This file documents FreeSnell 1c4 (released January 2024), a simulator for thin-film optics.
Copyright © 2003, 2004, 2007, 2009, 2010 Aubrey Jaffer
Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies.
Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one.
Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that this permission notice may be stated in a translation approved by the author.
Next: Optical Properties of Materials, Previous: FreeSnell, Up: FreeSnell [Contents][Index]
Some wondrous optical technology can result from depositing coatings less than a few micrometers thick on glass, plastic, and other surfaces. These coatings are used to enhance the reflectivity of astronomical mirrors or diminish the reflections from visual displays and lenses; they can improve the efficiency of window glass and solar cells.
FreeSnell computes these effects for parallel layers of dielectric and conductive materials.
Next: Theory of Operation, Previous: Overview, Up: Overview [Contents][Index]
I couldn’t find a free implementation of thin-film optical calculations I needed for a project. So I rolled my own.
The first versions were based on webpages [NCSU] and [Nave], but differences in signs and conventions of the complex index of refraction caused havoc with metallic layers. [Sernelius] has a comprehensive treatment with signs consistent from start to finish. The current version is based on that.
The properties of granular films are taken from [Heavens] discussion of Maxwell Garnett theory. [Granfilm] computes properties of granular films with great sophistication, but appears to require a PhD in physics in order to use it.
Optics is wavelength based; so this package is also. These routines work out the complex voltages in the forward and reverse directions to find the transmitted and reflected amplitudes. This works only for intensities where the layers act linearly (superposition).
Each layer 0:n has an index of refraction and height. Because the P and S polarizations are independent, they are calculated separately. The square of the absolute value of computed field values expressing power ratios are the returned quantities.
Next: Wrinkles, Previous: Background, Up: Overview [Contents][Index]
The effects of coatings on light are determined by Snell’s law and Fresnel’s equations, which model the light’s electric and magnetic fields.
Taking the Laplace-transform of the differential equations relating the fields at the surface of each parallel layer of materials yields algebraic equations relating the indexes-of-refraction and the (complex) attenuation and phase as functions of wavelength.
These algebraic equations can be organized into products of 2x2 matrices and 2-vectors. The 2-vectors represent the Laplace transforms of the forward and reverse radiation. Each interface between adjacent materials corresponds to a 2x2 matrix.
The product of the chain of 2x2 matrices produces a single 2x2 matrix expressing the transmittance and reflectance of the layered stack as a whole, solving the system of equations.
This method is not unique to thin-film optics; it is essentially the same as the 2-port method for analysis of linear electrical circuits.
Next: Bibliography, Previous: Theory of Operation, Up: Overview [Contents][Index]
Because these optical systems are passive and linear, the attenuation of radiation passing through in one direction must be the same as the attenuation of radiation passing through in the opposite direction.
Radiation that is not transmitted through the stack must be either absorbed or reflected. The absorption at the top is not necessarily the same as the absorption at the bottom.
Rays impinging on the stack with non-normal incidence will leave the stack with non-normal incidence; the angles being identical if the indexes of refraction of the top and bottom materials are identical.
Rays impinging on the stack with non-normal incidence have different attenuation and reflectance depending on the polarization of the impinging radiation. FreeSnell computes outcomes for both polarizations; and can report these separately or averaged.
Heavens, O. S., “Optical Properties of Thin Solid Films”, ISBN: 0486669246, Dover Pubns, Dec 1991
Bo E. Sernelius,
“Electrodynamics”,
Dept. of Physics and Measurement Technology, Linköping University
http://www.ifm.liu.se/~boser/elma/, especially
“REFLECTION FROM A METALLIC SURFACE”
http://www.ifm.liu.se/~boser/elma/Lect13.pdf
Lide, D.R., Dr. Editor, “CRC Handbook of Chemistry and Physics (3rd Electronic Edition)”, CRC Press, 2000
“Fresnel’s equations” from the chemistry department of
North Carolina State University.
http://web.archive.org/web/20041029131241/http://chsfpc5.chem.ncsu.edu/CH795Z/lecture/lecture8/fresnel/fresnel.html
“Fresnel’s Equations: Reflection and Transmission” by Carl R. Nave,
Department of Physics and Astronomy, Georgia State University.
