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A novel tunable and reconfigurable thermo-optical device is theoretically proposed and analyzed in this paper. The device is designed to be entirely compatible with CMOS process and to work as a thermo-optical filter or modulator. Numerical results, made by means of analytical and Finite-Difference Time-Domain (FDTD) methods, show that a compact device enables a broad bandwidth operation, of up to 830 GHz, which allows the device to work under a large temperature variation, of up to 96 K.
©2011 Optical Society of America
1. Introduction
Integrated optics based on silicon platform has been considered a promising technology, for present and future applications, due to its potential scalability in several fields of photonics, covering a broad spectrum of applications, ranging from telecommunication up to optical sensors for medical diagnostics [1–4]. One of the greatest advantages of this technology is the strong optical confinement achieved in high index contrast optical systems [1], as well as a mature fabrication technology compatible with CMOS systems [2].
For the past few years, several groups around the world have been proposing a great variety of active and passive devices, such as: electro-optic devices [4], thermo-optical devices [5], all optical devices [6], optical reflectors [7], tunable lasers [5], optical sensors [3], amongst many others.
However, even though several silicon photonics devices have been proposed and experimentally demonstrated, there still are several challenges that need to be overcome by science and technology in this field. One of the greatest, perhaps the most relevant weakness of silicon photonics, is its high sensitivity to temperature [8], as a direct consequence of the large silicon thermo-optical coefficient [9, 10].
Obviously, the large silicon thermo-optical coefficient cannot be always regarded as being a disadvantage; as a matter of fact, this is an important silicon’s property and several works, including this, have demonstrated its use in order to produce several active devices. On the other hand, the natural temperature oscillations, which are unintentional, are considered the great villain of silicon devices, which are highly dependent upon optical phase variations, such as modulators, switches and filters based on ring resonators, Bragg gratings, and other optical devices [3, 4, 7].
Some researchers have presented suggestions on how to solve this problem by means of intrinsic design. Amongst the presented solutions, it is noteworthy to point out some of them: the first solution consists of the use of a covering polymeric layer with negative thermo-optical coefficient as waveguide cladding in order to compensate the temperature variations, keeping a static effective index of refraction even with temperature variations [11, 12]. That solution is highly useful in many applications on the field of photonics, mainly, on the ones that require narrowband applications [1, 2, 8]; however, that solution makes silicon photonics lose an important advantage, the compatibility with CMOS process. Another solution has been presented by means of variations of the original Mach-Zehnder Interferometer, designing its arms in such a way that the phase difference between them is kept in a constant way [13, 14]. Finally, perhaps the most effective solution for various broadband applications comprises on the design of broadband devices that, due to its intrinsic broadband nature, are able to keep the device efficiently working under a large temperature variation [15–17].
In this paper, an innovative approach for a highly insensitive to temperature thermo-optical tunable and reconfigurable silicon device is theoretically presented and analyzed; such a device can be used either as a modulator or as an optical filter; its principle is based on the intrinsic broadband nature of the device, which is designed by means of several uncoupled ring resonators, which in turn are coupled to a bus waveguide. We call the principle of operation of our proposed device as the persiana effect, due to its physical similarity with the working of a window slat blind.
This paper is organized as follow: in the second section, the proposed device is mathematically analyzed and depicted, and some analytical and numerical results are presented; in the third section, the bandwidth of the device is analyzed, as well as the sensitivity to temperature; in fourth section, a tolerance fabrication analysis is presented; in the fifth section, a comparison with reported data of ring resonators is made; and finally, some conclusions are presented.
2. Theoretical analysis of the device
The proposed device is schematically shown in Fig. 1 , consisting of ten uncoupled ring resonators, which in turn are coupled to a bus waveguide; in addition, there is one micro-heater on each one of them.
The principle of operation of the device consists of using each ring resonator resonance, slightly and appropriately spaced, in order to develop a wideband resonator; each resonance is controlled by means of thermo-optic effect with a tailored heater configuration.
