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Abstract
The simulated multichannel comb filter [MCF] built on the stacking of the Fabry - Perot etalons that work in the telecommunication region between near-infra-red wavelengths (1538 −1558 nm) and (2333 - 2373 nm) has been demonstrated. Present work illustrates the dependence of defect modes produced on the stacked Fabry - Perot etalons. The FWHM of each channel is ∼0.043 picometers for the stacking of 20000 etalons. The spacing between the channels was ∼0.79 picometers and nearly uniform throughout the telecommunication band. The simulated MCF consists of ∼78 uniform channels within a range of ∼0.1 nm centered at 1550 nm.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The multichannel narrowband optical filters (MCNBOF) have gained more visibility in the view of their applications. MCNBOFs work especially in the prospect of filtering the Ultra-Dense Wavelength Division Multiplexing (UDWDM) system channels in telecommunication, and elements of imaging in space science. Ultra-Dense Wavelength Division Multiplexing (UDWDM) can be deployed to enhance the bandwidth in fiber-based networks/communication systems. Ultra-dense refers to the accommodation of many wavelengths in a single waveguide via maintaining the separation of individual wavelength modes. Incomplete isolation of channels in the UDWDM leads to inter-channel interferences (ICIs) and hence the spectral efficiency will be reduced. In that scenario, the simulated multichannel filters made up of the stacked Fabry-Perot etalons work as optical comb filters (OCF) which can display reflection/elimination of the unwanted band of wavelengths. Furthermore, the MCNBOFs play an essential role in the radio cognitive systems, and the manufacturing of large telescopes, etc. Because of their applications, manufacturing MCNBOFS that work in the Infrared range has become an exciting task. However, the limited commercial availability of the MCNBOFs in the infrared range always remains a challenge for the researchers as per the requirement. The MCNBOFs can be manufactured by employing the Acousto-optic tunable filters, concatenation of sampled Fiber Bragg Gratings (FBG), dielectric thin-film interference filters (one-dimensional photonic crystals), two-dimensional photonic crystals, unbalanced Mach-Zehnder interferometers, Microring resonator, and the Fabry Perot etalons in the combination with the Bragg grating. Amongst, the employment of the Fabry-Perot etalons to manufacture the MCNBOFs has its advantages, and hence in the present study stacking of the Fabry-Perot etalons has been considered. The Fabry-Perot etalon is an optical cavity made up of two parallel highly reflecting mirrors and works based on the interference of multiple reflections of a light beam by the two surfaces of a thin plate. The Fabry-Perot filter consists of two highly-reflecting multi-layers separated by a layer of space equivalent to an optical pathlength λ/2, where λ is the wavelength of the incident light. Multiple interferences that occur in the space layer lead to a spectral characteristic output that peaks over a narrow band of wavelengths which are multiples of the optical pathlength λ/2 of the spacer layer. When a highly reflective Fabry-Perot etalon is illuminated by a collimated beam of light results in an interferogram at a narrow bandwidth made it an effective spectral filter (bandpass filter). Thus, Fabry-Perot etalons have a broad range of applications such as multiplexers [1] frequency combs [2], laser resonators [3], filters with desired tunability [4], sensors in biomedical imaging [5]. Among the mentioned applications, Fabry-Perot etalons as optical comb filters (OCF) reflect the unwanted and transmit the anticipated band of wavelengths. These mentioned OCFs are the important elements in boosting up the fiber optic transmission bandwidths to enhance the internet speeds more and more to facilitate the buffering of videos and IoTs.
When the optical pathlength of the cavity of a Fabry-Perot etalon is equal to the integral multiple of the wavelength of the light, the cavity is said to be in resonance with the wavelength centered over a particular wavelength. Thus, the optical path thickness of a Fabry–Perot filter cavity is directly proportional to its central wavelength at which resonance occurs. Optical path thickness of Fabry–Perot filter cavities can be varied by employing the piezoelectric, electro-optic, and thermo-optic materials as the spacers in the Fabry - Perot filters [6–8]. An optical filter is a device that selectively transmits a particular range of wavelengths and the remaining wavelengths are blocked off. Fabry-Peron etalons can be prepared with the defective photonic crystal structures and later on these Fabry Perot etalons can be stacked to design an OCF. The one-dimensional photonic crystal (1DPhC) was first introduced in 1887 by Lord Rayleigh, who experimented with periodic multilayer dielectric stacks and discovered a one-dimensional photonic band-gap structure. After the pioneering work of Eli Yablonovitch and Sajeev john [9,10] on multi-dimensional periodic optical structures, the research interest has grown up in the design of photonic crystals. 1DPhC is a layered medium with a periodicity of different refractive indices and thicknesses [11–13]. The one-dimensional Photonic Crystal (1DPhC) is placed after the Erbium-doped fiber amplifier (EDFA) in telecommunication network to filter out the amplified spontaneous emission (ASE) noise because it allows only certain wavelengths and the rest of the waves will be stopped by the photonic bandgap (PBG). In this way, this 1DPhC structure improves the optical signal-to-noise ratio. The orientation of this filter is kept in such a way that whose thickness is perpendicular to the direction of light.
