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Abstract
Plasmonic electro-optic modulators might play a pivotal role in the development of compact efficient communication devices. Here, we introduce a novel electro-optic modulator based on a plasmonic Bragg microcavity and a pockels active material. We investigate detailed design and optimization protocols of the proposed structure. With 2D scanning of geometrical parameters, an extinction ratio of 19.8 dB, insertion loss of 2.8 dB and modulation depth of 0.99 with a driving voltage of ±5 V are obtained.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The ongoing technical revolution in the information technology requires a significant progress in miniaturization of photonic integrated devices to feature size of highly integrated electronic assemblies and circuits. But the diffraction limit of light constrains essential limitation on how compact the integrated photonic devices can be established. Surface plasmon (SP) waves enabled by coupling of light to the electron gas of a metal thin film can efficiently overcome this limitation and enable the smallest possible footprint by subwavelength confinement of light [1]. A range of passive and active plasmonic elements with the ability to create an intermediate link between electronic and photonic technologies have been successfully revealed [2–5].
Electro-optic modulators (EOMs) which map electrical signals onto an optical carriers are considered as one of the key elements in the optical interconnection scheme. In addition to small footprint and CMOS-compatible fabrication, communication EOMs should render low insertion loss (IL), high extinction ratio (ER), high modulation depth (M), and low bias voltages (U). These prospects can come closer to reality by confinement of photons and electronic control signal to the smallest possible area [5,6]. Plasmonic achieves the tightest confinement among all photonic technologies and their subwavelength field localization empowers the light-matter interaction which in turn paves the way for realizing efficient EOMs [7–11]. Also due to the plasmon-enhanced light-matter interaction, the structure length can be significantly reduced which is a critical prospect in densely co-integrated electronic photonic circuits. However, the overall losses i.e. metal ohmic losses and photon-plasmon coupling losses hinder the single-pass plasmonic EOMs to achieve IL values lower than 8 dB and even more [8–11]. This is a big hurdle to overcome and thus valuable researches have so far focused on this area [11–13]. Some of the state-of-the-art plasmonic EOMs prevail over losses and improve their modulation performance by taking advantages of resonance phenomena and multi-pass schemes [13–15]. In the on-state of the resonator, light is effectively couple to lossy SP waves during its successive round-trips in the resonator cavity. But in the resonator off-state, the incoming light wave can survive from the plasmonic losses and remains as a reflected or transmitted output signal. Therefore, the on/off-states of the resonator construct the “OFF”/“ON” states of the plasmonic modulator, respectively. Moreover, the resonance based EOMs significantly enhance the light-matter interaction reinforcing the modulator’s performances and notably reduce the footprint and the needed bias voltage by folding the required structure length into a multi-pass path. The reported progress in achieving low loss, high efficiency, compact footprint and low-electrical energy consumption encourage developing the resonant plasmonic modulators. Lou et al. theoretically investigated a hybrid plasmonic microring modulator with sub-micron radius and its performance’s dependence on the device parameters in order to reach an optimal design. They obtained M of 0.8 and IL of 0.97dB with a driving voltage of 3.6 V [14]. Haffner et al. studied a plasmonic ring resonator with Q-factor of ∼30, which reached IL of 2.5 dB and ER of 10 dB [13].
Here, we report a novel optical modulation scheme relying on a resonance assisted metal-insulator-metal (MIM) plasmonic waveguide with a pockels active material as its insulating slot. Periodic modulation of slot width in an MIM waveguide results in a structure with effective periodic refractive index changes. This can serve as a Bragg reflector with a band gap in certain wavelengths, known as plasmonic band gap, in which SPP propagation is forbidden. By introducing a longitudinal defect in the waveguide, a Fabry-perot (FP) resonator is established with two equal set of gratings in each side as its reflecting mirrors. This FP microcavity profits the lossy behavior of SP waves to meet the key performance metrics of modern optical communications links, achieving low IL, high ER, strong modulation, compact footprint and low consumption, simultaneously. To achieve the highest possible performance parameters, comprehensive optimization of the geometrical parameters presents in detail.
2. Theory and design
Surface plasmon MIM waveguides represent highly localized fields even compared with plasmonic insulator-metal-insulator (IMI) structures, albeit at the expense of higher losses. These deep subwavelength SPP modes and high field’s localization enable highly integrated plasmonic and photonic structures as well as strong light-matter interaction. The latter is essential when nonlinear interactions are utilized to enables efficient modulation process. In case of Kerr based modulators, the intensity of local fields will boost nonlinearity of metals as well as its adjacent dielectric medium. Although in pockels effect based modulators, the associated localized fields do not enhanced nonlinearity of material, but they enhance light-matter interaction and thus empowers sensitive response of the SPP dispersion relation to the refractive index (RI) changes of the pockels active medium.
