All Optical Technology PhotonicsCADUsers Manual Version 1.6 Your Best Choice forSimulation ofOptical CommunicationSystems & OpticalNetworks All Optical Technology Address Korea Techno Complex, Korea University 126-16, 5Ka, Anam-dong, Sungbuk-ku Seoul, 136-701, Korea Tel 82-2-3290-3233, 4088 Fax 82-2-924-9710 Email jcj@aotech.co.kr Home page http://www.aotech.co.kr/ AO Technology: AO Technology Korea Techno-complex Korea University 126-16, 5Ka, Anam-dong, Sungbuk-ku Seoul, 136-701, Korea Tel: 82-2-3290-3233, 4088 Fax: 82-2-924-9710 Email: jcj@aotech.co.kr Home page: http://www.aotech.co.kr/ 5 126-16 : 02-3290-3233, 02-3290-4088 : 02-924-9710 Sales outside Korea Sales inside Korea NetOptics 386 918 : 042-611-7550 : 042-611-7560 Technical Support: Prof. Jichai Jeong Microwave Photonics Lab. College of Communications and Information Dept. of Radio Communications Eng. Korea University 1, 5Ka, Anam-dong, Sungbuk-ku Seoul, 136-701, Korea Tel: 82-2-3290-3233 Fax: 82-2-924-9710 Email: jcj@korea.ac.kr URL: http://pulse.korea.ac.kr/ 5 1 : 02-3290-3233 : 02-924-9710 2002 AO Technology. All rights reserved. Reproduction of this manual is strictly prohibited without the written consent of AO Technology. Information in this manual is subject to change without notice and does not represent a commitment by AO Technology. AO Technology, 2002 i Contents Contents.........................................................................................................................................i 1. Introduction ............................................................................................................................. 1 1.1 System requirements ........................................................................................................ 1 1.2 Installing Photonics CAD................................................................................................. 2 1.3 Starting Photonics CAD................................................................................................... 2 2. Getting Started......................................................................................................................... 3 2.1 Main window.................................................................................................................... 3 2.1.1 Menu ...................................................................................................................... 3 2.1.2 Tree......................................................................................................................... 4 2.1.3 Toolbar ................................................................................................................... 5 2.1.4 Status bar................................................................................................................ 7 2.1.5 Zoom in and zoom out ........................................................................................... 7 2.1.6 Moving the focus of a workspace .......................................................................... 9 2.1.7 Keyboard.............................................................................................................. 10 2.1.8 Simulating schematics.......................................................................................... 11 2.2 Starting design of new schematics ................................................................................. 12 2.3 Drawing schematics ....................................................................................................... 13 2.3.1 Dragging and dropping tools................................................................................ 13 2.3.2 Flipping tools ....................................................................................................... 15 2.3.3 Changing parameters of selected tools................................................................. 15 2.3.4 Making connections between tools ...................................................................... 16 2.3.5 Copy and paste..................................................................................................... 17 AO Technology, 2002 ii 2.4 Saving and loading your project created on the window................................................ 19 2.5 Making your own projects or tools using input and output ports................................... 19 2.6 Simulating schematics.................................................................................................... 21 2.7 Result windows .............................................................................................................. 21 2.7.1 Result windows .................................................................................................... 22 2.7.2 Menu in result widow........................................................................................... 23 2.7.3. Changing axes ..................................................................................................... 27 3. Transmitter Models ............................................................................................................... 28 3.1 Electrical signal generator .............................................................................................. 28 3.1.1 Electrical signal generator for dual electrodes ..................................................... 28 3.1.2 Electrical signal generator for single electrode.................................................... 32 3.1.3 Analog signal generator........................................................................................ 34 3.2 Model of DFB laser........................................................................................................ 35 3.2.1 Complete DFB laser model from rate equations.................................................. 35 3.2.2 Analytical DFB laser model ................................................................................. 46 3.2.3 Ideal DFB laser model for CW sources ............................................................... 49 3.3. Time domain Fabry-Perot laser model .......................................................................... 50 3.4 Model of LiNbO3 external modulators........................................................................... 58 3.4.1 Ideal LiNbO3 external modulator ......................................................................... 58 3.4.2 Analytical LiNbO3 external modulator................................................................. 60 3.4.3 Measured LiNbO3 external modulator ................................................................. 63 3.5 EAMI-DFB lasers........................................................................................................... 65 3.5.1 Complete EAMI-DFB laser model from rate equations ...................................... 65 3.5.2 Analytical EAMI-DFB laser model ..................................................................... 79 3.6 Model of mode locked laser ........................................................................................... 85 3.7 Transmitter model using measured LI curve form laser diodes for analog applications 87 AO Technology, 2002 iii 3.8 Tunable EAMI-DBR lasers from rate equations ............................................................ 90 3.9 Transmitter model using measured pulse pattern and chirping .................................... 103 4. Receiver Models................................................................................................................... 107 4.1 Types of receivers......................................................................................................... 107 4.1.1 PIN diodes.......................................................................................................... 107 4.1.2 APD.................................................................................................................... 110 4.2.3 EDFA preamplifier + PIN.................................................................................. 112 4.2 Frequency response of PD to power amplifier ............................................................. 116 4.2.1 Butterworth filter................................................................................................ 116 4.2.2 Bessel-Thomson filter ........................................................................................ 118 4.2.3 Measured frequency response of receivers ........................................................ 119 5. Fiber Models ........................................................................................................................ 121 5.1 Nonlinear characteristics of fibers................................................................................ 121 5.1.1 Self-phase modulation (SPM) and cross-phase modulation (XPM) .................. 121 5.1.2 Stimulated Raman scattering (SRS)................................................................... 124 5.1.3 Polarization mode dispersion (PMD)................................................................. 126 5.1.4 Stimulated Brillouin Scattering (SBS) ............................................................... 128 5.2 Various types of Fibers ................................................................................................. 131 5.2.1 Single Model Fiber............................................................................................. 