- Email: [email protected]
Optical micro-multi-racetrack resonator filter based on SOI waveguides
Accepted Manuscript Title: Optical Micro-Multi-Racetrack Resonator Filter Based on SOI Waveguides Author: Dror Malka Moshik Cohen Jarek Turkiewicz Zeev Zalevsky PII: DOI: Reference:
S1569-4410(15)00056-5 http://dx.doi.org/doi:10.1016/j.photonics.2015.07.002 PNFA 513
To appear in:
Photonics and Nanostructures – Fundamentals and Applications
Received date: Revised date: Accepted date:
9-5-2015 12-7-2015 13-7-2015
Please cite this article as: D. Malka, M. Cohen, J. Turkiewicz, Z. Zalevsky, Optical Micro-Multi-Racetrack Resonator Filter Based on SOI Waveguides, Photonics and Nanostructures - Fundamentals and Applications (2015), http://dx.doi.org/10.1016/j.photonics.2015.07.002 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.
Highlights We present a new design of the optical FIR filter which based on 6 racetrack resonators and silicon waveguides. An FDTD simulation is being used to demonstrate optical pulses propagation in the filter and the filter's spectral response. The control over the spectral characteristics is carried out by changing the geometrical parameters of the racetrack resonators.
1
Ac
ce p
te d
M
an
us
cr
ip
t
The manufacturability of the filter is being demonstrated.
Page 1 of 13
Optical Micro-Multi-Racetrack Resonator Filter Based on SOI Waveguides Dror Malka1, Moshik Cohen1, Jarek Turkiewicz2 and Zeev Zalevsky1,* 1
Faculty of Engineering Bar-Ilan University, Ramat-Gan 52900, Israel 2
Warsaw University of Technology, Poland
*
Corresponding author’s email: [email protected]
Abstract: In this paper, we present a new design of optical Finite Impulse Response (FIR) filter based on combination of multi-racetrack resonators realized with Silicon waveguides. Numerical investigations were carried out on the spectral response of the proposed filters design, in order to obtain FIR band-pass filter around the photonic carrier wavelength of 1.55m. The proposed FIR filter was fabricated using electron beam lithography (EBL). The device was preliminary experimentally examined by a combination of scanning electron microscopy (SEM) and atomic force microscopy (AFM). Index Terms: Racetrack resonator, optical filter, Silicon photonics, Optical Communication
t
1. Introduction
ip
An optical racetrack resonator is a set of waveguides in which at least one is a closed loop waveguide coupled to the input and the output ports. A ring/racetrack resonator is a device that usually used as an optical Infinite
cr
Impulse Response (IIR) filter [1-3]. Many theoretical designs have been proposed to optimize the filter’s spectral response and other properties using various coupled resonator arrays [4-6]. The compact resonators have been
us
demonstrated using number of semiconductor materials [7] and glass waveguides [8]. Racetrack resonators play important role in the field of silicon photonics [9], due to the capability to realize them
an
at micrometric dimensions. A generic racetrack resonator consists of an optical waveguide which is looped back on itself, such that a resonance occurs when the optical path length of the resonator is exactly an integer
M
multiplication of the wavelengths injected into the device. FIR filter is a discrete-time filter with impulse response that contains a finite number of coefficients and which is designed usually by cascading Mach Zehnder
te d
Interferometer (MZI) and couplers components [3]. Optical waveguides [10] are dielectric structures that transmit electromagnetic waves in the direction parallel to 2
Ac
ce p
their axis at visible or infrared frequencies. They are fundamental building blocks of many optical systems,
Page 2 of 13
including optical filters. Similar to their microwave counterparts, optical filters are designed and analyzed by solving Maxwell's equations. These equations can e.g. be solved by numerical method called Finite Difference Time Domain (FDTD) [11]. Silicon photonic devices have been fabricated on top of Silicon on Insulator (SOI) wafers [12]. Optical lithography fabrication of silicon chip of one racetrack resonator and multi racetrack resonator structures is well known [13, 14]. Recently researchers have begun to design multi-tap microwave photonic FIR filter based on single-mode and multimode fibers [15]. An important consideration is the size of the components, and thus there is much interest in production of on-chip optical components. For example a radio-frequency photonics filter with dimension of 2mm x 8mm can be fabricated using SOI waveguide optical delay lines [16]. In this paper, we propose and investigate a new design of FIR photonic filter which is based on multi-racetrack resonator and which is fabricated on SOI. The advantage of this design is that although it is an FIR filter it uses the inherent properties of the racetrack resonator itself which is an IIR filter. Therefore, such filter should be extremely flexible, while our unique realization involves realizing plurality of racetrack resonators with slightly different Finesse instead of adding a delay line [15]. We show that by using racetrack resonators, instead of MZI or linear waveguide, the filter size can be maintain
t
i.e. the filter properties can be modified without any size change.
ip
Our findings may pave the way for designing novel on chip optical devices based on IIR components, like the
cr
multiple - racetrack architecture.
As a summary the novelties we present in our paper are as follows: we were able for the first time to the best of
us
our knowledge, to realize ultra-compact FIR spectral filter by folding the various optical paths through optical rings/racetracks. By interfering the output of adjacent rings/racetracks and adding a non-linear saturation optical
an
element we could realize spectral filter with flexibility in the position of its spectral peak as well as in its spectral width almost without the need to increase the size of the proposed filter.
M
Note that unlike conventional ring resonators our spectral filter is not based on interfering the temporal replications generated by the resonator but rather we use the last replicated term in order to realize effectively much longer optical path than its physical size. The interference between adjacent rings/racetracks and the
te d
passage through the non-linear element are needed to eliminate all the rest of the replications which are undesired
3
Ac
ce p
such that only the last replication of the inserted temporal signal is remained.
