Wavelength Conversion Four Wave Mixing in Silicon Waveguide

Wave space transmutation by Degenerate Four Wave f occasion in Silicon Waveguide Abstract Four- wander mixing (FWM) is one of the interesting nonanalogueities in optical systems. It is primarily used for wavelength revolution. To investigate the factors that affect the wavelength modulation dexterity, the growth of Four-wave mixing (FWM) in ti wave guide is pattern using matlab. The method acting of modeling is described. The knowects of remark watch male monarch and wave guide length on the conversion qualification atomic number 18 investigated.Results show that when propagating on a 0. 048m silicon wave guide, both the enter mettle motive and blow business leader flows, while anti- cam slice forefinger increases first and then decreases along the wave guide. It is also shown that for a 0. 048 silicon waveguide, siding anti-stroke government agency is the maximal when the enter warmness agent is 3W. Also, when the excitant nub fountain is k ept constant, there is a most useful waveguide length for wavelength conversion. Key names -FWM model conversion business leader stimulant drug nub magnate waveguide length 1 IntroductionFour-wave mixing (FWM) is an inter modulation phenomenon in optical systems, whereby interaction between three waves (two watch waves and a signal wave) fetch a fourth part wave (idler wave) 1. This phenomenon can be used for all optical wavelength conversion (AOWC) and entangled photon generation 2, 3. As extremely small core of si wires produce the non linear optical effect even down the stairs low optical proponent, Silicon is used as waveguide in our project for practical wavelength conversion by FWM process with all-night waveguide lengths and littler filename extension loss4.Factors that affect optical wavelength conversion atomic number 18 being studied to enhance the conversion efficiency. It has and so become alpha to study FWM in silicon waveguide theoretically to increase the conversion efficiency for get ahead experiment. In our project, FWM matlab to study the factors that affect the conversion efficiency. This report discusses the factors that affect FWMs conversion efficiency in silicon waveguide. Theoretical treatment is presented in section 2, where FWM in silicon waveguide is described. The method to model FWM in silicon waveguide using matlab is described in section 3.Results be shown in section 4. Results show that both the stimulant watch queen and the waveguide length play an important part in the FWMs conversion efficiency. 2 THEORY The FWM process involves the interaction of four waves (two warmness waves, one signal and one idler wave) as they propagates along a medium. In our project, silicon waveguide is used as the medium. The schematic plot of FWM in silicon waveguide is shown in figure 1. Here, E represents the electric field of the respective waves and normalized such that ply P=E2. Subscripts p, s and a represent ticker , signal and idler respectively.The superscript f represents forward propagating waves. pic jut 1 Schematic diagram of FWM in silicon waveguide . 3 methodological analysis The evolution of the three waves along the silicon waveguide can be modeled by the to a lower placementioned differential equations 1. picpicpicpic where Aeff is the waveguide strong core area, ? is the wavelength, ? is the linear propagation loss and ? is the TPA coefficient, ? is the FCA cross section and ? eff is the effective carrier lifetime. h and c keep abreast their usual physical meaning of Planks constant and free-space speed of light respectively. k denotes the linear phase mismatch and can be uttered aspic. ? is the nonlinear parameter assumed to be the aforesaid(prenominal) for three wavelengths and defined as pic where n2 is the nonlinear refractive index. To simulate the evolution of the three waves along the silicon waveguide, the above four differential equation are solved simultaneously u sing Runge-Kutta-Fehlberg (RKF) method 2. Parameters Input-Output model values ? 100/4. 34 m-1 Aeff 0. 17? 10(-12) m2 ? 0. 7? 10(-11) m/W ? p 1310? 10(-9) m ? eff 1? 10(-9) s c 2. 998? 10(8) h 6. 626? 10(-34) Js ? k 0 m/s ? p 1. 0297? 10-21m2 ? 2. 43 ? 10(-11) m/W 4 RESULTs and discussion . 1 Modelling of FWM in silicon waveguide disposed(p) Pp=1W, Ps=0. 001W, Pa=0W and L=0. 048m, Pump might, stroke military group and anti-stroke power are drawn with respect to the position in the waveguide. picpicpicThe figures above show that when propagating in the waveguide, both the pump power and stroke power decrease while the anti-stoke power increases. This is as expected, as the interaction of the pump wave and stroke wave produce the anti-stroke wave. The increase of the anti-stroke power comes from the decrease of the pump and stroke power.It can be seen that, at the end of the waveguide, the pump power is save 0. 26W and the stoke power is only 0. 