The existence of a photonic bandgap in 1DPhC forbids a certain range of wavelengths that falls within the photonic bandgap (PBG). Due to its simple structure, 1DPhC is the best choice for a channel filter design with particular specifications [11–13]. Due to the existence of PBG, 1DPhC can act as an efficient optical bandpass filter. Optical bandpass filters designed and fabricated to work in different regions of the electromagnetic spectrum using 1DPhC have been reported [14,15]. Optical filters have their applications in various areas of interest such as nano-technology, astronomy, and communication. Designing the optical filter is the primary step in making an effective channel filter in many applications. 1DPhCs uses the phenomenon of interference to transmit a desirable range of wavelengths. In recent times, many researchers have been working extensively on the doping of suitable elements to the pure Photonic Crystal (PC) and changing the thickness of the layer or removing the layer from it (known as defective PC) to achieve more controllable features of 1DPhC based channel filter. Introducing a defect in the design of the 1DPhC structure leads to various applications such as splitter and optical filter [16,17].
In the present study, a multichannel filter based on stacking of Fabry - Perot etalons made up of 1DPhC structure with defect layer was designed to use in de-multiplexing of Channels in UDWDM system [18,19]. This multichannel filter was numerically investigated using the transfer matrix method based on a common structural configuration of Fabry - Perot etalon
Where P indicates a dielectric material with a low refractive index, Q indicates a dielectric material with a high refractive index, D stands for defect layer and N indicates several stacking periods of Fabry-Perot etalons. The designed multi-channel filter consists of evenly spaced multiple channels in the near-infrared region centered at 1550 nm and 2400 nm.2. Materials and methods
To simulate the multi-channel transmission filter, a numerical method has been employed called the transfer matrix method (TMM) [20–22], to calculate the amplitude of the electric field of light transmitted inside 1DPhC. In this study, the multichannel filter so designed based on the stacking of Fabry – Perot etalons made of a defective photonic crystal structure as shown in Fig. 1.
Fig. 1. Schematic of stacked Fabry-Perot etalons made up of quarter-wave layers of different refractive indices.
The periodic layered medium (as shown in Fig. 1) consists of two different materials with refractive index profile along z-axis is given by
Here n stands for the nth unit cell and an, bn, cn, and dn are the constants. These constants are related by the continuity condition at the interface. In the case of Transverse Electric (TE) waves, imposing the continuity condition at the interfaces
These four equations can be rewritten as two matrix equations
In the matrix notation, the complex amplitudes of the two plane waves in each layer constitute the components of a two-component column vector. The electric field in each layer of a unit cell can thus be represented by a column vector. These column vectors are not independent and are related to the continuity conditions at the interfaces. Consequently, only one column vector can be expressed arbitrarily.
By eliminating the column vector
the matrix equationThe transfer matrix for PQ layers is denoted as $\left[ {\begin{array}{{cc}} A&B\\ C&D \end{array}} \right]$ where the matrix elements are
Here. a represents the thickness of the P-layer, b represents the thickness of the Q-layer, ${k_{1z}}$ and ${k_{2z}}$ are the propagation constants along the z-direction in the respective P and Q layers. The structure ${({PQ} )^3}/D/{({PQ} )^3}$ represents the Fabry - Perot etalon with low reflectivity and high transmission because the numbers of layers are low. By stacking the appropriate number of these etalons. one can achieve the required number of uniform transmission channels in the photonic bandgap (PBG).
The matrix equation relating the incident electric field amplitude ${a_0}$ and the transmitted amplitude ${a_N}$ for the above-proposed structure can be written as
3. Results and discussion
Fabry-Perot etalon’s P-layer was chosen as material Silica with a lower refractive index $n$ 1 = 1.45 at a thickness $a$ = 333 nm. Similarly, the Q layer was taken as a high refractive index material (when compared with the P-layer), i.e. Lithium Niobate (LiNbO3) whose refractive index is $n$2 = 2.25 at a thickness $b$ = 218 nm.
These mentioned layers were chosen deliberately to create a multichannel filter to work in the telecommunication band. The P layer with a low refractive index was introduced in between the PQ pentad stacks as a defect layer which also acts as a spacer in the Fabry-Perot etalon. Figure 2(a) depicts the transmission spectrum of stacking of ten PQ layers with a photonic bandgap (PBG) is introduced in between 1500 nm to 2470 nm.