131 5.2.2 Dispersion compensating fiber........................................................................... 141 5.2.3 Dispersion shifted fiber ...................................................................................... 142 5.2.4 Non-zero dispersion-shifted fiber (+), non-zero dispersion-shifted fiber (-) and generalized non-zero dispersion-shifted fiber ............................................................. 143 5.2.5 TrueWave Fiber and TrueWave RS fiber ........................................................... 144 5.2.6 LEAF Fiber ........................................................................................................ 146 5.2.7 Measured Fiber Types ........................................................................................ 147 AO Technology, 2002 iv 5.2.8 Bidirectional Fiber ............................................................................................. 149 6. Model of Passive Components ............................................................................................ 155 6.1 Electrical filter.............................................................................................................. 155 6.2 Attenuator ..................................................................................................................... 159 6.3 Delay line ..................................................................................................................... 160 6.4 Long period fiber Bragg grating................................................................................... 161 6.5 Short period fiber Bragg gratings................................................................................. 170 6.6 Optical filter ................................................................................................................. 179 6.7 Isolator.......................................................................................................................... 181 6.8 Connector ..................................................................................................................... 182 6.9 Coupler ......................................................................................................................... 183 6.10 Combiner .................................................................................................................... 184 6.11 Splitter ........................................................................................................................ 185 6.12 Phase Shifter............................................................................................................... 186 7. Model of Functional Components ...................................................................................... 188 7.1 Multiplexer ................................................................................................................... 188 7.2 Demultiplexer............................................................................................................... 191 7.3 Add/Drop Multiplexer .................................................................................................. 193 7.4 Time Domain Demultiplexer........................................................................................ 196 7.5 Differentiator ................................................................................................................ 198 7.6 Rectifier........................................................................................................................ 199 7.7 Space switch................................................................................................................. 200 7.8 OXC ............................................................................................................................. 204 7.8.1 OXC with Sp/Com (Splitter and Combiner) ...................................................... 204 7.8.2 OXC with Mux/Demux (Multiplexer and Demultiplexer) ................................ 205 7.8.3 OXC LM (Link modular)................................................................................... 207 AO Technology, 2002 v 7.8.4 OXC WM (Wavelength modular) ...................................................................... 208 7.9 AWG............................................................................................................................. 209 7.10 Optical Packet Switch ................................................................................................ 212 7.10.1 Input-Buffered Optical Packet Switch (IBOPS) .............................................. 212 7.10.2 Output-Buffered Optical Packet Switch (OBOPS) .......................................... 214 7.10.3 Broadcast and Select Optical Packet Switch (BSOPS) .................................... 215 7.10.4 Wavelength Routed Optical Packet Switch (WROPS) .................................... 217 7.11 FEC Encoder .............................................................................................................. 219 7.12 FEC Decoder .............................................................................................................. 224 7.13 Phase Modulator......................................................................................................... 226 7.14 PMD compensator...................................................................................................... 227 7.15 PMD emulator ............................................................................................................ 235 8. Model of Wavelength converters........................................................................................ 237 8.1 XGM (cross gain modulation) method......................................................................... 237 8.2 XPM (cross phase modulation) method ....................................................................... 244 8.3 FWM method in time domain ...................................................................................... 248 8.4 FWM method in wavelength domain........................................................................... 257 9. Optical amplifiers ................................................................................................................ 262 9.1 C-band EDFA............................................................................................................... 262 9.1.1 Gain block model ............................................................................................... 262 9.1.2 Spectrally resolved model .................................................................................. 263 9.2 L-band EDFA............................................................................................................... 274 9.3 Semiconductor Optical Amplifiers............................................................................... 277 10. Port and Repeated Link.................................................................................................... 281 10.1 Input port .................................................................................................................... 281 10.2 Output port ................................................................................................................. 282 AO Technology, 2002 vi 10.3 Repeated link.............................................................................................................. 284 11. System Viewers................................................................................................................... 286 11.1 Oscilloscope ............................................................................................................... 286 11.1.1 Pulse shape....................................................................................................... 286 11.1.2 Eye diagram ..................................................................................................... 287 11.2 Eye opening penalty ................................................................................................... 288 11.3 Error detector.............................................................................................................. 290 11.4 Eye margin.................................................................................................................. 295 11.5 Eye contour................................................................................................................. 299 11.6 ASE spectrum of EDFAs ............................................................................................ 302 11.7 Q Factor ...................................................................................................................... 304 11.8 Chirp viewer ............................................................................................................... 305 11.9 Spectrum analyzer ...................................................................................................... 306 11.10 Vrms viewer.............................................................................................................. 308 11.11 BER Calculator......................................................................................................... 309 11.12 Optical signal-to-noise ratio (OSNR) viewer ........................................................... 