The investigated structure consists of an MIM Bragg grating obtained by stepping the width of the insulator slot accompanied by a longitudinal defect which serves as a resonant FP microcavity [Fig. 1(a)]. Efficient light coupling to the plasmonic waveguides can be realized using optical elements such as prisms [16], gratings [17], optical fibers and silicon tapered waveguides [18,19], and photonic nanowires [20]. We exploit end-fire coupling mechanism due to its high efficiency and adaptability in on-chip applications [21]. To discuss further the physical mechanisms of the plasmonic EOMs, we carry out finite-element simulations in the frequency domain using a commercial numerical package COMSOL Multiphysics. We performed Electromagnetic waves and Electrostatics physics which are coupled trough material definition of the pockels active medium. Free meshing with user-controlled triangular elements was applied with the predefined mesh size ‘normal’. For electrostatics, a constant bias voltage (negative or positive) was applied to the upper boundary and zero volt (ground) was applied to the lower boundary of lower metallic cladding. These two boundaries which are illustrated with blue lines in Fig. 1(b) were the perfect electric conductor in ‘Electromagnetic waves’ physics. Moreover, in this figure the excitation port is shown by red arrows. Silver is considered as the metal claddings, the permittivity of which is obtained from the Drude model [22]:
Fig. 1. (a) Plasmonic modulator structure consists of an MIM Bragg grating with a resonant FP microcavity, (b) real and imaginary part of MIM waveguide’s effective index versus slot width, (c) illustration of boundary conditions in structural modelling.
The dispersion relation of a plasmonic MIM structure [inset of Fig. 1(b)] clarifies the dependence of the effective index (neff) on the insulating slot width (ws) [15]. As shown in Fig. 1(b), by increasing the slot width, both real and imaginary part of effective index increase. The higher the real part of neff more confined SPP’s field and thus stronger the light matter interaction. Therefore, the electro-optic effect is more efficient for smaller slot widths which cause the mutual destructive effect of enhancing the plasmonic loss. With decreasing the slot width, the field penetrates further into the metal which yields to higher ohmic loss.
Modification of the MIM slot width alters the real part of effective index of the SPP mode. Thus by stepping the insulating slot width and initiating periodic variation of the effective index, a Bragg reflection response in a manner analogous to the traditional fiber Bragg gratings can be obtained [23]:
where m is an integer, neff,1 and neff,2 are the effective indices for the narrower and wider sections of the slot with width of W1 and W2, respectively. Also, L1 and L2 denote the length of the narrower and wider sections of the slot, respectively as indicated in Fig. 1(a). Satisfaction of the Bragg reflection condition prevents propagation of light through the structure, creating a propagation forbidden spectral band. As an example, by considering W1=100 nm and W2=150 nm, neff,1=2.19 and neff,2=2.08 are obtained. Then setting L1 = 190 nm and L2=140 nm adjusts the reflectance of the MIM plasmonic Bragg reflector in the wide range of telecom optical wavelength band, as shown in Fig. 2 for TM polarized incident plane wave. It is evident that altering the plasmonic resonance condition and thus modulating a signal through pockels effect in such a broad spectrum is definitely inefficient.Fig. 2. Reflectance spectrum of an SPP MIM Bragg waveguide with U=0 V, W1=100 nm, W2=150 nm, L1=190 nm and L2=140 nm.
By applying a longitudinal defect in this structure, a resonant FP microcavity forms for which N gratings in each side serve as the Bragg reflectors. In Fig. 1(a), this defect is characterized by an inconsistency with length of LR. This resonance characteristics can be investigated using the normal magnetic field distribution, as illustrated in Fig. 3(a) for off/on-resonance conditions considering λ0=1402 nm and 1550 nm, respectively. It can be seen how the plasmonic mode is well resonated in this intentional added defect. Thus, an efficient light-matter interaction and consequently an improved modulation performance can be confidently expected although the MIM waveguide is essentially lossy.
Fig. 3. (a) Field mapping for the magnetic field magnitude in the plasmonic Bragg EOM structure with U=−5 V, W1=100 nm, W2=150 nm, L1=190 nm and L2=140 nm for off (λ0=1450 nm) and on-resonance (λ0=1550 nm) conditions, (b) The normalized reflectance considering U=±5 V and unbiased condition (U=0 V), (c) its zoomed view for applied bias of U=±5 V, (d) The normalized reflectance at λProbe=1550 nm and Δλres for applied bias from −5 V to +5 V.