Fig. 2. Transmission spectrum of Fabry Perot etalon (a) without defect layer (b) with single defect layer (N=1) (c) stacking of two Fabry Perot etalons (N=2) and (d) stacking of three Fabry Perot etalons (N=3).
By introducing a single defect layer, we can observe a single transmission channel centered at λ = 1825.5 nm in the photonic bandgap in Fig. 2 b. Figure 2 c and Fig. 2 d are observed by stacking of two (N=2) and three (N=3) Fabry-Perot etalons, respectively.
Figure 2 c demonstrates the two additional transmission channels centered at λ Left = 1550 nm and λ Right = 2349 nm are observed on both sides of the central transmission channel which is centered at λ=1825.5 nm. The creation of new channels resembles the Raman effect, however, the channels created had uniform transmission coefficient, unlike the Raman effect.
The channels which are having a round trip phase equal to 2 $\pi $ or 2n $\pi $ where n=0,1,2,3,4,….etc. appears as the defect mode due to the constructive interference. In Fig. 2(d) two channels are visible on both sides of the center channel. Figure 3 illustrate the transmission spectrum of Fabry-Perot etalons, Fig (a) (N=4), (b) (N=5), (c) (N=6), (d) (N=7), (e) (N=8) and (f) (N=9) respectively. From these figures, it is evident that the number of sideband channels is increasing with the number of stacking of etalons which are following a relation 2*(N-1) channels are created on both sides with stacking of N number of etalons. The channels so created are almost uniform and channel spacing is gradually increasing towards higher wavelength sides. It is because of the phase-matching condition of higher wavelengths for a round trip phase.
Fig. 3. Transmission spectrum of stacking of N numbered Fabry- Perot etalons (a) (N=4), (b) (N=5), (c) (N=6), (d) (N=7), (e) (N=8) and (f) (N=9)
Figure 4 depicts the transmission spectrum of Fabry-Perot etalons for (N=50) and the full width at half maximum (FWHM) of the transmission channel is 0.05 nm (6.243 GHz) for a wavelength centered at 1550 nm. The channel spacing or guard band is around 0.48 nm (59.94 GHz). For N = 100 the FWHM of the transmission channel centered at 1550 nm is 0.023 nm (2.872 GHz). The channel spacing or guard band is around 0.25 nm (31.22 GHz). For N = 200 the FWHM of transmission channels is 0.0143 nm (1.786 GHz). The channel spacing or guard band is around 0.125 nm (15.6 GHz) centered at wavelength 1550 nm. As per the recommendations of the international telecommunication unit (ITU), the channel spacing for UDWDM channels is 6.25 GHz to 100 GHz which can be achieved by choosing an appropriate number of etalons stacking. Since the FWHM of the transmission channels and the channel spacing can be engineered by the selection of the required number of etalons stacking which gives the flexibility to design comb filter better suited to the UDWDM system as it is obvious from Fig. 4. Figure 5 represents the transmission spectrum of N Fabry-Perot etalons (a) for N=1000 etalon stacking the channels created in the wavelength range 1538 nm to 1558 nm, (b) is the magnified view of figure (a) within the wavelength range 1550 nm to 1551 nm. From Fig. 5 b, it is obvious that 38 transmission channels at a uniform bandwidth with FWHM 2.25 pm or 280.9 MHz with a channel spacing is 25 pm or 3.122 GHz are observed in the one-nanometer range.
Fig. 4. Transmission spectrum of N Fabry- Perot etalons (a) (N=50), (b) magnified version of (a), (c) (N=100), (d) in the wavelength range 1535 nm to 1560 nm, (e) (N=200) in the wavelength range 1538 nm to 1558 nm, and (f) in the wavelength range 1543 nm to 1553 nm.