Page 3 of 13
2. Theory of operation Fig. 1 demonstrates a schematic sketch of our proposed optical FIR filter based on multi-racetrack resonator structure. In this figure, the yellow areas represent silicon, blue area represent silicon-nanocrystals [17], the black areas represent silica. The reason for using silicon-nanocrystals is to obtain optical gain in the saturation area (blue color). The filter design includes two sets of racetracks where each set contains three different racetracks resonators. The only difference between the two sets is the coupling distance between the racetrack and the input/output waveguide. In the first set, the coupling distance between the input/output waveguide and the racetrack is LC1=260nm and for the second it is LC2=220nm. Due to the change of the coupling distances in the two sets we obtain slightly different Finesse in each set (difference of one in the Finesse value). The idea of using the two sets is because we interfere the overall output of each set in such a way that they are subtracted. The subtraction, in case of Finesse having a difference of one in its value, allows eliminating all the replications of the signal coming out of each racetrack except of the last replica in the set of the higher Finesse. This way we may generate large temporal delay of the original signal (needed to realize spectrally narrow FIR filter) while the undesired
M
an
us
cr
ip
t
replications are eliminated (we mathematically prove the above mentioned claim below).
Fig. 1. Schematic illustration of the optical FIR filter.
te d
The silicon waveguides forming the structure have a cross section area with width of 450nm and height of 220nm. The optical signal wavelength is 1550nm. The dimensions of the filter are as follows: dc=6m, L=2(Ri+dc), 4
Ac
ce p
Ri=5+1.36i(m), i=0,1,2. where dc is the coupler straight section and L is the overall optical path of the racetrack. Each
Page 4 of 13
optical path is realized as a racetrack resonator as shown in Fig. 1, with zoom into the racetrack area that is shown at the inset. The operating principle of the introduced FIR filter is based on optical wave's interference. The Gaussian pulse that is injected at the input is split to six waveguiding traces and the waves as each of the branches undergoes phase accumulation through the racetrack structure. In the saturation and combining section we use saturated optical amplification to equalize the amplitudes of all the incoming signals, resulting in phase interference which realizes the filter functionality. The dimensionality compression of the FIR filter is obtained by using racetrack resonator to achieve the desired interference response. The Finesse of each racetrack generates replications of the incoming pulses of information while the replicated pulse that traveled more times in the racetrack waveguide experienced equivalently larger optical path. The reason that a racetrack and not ring resonator structure was used is due to our desire to increase the coupling efficiency since the racetrack device has better interaction with the input/output waveguide so longer coupling distance is obtained. In the input waveguide we transmit pulse having a Gaussian envelope multiplied by a sinusoidal carrier: s(t) exp[(
t 2 t d ) 2 ]sin( (t) Ct 2 ) , p
(1)
where 1.55 m is the wavelength of the carrier, C is the chirp coefficient, p is the time pulse and td is the delay time. The round trip time delay in each racetrack is given by:
L , c / ng
t
(2)
ip
t
where ng is the group index of the waveguide mode. The input signal is split into 6 optical racetrack resonators
cr
and eventually is recombined at the output. The principle of operation of the FIR filter is based on controlling the Finesse value in each racetrack resonator. To illustrate this concept we take a common optical path in both sets
us
and describe the obtainable output fields. The output field from the racetrack from the first set will be:
m 1
an
E1 (t) ( 1 12 )s(t) 12 ( 1 12 )m 1 s(t mt) ,
(3)
M
The output from the racetrack from the second set will be: E 2 (t) ( 1 )s(t)
2 2
( m 1
te d
2 2
1 22 ) m 1 s(t mt) ,
(4)
where 1 and 2 are the coupling coefficients between the waveguide and the racetrack resonator. We assume
5
Ac
ce p
that the fields are subtracted and then they pass through an amplifier which basically realizes a threshold function.
Page 5 of 13
As s(t) is a binary set of pulses the threshold function will not distort this pulse sequence. We will assume that the threshold of the amplifier is Ω. (denoted as T{…}Ω) Thus, in order to obtain the desired output, the threshold difference between E1 and E2 should be equal to: T E1 (t) E 2 (t) A s(t Mt) ,
(5)
As all the terms in both sets (in Eq. 3 for the first set and in Eq. 4 for the second set) after the threshold operation will have the same coefficient A for all terms up to the term of M in the first set and up to the term of M-1 in the second set, after the subtraction only one term of s(t-Mt) will remain. Where A is the output level of the amplified device, i.e. its saturation level (the amplifier output is zero for all values below Ω and they are A for all valued above it). The desired output as presented in Eq. 5 will be obtained if the following condition is fulfilled:
12 ( 1 12 )M1 22 ( 1 22 )M 2 ,
(6)
Then indeed the saturated subtraction will fully cancel all the not desired terms (undesired replications) in both series. As we want to obtain relatively large M we can assume that all are relatively close to 1 and then we can approximate according to Taylor series that: 1 12
M 1
1 2(1 1 ) 2(1 1 )
(M 1)
2
(M 1) (M 1) 2 , (1 1 ) 2(1 1 ) 1 4
(7)
t
and thus: (M 1)
, 2 1 2
2
(M 2)
,
cr
2
(8)
us
1 1 2
ip
12
Consequently we obtain only the optical signal with delay and without its undesired duplicates. Due to the path length difference, a delay is generated between each one of the 6 interferometers. The
an
combination of the 6 paths generates FIR filter while the relative delays between the 6 paths determine the position of the spectral band pass of the FIR filter.