Before demonstrating its principle of operation, it is beneficial to show our mathematical approach used to design the device. In this paper, the device was analytically analyzed by means of the scattering parameters method and numerically simulated by means of FDTD commercial tools from Rsoft Design Group; moreover, it is noteworthy to point out that several authors have shown the efficiency of both tools by means of the good agreement with experimental results [16–21].
A typical analytical mathematical approach for ring resonators and other structures based on ring resonators have been demonstrated in our previous works, as well as by other authors [22,23], in which the approach of each ring resonator may be analyzed by means of scattering parameters considering a directional coupler with one input port optically connected on one output port [23]. The mathematical approach for only one ring resonator is given by [23]:
where τ and κ are the electric field transmission and coupling coefficient between the ring resonator and the bus waveguide, and ϕ is the optical phase due to the propagation inside the ring resonator, which is given by:where λ0 is the free space wavelength, neff is the complex effective index of refraction of the waveguide, and R is the radius of the ring resonator.However, the structure which is being proposed consists of a sequence of ten ring resonators; thus, the complete optical response of the device is easily obtained by multiplying each ring resonator transmittance, being given by:
where the subscribe n, in all parameters of the design, means the n-th ring resonator (n = 1,2,3…10).Therefore, in order to demonstrate the principle of operation of the device, it was considered the design parameters specified on Table 1 , where each one of them was carefully chosen, based on typical results found in the literature [4, 6, 21, 32–37]:
Table 1. Parameters used on the modulator design
The coupling coefficient, κ, is related to the transmission coefficient by means of the principle of conservation of energy, i.e., κ = (1-τ2)1/2 [1, 2, 6]
Thereby, the optical response of the device can be assessed. Figure 2(a) shows the optical response of the device without any bias voltage applied on the micro-heaters; in this figure, it is emphasized where the resonances are spectrally positioned under this state, i.e., the resonance of the rings one, two, three, four, and five are spectrally positioned on the same wavelength, whereas the other resonances are slightly and periodic spaced. Thus, in order to create an overall broadband resonator, we consider a bias voltage applied on the micro-heaters, named from one to five, where such resonances become equally spaced, as it is shown in Fig. 2(b).
Fig. 2 Optical response of the proposed device; a) without bias and b) with bias, (Quasi-TM00 Polarization).
The required change of effective index of refraction, Δneff, to change from the state showed in Fig. 2(a) to the state showed in Fig. 2(b) is given on Table 2 . It is noteworthy to point out that on the tables, the ring status On means that a bias voltage is applied on the respective ring resonator heater, while Off means the opposite.
Table 2. Parameters for state shown in Fig. 2
The state showed on Fig. 2(b) is a configuration for a broadband filter or one level of modulation, which is defined in our analysis as level 0; on the other hand, our main purpose for this device is to demonstrate its capability of processing an optical signal, in such a way it can be used as a reconfigurable and tunable thermo-optical filter or modulator. Of course, the intrinsic speed limitation of the thermo-optic effect [24–26] implies that the device has to be used in processing speeds in the range of up to a few MHz [25], which is enough for several applications in the field of photonics [24].
The next stage to be showed is depicted in Fig. 3 , where we demonstrate the so called persiana effect. Figure 3(a) consists of the same state showed in Fig. 2(b), and Fig. 3(b) consists of our second level of operation, i.e., level 1, which is obtained by the tuning of the ring resonators resonances of resonators labeled six to ten; this is attained by means of a bias voltage applied on the respective ring resonators, while the others resonances, labeled one to five, are just turned off, thus establishing a modulated and processed signal.
Fig. 3 Optical response of the device; (a) not-modulated (corresponds to the logic level 0), and (b) modulated (corresponds to the logic level 1), Quasi-TM00 Polarization.
