching devices [1, 2], sensors [3, 4], demultiplexers [5-10], T- and Y-shaped branches and power splitters [11], low-threshold logic gates

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[12, 13] and analog-to-digital converters [14-20], slow light [21-24], and add-drop (ADFs) and

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channel drop filters (CDFs) [25-28]. Few of out-of-plane applications are as follow: enhanced light-emitting devices [29], light-trapping applications [30], beam steering [31, 32], and spoof

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surface plasmon to terahertz wave conversion [33-36].

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In-plane application of photonic crystals requires in-defect introduction within the lattice. The defects are usually categorized in point, line, and/or combination of these two, e.g., a ring or a

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disk. As the basic unit for all other possible in-plane applications of PhCs, CDFs have attracted

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much attention. Moreover, the ultimate occupied size of such filters is at least 1/1,000 to 1/10,000 less than that of conventional optical devices (such as fiber-based ones) [37]. In-plane seriescoupled hetero PhCs have already been proposed using different connecting scheme concepts such

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as lattice constant variation within each forming unit [38, 39], lattice refractive index, and/or material variation within each forming unit [8], although such structures have been used to validate

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multiwavelength ADF operations. In addition, reflection at the heterostructure interfaces have also been extensively studied and properly minimized [40].

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Here in this paper, an in-plane PhC-based filtering device is extensively studied and designed,

for which the light could be trapped in a ring-type defect and then efficiently extracted to the neighboring waveguide. The proposed unit could be considered as a key platform upon which countless practical elements, such as logic gates, switches, analog-to-digital convertors, buffers, optical limiters, optical transistors, and optical memories, could easily be integrated on a single chip. Recently, a single-channel in-plane filter for which ultra-high Q nanosized cavity that is

placed between two parallel waveguides had been experimentally demonstrated; however, theoretical studies predicted a maximum of 25% limit in drop efficiency [41]. More recently, another in-plane single CDF with more than 80% drop efficiency was experimentally utilized. This filter implemented destructive interference to manage and limit undesired outputs [42]. In this work, we theoretically design and propose an in-plane multiwavelength CDF (MCDF)

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device based on the well-developed concept of heterostructure PhCs. A few number of basic CDF units are serially connected to produce the multiwavelength CDF. To the best of our knowledge, none of the previous studies have implemented full-spectrum transmission behavior of the basic unit to find the wideband behavior of the tuning parameters, which would significantly help to design MCDFs with more denser channels and also easily tune them at specific required

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wavelengths using the red or blue shift behavior of each tuning parameter/channel.

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In this paper, in section 2, the concept of the basic CDF unit is presented. In section 3, the MCDF is proposed and investigated. Our MCDF shows a high dropping efficiency with reasonable

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drop efficiencies as low as 76%, up to its best of 100%. The crosstalk across all channels differs

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from -10 db for the poorest case down to -50 db for the best case. At the end, section 4 concludes

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2. Materials and Methods

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the paper.

2. 1. Basic CDF unit: design concept and tuning Our MCDF device is built by serially connecting multiple PhC-based ISO-centric ring

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resonator units that are named as CDFi, i=1, 2, …m, where m is the number of channels. For each of these units, the lattice constant is proportional to a photonic bandgap (PBG) that may differ with

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other units; however, there would remain an overlapped region. The CDF units are tuned such that when a multiwavelength light is incident upon the device, because of the different wavelength

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selection rule of each unit (for the trapped light within each resonator), only those wavelengths that have the same wavelength as that of the proper output channel are allowed to be extracted from that channel [37, 39, 43].

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Fig. 1: (a) Illustration of a square-type PhC lattice configuration, (b) Illustration of all-circular

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ring resonator based on a square-type PhC, (c) The ADF configuration that is used for tuning.