M
As known from the FIR theory [18] if we assume that an incoming sequence s(t), is duplicated 6 times and
te d
summed each after delaying each duplication by t, then the obtained output is:
5
sT (t) a ns(t n t) ,
(9)
n 0
6
Ac
ce p
The Fourier transform of sT equals to:
Page 6 of 13
5
ST ( ) sT (t) exp(2 i t)dt a n s(t n t) exp(2 i t)dt S( )F( ) n 0
S( ) s(t) exp(2 i t)dt
(10)
5
F( ) a n exp(2 i n t), n 0
The filter F is an FIR filter. By tuning the delay between the sequences the spectral position of the realized filter may be changed.
3. Simulation results We simulated operation of the micro-multi-racetrack resonator FIR filter structure using RSoft Photonics CAD Suite software, which is based on FDTD method. We performed 2 dimensional (2D) simulations on a 135m x 152m filter, as shown in Fig. 2(a). We transmitted Gaussian pulses with a wavelength centered at 1.55m into the waveguide input. The optical pulses split into 6 paths, as shown in Fig. 2(b). The coupling exists in all 6 optical paths. For clarity, we have also presented in Fig. 2(c) the coupling between waveguide and racetrack resonator, with zoom in area of radius R 0 Subsequently the interaction between the waveguides and the multi-racetrack resonator began. Fig. 2(d) shows the
Output Area
ip
t
propagation of the optical pulses at the output.
an
us
cr
Coupling Area
(b)
7
Ac
ce p
te d
(a)
M
Input Area
Page 7 of 13
Saturation Area
(c)
(d)
Fig. 2. Gaussian pulses propagation in the FIR filter: (a) Full view. (b) Zoom into the input area. (c). Zoom into the racetrack resonator area of radius R0. (d) Zoom into the output area.
Next, we used FDTD method to sample the electric field at the output. The electric field samples went through Fast Fourier Transform (FFT) in order to calculated the spectral responses of the micro-multi-racetrack resonator
an
t ip cr
us
Intensity [Arb. Units]
Intensity [Arb. Units]
for different sizes of the racetrack (L) and coupling distances ( LC1 , L C2 ).
(a)
Wavelength [µm]
M
Wavelength [µm]
(b)
Fig. 3. Spectral response of the optical FIR filter for two different coupler straight sections: (a) d c 6 m . (b) d c 3 m .
te d
Finally, after finding the optimal coupling distances, we found the appropriate values for L, LC1 and LC2, which are suitable for realizing the optical FIR filter, with a coupler straight sections of dc=6m. Fig. 3(a) shows the 8
Ac
ce p
spectral response obtained at the output of the proposed optical device.
Page 8 of 13
From Fig. 3(a) it can be seen that FWHM=15nm and FSR=40nm (FWHM=full width half maximum, FSR=free spectral range) has been obtained. The spectral position can be tuned by changing the value of the coupler straight sections, as shown in Fig. 3(b). For dc=3m, FWHM=20nm and FSR=35nm has been obtained. The ripples in both transmission spectra 3(a) and 3(b) are due to the finiteness of the waveguides, that is, the finite number of racetrack (in our case 6 racetracks). It can be assumed that by increasing the number of racetrack, the degradation caused by the ripple can be overcome. The optimal size of the saturation area was found by optimization the gain level at the output filter which lead to the best result in the extinction ratio. Fig. 4 shows the normalized extinction ratio as a function of the saturation area size.
1
0.8
0.6
0.2
0 0
2
4
cr
ip
t
0.4
us
] st i n U . br A [ oi t ar n oi ct ni t xe de zi l a m r o N
6
8
Saturation area size [um]
an
Fig. 4. Normalized extinction ratio as a function of the saturation area size.
From Fig. 4 it can be noticed that the optimal size of the saturation area is about 4µm. It can be noticed that we
M
obtained a passive filter that is operated over a photonic carrier (1.55m) and allows realization of e.g. band pass
9
Ac
ce p
te d
microwave filter around the photonic carrier.
Page 9 of 13
4. Fabrication The multi-racetrack resonator patterns were defined on SOI wafers with a Si layer thickness of 220nm, on top of a 2μm SiO2 buried oxide layer. It was done using CRESTEC CABLE-9000C high-resolution electron-beam lithography system [19] using different doses to control line and gap width. Zeon (ZEONREX® Electronic Chemicals) was spin coated at 5000 rpm and baked at 180°C for 20 min before exposure with a 105 KeV electron beam. After development, patterns were placed in an oven at 160°C for 5 min to cause the resist to reflow, reducing pattern roughness. The waveguide patterns were transferred using an anisotropic dry etch in an inductively coupled plasma reactive ion etcher mixed mode plasma etch [20]. Fig. 5(a) shows the fabrication results of the micro-multi-racetrack resonator FIR filter, with zoom into the racetrack area which is presented in Fig. 5(b). For complete verification of the fabrication process, we carried out three dimensional topography analysis using atomic force microscopy (AFM). All AFM measurements were performed at room temperature and free ambient conditions (no vacuum), using Dimension Icon AFM system with NanoScope V controller (Bruker®). We used NanoWorld probes SSS-NCH, SuperSharpSilicon - Non-contact / Tapping™ mode - High resonance frequency; with typical diameter of 2nm, resonance frequency of 320 kHz and spring constant of 42N/m. typically, voltages of 2V, AC capacitance frequencies of 880MHz, lift heights of 30nm - 50nm and line rates of 0.1 KHz were employed. Figs. 5(c) and 5(d) presents the 3D AFM analysis of a single racetrack and splitting section,
t
respectively. The entire device could not be analyzed at a single scan due to the maximum scan size limitation of
ip
the microscope (35µmX35µm). From the AFM analysis, we observe smooth waveguide faces with excellent
10
Ac
ce p
te d
M
an
us
cr
agreement to the desired patterns.
