MulDipSolveMultiSphere

 Solves the problem of dipole emission close to a multilayer spherical system with Mie theory
 Note that only dipoles outside the largest spheres (at a distance d) are
 considered.
 The parameters are given as arguments or may also be given in a
 structure stMP when called as MulDipSolveMultiSphere(stMP,sPlot,sCoeff)
 where stMP contains the parameter fields.
 The dipole is assumed to be on the positive z-axis (theta=0)
 and aligned in the plane (xOz) (i.e. p_y=0), and at a
 distance d from the sphere surface (i.e. at r=a+d).
 Note that in this case, we have for the Mie coefficients:
 either |m|=1; a,c even in m; b,d odd in m.
 or |m|=0; a,c=0; only b and d.
 For example, the scattered field is entirely defined by
 c_{n,1}, d_{n,1}, and d_{n,0}
 (c_{n,-1}=c_{n,1}, d_{n,-1}=-d_{n,1}, c_{n,0}=0 and
 all other coefficients are zero).

 Results are obtained for a perpendicular and parallel dipole.
 Results for the case of a general dipole can then be easily derived from
 them.

 Parameters:
 - nNmax:     integer [1 x 1]
              number of n in series
 - Ca:        cell of integer {K x [1 x 1]}
              K is number of interfaces (K=1 for single sphere)
              radii of spherical interfaces (typically in NANOMETERS)
              Ca{K} is outer interface (largest sphere)
 - lambda:    possibly column vector [L x 1]
              wavelengths (typically in NANOMETERS)
 - Cepsilon:  cell of scalars or column vectors {K+1 x [L x 1]}
              epsilon of media (possibly
              wavelength-dependent) for k=0 (inside sphere)
              to k=K (embedding medium).
 - d:         integer [1 x 1]
              distance from sphere (typically in NANOMETERS)
 - nNmaxESA:  integer [1 x 1]
              number of n in series for evaluation of MTot in
              the ESA for n>nNmax
 - sPlot:     optional (default does nothing)
              'plot' will produce a new figure with a plot
              of MRad and MTot (Perp and Para cases)
 - sCoeff:    optional (default does nothing)
              'coeff' will return the Mie coefficients for the regular
              field expansions(alphakn1, betakn1, betakn0), and for the
              irregular field expansions (gammakn1, deltakn1, deltakn0),
              and for the non-modified (incident) dipole radiated field
              (en1, fn1, fn0)
              'suscep' will return the Mie susceptibilities Gamma^k, Delta^k,
              A^, and B^k
              'both' will return both Mie coefficients and
              susceptibilities 

 Returns: structure stMdip with fields containing the parameters for
          future reference and additional fields for the results
 - stMdip.nNmax: scalar
 - stMdip.nNmaxESA: scalar
 - stMdip.a: scalar
 - stMdip.lambda: [L x 1]
 - stMdip.epsilonM: scalar or [L x 1]
 - stMdip.d: scalar
 - stMdip.x: [L x 1] x=kM*a
 - stMdip.xp: [L x 1] xp=kM*(a+d)
 - stMieRes.nK: scalar, number of interfaces
 - stMieRes.Ca: cell of {K scalars}
 - stMieRes.CepsilonM: cell of {K+1 x (scalar or [L x 1])}
 - stMieRes.Cx: cell of {K x [L x 1]}
 - stMieRes.Cs: cell of {K x [L x 1]}
 - stMdip.MRadPerp: [L x 1] wavelength-dependent radiative decay rate EF
                    for perpendicular dipole
 - stMdip.MTotPerp: [L x 1] wavelength-dependent total decay rate EF
                    for perpendicular dipole
 - stMdip.MRadPara: [L x 1] wavelength-dependent radiative decay rate EF
                    for parallel dipole
 - stMdip.MTotPara: [L x 1] wavelength-dependent total decay rate EF
                    for parallel dipole
 - stMdip.MRadPerpCoeffs [L x nNmax] (if sCoeff='coeffSum'): coeffs of the sums over n
 - stMdip.MRadParaCoeffs [L x nNmax] (if sCoeff='coeffSum'): coeffs of the sums over n
 - stMdip.MTotPerpCoeffs [L x nNmaxESA] (if sCoeff='coeffSum'): coeffs of the sums over n
 - stMdip.MTotParaCoeffs [L x nNmaxESA] (if sCoeff='coeffSum'): coeffs of the sums over n
 - stMdip.cn1 (if sCoeff='coeff' or 'both'): [L x nNmax]
 - stMdip.dn1 (if sCoeff='coeff' or 'both'): [L x nNmax]
 - stMdip.dn0 (if sCoeff='coeff' or 'both'): [L x nNmax]
 - stMdip.en1 (if sCoeff='coeff' or 'both'): [L x nNmax]
 - stMdip.fn1 (if sCoeff='coeff' or 'both'): [L x nNmax]
 - stMdip.fn0 (if sCoeff='coeff' or 'both'): [L x nNmax]
 - stMdip.Gamma (if sCoeff='suscep' or 'both'): [L x nNmax]
 - stMdip.Delta (if sCoeff='suscep' or 'both'): [L x nNmax]
 - stMdip.CstMulGDAB (if sCoeff='suscep' or 'both'): [L x nNmax]
 - stMdip.Cgammakn1 (if sCoeff='coeff' or 'both'): cell {K+1 x [L x nNmax]}
 - stMdip.Cdeltakn1 (if sCoeff='coeff' or 'both'): cell {K+1 x [L x nNmax]}
 - stMdip.Calphakn1 (if sCoeff='coeff' or 'both'): cell {K+1 x [L x nNmax]}
 - stMdip.Cbetakn1 (if sCoeff='coeff' or 'both'): cell {K+1 x [L x nNmax]}

