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n_ice_zhang01

PURPOSE ^

Function for calculating the complex refractive index

SYNOPSIS ^

function n = n_ice_zhang01(f,TK)

DESCRIPTION ^

 Function for calculating the complex refractive index
 of pure ice in the submillimeter region, according to 
 Zhang ...
 (Zhang et al. do not provide a formula for real part of refractive index,
 but have measured it and showed variations from 1.787-1.793 between 250
 and 1000GHz with no significant temperature variation. Here, we fix the
 real part to the mean value of 1.790)

 FORMAT   n = n_ice_zhang01(f,TK)
        
 OUT   n   Complex refractive index
 IN    f   Frequency [Hz]. 0.01-3000 GHz.
       TK  Temperature [K]. 20-273.15 K.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

DOWNLOAD ^

n_ice_zhang01.m

SOURCE CODE ^

0001 % Function for calculating the complex refractive index
0002 % of pure ice in the submillimeter region, according to
0003 % Zhang ...
0004 % (Zhang et al. do not provide a formula for real part of refractive index,
0005 % but have measured it and showed variations from 1.787-1.793 between 250
0006 % and 1000GHz with no significant temperature variation. Here, we fix the
0007 % real part to the mean value of 1.790)
0008 %
0009 % FORMAT   n = n_ice_zhang01(f,TK)
0010 %
0011 % OUT   n   Complex refractive index
0012 % IN    f   Frequency [Hz]. 0.01-3000 GHz.
0013 %       TK  Temperature [K]. 20-273.15 K.
0014 
0015 % 2014-07-14   Created by J. Mendrok
0016 
0017 function n = n_ice_zhang01(f,TK)
0018 
0019     f = f/1e9;
0020 
0021     if f<1.  |  f>1000
0022       error('Valid range for frequency is 1-1000 GHz'); 
0023     end
0024     if TK<100  |  TK>273.15
0025       error('Valid range for temperature is 100-273.15 K'); 
0026     end
0027     
0028     n1=1.79d0;
0029 
0030     h   = 6.6260693d-34;    % [Js]                ; from wikipedia: h = 6,626 069 3(11) * 10^-34 Js
0031     c   = 2.99792458d+10;    % [cm/s]            ; from wikipedia: c = 2,997 924 58 * 10^8 m/s
0032     k   = 1.3806504d-23;    % [J/K]                ; from wikipedia: k = 1,380 650 4(24) * 10-23 J/K
0033     hck   = h*c/k;
0034     Pi4c = 4.*pi*c;
0035 
0036     A  = 4.044d-5;    % [GHz]         ; it's not fully clear from paper, whether A is T-dependent
0037     B0 = 1.391d+5;    % [cm^(-1)*K]
0038     v0 = 233.d0;    % [cm^(-1)]
0039 
0040     hckv = hck * v0;
0041     v02 = v0^2;
0042     c1 = A / (2.d0*n1);                                         % [GHz]
0043     expVT = exp( hckv / TK );
0044     c2 = 1.d9/Pi4c * B0/TK * ( expVT/(expVT-1.0d0).^2 ) / v02;  % 1e9*[1/Hz]=[1/GHz]
0045     
0046     n = n1 + i*(shiftdim(c1/f,1) + c2*f);

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