Page 10 of 13
(b)
ip
t
(a)
cr
(c)
(d)
an
us
Fig. 5. Fabrication of the micro-multi-racetrack resonator FIR filter: (a) Full view (2D). (b). Zoom into the racetrack resonator area (2D). (c) 3D AFM analysis of a single racetrack section of the filter (d) 3D AFM analysis of the splitting/combining section.
5. Conclusions
M
Through experiment and simulation results, it has been shown that FIR filter can be realized using multi-racetrack resonator structures which are based on SOI waveguides.
te d
The novelty that we present in this letter is related to the fact that we propose a unique realization scheme that allows for the first time, to the best of our knowledge, to realize ultra-compact FIR spectral filter by folding the
11
Ac
ce p
various optical paths (needed to realize the FIR filter) via the optical rings/racetracks whose outputs are interfered
Page 11 of 13
and passed through a non-linear saturation optical elements. This unique scheme eventually yields spectral filter with flexibility in the position of its spectral peak as well as in its spectral width. Unlike conventional ring resonators our spectral filter is not based on interfering the temporal replications generated by the resonator but rather we use the last replicated term in order to realize effectively much longer optical path than its physical size. This new design can be used for realization of narrow band microwave filters as those used in passive optical communication networks or in electronic warfare applications. Such a filter can be used in a wide range of applications, e.g. in the opto-telecommunication systems. It can serve there as a signal shaper, interleaving demultiplexer, for wavelength selective power monitoring or as a demultiplexing filter in WDM-Passive Optical Network (PON) systems.
References 1.
A. Yariv and P. Yeh," Photonics," 6 Ed., Ch. 4, Oxford university press (2007).
2.
D. G. Rabus, M. Hamacher, U. Troppenz and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GalnAsp-Inp," J. Quantum electronics, 8, 1405-1411 (2002).
3.
C.K. Madsen and J.H. Zhao, "Optical Filter Design and Analysis: A Signal Processing Approach," Ch. 1, Wiley (1999).
4.
R.Otra, P. Savl, R. Tascone and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical system," IEEE photonics
t
technology, Lett.7, 1447-1449 (1995). G. Griffel, "Synthesis of optical filters using ring resonator arrays," IEEE photonics technology, Lett.12, 810-812 (2000).
6.
W.Bogaerts, P. D. Heyn, T.V. Vaerenmbegh, K. Devos , S. Selvaraja, T. Claes, P. Dumon, P. Bienstmen, D.V. Thourhout and
ip
5.
7.
B. E. Little, J. Forsei, H. A. Haus , E. P. Ippen, W. Greens and S. T. Chu, "Ultracompact Si/SiO2 micro-ring resonator channel T. Kominato, Y. Ohmori, N. Takato, H. Okazaki and M. Yasu, "Ring resonators composed of GeO2-doped silica waveguides," IEEE Lightwave Tech.10, 1781-1788 (1992).
G. T. Reed, "Silicon photonics the state of the art," Wiley (2008).
an
9.
us
dropping filter," IEEE photon. Technol. Lett. 10, 549-551 (1998). 8.
cr
R. Baets, "Silicon microring resonators," Laser photonics Rev. 6, No.1, 47-73 (2012).
10. K. Okamoto, "Fundamentals of Optical Waveguides," Ch. 2, Academic press (2000). 11. S. C. Hagness, D. Rafizadeh, S. T. Ho and A. Taflove, "FDTD microcavity simulations: design and experimental realization of
M
waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators," Lightwave Technology, 15, 2154-2164 (1997).
12. G. T. Reed and A. P. Knights, "Silicon Photonics: An Introduction," Ch.4, Wiley (2004).
te d
13. M. Soltani, S. Yegnanarayanan, Q. Li and A. Adibi, "Systematic Engineering of Waveguide-Resonator Coupling for Silicon Microring/Microdisk/Racetrack Resonators: Theory and Experiment," J. Quantum elecrronics, 46, (2010). 14. R. Boeck, N. A. F. Jaeger, N, Rouger, and L. Chrostowski, "Series-coupled silicon racetrack resonators the Vernier
12
Ac
ce p
effect: theory and measurement," Optics Express, 18, 25151-25157 (2010).
Page 12 of 13
15. N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, J. B. Luff, A. Agarwal, T. Banwell, R. Menendez,P. Toliver,T. K. Woodward and M. Asghari1, "Thermally-efficient reconfigurable narrowband RF-photonic filter," Optics Express, 18, 2464824653 (2010). 16. J. Chang, M. P. Fok, J. Meister and P. R. Prucnal1, "A single source microwave photonic filter using a novel single-mode fiber to multimode fiber coupling technique," Optics Express, 21, 5585-5593 (2013). 17. L. Paves, L. Dal Negro, C. Mazzoleni, G. Franzo and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000). 18. B. Porat, "A Course in Digital Signal Processing," Ch. 11, Wiley, (1997). 19. M. Cohen, R. Shavit, Z. Zalevsky, "Towards Integrated Nanoplasmonic Logic Circuitry," Nanoscale 5(12), 5442-9 (2013). 20. M. D. Henry, S. Walavalkar, A. Homyk, and A. Scherer, "Alumina etch masks for fabrication of high-aspect-ratio silicon
13
Ac
ce p
te d
M
an
us
cr
ip
t
micropillars and nanopillars," Nanotechnology 20, 255305 (2009).