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Fig. 1a illustrates the zero-configured square-type PhC lattice, in which r is the radius of rods, and az and ax are lattice constants in z and x directions, respectively. Usually it is assumed that

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a=az=ax; however, in this paper, they are disconnected and their effect on the overall transmission

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spectrum is investigated separately. Fig. 1b shows the proposed ring resonator, which is based on a square-type PhC and an iso-centric all-circular hub with an empty bore and modified rim. rc1 and

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rc2 are corner rods, which are added to modify the rim and prevent backreflections; thus, the transmission will significantly enhance. The hub is formed by four layers of iso-centric all-circular

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arranged rods with an overall radius of R=4a. Each hub ring is at a distance of aRing=a from the previous layer ring. The surrounding medium of structure is assumed to be air, whereas the PhC lattice and iso-centric hub are made of a material with a refractive index (RI) of nr=nh=4.34 (nr

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denotes the RI of PhC lattice and rim, and nh denotes the RI of hub). The CPR denotes the coupling region rods by which the coupling between a ring and the adjacent waveguide is provided. Fig. 1c proposes a single unit of CDF configured according to parameters presented in Table 1. A Gaussian wave is incident upon the entrance port (Ein1). Because of the instructive and destructive formation of standing waves within the ring resonator, some of the wavelengths are passed from

through port (P1); however, the others will resonate out through forward drop (P2) and backward drop ports (P3). Fig. 2a shows the calculated forbidden PBG of square-type PhC lattice, in which two PBG regions exist for TM propagating waves, i.e., a/λ=0.25-0.41 and a/λ=0.685-0.705, respectively. Considering λ0=1550 nm as the central operating wavelength and the PhC lattice constant as

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a=549nm, these regions correspond to λ=1339-2192 and λ=778-801 nm, respectively. Fig. 2b shows the transmission spectrum characteristics of the proposed filter for the values proposed in Table 1, for which a transmission dip occurs at λ0=1550 with 100% efficiency in through port (P1) and 94.8% efficiency in drop port (P3). With a full-width half-maximum (FWHM) of 1nm, the quality factor of λ/Δλ=1550 is achieved. The value of PBG is obtained by the plane wave expansion method, and the transmission spectrum is obtained by the finite time-domain difference method

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(FDTD). The simulation medium is surrounded by perfectly matched layers (PMLs), and the

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courant condition is satisfied for which the simulation accuracy is promised.

Fig. 2: (a) Illustration of a square-type PhC lattice PBG, in which two PBG regions exist for TM propagating waves, i.e., a/λ=0.25-0.41 and a/λ=0.685-0.705. (b) Transmission spectrum characteristics of the proposed filter with a transmission dip occurring at λ0=1550 with 100% efficiency in through port (P1) and 94.8% efficiency in drop port (P3). The PBG and filter are configured according to the data in Table 1.

3. Results and discussions 3.1 Single-channel investigations In this section, an intensive study is performed on various parameters of the single CDF to fully understand the behavior of that parameter on the transmission spectrum of through port (P1)

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and backward drop (P3). Because the CDF is configured at critical coupling condition, no light is transmitted to forward drop port (P2). The very first and important parameter that can affect the transmission spectrum is the PhC lattice constant itself. In Figs. 3a-c and Figs. 4a-c, the effect of variation in this parameter on wavelength shift is investigated both in full-spectrum transmission map (2D) and simple transmission peak plots in 1D. In these figures, the effects of variations in lattice constant in different x and z directions are studied. As shown in Fig. 3a, when assuming

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a=az=ax, any changes in the lattice constant result in a linear redshift of wavelength; however,

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when they are separated and either ax or az is varied (the other is held at a=549nm) from 0.52µm to 0.59µm, the fully linear behavior vanishes and a slight nonlinearity is seen. In fact, yet the

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wavelengths are redshifted toward higher values as the corresponding side lattice constant slightly

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increases, but with a slower rate compared to that shown Fig. 3a.

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Fig. 3: Illustration of full-spectrum transmission map versus PhC lattice constant (a) in both x and

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z directions, (b) in x direction, and (c) in z direction.