Instead of designing the modulator with the ring resonators labeled six to ten slightly different in size, in order to get the effect shown in Fig. 3(a) and 3(b), it is noteworthy to point out that the same effect could have been obtained by using ten ring resonator with the same size and, by means of an appropriate heating scheme, having their resonances slightly tuned, as shown in Fig. 3(a) and (b); however, that approach would require a higher electrical power consumption [24, 25].
In order to better clarify the persiana effect and the principle of operation of our device, Fig. 4 depicts the schematic representation of operation of the device and it emphasizes the scheme for the micro-heaters feeding, which establish the Levels 0 and 1, as well as its optical responses. To see more details, check Media 1.
Fig. 4 Optical response of the device (a) not-modulated and (b) modulated (Quasi-TM00 Polarization). Media 1.
The required change of index of refraction to establish, from state shown in Fig. 3(a) into that in Fig. 3(b), which is the same requirement to that from Fig. 4(a) into Fig. 4(b), is given by Table 3 .
Table 3. Parameters for state shown in Fig. 3
Figure 2, Fig. 3, and Table 3, show the principle of operation of the proposed device, the persiana effect, and, as far as the authors know, this is the first time that it has been proposed and demonstrated in the literature.
Up to now, we have presented only the mathematical approach of the device with the help of simple analytical tools; however, we have also made simulations with analytical and FDTD methods, using a professional computational designing tool from R-Soft Design Group.
Our FDTD simulation consists of a 2D simulation of a structure equivalent to the 3D counterpart [27]; the simulation takes into account the material dispersion, waveguide dispersion, and losses in general; moreover, it is noteworthy to point out that our analytical method also takes into account the dispersion characteristics of the device; thereby, in Fig. 5 , it is demonstrated the sensitivity to the losses of the optical response of the device, as well as a comparison between our analytical results and our FDTD simulations; these results are, respectively, shown in Fig. 5(a) and (b).
Fig. 5 Optical response of the device when is applied a modulation signal and when is not applied (Quasi-TM00 polarization): (a) analytical optical response as a function of wavelength and general loss; (b) comparison between analytical optical response and FDTD-2D simulations.
Based on Fig. 5(b), one can notice the excellent agreement between our analytical methods and the FDTD simulations. In addition, FDTD simulations indicate that the bending losses for the ring resonator leads to an electric field loss coefficient α = 26 cm−1 (52 cm−1 for optical power loss coefficient). It is noteworthy to point out that similar results have been reported in the literature, showing good agreement with our simulation [6, 38]. Moreover, ring resonators have been reported as being fabricated with similar dimensions [5, 6, 25, 31–33].
An important remark should be made concerning the control of waveguide losses, which has already been reported in the technical literature, by means of fabrication processes [34–37].
Based on the results presented on this section, one can observe the wideband achieved with this device and owing to this intrinsic nature, one can use it to inhibit the natural temperature variations and keep a static characteristic of operation [15, 16, 17]; the relevant figure-of-merit to be observed is the extinction ratio, i.e., the ratio between the maximum and minimum value achieved on the two levels.
3. Wideband analysis and temperature analysis
Based on the results presented on the last section, one can observe a large modulation depth, which establishes an excellent extinction ratio. For that reason, in this section, we analyze the broadband nature of the device, as well as its intrinsic nature of insensibility to temperature.
Therefore, in order to quantify how broadband the device is, Fig. 6 shows the extinction ratio of the device as a function of the wavelength. Based on Fig. 6, one can observe that the bandwidth of operation of the device is approximately of 6.5 nm, which translates into approximately 830 GHz in frequency span, for an extinction ratio of, at least, 10 dB. Obviously, the device is considered a broadband device as compared with other typical devices, such as single ring resonators [4, 6].
In fact, the broadband nature of the device is an important characteristic; however, our main purpose with this particular feature is to demonstrate that, for a central wavelength of operation, the device can work under a large range of temperature, either for positive or negative variations.