Page 13 of 13
S1569-4410(15)00056-5 http://dx.doi.org/doi:10.1016/j.photonics.2015.07.002 PNFA 513
To appear in:
Photonics and Nanostructures – Fundamentals and Applications
Received date: Revised date: Accepted date:
9-5-2015 12-7-2015 13-7-2015
Please cite this article as: D. Malka, M. Cohen, J. Turkiewicz, Z. Zalevsky, Optical Micro-Multi-Racetrack Resonator Filter Based on SOI Waveguides, Photonics and Nanostructures - Fundamentals and Applications (2015), http://dx.doi.org/10.1016/j.photonics.2015.07.002 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.
Highlights We present a new design of the optical FIR filter which based on 6 racetrack resonators and silicon waveguides. An FDTD simulation is being used to demonstrate optical pulses propagation in the filter and the filter's spectral response. The control over the spectral characteristics is carried out by changing the geometrical parameters of the racetrack resonators.
1
Ac
ce p
te d
M
an
us
cr
ip
t
The manufacturability of the filter is being demonstrated.
Page 1 of 13
Optical Micro-Multi-Racetrack Resonator Filter Based on SOI Waveguides Dror Malka1, Moshik Cohen1, Jarek Turkiewicz2 and Zeev Zalevsky1,* 1
Faculty of Engineering Bar-Ilan University, Ramat-Gan 52900, Israel 2
Warsaw University of Technology, Poland
*
Corresponding author’s email: [email protected]
Abstract: In this paper, we present a new design of optical Finite Impulse Response (FIR) filter based on combination of multi-racetrack resonators realized with Silicon waveguides. Numerical investigations were carried out on the spectral response of the proposed filters design, in order to obtain FIR band-pass filter around the photonic carrier wavelength of 1.55m. The proposed FIR filter was fabricated using electron beam lithography (EBL). The device was preliminary experimentally examined by a combination of scanning electron microscopy (SEM) and atomic force microscopy (AFM). Index Terms: Racetrack resonator, optical filter, Silicon photonics, Optical Communication
t
1. Introduction
ip
An optical racetrack resonator is a set of waveguides in which at least one is a closed loop waveguide coupled to the input and the output ports. A ring/racetrack resonator is a device that usually used as an optical Infinite
cr
Impulse Response (IIR) filter [1-3]. Many theoretical designs have been proposed to optimize the filter’s spectral response and other properties using various coupled resonator arrays [4-6]. The compact resonators have been
us
demonstrated using number of semiconductor materials [7] and glass waveguides [8]. Racetrack resonators play important role in the field of silicon photonics [9], due to the capability to realize them
an
at micrometric dimensions. A generic racetrack resonator consists of an optical waveguide which is looped back on itself, such that a resonance occurs when the optical path length of the resonator is exactly an integer
M
multiplication of the wavelengths injected into the device. FIR filter is a discrete-time filter with impulse response that contains a finite number of coefficients and which is designed usually by cascading Mach Zehnder
te d
Interferometer (MZI) and couplers components [3]. Optical waveguides [10] are dielectric structures that transmit electromagnetic waves in the direction parallel to 2
Ac
ce p
their axis at visible or infrared frequencies. They are fundamental building blocks of many optical systems,
Page 2 of 13
including optical filters. Similar to their microwave counterparts, optical filters are designed and analyzed by solving Maxwell's equations. These equations can e.g. be solved by numerical method called Finite Difference Time Domain (FDTD) [11]. Silicon photonic devices have been fabricated on top of Silicon on Insulator (SOI) wafers [12]. Optical lithography fabrication of silicon chip of one racetrack resonator and multi racetrack resonator structures is well known [13, 14]. Recently researchers have begun to design multi-tap microwave photonic FIR filter based on single-mode and multimode fibers [15]. An important consideration is the size of the components, and thus there is much interest in production of on-chip optical components. For example a radio-frequency photonics filter with dimension of 2mm x 8mm can be fabricated using SOI waveguide optical delay lines [16]. In this paper, we propose and investigate a new design of FIR photonic filter which is based on multi-racetrack resonator and which is fabricated on SOI. The advantage of this design is that although it is an FIR filter it uses the inherent properties of the racetrack resonator itself which is an IIR filter. Therefore, such filter should be extremely flexible, while our unique realization involves realizing plurality of racetrack resonators with slightly different Finesse instead of adding a delay line [15]. We show that by using racetrack resonators, instead of MZI or linear waveguide, the filter size can be maintain
t
i.e. the filter properties can be modified without any size change.
ip
Our findings may pave the way for designing novel on chip optical devices based on IIR components, like the
cr
multiple - racetrack architecture.
As a summary the novelties we present in our paper are as follows: we were able for the first time to the best of
us
our knowledge, to realize ultra-compact FIR spectral filter by folding the various optical paths through optical rings/racetracks. By interfering the output of adjacent rings/racetracks and adding a non-linear saturation optical
an
element we could realize spectral filter with flexibility in the position of its spectral peak as well as in its spectral width almost without the need to increase the size of the proposed filter.
M
Note that unlike conventional ring resonators our spectral filter is not based on interfering the temporal replications generated by the resonator but rather we use the last replicated term in order to realize effectively much longer optical path than its physical size. The interference between adjacent rings/racetracks and the
te d
passage through the non-linear element are needed to eliminate all the rest of the replications which are undesired
3
Ac
ce p
such that only the last replication of the inserted temporal signal is remained.