312 12. Device Viewer and Data Storage ...................................................................................... 314 12.1 Photon / Carrier viewer .............................................................................................. 314 12.2 Effective refractive index (neff) viewer ....................................................................... 316 12.3 LI / LV Characteristics ............................................................................................... 317 12.4 Lasing spectrum of DFB lasers .................................................................................. 318 12.5 Frequency response of DFB lasers............................................................................. 319 12.6 Waveguide analysis using effective index method (EIM) .......................................... 322 12.7 Long period fiber Bragg grating viewer..................................................................... 326 12.8 Short period fiber Bragg grating viewer..................................................................... 326 12.9 Optical Signal Storage................................................................................................ 327 AO Technology, 2002 vii 13. Sample Simulations ........................................................................................................... 330 13.1 Single channels........................................................................................................... 330 13.2 WDM channels........................................................................................................... 342 13.3 Bidirectional transmissions ........................................................................................ 353 13.4 Analog and CATV transmissions................................................................................ 358 14. Insertion of Icon and Library into Photonics CAD........................................................ 361 14.1 Generating dll file.......................................................................................................361 14.1.1 Getting started.................................................................................................. 361 14.1.2 Generating source codes of dll ......................................................................... 362 14.1.3 Generated files ................................................................................................. 366 14.1.4 Creation of main program................................................................................ 367 14.1.5 Modification of toolbar button......................................................................... 373 14.2 Finalizing users library.............................................................................................. 374 AO Technology, 2002 1 1. Introduction Photonics CAD is a user-friendly simulator capable of accurately predicting optical transmission performance of digital and analog optical networks based on the experimentally confirmed optical component models, and characteristics of optical devices and components with varying physical and material parameters. This simulation tool provides savings of cost and time for development of systems and devices from the accurate prediction of transmission performances in optical transmission systems and operating characteristics of optical devices. Photonics CAD is capable of handling Tbps data transmissions and bi-directional transmissions in ring networks. It can simulate performance of all optical networks including more functional optical components related to optical cross-connect switches and photonic packet switches. 1.1 System requirements To use Photonics CAD, the following computer system is required: IBM PC or compatible 128MB of RAM of RAM (256MB preferred to simulate fiber non-linearity) 50MB of hard-drive disk space CD-ROM driver MS Windows 95, 98, NT, XP, or 2000 AO Technology, 2002 2 1.2 Installing Photonics CAD To install the Photonics CAD, insert the Photonics CAD CD-ROM disk in your CD-ROM driver. Run setup.exe by double-clicking and then follow the instructions in the installing program: If you want to continue the setup, click the NEXT button. If you agree to the Software License, click the YES button. Enter the serial number. Select the Destination Folder using the Browser, and then click the NEXT button. Click the NEXT button. If the setup is completed, click the Finish button. 1.3 Starting Photonics CAD Photonics CAD is started in Windows from the file manager by changing the directory that contains the executable file and double clicking the Photonics CAD.exe. A hard key provided by AO Technology should be installed in the printer port in your computer. Its recommended to make an icon for Photonics CAD.exe. To start the simulator, construct your schematic related to transmission systems or devices by drag and drop from the Tool box. AO Technology, 2002 3 2. Getting Started 2.1 Main window To draw schematics, you should open a new workspace window at first. You can also create several workspace windows to draw. Fig. 2.1 -1 Workspace window 2.1.1 Menu The display and operation of the menu in schematics follow a standard window layout and operation. You can run the schematic and arrange the result windows. Fig. 2.1.1 -1 Menu AO Technology, 2002 4 Through the File menu, we can make new schematic, open schematic, save and print a schematic. The Edit menu includes the function of copy and paste. The View and Tools menus explain components and devices used for Photonics CAD. We can start the simulation with the Run menu and arrange the display of simulation results with the Window menu. The Help menu shows the version of Photonics CAD. After simulation, if the Window menu is selected, submenu will appear. In the File menu, we can export the simulated raw data into an ASCII file. With the Setting menu, we can change the axis and the color of result windows. Also, the Window menu includes the function of window arrangement. Following sections will explain these functions in detail. 2.1.2 Tree The tree can display different levels of hierarchy and several schematics that are saved in Photonics CAD. You can select the schematic that you want and can use the schematic in the current project window. Fig. 2.1.2 -1 Tree AO Technology, 2002 5 2.1.3 Toolbar The Toolbar icons provide shortcuts for initiating common actions. When you move the cursor onto an icon, the status bar shows the operation of the icon. Fig. 2.1.3 -1 Toolbar Also, many toolbars are created with the dll files in Photonics CAD. The toolbars are divided into transmitters, receivers, fibers, optical amplifiers, wavelength converters, functional blocks, passive components, repeated link, system viewers, and device viewers. Fig. 2.1.3 -2 Transmitters Fig. 2.1.3 -3 Receivers Fig. 2.1.3 -4 Fibers Fig. 2.1.3 -5 Passive components AO Technology, 2002 6 Fig. 2.1.3 -6 Functional blocks Fig. 2.1.3 -7 Wavelength converters Fig. 2.1.3 -8 Optical amplifiers Fig. 2.1.3 -9 Port and Repeated link Fig. 2.1.3 -10 System viewers Fig. 2.1.3 -11 Device viewers and data storage If the question mark toolbar is clicked, we can show following dialog box. Fig. 2.1.3 -12 Information of Photonics CAD AO Technology, 2002 7 2.1.4 Status bar The status bar is located at the bottom of the workspace window and shows a message of the operation and the current state of the workspace window. If the schematic is run, the status bar shows a progress of simulation of the schematic. Therefore, we can find the progress state of simulation through the status bar. Fig. 2.1.4 -1 Status bar 2.1.5 Zoom in and zoom out Photonics CAD provides a zoom in/out function through the Zoom In and Zoom Out commands of the View menu. Clicking the Zoom In command enlarges the schematic by 200% and clicking the Zoom Out command reduces it by 50%. The maximum and minimum sizes we can obtain are 400% and 50% of the original schematic size, respectively. AO Technology, 2002 8 Fig.2.1.5-1 Zoom In/Out commands of View menu Fig.2.1.5-2 50% of the original schematic size (minimum size) Fig.2.1.5-3 original schematic size AO Technology, 2002 9 Fig.2.1.5-4 200% of the original schematic size Fig. 2.1.5-5 400% of the original schematic size (maximum size) 2.1.6 Moving the focus of a workspace AO Technology, 2002 10 Fig. 2.1.6-1. Moving the focus of a workspace We can move the focus of a workspace as shown in Fig. 2.1.6-1 using the two methods in the following: 1) Move the scroll bar directly. 2) Lay the mouse cursor at the region shaded in blue in Fig. 2.1.6-1 and the focus of a workspace moves automatically. If you put the mouse cursor at the right, left, upper and bottom sides in that region, the focus moves right, left, up and down, respectively. 