Our modal simulations, using RSoft Design tools, indicate that the effective index sensitivity to temperature of a channel silicon waveguide, 400 nm wide and 200 nm thick, is 0.942 x10−4 for the Quasi-TM00 polarization state, at a wavelengths around 1.55 μm.
Therefore, in order to demonstrate this advantage of the proposed device, Fig. 7 shows the same analysis made in Fig. 6 for three different values of temperature variations: −15 K, 0 K, and 10 K. Special attention has to be given to the central wavelength of resonance, around 1.550 μm. To see more details, see Media 2.
Fig. 7 Extinction ratio of the device as a function of the wavelength (Quasi-TM00 polarization) for some values of temperature variation. Media 2.
Based on the Fig. 7 one can observe that, for the central wavelength of operation, the device preserves its extinction ratio and can be exposed to high temperature variations; thereby, in order to quantify how insensitive to temperature the device is, we have made an analysis of temperature sensibility, which consists of selecting the central wavelength of working (around 1.550 μm) and assessing the extinction ratio as a function of temperature; this analysis is shown in Fig. 8 for Quasi-TM00 fundamental mode.
Therefore, based on Fig. 8, one can notice that the device can stay working with a temperature variation of up 96 K, keeping at least 10 dB of extinction ratio for Quasi-TM00 polarization.
4. Tolerance fabrication analysis
On the previous sections, we have demonstrated the potentialities of the proposed device, where one can observe its important characteristics. In this section, we present a tolerance fabrication analysis in order to verify how sensitive to fabrication process variations the device in fact is.
Our analysis consists of three different analyses; we assess the modulated and not-modulated optical response of the device, the broadband analysis, and the temperature sensibility as a function of the transmission coefficient, covering the range from τ = 0.8 to 1. In other words, our analyses show how sensitive the device is to fabrication variations of the gap between the bus waveguide and each ring resonator.
The first analysis is shown in Fig. 9 , where we analyze the normalized optical response of the device as a function of the wavelength and of the transmission coefficient for both levels, 0 and 1. Figure 9(a) and (b) show the contour map and a perspective graphic of the optical response that corresponds to the Level 0, respectively; Fig. 9(c) and (d) show a similar analysis for the Level 1.
Fig. 9 Normalized optical intensity as a function of the wavelength and transmission coefficient, (a) contour map and (b) perspective view of the optical response on level 0, and (c) contour map and (d) perspective view of the optical response on level 1.
An important remark has to be made regarding the range of our analysis, in particular when τ = 1, which means that the ring resonator and the bus waveguide are at an appropriate coupling distance, such that no electric field is coupled into the ring resonators; as a consequence, this state makes the device work such as a straight waveguide and no resonant effects occur. Indeed, this state is completely undesirable, but it reveals what happens with high transmission coefficients, near τ = 1. Besides, based on Fig. 9, one can observe that the device can work very well even with significant variations during the fabrication process; the range of transmission coefficients reveals that even for a 10% positive or negative tolerance for this parameter, the device can still work satisfactorily. Obviously, these is a large fabrication variation, since researchers have achieved precision of up to 2 nm or less in some devices [29, 30 , 31]; notice that a 1 nm deviation in our analysis means less than 0.4% of variation on the transmission coefficient in our model.
Another point deserves special attention, which is related to the response amplitude at the central wavelength as a function of the transmission coefficient; by selecting the central wavelength of resonance around 1.550 μm, Fig. 9(c) and (d), reveal that, as the transmission coefficient is reduced its amplitude is also reduced, because of different Q-factor values, which in turn is determined by the transmission coefficient; thereby, the level of the output amplitude may be significantly decreased if the coupling coefficient is increased. However, it does not mean that the extinction ration will be totally hindered, since the amplitude of the level 0 is near of the transmission null; as a consequence, the behavior of the extinction ratio may assume different behaviors, because it is a ratio between a maximum and a minimum amplitude, and this is the main figure-of-merit to be analyzed; in addition, for several applications, a 10 dB extinction ratio is considered reasonably enough.