Page 3 of 13
2. Theory of operation Fig. 1 demonstrates a schematic sketch of our proposed optical FIR filter based on multi-racetrack resonator structure. In this figure, the yellow areas represent silicon, blue area represent silicon-nanocrystals [17], the black areas represent silica. The reason for using silicon-nanocrystals is to obtain optical gain in the saturation area (blue color). The filter design includes two sets of racetracks where each set contains three different racetracks resonators. The only difference between the two sets is the coupling distance between the racetrack and the input/output waveguide. In the first set, the coupling distance between the input/output waveguide and the racetrack is LC1=260nm and for the second it is LC2=220nm. Due to the change of the coupling distances in the two sets we obtain slightly different Finesse in each set (difference of one in the Finesse value). The idea of using the two sets is because we interfere the overall output of each set in such a way that they are subtracted. The subtraction, in case of Finesse having a difference of one in its value, allows eliminating all the replications of the signal coming out of each racetrack except of the last replica in the set of the higher Finesse. This way we may generate large temporal delay of the original signal (needed to realize spectrally narrow FIR filter) while the undesired
M
an
us
cr
ip
t
replications are eliminated (we mathematically prove the above mentioned claim below).
Fig. 1. Schematic illustration of the optical FIR filter.
te d
The silicon waveguides forming the structure have a cross section area with width of 450nm and height of 220nm. The optical signal wavelength is 1550nm. The dimensions of the filter are as follows: dc=6m, L=2(Ri+dc), 4
Ac
ce p
Ri=5+1.36i(m), i=0,1,2. where dc is the coupler straight section and L is the overall optical path of the racetrack. Each
Page 4 of 13
optical path is realized as a racetrack resonator as shown in Fig. 1, with zoom into the racetrack area that is shown at the inset. The operating principle of the introduced FIR filter is based on optical wave's interference. The Gaussian pulse that is injected at the input is split to six waveguiding traces and the waves as each of the branches undergoes phase accumulation through the racetrack structure. In the saturation and combining section we use saturated optical amplification to equalize the amplitudes of all the incoming signals, resulting in phase interference which realizes the filter functionality. The dimensionality compression of the FIR filter is obtained by using racetrack resonator to achieve the desired interference response. The Finesse of each racetrack generates replications of the incoming pulses of information while the replicated pulse that traveled more times in the racetrack waveguide experienced equivalently larger optical path. The reason that a racetrack and not ring resonator structure was used is due to our desire to increase the coupling efficiency since the racetrack device has better interaction with the input/output waveguide so longer coupling distance is obtained. In the input waveguide we transmit pulse having a Gaussian envelope multiplied by a sinusoidal carrier: s(t) exp[(
t 2 t d ) 2 ]sin( (t) Ct 2 ) , p
(1)
where 1.55 m is the wavelength of the carrier, C is the chirp coefficient, p is the time pulse and td is the delay time. The round trip time delay in each racetrack is given by:
L , c / ng
t
(2)
ip
t
where ng is the group index of the waveguide mode. The input signal is split into 6 optical racetrack resonators
cr
and eventually is recombined at the output. The principle of operation of the FIR filter is based on controlling the Finesse value in each racetrack resonator. To illustrate this concept we take a common optical path in both sets
us
and describe the obtainable output fields. The output field from the racetrack from the first set will be:
m 1
an
E1 (t) ( 1 12 )s(t) 12 ( 1 12 )m 1 s(t mt) ,
(3)
M
The output from the racetrack from the second set will be: E 2 (t) ( 1 )s(t)
2 2
( m 1
te d
2 2
1 22 ) m 1 s(t mt) ,
(4)
where 1 and 2 are the coupling coefficients between the waveguide and the racetrack resonator. We assume
5
Ac
ce p
that the fields are subtracted and then they pass through an amplifier which basically realizes a threshold function.
Page 5 of 13
As s(t) is a binary set of pulses the threshold function will not distort this pulse sequence. We will assume that the threshold of the amplifier is Ω. (denoted as T{…}Ω) Thus, in order to obtain the desired output, the threshold difference between E1 and E2 should be equal to: T E1 (t) E 2 (t) A s(t Mt) ,
(5)
As all the terms in both sets (in Eq. 3 for the first set and in Eq. 4 for the second set) after the threshold operation will have the same coefficient A for all terms up to the term of M in the first set and up to the term of M-1 in the second set, after the subtraction only one term of s(t-Mt) will remain. Where A is the output level of the amplified device, i.e. its saturation level (the amplifier output is zero for all values below Ω and they are A for all valued above it). The desired output as presented in Eq. 5 will be obtained if the following condition is fulfilled:
12 ( 1 12 )M1 22 ( 1 22 )M 2 ,
(6)
Then indeed the saturated subtraction will fully cancel all the not desired terms (undesired replications) in both series. As we want to obtain relatively large M we can assume that all are relatively close to 1 and then we can approximate according to Taylor series that: 1 12
M 1
1 2(1 1 ) 2(1 1 )
(M 1)
2
(M 1) (M 1) 2 , (1 1 ) 2(1 1 ) 1 4
(7)
t
and thus: (M 1)
, 2 1 2
2
(M 2)
,
cr
2
(8)
us
1 1 2
ip
12
Consequently we obtain only the optical signal with delay and without its undesired duplicates. Due to the path length difference, a delay is generated between each one of the 6 interferometers. The
an
combination of the 6 paths generates FIR filter while the relative delays between the 6 paths determine the position of the spectral band pass of the FIR filter.
