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					EOP3046 Optical Waveguides and Devices

2008/2009

OW2: Simulation of Optical Planar Waveguide I. Objective of Experiment   To learn how to create a 2D waveguide structure, define variables, set appropriate launch fields and perform mode calculations using BeamProp. To find the modes supported by this 2D symmetric slab waveguide. (Since this will be a scalar calculation, polarization dependencies will not be considered).

II. BeamPROP* BeamPROP is a highly integrated CAD tool and simulation engine for the design of photonic devices and photonic integrated circuits. The software incorporates advanced finite-difference beam propagation (BPM) techniques for simulation with RSoft’s modern graphical user interface for ease of circuit layout and analysis. The benefit of good design and modeling tools is well known in the electronics industry, where both device and circuit simulation programs, such as PICSES and SPICE have been instrumental in advancing the availability and use of integrated electronic circuits. BeamPROP brings this important capability to the photonics area, and can be an extremely useful tool for research and development groups in both university and industrial environments. The objective of BeamPROP is to provide a general simulation package for computing the propagation of light waves in arbitrary waveguide geometries and it has the capability for computing the waveguide modes. There are several reasons for the popularity of BPM; perhaps the most significant being that it is conceptually straightforward, allowing rapid implementation of the basic technique. This conceptual simplicity also benefits the user of a BPM-based modeling tool as well as the implementer, since an understanding of the results and proper usage of the tool can be readily grasped by a non-expert in numerical methods. In addition to its relative simplicity, BPM is generally a very efficient method, and has the characteristic that its computational complexity can, in most cases, be optimal, that is to say the computational effort is directly proportional to the number of grid points used in the numerical simulation. Another characteristic of BPM is that the approach is readily applied to complex geometries without having to develop specialized versions of the method. Furthermore the approach automatically includes the effects of both guided and radiating fields as well as mode coupling and conversion. Finally, the BPM technique is very flexible and extensible, allowing inclusion of most effects of interest (e.g. polarization, nonlinearities) by extensions of the basic method that fit within the same overall framework. III. Introduction The simplest optical waveguide structure is the step-index planar slab waveguide. This waveguide consists of a high-index dielectric layer (core) surrounded on either side by lower-index material (cladding) as shown in Figure 1. The slab is finite in the x direction and infinite in extent in the yz-plane. The index of refraction of the guiding core layer is larger than that of the * RSoft BeamProp 5.1.1 manual cover material (top cladding layer) and substrate material (bottom cladding layer) in order for total internal reflection to occur at the interface. The waveguide is symmetry if the cover and substrate materials have the same index of refraction, otherwise the waveguide is called asymmetric guide. Both types are used in the integrated optics. Figure 1 shows the light rays making angles  greater than the critical angle, undergoes multiple total internal reflections at the slab boundaries.

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EOP3046 Optical Waveguides and Devices

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x

z cladding n2 n1 0 cladding n2 -d/2 d/2  y Guided ray

core

Figure 1: Geometry of the Slab Optical Waveguide.
Considering a symmetric waveguide, with a sinusoidally time-varying wave propagates in the z direction. The propagation constant in the z direction is . The electric and magnetic components of the wave are expressed as

E  E0 ( x, y )e j (  z t )

H  H 0 ( x, y )e j (  z t )
The term E and the corresponding magnetic field distribution H describes the transverse structure of the field and is call the mode structure or mode shape. A mode is the field configuration or distribution in the waveguide. Two family of modes can be supported by this slab waveguide, transverse electric (TE) and transverse magnetic (TM). The TE modes have their electric field parallel to the y-axis and no longitudinal electric field, that is, Ez = 0. The TM modes have their magnetic fields parallel to the y-axis and no longitudinal magnetic field, that is Hz = 0. The TE and TM modes are denotes as TEm and TMm modes. The subscripts m is call the order of the mode or the mode number. The lowest-order or fundamental mode corresponding to m = 0. Figure 2 shows the field patterns of several of the lower-order TE modes. The order of a mode is equal to the number of field zeros across the guide. The mode patterns in Figure 2 shows that the electric fields of the guided modes are not completely confined to the central of the waveguide(core), i.e. they do not goes to zero at the guide-cladding interface, but, instead, they extend partially into the cladding. The fields vary harmonically in the core and decay exponentially at the cladding region. For lower-order modes, the fields are tightly concentrated near the center of the core, with little penetration into the cladding region. For higher-order modes the fields are distributed more towards the edges of the guide and penetrate further into the cladding region.