2.1.7 Keyboard You can edit a schematic using the keys in the keyboard of your computer. Ctrl + C, Ctrl + V, Ctrl + N, Ctrl + O, Ctrl + S and Ctrl + P are used to copy, paste, new, open, save and print respectively. AO Technology, 2002 11 Keyboard Function Ctrl + C Copy Ctrl + V Paste Ctrl + N New Ctrl + O Open Ctrl + S Save Ctrl + P Print Fig. 2.1.5 -1 Key function 2.1.8 Simulating schematics If you made your own schematic, you can simulate it. To simulate that schematic, you can select the Analysis command from the Run menu. Then, the simulation starts and the progress state are shown in the status bar. Fig 2.1.8 -1 Analysis submenu from the Run menu If you run the schematic, a new dialog box appears. Through this dialog box, we can change the number of sampling points in optical signals in the time domain and the range of ASE noise. Because the number of sampling points may affects your simulation results such as numerical errors in optical signals, you need to use enough sampling points. Photonics CAD suggests a proper number of sampling points, which appears automatically on this dialog box. Note that larger number of sampling points takes longer simulation execution time and more memories. If the number of sampling points exceeds 220, simulation execution time and memories are required prohibitively. AO Technology, 2002 12 Fig 2.1.8 -2 Dialog box in the Run menu 2.2 Starting design of new schematics To start the schematic editor, you can double-click on the MFC_DB_B.exe icon. Then, an empty window page is showed up. If you already use the schematic page, click the New File icon to start a new schematic. Fig. 2.2 -1 New schematic icon Fig. 2.2 -2 New project icon AO Technology, 2002 13 2.3 Drawing schematics The following sections 2.3.1~2.3.5 explain how to draw schematics. 2.3.1 Dragging and dropping tools There are two methods for dragging and dropping tools. One is to use the toolbar button and the other is to use the Tools menu. Well drag and drop oscilloscope using the two methods in the following. 1) Using the toolbar button Fig 2.3.1-1. Dragging and dropping an oscilloscope using the toolbar button Move the cursor onto the toolbar button labeled with an oscilloscope. Leave the cursor on the button for several seconds and a message box will appear to be giving a brief description of that button. This message is called ToolTip and is available for all the toolbar buttons. Click on the left mouse button to call an oscilloscope. If you move the cursor into the workspace, the oscilloscope icon appears on the AO Technology, 2002 14 workspace. When you have picked a position, click on the left mouse button to fix the oscilloscope icon. 2) Using the Tools menu. Fig 2.3.1-2. Dragging and dropping an oscilloscope using the Tools menu Move the cursor onto the Tools menu and click on the left mouse button. If you left-click tools menu, you can see various tool types (Transmitter, Receiver, Fiber, Optical Amplifiers, Wavelength Converters, Functional Blocks, Passive Components, Port, Repeated Links, System Viewers, Device Viewers). To select an oscilloscope, move the cursor onto Oscilloscope of System Viewer and click on the left mouse button. If you move the cursor into the workspace, the oscilloscope icon appears on the workspace. When you have picked a position, click on the left mouse button to fix the oscilloscope icon. AO Technology, 2002 15 2.3.2 Flipping tools During drawing schematics, we sometimes need to flip tools. Well flip the combiner in the following. Fig 2.3.2-1. Flipping combiner Drag and drop combiner on the workspace. If you move the cursor on to the combiner icon and click on the right mouse button, the pop-up menu appears. Then clicking the Flip command flips the combiner icon. 2.3.3 Changing parameters of selected tools The following example which is changing parameters for a PIN receiver explains how to change parameters of a tool selected by double clicking the icon. AO Technology, 2002 16 Fig 2.3.3-1. Dialog box of input parameters for PIN receiver There are two methods to display dialog box of input parameter for tools. Move the cursor onto the PIN receiver icon on the workspace and Double-click the left mouse button. Or Click on the right mouse button. If you do so, a pop-folder appears. Move the cursor onto the Properties at the pop-folder and click on the left mouse button. Change the parameter of input parameter for the PIN receiver as you want and then click yes button. 2.3.4 Making connections between tools The next step is to connect the tools together. Our goal is to make the schematic as shown in Fig 2.3.4-1. AO Technology, 2002 17 Fig 2.3.4-1 Example schematic for making connections Put the cursor on the end point of the upper arrow for ESG(double)1. If you do so, the shape of the cursor changes from an arrow to a rectangular. Click on the left mouse button at that point. After clicking, if you were to move the cursor somewhere else, the shape of the cursor would change to a pencil and the line would continue to stretch to the new point. Move the cursor onto the start point of the upper arrow for MZ Mod 1. When the shape of the cursor changes from a pencil to a rectangular, click on the left mouse button. If the connection is established successfully between two points, a node will be generated at each point. Connect all the remaining parts as shown in Fig 2.3.4-1. 2.3.5 Copy and paste It is highly likely that after you compose a schematic, you will need to copy or paste it. To copy and paste follows the following three processes: AO Technology, 2002 18 Selecting the tool(s) or area(s) involved. Selecting a single tool: Click on the tool you want to copy. Notice it becomes highlighted in red to indicate that the tool is selected. Selecting multiple tools: Click and hold the left mouse button and then drag the cursor to create a rectangle. All the tools completely contained in the rectangle will become selected. Also, notice that they become highlighted in red to indicate that tools are selected. Copy what you select. There are three methods to copy what you select. Move the cursor onto one of the tools you select and click on the right mouse button. Then a pop-folder shows up, where click the Copy command. Click the Edit menu, where click the Copy command. Press Ctrl+C key. Paste what you copy. There are also three methods to paste. Move the cursor onto the empty workspace and click on the right mouse button. Then, a pop-folder shows up, where click the Paste command. When what you copy appear(s), move the cursor onto the position where you want to paste and click on the left mouse button to fix them (it). Click the Edit menu, where click the Paste command. If you move the cursor onto the workspace, what you copy appear(s). Move the cursor onto the position where you want to paste and click on the left mouse button to fix them (it). AO Technology, 2002 19 Press Ctrl+V key. When what you copy appear(s), move the cursor onto the position where you want to paste and click on the left mouse button to fix them (it). 2.4 Saving and loading your project created on the window To save a schematic, you can click the Save icon or use the key function Ctrl + S or choose the Save from the File menu. If it is a new schematic, you can enter a file name where the new schematic will be saved. To open your saved schematic, you can click the Open icon or use the key function Ctrl + O or choose the Open from the File menu. Fig. 2.4 -1 Save icon Fig. 2.4 -2 Open icon 2.5 Making your own projects or tools using input and output ports You can make your own projects or tools using input and output ports. First, you make a schematic that you want. If the schematic has the input (the output), input port (output port) is combined. Then, save the schematic and the new project item will appear in the tree. The new project item is dragged using the left button of mouse in the schematic window and you can make your own tools thorough this work. AO Technology, 2002 20 Fig. 2.5 -1 Schematic you have saved as port-test Fig. 2.5 2 Project port-test made newly in Project created by user folder of the tree Fig. 2.5 -3 Create your own tools or projects If you move the cursor onto project icon and double-click on the left mouse button, you can see the composition of projects. AO Technology, 2002 21 2.6 Simulating schematics If you made your own schematic, you can simulate it. To simulate that schematic, you can select the Analysis submenu from the Run menu. Then, the simulation starts and then the progress state can be shown in the status bar. The detail is described in section 2.1.8 Fig. 2.6 -1 Analysis submenu from the Run menu 2.7 Result windows The following sections 2.7.1~2.7.3 explain the windows displaying simulated results briefly. Fig 2.7-1 Example of result windows AO Technology, 2002 22 2.7.1 Result windows A result window shows calculated results and other parameters on each viewer after or during signal propagation through optical fibers. The result window in Fig 2.7.1-1 shows the eye diagram on the oscilloscope. Fig 2.7.1-1 Example of a result window eye diagram If you want to change the properties of the x or y axis, move the cursor onto x or y axis and double-click on the left mouse button. The input dialog box for properties of the axis of graph (look figure 2.7.2-3) will appear. And you can extend the region you want to watch in detail. Click and hold the left mouse button and then drag the cursor to create a rectangle on that region. Click to undo. There are lines, the meaning of lines and some values in the right side of the result window. When you double-click the line, input dialog box for properties of colors of graph (look figure 2.7.2-4) will appear. And double-clicking the values displays the information window showing the values. AO Technology, 2002 23 2.7.2 Menu in result widow Result window has three menus: File, Setting, and Window. File menu Fig 2.7.2-1 commands of File menu Export data into ASCII file: export calculated raw data into an ASCII file and store them in the location you indicate. Print: print the active window. Setting menu Fig 2.7.2-2 commands of Setting menu Axis: change the scaling, grid, title, and format of X or Y-axis using this command. AO