 This file is part of the SPlaC v1.0 package (copyright 2008)
 Check the README file for further information

0001 disp ' ';
0002 global noCheckSum;
0003 if (isempty(noCheckSum) || ~noCheckSum)
0004     disp 'MulDipSolveMultiSphere: Solving dipole Mie for sphere multilayer- CheckSum ON'
0005 else
0006     disp 'MulDipSolveMultiSphere: Solving dipole Mie for sphere multilayer - CheckSum OFF'
0007 end
0008 
0009 % rearrange function parameters and define optional parameters
0010 % number of parameters is 1,2, or 3 if called as stMP,sOption,sCoeff
0011 % or 6,7, or 8 if nMax,Ca,lambda,Cepsilon,d,nNmaxESA,sOption,sCoeff
0012 nNbParam=nargin;
0013 if ((nNbParam==1) || (nNbParam==6))
0014     sPlot='No';
0015     sCoeff='No';
0016 end
0017 if ((nNbParam==2) || (nNbParam==7))
0018     sCoeff='No';
0019 end
0020 if (nNbParam<4)
0021     nNmax=stMP.nNmax;
0022     Ca=stMP.Ca;
0023     lambda=stMP.lambda;
0024     Cepsilon=stMP.Cepsilon;
0025     d=stMP.d;
0026     nNmaxESA=stMP.nNmaxESA;
0027 end
0028 
0029 nK=length(Ca); % number of spherical interfaces K
0030 
0031 % Get s_k and x_k for k=1..nK
0032 [Cs,Cx]=MulGetCsCx(lambda,Ca,Cepsilon);
0033 
0034 % Calculate xp=k_M (a+d) for dipole position
0035 xp=Cx{nK}/Ca{nK}*(Ca{nK}+d);
0036 
0037 if nNmax>0
0038     % Calculate susceptibilities Gamma^k_n, Delta^k_n, A^k_n, and B^k_n
0039     % (defined in Eqs. H.108 and H.117)
0040     % for all n,k and all lambda
0041     CstMulGDAB=MulSuscepGDAB(nNmax,Cs,Cx);
0042     % CstMulGDAB is a cell of K structures, each with the corresponding
0043     % susceptibilities
0044     % Gamma^k_n, Delta^k_n, A^k_n, and B^_n as matrices [L x Nmax]
0045 
0046     % Calculate M coeffs for dipole emission
0047     % return coeffs in the sum if sCoeff='coeffSum'
0048     stMdip=DipMcoeff(xp,CstMulGDAB{nK},Ca{nK},d,Cs{nK},nNmaxESA,sCoeff);
0049 else % nNmax=0 means ESA calculation only
0050     stMdip=DipMcoeff(xp,[],Ca{nK},d,Cs{nK},nNmaxESA,'ESAonly');
0051     sCoeff='No'; % deactive additional options (sCoeff is ignored if nNmax=0)
0052 end
0053     
0054 % return results
0055 stMdip.nNmax=nNmax;
0056 stMdip.nNmaxESA=nNmaxESA;
0057 stMdip.a=Ca{nK};
0058 stMdip.lambda=lambda;
0059 stMdip.epsilonM=Cepsilon{nK+1};
0060 stMdip.d=d;
0061 stMdip.x=Cx{nK};
0062 stMdip.xp=xp;
0063 
0064 stMdip.nK=nK;
0065 stMdip.Ca=Ca;
0066 stMdip.Cepsilon=Cepsilon;
0067 stMdip.Cx=Cx;
0068 stMdip.Cs=Cs;
0069 
0070 if (strcmpi(sCoeff,'suscep') || strcmpi(sCoeff,'both'))