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EOP3046 Optical Waveguides and Devices

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TE0 Cladding, n2

TE1

TE2 Exponential decay

Core, n1

Exponential decay

Figure 2: Electric field distribution of TE modes for several of the lower-order guided modes in a symmetrical waveguide. We often use the terms single-mode or multimode to characterize a waveguide. A waveguide can support a different number of modes depending on its thickness. For a symmetric waveguide, it can always support at least one mode. By changing the relative indices between the layers, the number of modes will vary. The approximations of the number of the guided modes can be found from,
1

M 
where, k 

2 kd(n12  n 2 ) 2



2



is the propagation constant, d is the thickness of the core and n1 and n2 is the index of

refraction of the core and cladding respectively. The approximation is best when M is a large integer. The number of modes, N is an approximation and usually should be rounded up to the next larger integer to get the accurate number of modes that will be guided by the structure. Note that the mode count increases with the thickness, d, of the guide, with the 2 difference in index ( n12  n2 ) between the core and cladding, and as the wavelength of the guided light gets shorter. We usually characterize a waveguide by normalized frequency, defined as,
2 V  kd (n12  n2 ) 2 1

In terms of normalized frequency, the number of modes,

M 

V



When a pulse is launched on a waveguide, in digital communication system, the pulse energy will become distributed over all the allowed modes that are excited in the waveguide. Each mode however has a different propagation constant and hence travels at a slightly different velocity. Thus each mode arrives at

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EOP3046 Optical Waveguides and Devices

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the receiving point at a different phase and the signal is distorted. This distortion is called mode dispersion. A signal in a single-mode waveguide is not distorted by mode dispersion. IV. 2D Waveguide Types in BeamProp 2D structures are very simple to define in the RSoft CAD interface. They consist of only a Waveguide Width, Index Difference, and a starting and ending vertex as shown in Figure 2. By default, the cross section of the segment is assumed to be step-index; however, this can be changed via a profile function. Note: the index difference, n, is equal to the difference between the core refractive index and the cladding refractive index in the context of a symmetric slab waveguide, and n0 is the background index. This is the index of refraction for the background material in which the waveguide components will be embedded. It is essentially the index of the cladding material for the case of symmetric slab waveguide.

Figure2*: The basic 2D structure definition. Note that the propagation direction is along Z. V. Simulation Procedures (Students are advised to familiarise with the icons/commands of the softwares) 1. Launch the RSoft CAD program from the window’s Start>Program>RSoft Photonics CAD Suite>RSoft CAD-Layout. 2. Click on the New Circuit icon in the toolbar. We are going to create a 2D symmetric slab waveguide with a core index ncore a cladding index ncladding, and a width of 10 µm at a wavelength of 1.3 µm. 3. Enter the information below into startup dialog:  Free Space Wavelength = 1.3  Background Index = 3.378 (this refers to the cladding index)  Index Difference = 0.0067  Waveguide Width = 10

