BandSOLVE 4.2
RSoft Design Group, Inc.
400 Executive Blvd. Ste 100
Ossining, NY 10562 USA
ph: 1.914.923.2164
fax: 1.914.923.2169
info@rsoftdesign.com
www.rsoftdesign.com
Copyright © 1993-2010
All Rights Reserved.
REVISON A
BandSOLVE 4.2 iii
Contents
Preface 1
Foreword.................................................................................................................................... 1
How to Read This Manual.........................................................................................................1
Notices....................................................................................................................................... 3
Chapter 1: Introduction 5
1.A. Program Installation & System Requirements................................................................... 5
1.B. Physical Conventions.........................................................................................................5
1.C. Program Executables..........................................................................................................6
1.D. Program Operation.............................................................................................................6
1.D.1. GUI Program Operation ...................................................................................6
1.D.2. CLI Operation................................................................................................... 8
1.E. Simple Tutorial - Propagation in a photonic crystal waveguide......................................... 8
1.E.1. Photonic crystal T-junction............................................................................... 8
1.E.2. Explaining the results........................................................................................ 9
2.B. Applying BandSOLVE .....................................................................................................9
1.F. Example Files ................................................................................................................... 12
1.G. README Files................................................................................................................ 12
1.H. Product Support & Upgrades ........................................................................................... 12
Chapter 2: Theory of photonic band structures 13
2.A. Geometry of periodic structures.......................................................................................13
2.A.1. The reciprocal lattice ......................................................................................15
2.A.2. The first Brillouin zone................................................................................... 15
2.B. Theory of band structures.................................................................................................16
2.B.1. Bloch’s theorem..............................................................................................16
2.B.2. Eigenvalue formulation of Maxwell’s equations ............................................ 17
2.B.3. Band structures, band gaps and their meanings ..............................................18
2.B.4. Reduced and projected band structures........................................................... 20
2.C. Scaling laws .....................................................................................................................20
2.D. Polarization ......................................................................................................................21
2.E. Parity ................................................................................................................................21
2.F. Numerical approaches ......................................................................................................22
2.F.1. Limitations of the PWE................................................................................... 22
2.G. Further reading................................................................................................................. 23
Chapter 3: Creating periodic structures in the RSoft CAD 25
3.A. Array Layout Utility and lattice vectors in the CAD .......................................................25
3.A.1. Creating a hexagonal array .............................................................................26
3.A.2. 2D X-Y lattices............................................................................................... 27
3.A.3. Photonic crystal fibers ....................................................................................28
BandSOLVE 4.2 iv
3.A.4. Selecting elements in multiple-Y layers .........................................................29
3.B. Layout of 3D structures.................................................................................................... 29
3.B.1. Cubic lattice of spheres................................................................................... 29
3.B.2. Viewing the 3D index profile..........................................................................30
3.B.3. FCC and BCC lattices of cubes.......................................................................30
3.B.4. Woodpile lattice..............................................................................................30
3.C. Specifying 1D and 2D periodic structures using formulae or data files........................... 30
3.C.1. Creating a 1D user profile............................................................................... 30
3.C.2. Creating a 2D user profile............................................................................... 31
3.D. Index cut planes ............................................................................................................... 31
3.E. Using lattice vectors and coordinate orientations effectively........................................... 31
3.E.1. Defining lattice vectors ................................................................................... 32
3.E.2. Other variables ................................................................................................32
3.F. References .......................................................................................................................33
Chapter 4: Using BandSOLVE: creating band structures 35
4.A. Generating a 2D band structure .......................................................................................35
4.A.1. Laying out the photonic crystal design ........................................................... 36
4.A.2. Selecting BandSOLVE as the design tool ...................................................... 36
4.A.3. Choosing the BandSOLVE numerical method ...............................................36
4.A.4. Choosing the number of dimensions ..............................................................37
4.A.5. Defining the lattice properties ........................................................................37
4.A.6. Lattice resolution and numerical properties.................................................... 40
4.A.7. Choosing the number of bands ....................................................................... 41
4.A.8. Choosing the wavevector k-path.....................................................................41
4.A.9. Choosing the polarization of the calculation ..................................................43
4.A.10. Activating mode output and other features................................................... 43
4.A.11. Starting the calculation .................................................................................43
4.B. Other controls................................................................................................................... 44
Chapter 5: Using BandSOLVE II: analyzing and controlling output 47
5.A. Creating and viewing mode profiles ................................................................................ 47
5.A.1. Generating the band structure......................................................................... 48
5.A.2. Selecting modes..............................................................................................48
5.A.3. Viewing modes...............................................................................................52
5.B. Other features of the Output dialog.................................................................................. 55
5.B.1. Analysis and diagnostics................................................................................. 56
5.B.2. Auxiliary .........................................................................................................59
5.B.3. Units................................................................................................................ 59
5.B.4. Plotting............................................................................................................59
5.B.5. Filters .............................................................................................................. 60
5.B.6. Logging........................................................................................................... 60
5.B.7. References.......................................................................................................60
Chapter 6: Advanced topics 61
6.A. Inversion symmetry ......................................................................................................... 61
6.A.1. Ensuring validity.............................................................................................61
6.B. Advanced numerical options............................................................................................62
6.B.1. Index profile settings.......................................................................................62
6.B.2. Finding modes of definite parity..................................................................... 64
6.B.3. Mode seeding..................................................................................................65
6.C. Adjustable K-path symmetry points................................................................................. 66
6.D. Equi-frequency contours, band surfaces and dispersion engineering ..............................67
6.D.1. Activating Full Zone analysis.........................................................................68