Technology, 2002 24 Fig 2.7.2-3 Input dialog box of properties for the axis of graph Color: change the color of background or the name, color, type, thickness and text of the lines using this command. Fig 2.7.2-4 Input dialog box for properties of colors in graph AO Technology, 2002 25 Window menu Fig 2.7.2-5 commands of Window menu Cascade: display all of the result windows in cascade. Fig 2.7.2-6 Display of all the result windows in cascade AO Technology, 2002 26 Tile: display all of the result windows simultaneously in tile format. Fig 2.7.2-7 Display all the result windows in tile Windows: display the window you select. Fig 2.7.2-8 window of Window command AO Technology, 2002 27 2.7.3. Changing axes To change properties of axes, you can use the Axis command of the Setting menu or double-click the axis you want to change. Fig 2.7.3-1 Input dialog box for changing properties of axes Description of input dialog box for changing properties of axes Parameter Description Auto Scaling Auto scaling Scaling Manual Scaling Require minimum and maximum values Major Grids Show major grids Number of Major Number of major grid. Limited to 20. Minor Grids Show minor grids Grid Number of Minor Grids Number of minor grids per major grid. Limited to 4. Unit Unit of the value on the axis Engineering Form Represent the value on the axis in the engineering form (exponentially) Field Width Field width Precision Precision of the value on the axis Tile and Format Title of Axis Change the title and font of the axis AO Technology, 2002 28 3. Transmitter Models Transmitters convert electrical signals to optical ones for transmission through optical fibers. Distributed-feedback Bragg grating (DFB) lasers, Fabry-Perot (FP) lasers, electroabsorption modulator integrated (EAMI) DFB lasers, LiNbO3 external modulators, EAMI-DFB laser based tunable lasers, soliton pulses, and measured transmitter characteristics can be used in the transmitter for optical transmission systems. For optical components for transmitters, large signal analysis including the extinction ratio and the frequency chirping are modeled and used in Photonics CAD to generate optical pulses propagated through optical fibers. 3.1 Electrical signal generator 3.1.1 Electrical signal generator for dual electrodes Icon Theory The frequency characteristics of a raised cosine signal consists of a flat portion and a roll-off portion that has a sinusoidal form as follows:

\| < < =11 112 , 02 , 4 / 10 , 2 / 1) (f W f f W f f W f f Wf P (3.1.1-1) AO Technology, 2002 29 where the frequency parameter 1f and the bandwidth W are related by Wf11 = (3.1.1-2) The parameter is called the rolloff factor, which indicates the excess bandwidth over the ideal solution of the ideal Nyquist channel, W. The time response ) (t p is the inverse Fourier transform of the function ) ( f P . ( ) ( )|.|

\||.|

\|=2 2 216 12 cos22 sin) (t WWtWtWtt p (3.1.1-3) A super Gaussian shape can be used to model the effects of steep leading and trailing edges on dispersion-induced pulse broadening. The equation of a super Gaussian pulse is given by

||.|

\| =mTtt p2021exp ) ( (3.1.1-4) where m controls the degree of the edge sharpness. Input dialog box AO Technology, 2002 30 Fig. 3.1.1-1 Input dialog box of pulse shapes for electrical signal generator for dual electrodes Fig. 3.1.1-2 Input dialog box of parameters for electrical signal generator for dual electrodes AO Technology, 2002 31 Description of parameters for electrical signal generator for dual electrodes Parameter Description Default value / Units Data rate Data Rate 10 Gb/s No. of bits Total number of data bits 27 bits Data format Select a data format from NRZ, RZ, or Clock signal NRZ Raised Cosine Pulse Raised cosine shape as an output pulse shape - Super Gaussian Pulse Super Gaussian shape as an output pulse shape - Sine Pulse Sine shape as an output pulse shape - Square Pulse Square Pulse as an output pulse shape - Super Gaussian Factor Degree of edge sharpness of super Gaussian pulse 3 Pulse width ratio for the bit period Pulse width ratio for the bit period 1 Rolloff Factor Degree of edge sharpness of raised cosine pulse 1 Users PRBS PN sequence defined by user 0000100100110100111.. Automatic 5 bit delayed PRBS generation between channels Automatically generate 5 bit delayed PRBS between WDM channels - V1_offset Offset voltage of electrode 1 (Q) 0 V V2_offset Offset voltage of electrode 2 (Q bar) 2 V V1_pp Peak to peak voltage of electrode 1(Q) 2 V V2_pp Peak to peak voltage of electrode 2 (Q bar) 2 V Use duobinary precoder Use duobinary precoder for optical duobinary transmissions - AO Technology, 2002 32 3.1.2 Electrical signal generator for single electrode Icon Theory The theory of electrical signal generator for single electrode is described in 3.1.1. Input dialog box Fig. 3.1.2 -1 Input dialog box of pulse shapes in the electrical signal generator for single electrode AO Technology, 2002 33 Fig. 3.1.2 -2 Input dialog box of parameters for electrical signal generator for single electrode Description of parameters for electrical signal generator for single electrode Parameter Description Default value / Units Data rate Data Rate 10 Gb/s No. of bits Total number of data bits 27 bits Data format Select a data format from NRZ, RZ, or Clock signal NRZ Raised Cosine Pulse Raised cosine shape as an output pulse shape - Super Gaussian Pulse Super Gaussian shape as an output pulse shape - Sine Pulse Sine shape as an output pulse shape - Square Pulse Square Pulse as an output pulse shape - Super Gaussian Factor Degree of edge sharpness of super Gaussian pulse 3 Pulse width ratio for the bit period Pulse width ratio for the bit period 1 Rolloff Factor Degree of edge sharpness of raised cosine pulse 1 AO Technology, 2002 34 Users PRBS PN sequence inputted by users 00001001001101001111. Automatic 5 bit delayed PRBS generation between channels Automatically generate 5 bit delayed PRBS between WDM channels - V_offset Offset voltage of electrode 2 V V_pp Peak to peak voltage of electrode 2 V 3.1.3 Analog signal generator Icon 3.1.3.1 Multi-tone signal generator Theory The equation used for a single tone signal is ) f cos(2 A f(t)1 1 t = (3.1.3.1 -1) In order to generate multi-tone signals, signals should be combined using the multiplexer after each signal generation. Input dialog box AO Technology, 2002 35 Fig. 3.1.3.1 -1 Input dialog box of input parameters for multi-tone signal generator Description of parameters for multi-tone signal generator Parameter Description Default Value/Units No. of channels Number of channels for Analog signal generator 2 Channel spacing Channel spacing 1.25 MHz Oscillation frequency Oscillation frequency of channel 1 1851.25 MHz Avg. power Average power of one channel 25 dBm 3.2 Model of DFB laser 3.2.1 Complete DFB laser model from rate equations Icon AO Technology, 2002 36 Theory Single-wavelength semiconductor lasers undoubtedly play an important role as light sources for long-haul high-bit-rate optical communication systems both in direct intensity modulation and in wavelength division multiplexing (WDM) transmissions. In these systems, the light sources require superior spectral properties (spectral sharpness and stability) such as low wavelength chirping under high-speed modulation and narrow static spectral linewidth. A number of large-signal dynamic DFB laser models have been developed including the longitudinal spatial hole-burning (z-HB) and the gain saturation which affect the chirp behavior under direct current modulations. Among the models, a large-signal dynamic DFB laser one based upon the transfer matrix method (TMM) has the core capability to analyze various device structures. In Photonics CAD, large-signal analysis for DFB lasers is necessary with using the time dependant TMM to calculate optical pulse waveforms, the extinction ratio, and the frequency chirping in DFB lasers by self-consistently solving the pulse propagation equation and rate equations. The time dependent TMM has been proposed for the purpose of characterizing multi-electrode DFB lasers [3.2.1-1]. In order to simulate more realistic DFB lasers, the propagation part of the transfer matrix is modified using the pulse propagation equation that describes the propagation of pulses in DFB lasers. The evolution of slowly varying amplitude A(z, t) inside DFB lasers is governed by the pulse propagation equations [3.2.1-1, 2]: ) , ( ) , (21) , (2) , ( 1 ) , (t z t z gA t z A git t z Av z t z Amg + + =+ (3.2.1-1) where A(z, t) is the normalized pulse envelope such that |A(z, t)|2 represents the optical power, is the chirp parameter which accounts for carrier-induced index changes, vg is the group velocity, is the confinement factor, gm is the material gain, and g is the net gain. Seeding of the traveling-wave amplitudes can be done with the use of lumped AO Technology, 2002 37 spontaneous emission-type input flux (z, t): ) ( ) ' ( ) ' ( ) , ( cross w g SP A E v z z t t R t z = (3.2.1-2) where is the spontaneous coupling factor, RSP the spontaneous emission rate assuming bimolecular recombination (c 2 N 2 ), (x) the function, EW the photon energy, and Across the cross sectional area of the active layer. To consider the interaction between the carrier density N and the photon density S, the cavity is divided into a number of small sections, and the rate equation is solved in each section as i i m g i i iiS g v N c N c c NqVItN + + =) (23 2 1 (3.2.1-3) where index i corresponds to a different section, I is the injection current, V is the active volume, q is the electronic charge, and c1 , c2 , and c3 are related to recombination constants. The average photon density S i is calculated by cross gi i i iiA E v B B A AS2| | | | | | | |212 212+ + + + += (3.2.1-4) where Ai is the amplitude of forward-traveling wave and Bi that of backward-traveling wave. In order to model the asymmetric gain profile, the gain spectrum is assumed to be cubic and the material gain is approximated to ( )Sa N N aN g p ii i m + =1) ( ) (,21 0 0 (3.2.1-5) where a0 and a1 are the gain constants, p is the gain peak wavelength assumed to shift linearly with the carrier density, and is the gain compression factor. The net gain is given by: AO Technology, 2002 38 loss i m i g g = (3.2.1-6) The effective refractive index is related to the carrier density by N a n n eie 0 04 = (3.2.1-7) where neo is the refractive index without current injection. The lasing wavelength is obtained by the minimizing technique on | a22 | where a22 is an element of the overall transfer matrix for the structure given by the product of the subsection transfer matrices. The Bragg wavelength is obtained from [3.2.1-2]. 