026W. Both of them decr ease 74% of their original power. Both the pump power and stroke power decrease fast at the bloodline, and then their decrease rate becomes slower when propagating further in the waveguide. This implies that the higher the pump power and the stroke power, the higher the propagation loss. As a result, the anti-stroke power increases fast at the beginning and then its change magnitude rate slows down. At the length of 0. 42m, the power of the anti-stroke reaches its maximum value which is about 3. 2*10-5W. accordingly the anti-stroke power starts to decrease slowly. This may be because when the pump and stroke power is small, the gain of the anti-stroke power is slight than its propagation loss. 4. 2 Effects of input pump power on conversion efficiency Given Ps=0. 001W, Pa=0W and L=0. 048m, Pp changes from 0 to 10W with measuring stick 0. 2W. The graphical record of the railroad siding stroke power and the turnout anti-stroke power are drawn with respect to the input pump powe r. pic Figure 2. 1 Output stroke power with different input pump powerThis graph shows that the larger the input pump power, the smaller the output stroke power. This is as expected, as the larger the input pump power, the larger the propagation loss. The output stroke decreases slower when the input pump power is higher. pic Figure 2. 2 Output anti-stroke power with different input pump power This graph shows that when the input pump power is less than3W, the higher the input pump power, the higher the output anti-stroke power. This is as expected, as more(prenominal) input power can be converted to anti-stroke power when the input pump power is larger.When the input pump power is larger than3W, the output anti-stoke power decreases with the input pump power. As the higher the input pump power, the higher the propagation loss. When the input pump power is larger than3W, the propagation loss dominates. 4. 3 Effects of waveguide length on conversion efficiency To investigate the re lationship between the waveguide length and the conversion efficiency, input power are keep constant, Pp=1W, Ps=0. 001W, Pa=0W, L changes from 0. 001m to 0. 1m with timber 0. 001m. Output stroke power and output anti-stroke power are drawn with respect to different waveguide length. pic Figure 3. 1 Output stroke power with different waveguide length This graph shows that the longer the waveguide length, the smaller the output stroke power. This is as expected, as the longer the waveguide length, the larger the propagation loss. The decreasing rate of the output stroke power decreases with the waveguide length. pic Figure 3. 2 Output anti-stroke power with different waveguide length This graph shows that when the waveguide length is less than 0. 048m, the output anti-stroke power increases with the waveguide length.This implies that the gain is larger than the propagation loss in the waveguide. When the waveguide length is larger than 0. 48m, the output anti-stoke power decreases wi th the waveguide length. At waveguide length larger than 0. 048m, the propagation loss is larger than the gain of the anti-stroke power. The output anti-stroke power has a maximum value of 4. 5*103 when the waveguide is 0. 048m. Thus, the most effective waveguide length is 0. 048m. 5 Conclusion The completion serves the important function of drawing together the motley sections of the written report.The conclusion is a summary, and the developments of the previous sections or chapters should be succinctly restated, important findings discussed and conclusions drawn from the alone study. In addition, you may list questions that train appeared in the course of the study that require additional research, beyond the limits of the project being reported. Where appropriate, recommendations for future work may be included. The conclusion should, however, leave the reader with an ruling of completeness and of gain. AcknowledgmentThe author would like to express her deepest gratitude to A/P Luan Feng and PhD student Huang Ying for their guidance, assistance and advices. The author also wishes to own the funding support for this project from Nanyang Technological University under the Undergraduate Research Experience on Campus (URECA) programme. References The guide will number extensions consecutively wi cut down brackets 1. The judgment of conviction punctuation follows the bracket 2. Refer simply to the persona number, as in 3do not use Ref. 3 or reference 3 except at the beginning of a sentence Reference 3 was the first look pens separately in superscripts. Place the actual footnote at the bottom of the column in which it was cited. Do not put footnotes in the reference list. mapping letters for table footnotes. Unless there are sixsome authors or more founder all authors name do not use et al. Papers that have not been published, even if they have been submitted for upshot, should be cited as unpublished 4. 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