Fig. 4: Illustration of transmission peaks versus PhC lattice constant (a) in both x and z directions, (b) in x direction, and (c) in z direction.

Figs. 4a-c convey the same information, but in another point of view. For example, as seen in these figures, it is found that a rapid variation in the lattice constant, as shown in Fig.4a, results in

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a larger number of immature unwanted adjacent resonant peaks near the main peak; however, in a slow varying case, as shown in the other two figures, this problem is limited by restraining the speed of variations.

The next parameter to study is the ISO-centric hub ring-to-ring constant (aRing). As shown in Figs. 5 a-b, with the increase in aRing from 0.519µm to 0.599µm (a=0.549µm), the wavelength peak is downshifted (blue shift). This result is in contrast to the result of PhC lattice constant study, in

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which the increase in a resulted in transmission peak being redshifted. Fig. 5b demonstrates the

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same information in another plot. It is seen that the adjacent immature peaks are far away from affecting the main peak. Here, again the variations of peaks are not fully linear, and just by

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increasing aRing to values above 0.565µm, a linear response is perceived.

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Fig. 5: (a) Illustration of full-spectrum transmission map versus hub ring-to-ring constant (aRing)

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(b) Illustration of transmission peaks versus hub ring-to-ring constant (aRing) variations.

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Fig. 6: Illustration of full-spectrum transmission map versus PhC rod radii variations for (a) when only PhC lattice and rim rod radius is varied and hub radius is constant (rh/a=0.165). (b) when all

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the PhC lattice, rim and hub radii are varied.

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The PhC rod radii variations also affect the transmission spectrum. In Figs. 6a-b, this fact is studied. In Fig. 6a, only PhC lattice rod radius is varied, whereas the hub radius is held constant

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(rh/a=0.165). This study shows that until a radius of 105 nm, the transmission peak redshifts

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linearly toward higher values; however, for larger variations in radius (>105 nm), the transmission suddenly vanishes from the desired interval. The same result is obtained in Fig. 6b in which the

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PhC lattice and hub radius are both varied simultaneously; however, here the slope of wavelength redshift is larger by a fewer magnitude. In Figs. 7a-b, this slope is shown with a more clear point

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of view for which Fig. 7b shows a faster redshift of peak toward higher values than Fig. 7a, when

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the radius is varied from 77 nm to 102 nm.

Fig. 7: Illustration of transmission peaks versus PhC rod radii variations for (a) when only PhC lattice and rim rod radius are varied and the hub radius is constant (rh/a=0.165). (b) when all the

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PhC lattice and rim and hub radii are varied.

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Fig. 8: (a) Illustration of full-spectrum transmission map versus lattice normalized hub ring radius (rh/a) variations, when the PhC lattice and rims radius are r/a=0.165 (b) Illustration of transmission

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peaks versus lattice normalized hub ring radius (rh/a) variations, when the PhC lattice and rim

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radius are r/a=0.165.

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In Figs. 8 a-b, the variations in lattice normalized hub ring radius (rh/a) and its effect on the

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transmission spectrum of P3 are studied. As shown in Fig. 8 a, the transmission spectrum has a Slike-shaped redshift beginning from rh/a =0.1 and vanishing at rh/a=0.2. The best useful part of this map is for rh/a=0.13-0.2, for which the linear response from full-spectrum transmission map

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is obtained. The transmission peaks for this usable range are plotted and compared in Fig. 8b for

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various values of rh/a.

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Fig. 9: Illustration of full-spectrum transmission map versus refractive index variations for (a) when all the PhC lattice, rim and hub RIs are varied (r/a=0.165). (b) when only the hub RI is

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varied. The PhC lattice and rim radius and RI are r/a=0.165, nr=4.345.