000 BeeB Bnn + = (3.2.1-8) where B0 is the Bragg wavelength when the current is not injected and en the average of the carrier-induced index changes for the whole structure given by [3.2.1-2]. = i i eSe N nNn ) (1 (3.2.1-9) The summation is carried out all over the subsections, where NS is the total number of subsections. A rectangular effective refractive index profile in a DFB structure is shown in Fig. 3.2.1-1. The coupling coefficient of the structure and the Bragg wavelength given by the Bragg condition are obtained by [3.2.1-3]-[3.2.1-5]: effn l n n2) (1 2 = ,m l neffB4= (3.2.1-10) AO Technology, 2002 39 ...ieffn2effn1effn1 peffn peffnARn HRn... .. .. .. .. M..2= l in2in1) (z nz+ = =) 1 () 1 (, , 2, , 1l n n l n ni eff ii eff i Fig. 3.2.1-1 Grating structure in DFB lasers where m is the Bragg order considered equal to 1 in this connection, and 2 / ) (2 1 n n neff + = . It is obvious that when the parameters , B, and neff of a structure are given, n1, n2 , and l, the parameters of equivalent periodic structure can be found from Eq. (3.2.1-10). ni-1 Ni-1gm, i-1ni Nigm, ini+1 Ni+1gm, i+1 ARLOutput signalPSIG atSIGHR Ai-1(t) Bi-1(t) Ai (t) Bi (t) Ai+1(t) Bi+1(t) Fig. 3.2.1-2 Schematic of the modified TMM-based dynamic DFB laser model In order to perform a dynamic analysis of DFB lasers, a model based on TMM is developed by using the modified transfer matrix: AO Technology, 2002 40

+

=

+ +) 1 () () (1) () () () () () ( ) () () () (22 222122122221 1211t E t Et a t a t a t a t at a t a t at at t E t t EBABA (3.2.1-11) Fig. 3.2.1-2 shows the schematic of the modified TMM-based dynamic DFB-laser model. Assuming that various material and structural parameters remain unchanged throughout section i in a time from t to t+t, the output amplitudes A i+1 and B i at time t+t can be calculated from the input amplitudes A i and B i+1 at time t by Eq. (3.2.1-11). Transfer matrix elements amn(t) of a section i are obtained from ni, Ni, gmi, and i at time t. Typical buried-heterostructure (BH) DFB-LD operating at 1.55m is considered in this simulator. Also, 1.3m DFB lasers can be modeled by changing some material parameters explained in below. Calculated and measured pulse pattern and chirp are shown below Fig. 3.2.1.-4 and Fig.3.2.1.-5. These calculated results are similar to the measured data. Fig. 3.2.1-3 Calculated pulse shapes and chirping in DFB lasers AO Technology, 2002 41 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4-0.06-0.030.000.030.060.090.12Wavelength Chirp [nm] Time [ns] Optical Power [Arb. Unit] Fig. 3.2.1-4 Measured pulse shapes and wavelength chirping in DFB lasers 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4-0.06-0.030.000.030.060.090.12Wavelength Chirp [nm] Time [ns] Optical Power [Arb. Unit] Fig. 3.2.1-5 Calculated pulse shapes and wavelength chirping in DFB lasers If you want to simulate at 1300nm wavelength range, the above parameters should be modified in the simulation. The modified parameters are the Gain peak wavelength and the Delta n_12. The gain peak wavelength is changed from 1580 to 1330nm. The Delta n_12 is changed from 0.001725 to 0.0006915. Fig. 3.2.1-6, 7, and 8 show the input dialog box of the device and material parameters, and simulation conditions. You can easily change the default values in the AO Technology, 2002 42 input dialog box. Input dialog box Fig. 3.2.1-6 Input dialog box for physical parameters in the complete DFB laser AO Technology, 2002 43 model from rate equations Fig. 3.2.1-7 Input dialog box for material parameters in the complete DFB laser model from rate equations AO Technology, 2002 44 Fig. 3.2.1-8 Input dialog box for other parameters in the complete DFB laser model from rate equations Description of parameters for Complete DFB lasers model from rate equation Parameter Description Default Value / Units Grating period Half length of a grating pitch 0.1125 m AO Technology, 2002 45 Delta n (real) Real part of differential refractive index -0.001 Delta n (imag) Imaginary part of differential refractive index 0.001 Average n_eff Average refractive index (n1+n2)/2 3.45 Active layer width Active layer width of DFB laser 1.5 m Active layer thickness Active layer thickness of DFB laser 0.12 m Optical confinement factor Optical confinement factor 0.3 R_front_facet Front facet reflectance 1 % R_rear_facet Rear facet reflectance 70 % Phase_front_facet Grating phase of front facet 0 deg. Phase_rear_facet Grating phase of rear facet 150 deg. Ao Material gain constant 2.5 10-20 m2 A1 Material gain constant 1.5 1019 m-3 A2 Material gain constant 2.7 10-32 m4 No Carrier density at transparency 9 1023 m-3 Eff. Loss Effective loss ( loss ) 2500 m-1 C1 Recombination rate 2500000 s-1 C2 Recombination rate 1 10-16 s-1 C3 Recombination rate 3 10-41 s-1 Alpha parameter Alpha parameter ( ) 5 Wavelength for peak gain Gain peak wavelength ( peak ) 1.58 10-6 m Gain compression factor Nonlinear gain compression factor ( ) 1.5 10-23 m3 Length of section Length of each divided section 22.5 um No. of divided sections Number of sections in DFB laser 20 I_bias Bias current of steady state condition 0 mA Electrical confinement factor Electrical confinement factor 0.9 Fiber coupling loss Fiber coupling loss 1 dB Impedance Matching impedance for DFB laser 50 ohm AO Technology, 2002 46 References [3.2.1-1] M. G. Davis and R. F. ODowd, "A Transfer Matrix Method Based Large-Signal Dynamic Model for Multi- electrode DFB Lasers," IEEE J. Quantum Electron., vol. 30, pp. 2458-2466, Nov. 1994. [3.2.1-2] G. P. Agrawal and N. A. Olsson, Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers, IEEE J. Quantum Electron., vol. 25, pp. 2297-2306, Nov. 1989. [3.2.1-3] Gunnar Bjork and Olle Nilsson, A New Exact and Efficient Numerical Matrix Theory of Complicated Laser Structures: Properties of Asymmetric Phase-Shifted DFB Lasers, J. Lightwave Technol., vol. LT-5, pp. 140-146, Jan. 1987. [3.2.1-4] Hans Bissessur, Effects of Hole Burning, Carrier-Induced Losses and the Carrier-Dependent Differential Gain on the Static Characteristics of DFB Lasers, J. Lightwave Technol., vol. 10, pp. 1617-1630, Jan. 1992. [3.2.1-5] Orfanos, Thomas Sphicopoulos, A. Tsigopoulos, and C. Caroubalos, A tractable above-threshold model for the design of DFB and Phase-shifted DFB lasers, IEEE J. Quantum Electron., vol. 27, pp. 946-956, 1991. 3.2.2 Analytical DFB laser model Icon Theory The complex electrical field E(t) at the laser output is given by )] ( ) ( exp[ ) , ( ) , (0 t t j x t A z t E c + = (3.2.2-1) AO Technology, 2002 47 =k k z kT t g a P z t A ) , ( ) , ( (3.2.2-2) where A(t) is the field envelope, 0 is the optical carrier frequency, P1 is the optical peak power for a "1" pulse , T is the pulse duration, and ak is the pseudorandom bit sequence (PRBS) taking values of "0" and "1". The chirp of transmitters using DFB lasers is analyzed by using the time dependent phase ) (t in Eq. (3.2.2-1). For directly modulated lasers, the time-dependent frequency change ) (t f (chirp) is given in terms of optical power as ) ) 0 , ( ln (4) (2= = z t Edtdt f (3.2.2-3) where is the linewidth enhancement factor. For semiconductor lasers, the -parameter varies between 2 and 8, depending on the laser structure. Integration of the instantaneous frequency yields the phase used in Eq. (3.2.2-1). .2) ( ln2) ( 2 ) ( = = t E dt t f t (3.2.2-4) The A(t,z) is used for the non-linear Schrodinger equation to calculate pulse distortions. Fig. 3.2.2-1 Calculated pulse shapes and chirping from the analytical DFB laser model using the Super Gaussian pulse shape AO Technology, 2002 48 Input dialog box Fig. 3.2.2 -2 Input dialog box of parameters for the analytical DFB laser Description of parameters for analytical DFB laser Parameter Description Default value / Units Lasing wavelength Lasing wavelength 1.55 m Average power Average power of laser output 0 dBm Chirp parameter Chirp parameter 5 Extinction ratio Extinction ratio 10 dB References [3.2.2-1] M.Schiess, Chirp and Dispersion Compensation in Nonlinear Fibers for High Bit-Rate IM/DD Systems, ECOC, Paper We18, pp. 481-484, 1994. [3.2.2-2] Govind P. Agrawal, Nonlinear Fiber Optics, 2nd, Academic Press. AO Technology, 2002 49 3.2.3 Ideal DFB laser model for CW sources Icon Theory The output of the ideal DFB laser model is considered to be continuous wave (CW). Therefore a time dependent field