In this structure, two mechanisms simultaneously enhance light-matter interaction and boost the EOM performances: First, utilizing MIM structure renders high confinement of field into pockels active medium and second, the resonant assisted multiple-pass of SP waves in pockels medium which results in high effectiveness of the pockels induced RI changes.
The normalized reflectance is shown in Fig. 3(b) and its zoomed view in logarithmic scale in Fig. 3(c) for applied bias of U=±5V. In Fig. 3(c), method of calculating ER and IL value is shown. Also modulation depth can be estimated by M=(ION-IOFF)/ION. The geometrical parameters are set up to obtain the resonant condition at telecom wavelength of λres=1550 nm: W1=100 nm, W2=150nm, L1=190 nm, L2=140 nm, LR=751.3 nm, and N=4. Modulating the active material’s RI by an applied voltage shifts the cooperated SP-FP resonance wavelength by Δλres. Subsequently, the information is encoded on the cooperated SP-FP resonance and obviously on the reflectance at the probe wavelength of λProbe=1550 nm. The cooperated SP-FP resonance wavelength λres and the normalized reflectance at λProbe for applied bias from −5V to +5V are depicted in Fig. 3(d). These changes can be used for modulating the output signal (here, reflectance at λProbe) by applying appropriate voltage. Hereafter, for fixed wavelength of λProbe=1550 nm, U=+5V and U=−5V are off (λProbe = λres) and on (λProbe ≠ λres) resonance conditions which is considered as “ON” and “OFF” states of the modulator, respectively. This resonance assisted plasmonic modulator with the aforementioned geometrical parameters offers IL=1.15 dB, ER=6.45 dB, Δλres=53 nm and a Q-factor of 33 associated to a relative RI change of 0.0551 RIU in active slot material, all show an acceptable performance compared with reported plasmonic EOMs [13–15]. Moreover, sensitivity (Sλ=Δλres/Δn) of ∼961.88 nm.RIU−1, voltage sensitivity (Δλres/U) of 5.3 nm/V and FoM (Sλ/ΔFWHM=Δλres/(ΔFWHM·Δn)) of 20.21 RIU−1 are estimated. The performance of the proposed structure is comparable [24] with commercial SPR sensors with FoM of 50 RIU−1 with a free-space Kretschmann configuration.
3. Geometrical optimization
To realize highly integrated plasmonic EOM with efficient performance, a more favorable balance between localization and loss is required. One can vary the geometrical parameters, i.e. width and length of each sections as well as the number of gratings in each side. Therefore, in order to establish a desirable performance, we carried out geometrical parameters scanning while monitoring the changes in normalized reflectance at λProbe=1550 nm. The optimization process was performed by a 16 core -Core i9 (9900K) with up to 5 GHz computer and 64Gb of RAM with 3200 MHz Clock Speed. In independent attempts, the geometrical parameters were scanned in pairs. The results are shown in Fig. 4: each raw is related to scanning a pair of parameters while the rest were fixed to the aforementioned values (W1=100 nm, W2=150nm, L1=190 nm, L2=140 nm, LR=751.3 nm, and N=4). To avoid many data, only some cases are represented in Table 1, although all of possible pairs were scanned and investigated. U=−5V is considered as “OFF” state while applied bias of U=5V is assumed for the “ON” state of EOM.
Fig. 4. 2D scanning of geometrical parameters: In each raw, two geometrical parameters were scanned while the other parameters were fixed to W1=100 nm, W2=150 nm, L1=190 nm, L2=140 nm, LR=751.3 nm, and N=4. Columns from left to right illustrate the ER, IL, M and MF values.
Table 1. The device performance considering optimization on only one performance parameter.
The results of these 2D scans (Fig. 4) demonstrate that distinguished performance parameters (ER, IL and M) can be reached which does not necessarily mean that the modulator with these specific geometrical parameters acts effectively in all respects. Some examples are listed in Table 1, which shows that in certain points of these 2D scans, remarkable values of ER>37 dB, M∼1, and IL=0.3 dB can be obtained. But it is clear that optimizing just one of the performance features can simply lead to degradation of others. For example, as depicted in the first line of Table 1, by changing L2 and LR, ER of more than 37 dB can be achieved but at the expense of a high inappropriate IL of 23 dB. Further investigation illustrates that λProbe in this case is placed in the sidelobes of the resonant spectrum [Fig. 5(a)] and thus signal modulation could not effectively achieved due to the ultra-low probe signal changes.