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Fig. 10: Illustration of transmission peaks versus refractive index variations for (a) when all the PhC lattice, rim and hub RIs are varied (r/a=0.165). (b) when only the hub RI is varied. The PhC

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lattice and rim radius and RI are r/a=0.165, nr=3.435.

The simplest type of study usually is to investigate the RI variations within each region of

design. As an example, in Fig. 9a, the variations in refractive index for the whole CDF (nr)-when all the PhC lattice, rim and hub RIs are varied (r/a=0.165)-are studied. As concluded from this figure, it is obvious that a large redshift of wavelength, from λ=1.45 to 1.56 µm, arises due to the

increase in nr. Considering a limited variation in RI within the structure, the best choice is to vary the RI of the hub itself, because the region with the most interaction with the incident light is hub. In Fig. 9b, this limited RI study is shown in which the nh denotes the hub RI. Here, the PhC lattice and rim radius and RI are r/a=0.165 and nr=4.345, respectively. By varying nh from 3 to 4.4, the transmission spectrum peak wavelength is only redshifted from λ=1.54 to 1.56µm.

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Learning the most important parameter variation behavior and their effect on transmission spectrum, now the design of multichannel operation of the proposed CDF unit is presented.

3.2 Multichannel investigations

Because the efficiency and quality factor are dimensionless parameters, by tuning the unit filter to operate at different wavelengths, their values should remain unaltered for other units. Thus,

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when the basic unit is designed and tuned, any simple serial connection of a few number of this

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unit should provide a multichannel drop filter, with expectation of the same efficiency and Q for all channels. According to this idea and based on the investigations of previous section, a five-

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channel filter is proposed in Figs. 11a, b. In Tables 2 and 3, two different configurations are

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presented. By varying the parameters in these two multi-CDFs, we have been able to manage the channel spacing and undesired crosstalk between channels. However, because of the existence of

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crosstalk of channels, the quality factor and transmission efficiency of channels have been altered

design applications.

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by a few percentage. Fortunately, these levels are not much and could easily be neglected for real

Fig. 12 shows that the crosstalk of channels could be extracted in decibel (db) units from

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10×log(transmission value), from which the worst crosstalk for CDF5 is found to be less than -10 db, and originates form CDF1 and CDF4. The worst crosstalk for CDF4 is less than -14db, which

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originates from CDF3. The worst crosstalk for CDF3 originates from CDF2 and has a value of -17 db. CDF2 shows a very interesting characteristic that almost no crosstalk larger than -50 db exists

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for this channel; however, the poorest level of crosstalk of CDF1 again equals to -16 db that is originated from CDF2.

Table 1. Summary of parameters for the basic configuration of CDF unit shown in Fig. 1c Parameter a, ax, az

Description Lattice constant

CDF

Unit

549

nm

ΔaRing

Radial lattice constant of hub

nh

nm

Refractive index of hub

3.435

nm

nr

Refractive index of rim

3.435

nm

rh

Rod radii of hub

0.165a

nm

r

Rod radii of rim

0.165a

nm

λ

Dropping Wavelength

1550.2

nm

?? %

Transmission efficiency

94.8%

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549

-

Table 2. Summary of parameters for configuration of multi-CDF shown in Fig. 11a Description