E(t) can be obtained from the below Eq. (3.2.3-1). ) 2 exp( ) ( t f j P t E c = (3.2.3 -1) where P is the average power, and cf is the carrier frequency which can be obtained from the lasing wavelength. Input dialog box Fig. 3.2.1 -1 Input dialog box of parameters for the ideal DFB laser model AO Technology, 2002 50 Description of parameters for ideal DFB laser model Parameter Description Default value / Units Lasing wavelength Lasing wavelength 1.55 m Optical output power of laser Average power of laser output 0 dBm 3.3. Time domain Fabry-Perot laser model Icon Theory With the advantage of relative low-cost, multi-longitudinal Fabry-Perot laser diodes are widely used in optical communication systems. However, the multi-mode characteristics limit the speed or the distance in transmission and the spontaneous emission noise can trigger the laser to oscillate in side-modes under intensity modulation conditions [3.3-1], [3.3-2]. Even though the transient response of laser diodes has been widely reported, most studies are concentrated on single mode laser diodes for high-speed communications. Also some published reports treated multi-longitudinal laser diodes dealt with them as nearly single mode cases [3.3-3]-[3.3-5]. Besides, the frequency chirp usually investigated in single mode lasers to understand the broadening of a propagating pulse in high-speed transmission has been of relatively low interests in multi-mode laser diodes [3.3-6]-[3.3-8]. In the view of the gain spectrum, the frequency shift (chirp) of modes can AO Technology, 2002 51 change the effective gain. The random spontaneous noise term, an important factor for multi-mode excitation, needs to be included in the simulation and should be considered as a stochastic process. The laser cavity is split into uniform sections with the forward and reverse propagating electric fields which have amplitude and phase information. Within a section all the relevant parameters are assumed to be homogeneous. A restriction on the sections is that they must all have the same length z = vg t. The forward and reverse input fields in section i at a given time t become ] 1 [ ] 1 [ ] [1 + = t rR t tF t F i ii (3.3-1) ] 1 [ ] 1 [ ] [1 + = +t rF t tR t R i ii (3.3-2) where r is the reflection coefficient and t is the transmission coefficient. Fi-1[t-1] and Ri+1[t-1] are the forward and reverse output fields in sections i-1 and i+1, respectively, at time t-1. In a time domain model [3.3-9], the output fields of a digital filter are given by the convolution of input field and impulse response h[n] of the filter. = =0] [ ] [ ] [n i i n h n t F t F (3.3-3) = =0] [ ] [ ] [n ii n h n t R t R (3.3-4) The frequency-dependent gain at the center gain frequency 0 with the section length L is modeled using the second order Lorentzian digital filter which has a peak amplitude gain } 2 / ) ) ( ( exp{ ) (0 0 L N t N b g i = (3.3-5) where b and are the differential gain and confinement factor, respectively, and N0 is the transparency carrier density. The phase shift term caused by changes in carrier density is multiplied to the amplitude gain. The phase shift calculated from the carrier density AO Technology, 2002 52 and the - parameter is given by 2 / ) (t LN b i = (3.3-6) Nonlinear gain is also included with the use of the gain compression factor (1+S) where =210-17cm3. To find an effective refractive index and a confinement factor depending on the structure of laser diodes in a section, the effective index method is used [3.3-10]. The effective index method is included in Photonics CAD to calculate modes in dielectric waveguides in chapter of device viewer. The effective refractive index and the confinement factor have been calculated to be 3.26 and 0.32, respectively. The effective refractive index is changed by the variation of carrier density with the relation of [3.3-11] ) 1 ( ) 1 , ( ) , ( + = t NdNdnt i n t i n i eff eff (3.3-7) The photon density Si[t] in section i and the output power P(t) from the right-hand side facet are given by hv t R t F t S i i i/ ) ] [ ] [ ( ] [2 2+ = (3.3-8) gv t S d w hv t P ] [ ) ( = (3.3-9) where h is the average photon energy, w the width, and d the depth of the active layer in lasers. The dynamics of a semiconductor laser are modeled by the noise driven rate equation for carrier density. ] [ 1) ( ) ) ( () ) ( ) ( ) ( () (0 3 2t S t S N t N b vt CN t BN t ANqVIdt t dNii i gi i ii + + + = (3.3-10) The random spontaneous emission process [3.3-12], [3.3-13] is modeled by the Gaussian white noise term (t) with zero mean and correlation = (t-t)nspb(Ni(t)-N0)h. It yields the mean photon number emitted by spontaneous emission and fluctuation. The effect of radiative and nonradiative carrier generation and recombination noise in the rate equation for Ni(t) is neglected since it is negligible AO Technology, 2002 53 compared with the photon density fluctuations. Calculated pulse patterns and chirp: 0 2 4 6 8 10 12 14 16 181.00E+0181.20E+0181.40E+0181.60E+0181.80E+0182.00E+018time (nsec)Carrier Density (cm-3)05101520Output Power (mW) Fig. 3.3-1 Pulse pattern and carrier density of FP lasers 0.0 0.5 1.0 1.5 2.0 2.5-400-2000200current pulse mode 1 mode 2 mode 3 mode 4 mode 5Frequency (GHz)time (nsec) Fig. 3.3-2 Frequency change of each mode in FP lasers during modulations AO Technology, 2002 54 Calculated analog signals: TimeOptical powerInjection current Fig. 3.3-3 Optical pulse shape of FP lasers output with the injection current Input dialog box Fig. 3.3-4 Input dialog box of parameters for the FP laser model for digital links AO Technology, 2002 55 Fig. 3.3-5 Input dialog box of material parameters for the FP laser model Description of modeling parameters used for FP lasers Parameter Description Default value / Units Lasing Wavelength Lasing wavelength 1.31 m No. of divided sections Number of divided sections 10 Cavity length Laser cavity length 300 m Active layer width Active layer width 1 m Active layer thickness Active layer thickness 0.15 m Front facet reflectance Front facet reflectance 0.3 Rear facet reflectance Rear facet reflectance 0.7 Injection current Injection current 10 mA Laser impedance Laser impedance 50 AO Technology, 2002 56 C1 Recombination rate 1 108 s-1 C2 Recombination rate 1 10-10 m3s-1 C3 Recombination rate 3 10-29 m6s-1 No Transparency carrier density 1 1018 cm-3 Alpha parameter The -parameter 5 Effective Loss Effective waveguide loss 20 m-1 References [3.3-1] M. M. Choy, P. L. Liu, and S. Sasaki, Origin of modulation-induced mode partition and Gb/s system performance of highly single mode 1.5m distributed feedback lasers, Appl. Phys. Lett., vol. 52, pp. 1762-1764, 1988. [3.3-2] J. C. Cartledge and A. F. Elrefaie, Threshold gain difference requirements for nearly single-longitudinal-mode lasers, J. Lightwave Technol., vol. 8, pp. 704-715, 1990. [3.3-3] A. Valle, P. Colet, L. Pesquera, and M. San Miguel, Transient multimode statistics in nearly single-mode semiconductor lasers, IEE Proc. Part J, vol. 140, pp. 237-242, 1993. [3.3-4] J. C. Cartedge, On the probability characterization of side mode fluctuations in pulse-modulated nearly single-mode semiconductor lasers, IEEE J. Quantum Electron., vol. 26, pp. 2046-2051, 1990. [3.3-5] A. Mecozzi, A. Sapia, P. Spano, and G. Agrawal, Transient multimode dynamics in nearly single-mode lasers, IEEE J. Quantum Electron., vol. 27, pp. 332-343, 1991. [3.3-6] J. C. Cartledge, G. S. Burley, The effect of laser chirping on lightwave system performance, J. Lightwave Technol., vol. 7, pp. 568-573, 1989. [3.3-7] O-K. Kwon, J-I. Shim, The effects of longitudinal gain distributions on the static and the dynamic properties in a /4 phase-shifted DFB laser, IEEE J. AO Technology, 2002 57 Quantum Electron., vol. 34, pp. 225-232, 1998. [3.3-8] B. W. Hakki, Evaluation of transmission characteristics of chirped DFB lasers in dispersive optical fiber, J. Lightwave Technol., vol. 10, pp. 964-969, 1992. [3.3-9] D. D. Marcenac and J. E. Carroll, Quantum-mechanical model for realistic Fabry-Perot lasers, IEE Proc. Part J, vol. 140, pp. 157-171, 1993. [3.3-10] J. Buus, The effective index method and its application to semiconductor lasers, IEEE J. Quantum Electron., vol. 18, pp. 1083-1089, 1982 [3.3-11] K. Inoue, Blue frequency shift due to external light injection in a distributed-feedback laser diode, Appl. Phys. Lett., vol. 67, pp. 1518-1520, 1988. [3.3-12] A. E. Siegman, Excess spontaneous emission in non-Hermitian optical systems. I. Laser amplifiers, Phys. Rev. A, vol. 39, pp. 1253-1263, 1989. [3.3-13] A. E. Siegman, Excess spontaneous emission in non-Hermitian optical systems. II. Laser oscillators, Phys. Rev. A, vol. 39, pp. 1264-1268, 1989. A. E. Siegman, Excess spontaneous emission in non-Hermitian optical systems. II. Laser oscillators, Phys. Rev. A, vol. 39, pp. 1264-1268, 1989. [3.3-14] Jeungyun Ko, Yunbum Kim, Hyunjae Yoon, Insik Park and Jichai Jeong "Missing modes in 1.3um InGaAsP/InP uncooled Fabry-Perot lasers and their effect on Transmission," accepted for Optical and Quantum Electronics AO Technology, 2002 58 3.4 Model of LiNbO3 external modulators 3.4.1 Ideal LiNbO3 external modulator Icon Theory When ) (1 t v and ) (2 t v are applied to each electrode of the Mach-Zehnder type LiNbO3 external modulator, the modulator output electric field is expressed by [3.4.1 -1]. ||.|

\|+||.|