Fig. 5. Normalized reflectance for a structure with modified geometrical parameters of (a) L2=58 nm, LR=720 nm, (b) L1=15 nm, W1=30 nm, and (c) L1=102 nm, W2=220 nm.
The second and third points listed in Table 1 are the result of optimizing IL regardless of a comprehensive optimization. Low IL of 0.35 dB, as depicted in Fig. 5(b), is the result of not benefiting from the resonant condition. For this parameter pair (L1=15 nm and W1=30 nm), the resonant wavelength of microcavity is 1682.68 nm for U=−5V, yielding to a poor performance from the extinction perspective. Also, as shown in the third raw of Table 1, low IL of 1.58 dB can be obtained by setting the values of W2=220 nm and L1=102 nm and aforementioned values for other structural parameters. The related reflectance spectra for U=−5 and +5 V are shown in Fig. 5(c) which shows in this case, broaden spectra with shallow dip are obtained. This can be attributed to the low coupling strength of light wave to SP wave due to the large slot width.
Therefore, the goal should be the structural comprehensive optimization to meet all the functional aspects of an efficient EOM, i.e. the largest possible modulation depth and extinction ratio as well as lowest possible insertion loss and also possess miniature feature size and small required bias voltage. To this end, we define a practical merit function as [25]:
When reviewing 2D scans, it should be noted that all the reverse performances are omitted by ceiling the negative values of ER and M to zero. These negative ER and M values are obtained due to the opposed trends for “ON” and “OFF” states of the modulator.
For the simulation being progressed we arrived with finding the best geometrical parameters which can establish a desirable plasmonic EOM with the best possible combination of properties, corresponding to the minimum of MF value as low as possible. Examples are listed in Table 2 along with performance parameters (ER, IL, and M). Again, only that geometrical parameters that have been changed are listed, and the rest of the parameters are set to the aforementioned value. The lowest possible value of MF is obtained for L2=96nm and considering 8 gratings in each side yielding to ER of 19.8dB and IL of 2.8 dB which shows remarkable performance compared to the efforts that have been made so far. Also, by further examining the resulted MF values, it is obviously proved that a device with a different but degraded function is obtained. It should be noted that by selecting different values of Wi, it is possible to design a device with a preferable performance parameter.
Table 2. The device performance considering comprehensive optimization
Table 3. Comparison of the performances of some of state-of-the art plasmonic EO modulator
In order to achieve a better sense of the proposed structure performance, we consider a fiber coupled Lithium Niobate EOM (LN81S-FC) from Thorlabs, Inc. [28], as an example, which presents typical IL of 4 dB and ER of 20 dB. Our 2D scanning optimization outcome, as represented in the first line of Table 2, i.e. ER of 19.8 dB and IL of 2.8 dB, demonstrates the comparable performance of the proposed plasmonic Bragg microcavity EOM. Also, Table 3 summarizes some of the results reported in literature. The results achieved with the proposed structure are competitive in the field of electro-optic modulators, especially considering that the proposed structure is compatible with highly integrated photonic circuits.
Moreover, using these 2D scanning diagrams, it is possible to predict how much the performance of the device will be degraded by manufacturing errors. As an example, for the optimized device with parameters represented in the first line of Table 2, if L2 is decreased by 2 nm, the performance parameters will be ER=20 dB, IL=3.91 dB and M=0.99 which results in MF=1.76.
