Luxpop    Index of refraction and photonics calculations.   Calculs d'indices de réfraction et de photonique.  折射率和光子计算

Index of Refraction
* Return the refractive index of a (fixed ratio) substance at a given wavelength, l (nm). Further information also may be given.
* The absolute refractive index (i.e. with resp. to vacuum) is returned, unless stated otherwise. Click here for more index of refraction terminology.
* See also our Long List of Index of Refraction Values (A-Z)... for other materials.
     l:nm        temperature (certain substances only) deg C     
variable compound category: return the index of refraction of variable atomic content compound materials at a given wavelength, l (nm), and material content proportion, x.
* For quaternary materials such as In1-xGaxAsyP1-y or AlGaInAs, Luxpop assumes there is a lattice match to InP. As such, there is no need to specify a value for y since entering a value for x will force a value of y.
* For H2SO4 (sulfuric acid) and HNO3 (nitric acid), x relates to the wt % of these substances in water. e.g. x=0.4 for H2SO4 means a 40% ratio of H2SO4 by weight in an aqueous solution.

Substance:     l: nm       x:      temperature:  deg C    

Light at Interface

Thin film stack model: reflectivity/transmissivity online calculation for light incident at an arbitrary angle on a thin film stack.
The algorithm returns full reflected/transmitted field, power, and phase information for incident TE (perp, or s) and TM (para or p) waves. Input power is unitary and flat across the spectrum unless centre_lambda box in section 1 below is blank.
There are up several sets of information to be entered:
    1 Incident angle, centre wavelength, wavelength sweep range, and number of points(max 20) to compute across the wavelength sweep range.
    2 Complex index of refraction of incident medium (n,k). For air, n=1 and k=0 is a good approximation.
    3a Thin film stack. Enter stack information using the following notation, where the top film is closest to the incident medium (see examples below):
Fixed index on each layer: notation Fully dispersive calculation: notation Variable thickness: notation Resistivity: notation
thickness1, n1,k1
thickness2, n2,k2
thickness3, n3,k3
thickness1, {Material1}
thickness2, n2,k2
thickness3, {Material3}

Deposition materials currently available are: Ag,Al,Au,Cr,Cu,GaAs,ITO,Mo,Ni,Si,Si3N4,SiO2a,Ti. (SiO2a is amorphous SiO2)
Contact Luxpop to get your favourite material added.
NOTE: if '{ }' characters do not work on your system, use '( )' characters. 		In lieu of one thickness, put semicolon-separated values in parentheses. Up to 3 sets are permitted.

thickness1, n1,k1
(thickness2a;thickness2b;thickness2c), n2,k2
(thickness3a;thickness3b;thickness3c), {Material3}

In this example, three sets of calculations are performed.
Set 1 has: layer 1 thickness1   layer 2 thickness2a   layer3 thickness3a
Set 2 has: layer 1 thickness1   layer 2 thickness2b   layer3 thickness3b
Set 3 has: layer 1 thickness1   layer 2 thickness2c   layer3 thickness3c 		Calculate resistance of thin film stack. Either user-supplied resistivity values or default values can be used. Resistance determined by multiplying by thickness and dividing by area assumed to be 1 mm^2.

thickness1, n1,k1,Res1
thickness2, n2,k2,Res2
thickness3, {Material3},Res3
thickness4, {Material4}

In this example, the resistivity values Res1,Res2, and Res3 are used, along with the default resistivity value of Material4 (the value Res3 overrides the default value of Material3).
4 Complex index of refraction of substrate (ns,ks): either enter a fixed value OR leave the ns,ks fields blank and choose a substrate material for a fully dispersive calculation.
Luxpop can usually do more layers or steps for fixed index layers compared to dispersive material layers, depending on system activity.
    Here are some examples of thin film stacks. Feel free to cut and paste into the "3a" box below.
Example#1: Fixed index layers(Born & Wolf, Principles of Optics, 9th Ed. p. 74) stack of 1/4 wavelength (for lambda=546 nm) High n / low n materials at n= 2.3 and 1.35

    59.348,2.3,0
    101.11,1.35,0
    59.348,2.3,0
    101.11,1.35,0
    59.348,2.3,0
 Example #2: Specify material using {Material} notation on some or all the layers to obtain dispersive calculations. Cut and paste into box #3a below.

    5.348,{Al}
    101.11,1.35,0
    5.348,{Ag}
    101.11,1.35,0
    59.348,2.3,0
 Example #3: Variable thickness notation on one layer to perform multiple sets of calculations simultaneously. Cut and paste into box #3a below.


    (3.348;5.348;7.348),{Al}
    101.11,1.35,0
    5.348,{Ag}
    101.11,1.35,0
    59.348,2.3,0
 Example #4: Include resistivity with fixed values, default material value, and fixed value overriding default material value.Cut and paste into box #3a below.