M
As known from the FIR theory [18] if we assume that an incoming sequence s(t), is duplicated 6 times and
te d
summed each after delaying each duplication by t, then the obtained output is:
5
sT (t) a ns(t n t) ,
(9)
n 0
6
Ac
ce p
The Fourier transform of sT equals to:
Page 6 of 13
5
ST ( ) sT (t) exp(2 i t)dt a n s(t n t) exp(2 i t)dt S( )F( ) n 0
S( ) s(t) exp(2 i t)dt
(10)
5
F( ) a n exp(2 i n t), n 0
The filter F is an FIR filter. By tuning the delay between the sequences the spectral position of the realized filter may be changed.
3. Simulation results We simulated operation of the micro-multi-racetrack resonator FIR filter structure using RSoft Photonics CAD Suite software, which is based on FDTD method. We performed 2 dimensional (2D) simulations on a 135m x 152m filter, as shown in Fig. 2(a). We transmitted Gaussian pulses with a wavelength centered at 1.55m into the waveguide input. The optical pulses split into 6 paths, as shown in Fig. 2(b). The coupling exists in all 6 optical paths. For clarity, we have also presented in Fig. 2(c) the coupling between waveguide and racetrack resonator, with zoom in area of radius R 0 Subsequently the interaction between the waveguides and the multi-racetrack resonator began. Fig. 2(d) shows the
Output Area
ip
t
propagation of the optical pulses at the output.
an
us
cr
Coupling Area
(b)
7
Ac
ce p
te d
(a)
M
Input Area
Page 7 of 13
Saturation Area
(c)
(d)
Fig. 2. Gaussian pulses propagation in the FIR filter: (a) Full view. (b) Zoom into the input area. (c). Zoom into the racetrack resonator area of radius R0. (d) Zoom into the output area.
Next, we used FDTD method to sample the electric field at the output. The electric field samples went through Fast Fourier Transform (FFT) in order to calculated the spectral responses of the micro-multi-racetrack resonator
an
t ip cr
us
Intensity [Arb. Units]
Intensity [Arb. Units]
for different sizes of the racetrack (L) and coupling distances ( LC1 , L C2 ).
(a)
Wavelength [µm]
M
Wavelength [µm]
(b)
Fig. 3. Spectral response of the optical FIR filter for two different coupler straight sections: (a) d c 6 m . (b) d c 3 m .
te d
Finally, after finding the optimal coupling distances, we found the appropriate values for L, LC1 and LC2, which are suitable for realizing the optical FIR filter, with a coupler straight sections of dc=6m. Fig. 3(a) shows the 8
Ac
ce p
spectral response obtained at the output of the proposed optical device.
Page 8 of 13
From Fig. 3(a) it can be seen that FWHM=15nm and FSR=40nm (FWHM=full width half maximum, FSR=free spectral range) has been obtained. The spectral position can be tuned by changing the value of the coupler straight sections, as shown in Fig. 3(b). For dc=3m, FWHM=20nm and FSR=35nm has been obtained. The ripples in both transmission spectra 3(a) and 3(b) are due to the finiteness of the waveguides, that is, the finite number of racetrack (in our case 6 racetracks). It can be assumed that by increasing the number of racetrack, the degradation caused by the ripple can be overcome. The optimal size of the saturation area was found by optimization the gain level at the output filter which lead to the best result in the extinction ratio. Fig. 4 shows the normalized extinction ratio as a function of the saturation area size.
1
0.8
0.6
0.2
0 0
2
4
cr
ip
t
0.4
us
] st i n U . br A [ oi t ar n oi ct ni t xe de zi l a m r o N
6
8
Saturation area size [um]
an
Fig. 4. Normalized extinction ratio as a function of the saturation area size.
From Fig. 4 it can be noticed that the optimal size of the saturation area is about 4µm. It can be noticed that we
M
obtained a passive filter that is operated over a photonic carrier (1.55m) and allows realization of e.g. band pass
9
Ac
ce p
te d
microwave filter around the photonic carrier.
Page 9 of 13
4. Fabrication The multi-racetrack resonator patterns were defined on SOI wafers with a Si layer thickness of 220nm, on top of a 2μm SiO2 buried oxide layer. It was done using CRESTEC CABLE-9000C high-resolution electron-beam lithography system [19] using different doses to control line and gap width. Zeon (ZEONREX® Electronic Chemicals) was spin coated at 5000 rpm and baked at 180°C for 20 min before exposure with a 105 KeV electron beam. After development, patterns were placed in an oven at 160°C for 5 min to cause the resist to reflow, reducing pattern roughness. The waveguide patterns were transferred using an anisotropic dry etch in an inductively coupled plasma reactive ion etcher mixed mode plasma etch [20]. Fig. 5(a) shows the fabrication results of the micro-multi-racetrack resonator FIR filter, with zoom into the racetrack area which is presented in Fig. 5(b). For complete verification of the fabrication process, we carried out three dimensional topography analysis using atomic force microscopy (AFM). All AFM measurements were performed at room temperature and free ambient conditions (no vacuum), using Dimension Icon AFM system with NanoScope V controller (Bruker®). We used NanoWorld probes SSS-NCH, SuperSharpSilicon - Non-contact / Tapping™ mode - High resonance frequency; with typical diameter of 2nm, resonance frequency of 320 kHz and spring constant of 42N/m. typically, voltages of 2V, AC capacitance frequencies of 880MHz, lift heights of 30nm - 50nm and line rates of 0.1 KHz were employed. Figs. 5(c) and 5(d) presents the 3D AFM analysis of a single racetrack and splitting section,
t
respectively. The entire device could not be analyzed at a single scan due to the maximum scan size limitation of
ip
the microscope (35µmX35µm). From the AFM analysis, we observe smooth waveguide faces with excellent
10
Ac
ce p
te d
M
an
us
cr
agreement to the desired patterns.