4. Conclusion
Plasmonic electro-optic modulators are interested due to their ability of efficient light matter interaction related to their ability in sub-diffraction confinement of light, and simultaneously carry both electric signals and optical waves. However, plasmonic based devices suffer from large insertion losses which limits their practical applications. In this work, we proposed a novel EOM based on plasmonic MIM Bragg waveguide which combat the high losses of plasmonic devices by using a Fabry-Perot microcavity. We presented a detail design and comprehensive optimization of the device geometrical parameters. The represented investigation could pave the way for application of low-loss high efficient plasmonic modulators in the future modern optical communications links.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. S. A. Maier, “Plasmonics: The promise of highly integrated optical devices,” IEEE J. Sel. Top. Quant. Electron. 12(6), 1671–1677 (2006). [CrossRef]
2. B. Ni and X. Jinbiao, “Ultracompact and broadband silicon-based TE-pass 1× 2 power splitter using subwavelength grating couplers and hybrid plasmonic gratings,” Opt. Express 26(26), 33942–33955 (2018). [CrossRef]
3. Z. B. Yang, D. F. Guan, P. You, X. Huang, S. D. Xu, L. Liu, R. Hong, and S. W. Yong, “Compact effective surface plasmon polariton frequency splitter based on substrate integrated waveguide,” J. Phys. D: Appl. Phys. 52(43), 435103 (2019). [CrossRef]
4. O. Ilic, N. H. Thomas, T. Christensen, M. C. Sherrott, M. Soljačić, A. J. Minnich, O. D. Miller, and H. A. Atwater, “Active radiative thermal switching with graphene plasmon resonators,” ACS Nano 12(3), 2474–2481 (2018). [CrossRef]
5. D. K. Gramotnev and I. B. Sergey, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]
6. I. A. Pshenichnyuk, S. S. Kosolobov, and V. P. Drachev, “Towards Deep Integration of Electronics and Photonics,” Appl. Sci. 9(22), 4834 (2019). [CrossRef]
7. T. Nikolajsen, L. Kristjan, and I. B. Sergey, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]
8. M. Ayata, Y. Fedoryshyn, W. Heni, B. Baeuerle, A. Josten, M. Zahner, U. Koch, Y. Salamin, C. Hoessbacher, C. Haffner, and D. L. Elder, “High-speed plasmonic modulator in a single metal layer,” Science 358(6363), 630–632 (2017). [CrossRef]
9. A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, and B. Chen, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014). [CrossRef]
10. C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, and C. Hoessbacher, “All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9(8), 525–528 (2015). [CrossRef]
11. W. Heni, C. Hoessbacher, C. Haffner, Y. Fedoryshyn, B. Bäuerle, A. Josten, D. Hillerkuss, Y. Salamin, R. Bonjour, A. Melikyan, and M. Kohl, “High speed plasmonic modulator array enabling dense optical interconnect solutions,” Opt. Express 23(23), 29746–29757 (2015). [CrossRef]
12. Y. Ding, X. Guan, X. Zhu, H. Hu, I. B. Sergey, L. K. Oxenløwe, K. J. Jin, N. A. Mortensen, and S. Xiao, “Efficient electro-optic modulation in low-loss graphene-plasmonic slot waveguides,” Nanoscale 9(40), 15576–15581 (2017). [CrossRef]
13. C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, and D. L. Elder, “"Low-loss plasmon-assisted electro-optic modulator”,” Nature 556(7702), 483–486 (2018). [CrossRef]
14. F. Lou, D. Dai, L. Thylen, and L. Wosinski, “Design and analysis of ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators,” Opt. Express 21(17), 20041–20051 (2013). [CrossRef]
15. C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, and D. L. Elder, “Bypassing Loss in Plasmonic Modulators,” In CLEO: QELS_Fundamental Science, pp. FTh4H-1. Optical Society of America, 2018.
16. L. Wendler and R. Haupt, “An improved virtual mode theory of ATR experiments on surface polaritons,” Phys. Status Solidi B 143(1), 131–148 (1987). [CrossRef]
17. G. Li, K. Li, L. Cai, and A. Xu, “Efficient free-space optical coupler into dielectric waveguide with great field enhancement,” In International Conference on Information Photonics and Optical Communications, pp. 1–2, 2011.
18. J. Gosciniak, V. S. Volkov, S. I. Bozhevolnyi, L. Markey, S. Massenot, and A. Dereux, “Fiber-coupled dielectric-loaded plasmonic waveguides,” Opt. Express 18(5), 5314–5319 (2010). [CrossRef]
19. R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010). [CrossRef]
20. X. Guo, M. Qiu, J. Bao, B. J. Wiley, Q. Yang, X. Zhang, Y. Ma, H. Yu, and L. Tong, “Direct coupling of plasmonic and photonic nanowires for hybrid nanophotonic components and circuits,” Nano Lett. 9(12), 4515–4519 (2009). [CrossRef]
21. C. Fisher, L. C. Botten, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Efficient end-fire coupling of surface plasmons in a metal waveguide,” J. Opt. Soc. Am. B 32(3), 412–425 (2015). [CrossRef]
22. S. A. Maier, Plasmonics: Fundamentals and Applications, (Springer, 2007).
23. Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photonics Technol. Lett. 19(2), 91–93 (2007). [CrossRef]
24. J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics 5(2), 161–167 (2010). [CrossRef]
25. J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit functions for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989). [CrossRef]
26. X. Sun, L. Zhou, H. Zhu, Q. Wu, X. Li, and J. Chen, “Design and analysis of a miniature intensity modulator based on a silicon-polymer-metal hybrid plasmonic waveguide,” IEEE Photonics J. 6(3), 1–10 (2014). [CrossRef]
27. W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009). [CrossRef]
28. https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3918