Fig. 5. (a) for N=1000 in the wavelength range, 1535 nm to 1560 nm, (b) magnified image of (a) for the wavelength range 1550 nm to 1551 nm, (c) for N=20000 in the wavelength range 1535 nm to 1560 nm, (d) is a magnified image of (c) in the wavelength range 1550 nm to 1551 nm
Figure 5(c) depicts the wavelength range 1538 nm to 1558 nm for N=20000 and Fig. 5(d) is the magnified view of Fig. 5(c) for the wavelength range 1550 nm to 1550.1 nm. This kind of transmission comb filter is useful for the suppression of the noise caused by the amplified spontaneous emission (ASE) generated by Erbium-doped fiber amplifier (EDFA) [23,24] in the communication window. The large transmission band in the telecommunication window ranging from 1510 nm to 1580 nm can be generated by the selection of the appropriate thickness of P, Q quarter-wave layers for the central wavelength of 1550 nm. Figure 5(a) and 5(b) represent the transmission spectrum of N Fabry- Perot etalons for (N=1000). The FWHM of the transmission channels is 2.25 pm (280.9 MHz). The channel separation is 25 pm (312.2 MHz) centered at wavelength 1550 nm. Figure 5(c) and 5(d) represent the transmission spectrum of N Fabry- Perot etalons for N=20000. The FWHM of transmission channels is 0.043pm (5.37 MHz). The channel separation is 0.79 pm (98.65 MHz) centered at wavelength 1550 nm. J. Lumeau et al [6] reported for a comb filter with FWHM of channels is 0.22 nm and channel spacing is 0.8 nm with a combination of Fabry-Perot etalon and a volume Bragg grating but these components integration is a difficult task. In the present paper, the stacking of 20000 Fabry-Perot etalons results in the formation of a frequency comb [25–33] of FWHM ∼0.043 pm and a 0.79 pm channel spacing and ∼78 channels are noticed in the 0.1 nm wavelength range in the telecommunication window. These transmission channels are very useful in de-multiplexing of UDWDM channels for tera-bits per second (TBPS) speed networks to fulfill the capacity crunch in the nearest future [19]. The thickness of the system consisting of 200 etalons is 1.1686 mm which can be used in photonic integrated circuits. The proposed design of Fabry Perot stacking-based MCP inherently has a very good optical signal-to-noise ratio (OSNR) and consists of uniform amplitude channels when compared with frequency combs generated by microring resonator (MRR), concatenated FBGs, and distorted Machzhender interferometer.
J. Kischkat et al. [34] have developed ultra-angle tunable Fabry-Perot bandpass interference filters and utilized them as tuning elements in the Infra-red lasers. The usage of angle-tuned Fabry-Perot etalons in the laser cavity helps to run the laser in a stable mode. Xin He et al. [35] numerically investigated the mid-infrared dual-band filter with an ultra-high resolving power which is composed of an Al2O3 layer in between a gold grating and a CaF2 substrate. However, the metal-based multichannel filters suffer from unwanted peaks over a broad spectral region [36]. Shun Zhou et al. [37] recently demonstrated the integrated dual-channel thin-film filter for the mid-Infrared region of the electromagnetic spectrum. Instead of following complex strategies such as precision cutting, dicing, and adhesive bonding, bandpass thin-film filters are designed by utilizing a 4-cavity Fabray–Perot (F-P) type filter to work in the infrared region. D. M. Marque et al. [38] have modeled the consequence of the Fabry-Perot etalons whey are illuminated by focused laser beams and demonstrated the multifarious applications of the stacking of Fabry-Perot etalons. Compared to these metal-based filters, multichannel filters based on the stacking of Fabry Perot etalons proposed are expected to work well since the spacing between the channels was ∼0.79 picometers and nearly uniform throughout the telecommunication band. The simulated MCF consists of nearly ∼78 uniform channels within a span of ∼0.1 nm centered at 1550 nm. Similarly, Xingyuan Xu et.al [39] reported a frequency comb with 1.3 pm FWHM channels and free spectral range 1.6 nm and it consists only of 18 useful channels in the wavelength range 1530 nm to 1560 nm. But our design supports 15600 channels in the wavelength range 1538 nm to 1558 nm with 0.043 pm FWHM channels and free spectral range 0.79 pm.
4. Conclusions
The multi-channel filter based on stacking of Fabry-Perot etalons in the telecommunication band in the near-infrared region ranging from (1500 nm - 1570 nm) and (2333 nm −2374 nm) was designed. The number of defect modes created in the cavity will be determined by the number of Fabry - Perot etalons stacked. The number of channels has created in the simulation is increasing with an increase in the number of Fabry-Perot etalons stacked. The frequency comb which is generated in the region (1538 nm to 1558 nm) within the Photonic band gap of stacking of 20000 Fabry-Perot etalons has 78 channels in the 0.1 nm range. The full width at half maximum of channels was obtained to be ∼0.043 pm and the channel spacing was∼0.79 pm. The proposed transmission comb filter suppresses the noise caused by the amplified spontaneous emission (ASE) in the Erbium-doped fiber amplifier (EDFA). The frequency combs so generated are of great applications in demultiplexing of ultradense wavelength division multiplexing system channels to deliver the terabits per second in high-speed networks.
Acknowledgments
The authors acknowledge the department of physics, GIS, GITAM, Visakhapatnam, India for their continuous support.
Disclosures
Authors do not have any conflict of interest with any author or with any funding agency.
Data availability
Data underlying the results presented in this article is not publicly available at this time, however data may be obtained from the corresponding author subject to a reasonable request.
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