\|= V t v j EV t v j EEout) (exp2) (exp22 0 1 0 (3.4.1 -1) where 0E the incoming electric field and V the switching voltage of the modulator. It is assumed that the device is biased at the midpoint of its transfer characteristic curve. Fig. 3.4.1 1 Calculated output pulse shape of the ideal LiNbO3 external modulator AO Technology, 2002 59 Input dialog box Fig. 3.4.1 -2 Input dialog box of ideal LiNbO3 external modulator Description of parameters for ideal LiNbO3 external modulator Parameter Description Default value / Units Switching Voltage Switching voltage of modulator (V ) 4 V Asymmetry Ratio Power ratio divided between upper and lower arm 1 References [3.4.1 -1] SungKee Kim and Jichai Jeong, "Transmission performance on frequency response of receivers and chirping shape of transmitters for 10 Gb/s LiNbO3 modulator based lightwave systems," Optics Comm., vol.175, pp.109-123, 2000. AO Technology, 2002 60 3.4.2 Analytical LiNbO3 external modulator Icon Theory The linewidth enhancement factor or chirp parameter, can be expressed by two methods: one is proposed by Koyama and Iga [3.4.2 -1], and the other is calculated by the voltage ratio applied to both electrodes [3.4.2 -2]. The two chirp parameters are given by Model 1 : ) () () ( 2t dSdtdtt dt S = (3.4.2 -1) and Model 2 : B AB AV V V V+= ~ (3.4.2 -2) where (t) and S(t) are the instantaneous phase and intensity of the optical output, and VA and VB are peak voltages applied to A and B electrodes, respectively. In the case of chirping model 1, by the definition of the chirp parameter in Eq. (3.4.2 -1), the electric field of the modulator output is given by ( )) () (120cos cos | | t dSt Sjjout out e t E e E E = = (3.4.2 -3) From the definition of m and ~ in Eq. (3.4.2 -2), the electric field of modulator output for chirping model 2 is ( )} cos~4 4{0cos cos~ t m jout e t E E = (3.4.2 -4) AO Technology, 2002 61 Fig. 3.4.2 -1 Calculated output pulse shape and chirping. Chirping model 1 is used for the negative chirp parameter with the extinction ratio of 12dB Fig. 3.4.2 -2 Calculated output pulse shape and chirping. Chirping model 2 is used for the negative chirp parameter with the extinction ratio of 12dB AO Technology, 2002 62 Input dialog box Fig. 3.4.2 -3 Input dialog box of parameters for the analytical LiNbO3 external modulator model Description of parameters for analytical LiNbO3 external modulator Parameter Description Default value / Units Chirp Model 1 Chirping model 1 (Eq. 3.4.2 -1) - Chirp Model 2 Chirping model 2 (Eq. 3.4.2 -2) - Modulation Model 1 Raised cosine shape as an output pulse shape of LiNbO3 modulator - Modulation Model 2 Super Gaussian shape as an output pulse shape of LiNbO3 modulator. - Chirp Parameter -parameter 0 Extinction Ratio Extinction ratio 12 dB Insertion Loss Insertion loss by LiNbO3 modulator 3 dB Super Gaussian factor Parameter which controls the degree of edge sharpness of super Gaussian pulse 3 AO Technology, 2002 63 References [3.4.2 -1] F. Koyama and K. Iga, Frequency chirping in external modulators, J. Lightwave Technol., vol. 6, pp. 87-92, 1988. [3.4.2. -2] A. H. Gnauck, S. K. Korotky, J. J. Veselka, J. Nagel, C. T. Kemmerer, W. J. Minford, and D. T. Moser, Dispersion penalty reduction using an optical modulator with adjustable chirp, IEEE Photon. Technol. Lett., vol. 3, pp. 916-918, 1991. 3.4.3 Measured LiNbO3 external modulator Icon Theory From measured characteristics of LiNbO3 external modulators, the optical output pulse can be determined by the measured extinction ratio and the measured rise/fall times. Fig. 3.4.3 -2 Calculated output pulse shape and chirping. Chirping model 1 is used for 0.1peak chirp with the extinction ratio of 12dB AO Technology, 2002 64 Fig. 3.4.3 -3 Calculated output pulse shape and chirping. Chirping model 2 is used for 0.1peak chirp with the extinction ratio of 12dB Input dialog box Fig. 3.4.3 -4 Input dialog box of parameters for the measured LiNbO3 external modulator model AO Technology, 2002 65 Description of parameters for analytical LiNbO3 external modulator Parameter Description Default value / Units Chirp Model 1 Chirping model 1 (Eq. 3.4.2 -1) - Chirp Model 2 Chirping model 2 (Eq. 3.4.2 -2) - Extinction Ratio Extinction ratio 12 dB Peak Chirp Peak chirp; for positive chirp input positive value, and for negative chirp input negative value 0.1 Rise/Fall Time Rise and fall times of output pulse 45 ps Insertion Loss Insertion loss by LiNbO3 modulator 3 dB 3.5 EAMI-DFB lasers In recent years, electroabsorption modulators have been attractive as transmitters for high bit rates and long haul optical fiber transmission systems because they have some advantages not only of a small negative chirp but also of the compactness and polarization control elimination through the monolithic integration with a DFB laser. 3.5.1 Complete EAMI-DFB laser model from rate equations Icon Theory Large signal chirp in electro-absorption modulators integrated with distributed AO Technology, 2002 66 feedback (EAMI-DFB) laser are caused by the combination of the two phenomena. One is the phase modulation in a modulator (= intrinsic modulator chirp). It is due to the refractive index change induced by variation of the absorption coefficient. It affects the wavelength shift at the rising and falling edges. The other is the lasing wavelength shift in a laser since the carrier density fluctuates by the optical feedback and the electrical coupling (= laser chirp) [3.5.1-1], resulting in a difference of the lasing wavelengths between a mark power level and a space power level. Fig. 3.5.1-1 shows the structure of EAMI-DFB lasers [3.5.1-10]. Along the longitudinal direction, a DFB laser is integrated with a modulator including a waveguide region. Fig. 3.5.1-2 is schematically illustrating the wave propagation in EAMI-DFB lasers. It is possible for the time dependent TMM to involve not only forward traveling waves but also backward reflected waves, and to consider the spatial hole burning, as the overall structure is divided into a number of small sections. HR coatingRLDI biasV modAR coatingRmodLLDLmodLtrDFB laser Waveguide modulator+ Vbias frisolation Fig. 3.5.1-1 Schematic showing cross-sectional view of an EAMI-DFB laser AO Technology, 2002 67 ... ...Ai-1 Ai Ai+1Bi+1 Bi Bi-1 Fig. 3.5.1-2 Schematic illustrating wave propagation on the time-dependent TMM-based large signal dynamic EAMI-DFB model The DFB laser can be modeled by interpreting grating structure with the transfer matrix [3.5.1-2]. In section 3.2.1, the DFB model is explained in detail. To apply TMM to the modulator as well as the laser, we modify the propagation part of the transfer matrix as follows ) t , z ( A ) i 1 (21t) t , z ( Av1z) t , z ( Achirpg =+ (3.5.1-1) where A(z,t) is the normalized pulse envelope such that |A(z,t)|2 represents the optical power, vg is the group velocity, and is the confinement factor. The chirp parameter is defined by [3.5.1-3]. ) V , () V , ( n 4) V , (chirp = (3.5.1-2) The absorption spectrum is assumed to be the Lorentzian function rather than calculating the exact absorption spectrum by the Schrdinger equation [3.5.1-4]. The absorption coefficient depends on wavelengths and drive voltages due to the quantum-confined Stark effect. 2 2p2p) 2 / ) V ( ( )) V ( () 2 / ) V ( ( ) V () V , ( + = (3.5.1-3) where p(V) is the peak absorption coefficient { p(V) = 0 (1+V/24) }, p(V) represents the wavelength with the peak absorption coefficient { p(V) = p0 410-9V }, and (V) stands for the spectral broadening { (V) = (10-1.28V3)10-9 }. The change of refractive index can be calculated from the change of the absorption AO Technology, 2002 68 coefficient through the Kramers-Kronig relation [3.5.1-5]. = d) V , (P2) V , ( n2 2 22 (3.5.1-4) where symbol P represents the Cauchy principal value. Fig.3.5.1-3 shows calculated absorption coefficients and refractive index changes (n) as a function of applied voltage with Eq.(3.5.1-3) and (3.5.1-4). When the applied voltage is higher than 0.5 V, n increases by decreasing the drive voltage. In this case, the chirp parameter becomes positive, as expected from Eq.(3.5.1-2). However, when the applied voltage is lower than 0.5 V, n reduces by decreasing the drive voltage and the chirp parameter becomes negative. -4 -2 0 2050000100000150000200000250000300000Applied Voltage [V]Absorption Coefficient [/m]-0.008-0.006-0.004-0.0020.0000.0020.0040.0060.008 n Fig. 3.5.1-3 Calculated absorption coefficient (solid line) and refractive index change (n) (dotted line) in modulators as a function of bias voltage In the waveguide region, the absorption was ignored since it was not important to determine large signal chirp, and the refractive index was linearly interpolated between the refractive index of the laser section and the modulator section. The length of a AO Technology, 2002 69 waveguide region plays a significant role in changing the laser chirp since the phase of optical wave shifts through the waveguide region. The reflectivity at the end of the laser section has a phase term since it is very difficult to control the grating phase at the end of DFB lasers. It is also a very important parameter determining characteristics of large signal chirp in the laser section. In addition, the drive voltage of modulators changes the bias current of the laser due to imperfect isolation between the laser and the modulator. We include the effect of electrical coupling with containing isolation resistance as shown in Fig. 3.5.1-1 [3.5.1-6]. For example, the modulator drive voltage of 2 V and isolation resistance of 2 k causes the leakage current of 1mA from the modulator to the laser. In order to perform a dynamic analysis of EAMI-DFB la