Therefore, in order to quantify how sensitive the extinction ratio is, the second analysis is presented on Fig. 10 , which shows it as a function of the wavelength and of the transmission coefficient. Figure 10(a) shows the contour map, while Fig. 10(b) shows the same analysis in a perspective graphic.
Fig. 10 Extinction ratio as a function of the wavelength and transmission coefficient, (a) 2D contour map and (b) the respective 3D contour map.
In Fig. 10 (a), the highlighted mark corresponds to the point of operation chosen in our model; however, one can observe that for τ = 0.915, a high extinction ration can be achieved, this is an excellent point and the extinction ratio may achieve up to 80 dB for a particular wavelength; this occurs for that particular value of τ because it establishes the critical coupling for all ring resonators [22]. On the other hand, one can notice that even with τ = 0.8, a good extinction ratio is achieved. Therefore, at least 10 dB of extinction ratio is achieved for a broadband operation, even with relatively large variation of the parameter τ.
Finally, Fig. 11 shows the extinction ratio as a function of both the temperature variation and the transmission coefficient, for the central wavelength (1.550 μm).
Fig. 11 Extinction ratio as a function of the temperature variation and transmission coefficient,, (a) 2D contour map and (b) the respective 3D contour map.
Based on Fig. 11, similarly to our previous analysis, one can observe that the device is able to keep the extinction ratio over 10 dB for a large range, of almost 100 K; this characteristic is observed for a large range of values of transmission coefficient, similar to the broadband analysis.
5. Final design and considerations
After discussing the main points of the proposed device, we then compare our designed device parameters with data from ring resonators already reported in the literature. Table 4 shows the optimized dimensions for our device, all ring resonators have the same waveguide cross-section and gap between the bus-waveguide and ring resonators. On the other hand, the length of the ring resonator are suitably and slightly spaced in order to attain the persiana effect. The micro-heaters are considered to be similar to the one proposed by Adibi [25].
Table 4. Optimized dimensions of the final design.
It is noteworthy to point out that other researchers have already experimentally achieved resolutions of about 1 nm for the circular length of ring resonators [31], as well as have being able to control the waveguide losses by means of fabrication processes [35–37].
Simulations made by means of FDTD method indicate that the gap shown in Table 4 corresponds to a τ = 0.9 for the quasi-TM00 polarization state. In addition, data from the literature, as well as from our FDTD simulations, indicate that the intrinsic electric field loss coefficient for such ring resonators stays around α = 26 cm−1 [4,6,38].
We have chosen this specific waveguide cross-section from a previous optimization with respect to the effective index thermo-optical response [15]; this cross-section also provides acceptable bending losses [34–37,39].
Ring resonators have been considered essential building blocks for several devices; thereby, in order to demonstrate the fabrication feasibility of our device, we have selected some data for ring resonators that have already been fabricated. Table 5 shows a comparison between our proposal and reported ring resonators.
Table 5. Comparison with reported ring resonators.
Based on the above referenced data, one can observe that our optimized proposed dimensions are close to the ones that have already been fabricated and reported. All parameters in our design have been optimized to attain the lowest sensitivity to temperature [15].
6. Conclusions
Based on results discussed in the previous sections, one can classify the persiana structure as a promising optical integrated device, compact and CMOS-compatible, due to its intrinsic broadband characteristic, of up to 830 GHz, and very low sensitivity to temperature, being able to support around 96 K of temperature variation, when it is tuned to the central resonance wavelength for the Quasi-TM00 polarization state,
Therefore, devices based on persiana effect may open the door for novel structural configurations of silicon optical devices, capable of mitigating one of the few remaining sources of criticism for widespread use of silicon photonics – the temperature sensitivity.
Acknowledgements
The authors thank CAPES and CNPq foundations (funded by the Brazilian Government) for the financial support, as well as the Electronic Warfare Laboratory at ITA and the Photonics Division at IEAv for the technical support.
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