0071     stMdip.Gamma=CstMulGDAB{nK}.Gamma; % for compatibility with single spheres
0072     stMdip.Delta=CstMulGDAB{nK}.Delta; % for compatibility with single spheres
0073     stMdip.CstMulGDAB=CstMulGDAB; 
0074 end
0075 
0076 if (strcmpi(sCoeff,'coeff') || strcmpi(sCoeff,'both'))
0077     % calculate incident field coefficient an1, bn1, and bn0
0078     stIncEabn1bn0=DipIncEabn1bn0(nNmax,xp);
0079     % results are [L x nNmax]
0080     
0081     % calculate Mie coefficients using a downward recurrence (pp. 623,624)
0082     % each cell of coeff corresponds to a given kk=0..nK
0083     stMdip.Cgammakn1=cell(1,nK+1);
0084     stMdip.Cdeltakn1=cell(1,nK+1);
0085     stMdip.Cdeltakn0=cell(1,nK+1);
0086     stMdip.Calphakn1=cell(1,nK+1);
0087     stMdip.Cbetakn1=cell(1,nK+1);
0088     stMdip.Cbetakn0=cell(1,nK+1);
0089     stMdip.Cgammakn1{1}=0; % no scattered field inside the smallest sphere
0090     stMdip.Cdeltakn1{1}=0;
0091     stMdip.Cdeltakn0{1}=0;
0092     % Initialize recurrence
0093     stMdip.Calphakn1{nK+1}=stIncEabn1bn0.an1;
0094     stMdip.Cbetakn1{nK+1}=stIncEabn1bn0.bn1;
0095     stMdip.Cbetakn0{nK+1}=stIncEabn1bn0.bn0;
0096     for kk=nK:-1:1
0097         % Eq. H.108 gamma^k=Gamma^k * alpha^k
0098         stMdip.Cgammakn1{kk+1}=CstMulGDAB{kk}.Gamma .* stMdip.Calphakn1{kk+1};
0099         stMdip.Cdeltakn1{kk+1}=CstMulGDAB{kk}.Delta .* stMdip.Cbetakn1{kk+1};
0100         stMdip.Cdeltakn0{kk+1}=CstMulGDAB{kk}.Delta .* stMdip.Cbetakn0{kk+1};
0101         % Eq. H.117 alpha^{k-1}=A^k alpha^k
0102         stMdip.Calphakn1{kk}=CstMulGDAB{kk}.A .* stMdip.Calphakn1{kk+1};
0103         stMdip.Cbetakn1{kk}=CstMulGDAB{kk}.B .* stMdip.Cbetakn1{kk+1};
0104         stMdip.Cbetakn0{kk}=CstMulGDAB{kk}.B .* stMdip.Cbetakn0{kk+1};
0105     end
0106     stMdip.cn1=stMdip.Cgammakn1{nK+1}; % for compatibility with single spheres
0107     stMdip.dn1=stMdip.Cdeltakn1{nK+1}; % for compatibility with single spheres
0108     stMdip.dn0=stMdip.Cdeltakn0{nK+1}; % for compatibility with single spheres
0109 
0110     % coefficient of expansion of incident dipole field in far field
0111     stIncEefn1fn0=DipIncEefn1fn0(nNmax,xp);
0112     stMdip.en1=stIncEefn1fn0.en1; % [L x nNmax]
0113     stMdip.fn1=stIncEefn1fn0.fn1; % [L x nNmax]
0114     stMdip.fn0=stIncEefn1fn0.fn0; % [L x nNmax]
0115 end
0116 
0117 % plot if required
0118 if strcmpi(sPlot,'plot')
0119     disp 'Drawing plot...'
0120     DipPlotM(stMdip);
0121 end
0122 
0123 disp 'MulDipSolveMultiSphere: done.'
0124 disp ' '