A MODEIG UTILITY

where F(x) and G(x) are complex electric-field functions.

OVERLAP has been redesigned so that up to 20 correlations against any one set of data may be performed in one run of the program. Double-click the OVERLAP icon. Upon running the program, OVERLAP will first ask you the "reference filename." This is the file against which all correlations will be performed. (Note: If you are using the regular version of OVERLAP, all files must be MODEIG near-field files!)

Next, you must input the number of correlations that you wish OVERLAP to perform (maximum of twenty). Then, enter each filename, followed by a 'return.' When the number of filenames agrees with the number of correlations, OVERLAP will continue.

Finally, you must tell OVERLAP where you wish the output to be written. Enter a filename or hit 'return' to have the output sent to the screen. (Warning: Any file having the same name as the destination file will be overwritten!)

A sample run of the program is listed below. Boldface signifies user input.

DATA1_NFIELD

INPUT NO. OF COMPARISONS (MAX=20 DEFAULT=1)

3

INPUT COMPARISON FILENAME(S)

DATA2_NFIELD

DESTINATION OF OUTPUT? (DEFAULT=SCREEN)

OVER.OUT

COMPUTING...

For each correlation, OVERLAP returns six values:

(1) c, the normalized area of the amplitude overlap given in the equation above

(2) kappa, the normalized area of the intensity overlap given in the equation above

(3) the non-normalized area of both c and kappa (the numerator of each equation)

(4) the area under each field intensity

NORMALIZED AMPLITUDE OVERLAP (C)= 1.00000 + j( .00000)

NORMALIZED INTENSITY OVERLAP (KAPPA)= 1.00000

AREA OF AMPLITUDE OVERLAP= 0.626657E+00 + j( 0.000000E+00)

AREA OF INTENSITY OVERLAP= 0.392699E+00

AREA UNDER INTENSITY1= 0.626657E+00

AREA UNDER INTENSITY2= 0.626657E+00

OVERLAP utilizes a cubic spline routine in order to find the field values at particular x-coordinates. Naturally, the accuracy of this interpolation algorithm is based on the number of data points supplied by the input files. OVERLAP can handle up to 500 points, and files containing at least 100 points have been found to produce rather accurate results. To test the accuracy of OVERLAP with a given file, merely run the file against itself.

If you find that you need more data points in your near-field file, edit the MODEIG file, adding the statement: CASE DXIN=0.05. This will double the number of data points in the near-field file. DXIN may be made smaller if needed.

OVERLAP_SA should be used if you wish to use standard files. The format of each line of a standard file must be as follows:

(x-value) <tab> (real part of electric field) <tab> (imaginary part of electric field)

When calculating the overlap of the near-fields of two waveguides, it is important to make sure that the quantum wells of each guide are lined up correctly. This is accomplished quite easily using MODEIG's looping capability. The following sample file illustrates one example where we desire to calculate the overlap between the gain section and DBR section of a GRINSCH-structure as the thickness of the pclad layer in the DBR section is varied.

CASE EPS1=1E-7 GAMEPS=1E-3 DXIN=0.05

CASE PRINTF=0 INITGS=1 AUTOQW=0 NFPLT=1 FFPLT=0

MODCON KPOL=1 APB1=0.25 APB2=0.25

STRUCT QW=.0100 NQW=3.64 GRW=.1 WVL=.8600

LAYER AIR=1.0

LAYER AIR=1.0 TL=1.00

LAYER ALPERC=.60 TL=0.00

LAYER ALPERC=.60

LAYER NSLC=10

LAYER ALPERC=.20

LAYER QWS=1

LAYER ALPERC=.20

LAYER NSLC=10

LAYER ALPERC=.60

LAYER ALPERC=.60 TL=0.0

OUTPUT PHMO=1 GAMMAO=1 WZRO=1 WZIO=0 QZRO=1 QZIO=0

OUTPUT FWHPNO=0 FWHPFO=0

OUTPUT SPLTFL=2 MODOUT=0 LYROUT=0 DBOUT=0

GAMOUT LAYGAM=15 COMPGAM=0 GAMALL=0

LOOPX1 ILX='TL' FINV=0.00 XINC=-.1 LAYCH=2

LOOPX1 ILX='TL' FINV=1.00 XINC=.1 LAYCH=3

Notice that a second layer of air has been inserted between the semi-infinite layer of air and the pclad layer. As the pclad thickness is increased, we simultaneously decrease the second air layer by the same amount. In this manner, the position of the quantum well remains the same! This makes finding the overlap a simple task.

To acquaint yourself with OVERLAP, first run MODEIG using the file "samp.mod" (the file shown above.) MODEIG will save a new near-field file for each loop it performs. Now, use OVERLAP as shown above, entering in the names of the various near-field files.

For more information on looping and saving files using MODEIG, please consult the MODEIG manual.

The following results were obtained using OVERLAP with "samp.mod_NFIELD_T0T100" as the reference file and with "samp.mod_NFIELD_T100T0" , "samp.mod_NFIELD_T50T50", and "samp.mod_NFIELD_T100T0" as the comparison files.

NORMALIZED AMPLITUDE OVERLAP (C)= .79256 + j( 0.00000)

NORMALIZED INTENSITY OVERLAP (KAPPA)= .62816

AREA OF AMPLITUDE OVERLAP= 0.792567E+00 + j(-0.297175E-07)

AREA OF INTENSITY OVERLAP= 0.628162E+00

AREA UNDER INTENSITY1= 0.100001E+01

AREA UNDER INTENSITY2= 0.999999E+00

NORMALIZED AMPLITUDE OVERLAP (C)= .97979 + j( .18843)

NORMALIZED INTENSITY OVERLAP (KAPPA)= .99549

AREA OF AMPLITUDE OVERLAP= 0.979799E+00 + j( 0.188430E+00)

AREA OF INTENSITY OVERLAP= 0.995512E+00

AREA UNDER INTENSITY1= 0.100001E+01

AREA UNDER INTENSITY2= 0.100001E+01

NORMALIZED AMPLITUDE OVERLAP (C)= .99964 + j( .00000)

NORMALIZED INTENSITY OVERLAP (KAPPA)= .99928

AREA OF AMPLITUDE OVERLAP= 0.999646E+00 + j( 0.000000E+00)

AREA OF INTENSITY OVERLAP= 0.999291E+00

AREA UNDER INTENSITY1= 0.100001E+01

AREA UNDER INTENSITY2= 0.100001E+01

R. PERLOW 1/90