    5.348,{Al},4e-7
    101.11,1.35,0,2e-3
    5.348,{Ag}
    101.11,1.35,0,5e-4
    59.348,2.3,0,5e-3

1 incident angle (theta_i): degrees     centre_lambda: (nm)     wavelength sweep range: +/-nm      # of sweep points:     
2 index of incident material (eg air) n:     k:     


3a Enter the thin film stack text information into the box below
3b Optional: custom power spectral profile of input.
* If centre_lambda in section 1 above is kept blank, the information in this box to the right will be used and will override the wavelength sweep range and the # of points.
* Max 15 wavelengths.
* Wavelengths must be monotonically increasing, but do not need to be uniformly spaced.
* Input power must be in linear units. Output power will be in the same units as input power.
* Format as follows:
lambda1,power1
lambda2,power2
lambda3,power3
...
Feel free to overwrite sample text in box==>

4 index of susbtrate material (eg glass) ns:     ks:     OR   leave the ns,ks fields blank and select a substrate material:   

Here is another simple example:
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Example#2: (Born & Wolf, Principles of Optics, 9th Ed. p. 757) Single layer metal film with thickness = 300nm, n=3.5,k=0.1

    300,3.5,0.1
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Arbitrary reflection on complex material. Calculate the reflected amplitude coefficients and phase shifts for linearly polarized light at an arbitrary polarization azimuth angle, incident at an arbitrary angle on a material of arbitrary real or complex index of refraction. Two sets of results are given: ideal zero smoothness and rough surface, with impact calculated per the Kirchoff approximation.
In the inputs below:
(i) n1 and k1 are respectively the real and imaginary values of the index of refraction(incident material), (ii) n3 and k3 correspond to the transmitted material, (iii) theta_i is the incident angle measured from the normal, (iv)angular sweep range is the angular range, centered on theta_i, across which the program will perform angle calculations, (v) d is the rms surface height in nm (vi) lambda is the wavelength at which the impact of surface roughness is calculated, and (vii) num sweep points is the number of points that will be computed during the sweeping.
(For the example given below, the default values below will allow the user to locate the approximate Brewster angle for BK7 in the visible.)

n1:     k1:     n3:     k3:     theta_i: degrees     d : nm     lambda: nm
angular sweep range: degrees      num sweep points: (max 25)        

Gaussian Beam Propagation

Perform calculations on Gaussian beam transformation by a lens. Notes: a) for these calculations the beam waists do not necessarily need to be at the focus, b) results for negative focal length lens may be suspect.
Parameters: d1,d2 (in millimetres): distance from beam waist to lens; w1, w2 (microns): 1/e2 beam radii at the waist; f (millimetres): lens focal length; l (nm): wavelength.

If you enter d1, w1, f and l, the algorithm will return d2 and w2; additionally, the algorithm will return wL, the 1/e2 beam radius (although wL is not at a waist) at the lens.

Additional "sweeping" feature: if one sweep value is entered, Luxpop will perform 15 calculations within a range bounded by the sweep parameter.

ModeMatching_GaussianBeam.gif (3034 bytes)

                 d1: mm   w1: mm            f:  mm       l: nm            
      sweep:    mm        mm               mm          nm

Return the Rayleigh range and far field divergence angle given an initial 1/e2 beam radius  at the waist , wo (mm), and a wavelength, l (nm).

wo: mm        l:nm   

Return the 1/e2 beam radius  (in mm) given a distance from the waist , z (mm), a beam radius at the waist, wo (mm), and a wavelength l (nm). Additional "sweeping" feature: if one sweep value is entered, Luxpop will perform 15 calculations within a range bounded by the sweep parameter.

z:   mm     sweep: mm about nominal values
wo:mm     sweep: mm about nominal values
l:   nm     sweep: nm about nominal values       

Conversions
Convert between photon energy (in eV) , wavelength (nm in vacuum), frequency (Hz), and wavenumber (cm-1).
Enter one parameter below and the three other equivalent values will be returned.
Scientific notation is acceptable. Example: entering 192.2e12 for the frequency will properly be interpreted to mean 192.2 THz.

Photon energy: eV           wavelength: nm                frequency: Hz                wave number: cm-1              

Return the differential frequency or wavelength  (in GHz or nm) for a given differential wavelength or frequency, centered at the given wavelength.
If dl is entered, then the differential frequency will be computed, and vice-versa.

 dl: nm    df: GHz     l: nm 

Convert complex index of refraction to complex permittivity   or vice versa.
Enter a value for either (i) n and k or (ii) the complex permittivities

        n:            k:              e1:               e2:                        

Convert absorption coefficient (alpha or a) to extinction coefficient (k)   or vice versa.
Enter a value for (i) either alpha or k and (ii) wavelength (nm)

        k:            alpha: dB/cm              l: nm

Return the finesse for a resonator with the given refractive index, thickness, and reflectivity.
refractive index:      thickness: mm      reflectivity: %  

Click here for more optical computing features.
Index v130