Page 10 of 13
(b)
ip
t
(a)
cr
(c)
(d)
an
us
Fig. 5. Fabrication of the micro-multi-racetrack resonator FIR filter: (a) Full view (2D). (b). Zoom into the racetrack resonator area (2D). (c) 3D AFM analysis of a single racetrack section of the filter (d) 3D AFM analysis of the splitting/combining section.
5. Conclusions
M
Through experiment and simulation results, it has been shown that FIR filter can be realized using multi-racetrack resonator structures which are based on SOI waveguides.
te d
The novelty that we present in this letter is related to the fact that we propose a unique realization scheme that allows for the first time, to the best of our knowledge, to realize ultra-compact FIR spectral filter by folding the
11
Ac
ce p
various optical paths (needed to realize the FIR filter) via the optical rings/racetracks whose outputs are interfered
Page 11 of 13
and passed through a non-linear saturation optical elements. This unique scheme eventually yields spectral filter with flexibility in the position of its spectral peak as well as in its spectral width. Unlike conventional ring resonators our spectral filter is not based on interfering the temporal replications generated by the resonator but rather we use the last replicated term in order to realize effectively much longer optical path than its physical size. This new design can be used for realization of narrow band microwave filters as those used in passive optical communication networks or in electronic warfare applications. Such a filter can be used in a wide range of applications, e.g. in the opto-telecommunication systems. It can serve there as a signal shaper, interleaving demultiplexer, for wavelength selective power monitoring or as a demultiplexing filter in WDM-Passive Optical Network (PON) systems.
References 1.
A. Yariv and P. Yeh," Photonics," 6 Ed., Ch. 4, Oxford university press (2007).
2.
D. G. Rabus, M. Hamacher, U. Troppenz and H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GalnAsp-Inp," J. Quantum electronics, 8, 1405-1411 (2002).
3.
C.K. Madsen and J.H. Zhao, "Optical Filter Design and Analysis: A Signal Processing Approach," Ch. 1, Wiley (1999).
4.
R.Otra, P. Savl, R. Tascone and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical system," IEEE photonics
t
technology, Lett.7, 1447-1449 (1995). G. Griffel, "Synthesis of optical filters using ring resonator arrays," IEEE photonics technology, Lett.12, 810-812 (2000).
6.
W.Bogaerts, P. D. Heyn, T.V. Vaerenmbegh, K. Devos , S. Selvaraja, T. Claes, P. Dumon, P. Bienstmen, D.V. Thourhout and
ip
5.
7.
B. E. Little, J. Forsei, H. A. Haus , E. P. Ippen, W. Greens and S. T. Chu, "Ultracompact Si/SiO2 micro-ring resonator channel T. Kominato, Y. Ohmori, N. Takato, H. Okazaki and M. Yasu, "Ring resonators composed of GeO2-doped silica waveguides," IEEE Lightwave Tech.10, 1781-1788 (1992).
G. T. Reed, "Silicon photonics the state of the art," Wiley (2008).
an
9.
us
dropping filter," IEEE photon. Technol. Lett. 10, 549-551 (1998). 8.
cr
R. Baets, "Silicon microring resonators," Laser photonics Rev. 6, No.1, 47-73 (2012).
10. K. Okamoto, "Fundamentals of Optical Waveguides," Ch. 2, Academic press (2000). 11. S. C. Hagness, D. Rafizadeh, S. T. Ho and A. Taflove, "FDTD microcavity simulations: design and experimental realization of
M
waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators," Lightwave Technology, 15, 2154-2164 (1997).
12. G. T. Reed and A. P. Knights, "Silicon Photonics: An Introduction," Ch.4, Wiley (2004).
te d
13. M. Soltani, S. Yegnanarayanan, Q. Li and A. Adibi, "Systematic Engineering of Waveguide-Resonator Coupling for Silicon Microring/Microdisk/Racetrack Resonators: Theory and Experiment," J. Quantum elecrronics, 46, (2010). 14. R. Boeck, N. A. F. Jaeger, N, Rouger, and L. Chrostowski, "Series-coupled silicon racetrack resonators the Vernier
12
Ac
ce p
effect: theory and measurement," Optics Express, 18, 25151-25157 (2010).
Page 12 of 13
15. N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, J. B. Luff, A. Agarwal, T. Banwell, R. Menendez,P. Toliver,T. K. Woodward and M. Asghari1, "Thermally-efficient reconfigurable narrowband RF-photonic filter," Optics Express, 18, 2464824653 (2010). 16. J. Chang, M. P. Fok, J. Meister and P. R. Prucnal1, "A single source microwave photonic filter using a novel single-mode fiber to multimode fiber coupling technique," Optics Express, 21, 5585-5593 (2013). 17. L. Paves, L. Dal Negro, C. Mazzoleni, G. Franzo and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000). 18. B. Porat, "A Course in Digital Signal Processing," Ch. 11, Wiley, (1997). 19. M. Cohen, R. Shavit, Z. Zalevsky, "Towards Integrated Nanoplasmonic Logic Circuitry," Nanoscale 5(12), 5442-9 (2013). 20. M. D. Henry, S. Walavalkar, A. Homyk, and A. Scherer, "Alumina etch masks for fabrication of high-aspect-ratio silicon
13
Ac
ce p
te d
M
an
us
cr
ip
t
micropillars and nanopillars," Nanotechnology 20, 255305 (2009).
Page 13 of 13