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4. Click OK button to continue. 5. Click on the Edit Symbols icon and the Symbol Table Editor will appear. 6. Set the length of the waveguide by defining a variable (symbol) and set it equal to 100000. Click New Symbol, enter the symbol Name (Length) and Value (100000), and then click Accept Symbol. The variable Length should now appear in the symbol table. Click OK button to continue. 7. Choose the straight waveguide component, or Segment Mode. Move the cross-hair cursor to the beginning of the straight waveguide section located at the coordinates (X=0, Z=0). Press, but do not release the left mouse button, and move the cursor to the end of the straight waveguide section located around the coordinates (X=0, Z=50). The length of the waveguide segment will use the variable defined previously. The waveguide segment is drawn with the center line displayed in black, and the left and right edges in red. Click Undo Last Change to restore to its previous state if a mistake is made when adding any waveguide component. 8. Open the Segment Properties window for this waveguide by right clicking on the segment in the CAD window. 9. Select the Reference Type of the Z coordinate of the Ending Vertex to be offset, and in Reference To: Component 1, Vertex 0. (This tells the software that the Z coordinate of the ending vertex of this segment, or Segment #1, should be computed as an offset from the starting vertex, or vertex 0, of this segment, or component 1. This offset will therefore equal the length of the segment.) 10. Set the Parameter Value equal to the variable Length. 11. To zoom in to see the whole structure choose the View/Full from the CAD menu, and then choose View/Regrid. 12. You may notice that the waveguide you have drawn does not have the same shape as the previous one. This is most likely due to the aspect ratio of the display window. To set the aspect ratio of the CAD window, choose View/Set View Parameters from the CAD menu. Check the box Lock Aspect, and change the Aspect Ratio to 1. This sets the aspect ratio of the CAD window to 1. 13. Click Display Index Profile icon in the left toolbar and press OK in this dialog that will display the index profile at the Z Domain Min value. It is very useful to measure the index distribution in order to verify the layout. 14. To save the index profile to a data file, enter an Output File Prefix in the simulation parameters dialog. After pressing OK, the graph will be displayed, and the index profile will be saved in the file <prefix>.ipf, and a corresponding WinPLOT command file for the graph will be saved in the file <prefix>.ppf, where <prefix> is the output prefix specified. 15. Click on the Edit Launch Field icon to define the launch field and choose the Launch Type equals to Slab Mode and Launch Position X equals to 0 and these will launch the field from the center of the waveguide. Click OK. 16. Click Compute Fundamental Mode icon from the left toolbar, this will bring up a Simulation Parameters dialog. Set the mode calculation parameters as bellow:

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17. Enter an Output File Prefix (e.g. mode). Click the Output… button and make sure the Slice Output is set to None; this will generate files at each point along Z, and is unnecessary for a mode calculation. Set the Display Mode to Contour Map (XY). Then click OK. When the simulation is completed, the computed fundamental mode will be displayed. Note that the mode files will only be saved if the Output File Prefix is specified. 18. To find the possible mode that can propagate through this waveguide, choose Run/Compute Mode/Option… from the menu and select the Iterative Mode Solver. Then go to Run/Compute Mode/All to bring up a Simulation Parameters dialog. Enter an Output File Prefix (e.g. mode). Click the Output… button and make sure the Slice Output is set to None. Set the Display Mode to Contour Map (XY). Click OK in the Simulation Parameters dialog box to run the mode solver. Note that only the fundamental mode will be displayed on the screen. To view the other resulting modes, use the View Graphs icon on the top of the screen and select the files that begin with the Output File Prefix (that set previously, e.g. mode). Each mode found will have two files: the mode data is contained in the file <prefix>.m##, and has a corresponding WinPLOT command file <prefix>.p##, where ## is the mode number. VI. Exercise 1. Use the Symbol Table to change each of the following values and find the resulting modes and observe the mode profiles for each case with respect to the original setting in the section V: a. width to 5m and 25m. b. core index to 3.3800 and 3.402 with the width set to 5m. (i.e need to find the index difference from these core index from the cladding index) c. wavelength to 0.89m and 0.63m with the width set to 5m and core index set to 3.3872. Note: Save the results in different Output File Prefix. 2. Using the value in part1 (a), (b) and (c), calculate the Normalize Frequency and number of possible modes that can supported by the waveguide.

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EOP3046 Optical Waveguides and Devices

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VII. Lab report format, evaluation and submission 1. The report should be nicely typed and should include the following:  Date of experiment  Objectives  Apparatus  Summary of procedures (in passive and past tense)  Results/answers for all the assignments  Discussions  Conclusions  References  Appendix A: Detailed contributions by each student in the group for the experiment (e.g. tasks, ideas, etc. during the session), and report (e.g. page numbers, sections, paragraphs, etc.), respectively.  Appendix B: Corrections to the experimental procedure in the labsheet 2. Duration of lab report submission: not more than 7 days after the date of your experiment. 3. Lab report submitted to the lab staff of Optical Laboratory. 4. Penalty for the late submission: deduct 1 mark and not accepted after the last day of Trimester.

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Lingjuan Ma Lingjuan Ma
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