CDF1

CDF2

CDF3

CDF4

CDF5

Unit

Δax

Lattice constant in x direction

0

0

0

0

0

nm

Δaz

Lattice constant in z direction

0

0

0

0

0

nm

ΔaRing

Radial lattice constant of hub

12

6

0

-6

-12

nm

Δnh

Refractive index of hub

-0.3

-0.15

0

0.15

0.3

nm

Δnr

Refractive index of rim

0

0

0

0

0

nm

Δrh

Rod radii of hub

-0.05a

0

0.025a

-0.05a

nm

Δr

Rod radii of rim

0

0

0

0

0

nm

λ

Dropping Wavelength

1529.6

1538.9

1550.2

1559.9

1569.4

nm

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Parameter

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-0.025a

Description

CDF1

CDF2

CDF3

CDF4

CDF5

Unit

Δax

Lattice constant in x direction

0

0

0

0

0

nm

Δaz

Lattice constant in z direction

0

0

0

0

0

nm

ΔaRing

Radial lattice constant of hub

20

10

0

-10

-20

nm

Refractive index of hub

-0.2

-0.1

0

0.1

0.2

nm

Refractive index of rim

0

0

0

0

0

nm

Rod radii of hub

-0.1a

-0.05a

0

0.05a

-0.1a

nm

Δr

Rod radii of rim

0

0

0

0

0

nm

λ

Droping Wavelength

1521

1533.6

1550.3

1563.8

1576.1

nm

Δnr

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Δrh

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Δnh

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Parameter

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Table 3. Summary of parameters for configuration of multi-CDF shown in Fig. 11b

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Fig. 11: Transmission peaks of the proposed five-channel filter in the desired spectra for two different configurations: (a) configured considering Table 2 parameters, (b) configured

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considering Table 3 parameters.

Fig. 12: Logarithmic presentation of transmission peaks in the desired spectra for proposed fivechannel filter, which is configured according to the parameters summarized in Table 3.

Figs. 13a-f demonstrate the time snapshots taken at 6 ps after the simulations are commenced. These figures verify that after excitation of the proposed multichannel filter with a continuous

wave whose wavelength corresponds to that of each CDF1, CDF2, … CDF5, the device works properly and the specific wavelength is properly selected from the incoming P1 port. The multiCDF for which these results are obtained is configured such that its transmission output is shown in Fig. 11b. The CDF1 selects λ1=1521 nm, CDF2 selects λ2=1533.6 nm, CDF3 selects λ3=1550.3 nm, CDF4 selects λ4=1563.8 nm, and CDF5 selects λ5=1576.1 nm from incoming wavelengths. The

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Ch1, Ch2, …, Ch5 indicate the output channel of the corresponding CDFs, respectively. The other wavelengths that are not within the selection range of CDFs are free to pass the structure. As an example, for λ0=1512.8nm, there is no selection by any output channel and is transmitted freely

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within P1.

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Fig. 13: Time snapshots at 6 ps after the simulation commenced, in which a continuous wave excitation is demonstrated for the proposed multi-CDF for (a) through port (P1) excited by

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λ0=1512.8nm, there is no selection by any output channel, (b) Ch1 selects λ1=1521 nm, (c) Ch2 selects λ2=1533.6 nm, (d) Ch3 selects λ3=1550.3 nm, (e) Ch4 selects λ4=1563.8 nm, (f) Ch5 selects

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λ5=1576.1 nm (the multi-CDF is configured such that its transmission output is as shown in Fig. 11b).

Conclusion In this paper, a photonic crystal-based all-circular ring resonator was designed and used as an optical filtering device. By conducting full-spectrum transmission studies on available tuning

parameters such as RR radius, RR refractive index, PhC lattice high and low refractive indices, and PhC lattice constant, the general transmission behavior of each parameter was found in terms of blue or red shift wavelength dependencies. This blue or red shift effect on resonance peak was used to easily design MCDFs with proper channel spacing and engineering crosstalks. Because the engineering of channel spacing and crosstalks was difficult without the implementation of a blue

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shift-inducing parameter, by increasing any other tuning parameter only red shifted the resonance peak, and the ISO-centric all-circular PhCRR was easily able to provide such a wavelength blue shift. By using these two red and blue wavelength shift mechanisms, we were able to easily retune the resonance wavelength at exactly desired values. These data were applied to design a fivechannel multiwavelength filter for which reasonable drop efficiencies from at least 76%, up to 100%, were obtained. Moreover, the crosstalk across all the channels was obtained from exact

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designs between -10 db as the worst case up to -50 db as the best case. These values promise a

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highly efficient MCDF. Moreover, the simulations were performed by FDTD method.

[4] [5]

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[6]

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