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/freseq.html
J. C. Maxwell Garnett,
“Colours in Metal Glasses and in Metallic Films”,
Phil. Trans. Roy. Soc. London 203A, 385 (1904).
http://rsta.royalsocietypublishing.org/content/203/359-371/385
R. Lazzari and I. Simonsen, “Granfilm: a software for calculating thin-layer dielectric properties and fresnel coefficients”, Thin Solid Films, 419:124, 2002. http://www.insp.jussieu.fr/axe2/Oxydes/GranFilm/GranularFilm.html
Bartl J, Baranek M (2004), “Emissivity of aluminium and its importance for radiometric measurement”, Measurement of Physical Quantities 43:31–36. http://www.measurement.sk/2004/S3/Bartl.pdf
Michael F Modest, “Radiative heat transfer”, second edition, Academic Press 2003
Next: Material Databases, Previous: Overview, Up: FreeSnell [Contents][Index]
The salient optical properties of a material are specified by its complex index of refraction; which differs from the common index of refraction, n, by incorporating the extinction-coefficient, k/n. There are several conventions for the complex index of refraction. The one employed here follows [Sernelius]: (n + k*i).
Dielectric materials typically have k equal to zero and n which varies little with the wavelength of light being analyzed. They are often computed using a single n value.
Metallic or conductive materials have non-zero k and n which can vary wildly with the wavelength of light being analyzed. These values can be determined through a process called ellipsometry.
The Sopra company manufactures spectroscopic ellipsometers. A bundle
of spectra for 278 materials available from
http://www.sopra-sa.com/more/database.asp (Nov 28, 2000) is
included in the FreeSnell distribution database.
The Software Spectra company also distributes the Sopra data, although
rewritten into their proprietary format. But their zip file
http://www.sspectra.com/files/misc/win/SOPRA.EXE
(Macintosh
http://www.sspectra.com/files/misc/mac/Sopra.sea.hqx)
contains
README.TXT identifying the Sopra files.
Included with FreeSnell are the following metal spectra from the CRC Handbook of Chemistry and Physics:
ag.nk: eV n k R(th=0) ; Silver al.nk: eV n k R(th=0) ; Aluminium au.nk: eV n k R(th=0) ; Gold, electropolished, Au (110) cr.nk: eV n k R(th=0) ; Chromium cu.nk: eV n k R(th=0) ; Copper fe.nk: eV n k R(th=0) ; Iron ge.nk: eV n k R(th=0) ; Germanium, single crystal li.nk: eV n k R(th=0) ; Lithium ni.nk: eV n k R(th=0) ; Nickel ta.nk: eV n k R(th=0) ; Tantalum ti.nk: eV n k R(th=0) ; Titanium (Polycrystalline) v.nk: eV n k R(th=0) ; Vanadium w.nk: eV n k R(th=0) ; Tungsten zn.nk: eV n k R(th=0) ; Zinc, E _|_ to c^28 zn-e.nk: eV n k R(th=0) ; Zinc, E || to c^28 zr.nk: eV n k R(th=0) ; Zirconium (Polycrystalline)
Many of these materials are included in the Sopra bundle; but the CRC data covers a wider wavelength span than the Sopra spectra. Combining the CRC and Sopra files produces wide bandwidth spectra with finer resolution in the visible and near-infrared bands.
Previous: Optical Properties of Materials, Up: Optical Properties of Materials [Contents][Index]
FreeSnell supports SOPRA textual formats with their evenly spaced wavelengths or energies, as well as textual formats where the wavelength or energy of each nk pair is individually specified.
If the first non-whitespace character in the file is a digit, then the file is interpreted as a SOPRA format file. The first number indicates the spectral unit (1 = eV, 2 = um, 3 = 1/cm, 4 = nm). The second and the third numbers indicate the spectral range and the fourth one the number of intervals. The n and k values are then stored in the order N,K,N,K...; each value may be followed by a semicolon, whitespace, or both.
For example, the SOPRA file al2o3.nk has 27 values for wavelengths from 0.25.um to 0.9.um:
2,.25,.9,26 1.7331,0 1.7163,0 1.7042,0 1.6951,0 1.6881,0 1.6825,0 1.678,0 1.6743,0 1.6713,0 1.6687,0 1.6665,0 1.6646,0 1.6629,0 1.6614,0 1.6601,0 1.659,0 1.6579,0 1.657,0 1.6561,0 1.6553,0 1.6546,0 1.6539,0 1.6532,0 1.6526,0 1.652,0 1.6515,0 1.6509,0
The other formats ignore the first line if it begins with a semicolon. The first non-ignored word read indicates the spectral unit, either eV, /cm, um, or nm; the rest of that line is discarded. Each line which follows is a triple of the spectral index, the n value, and the k value, separated by whitespace. Extra data on the line (the normal reflectance in some files) is ignored.
This example (blackbody.nk) specifies constant n and k values over all wavelengths:
um n k ; blackbody 01.0 1.0 0.038 25.0 1.0 0.038
Next: Specifying Designs, Previous: Optical Properties of Materials, Up: FreeSnell [Contents][Index]
The FreeSnell package includes a SCM script (program) named nk to create, manage, and query a refractive-index spectra database.
Recent versions of the FreeSnell distribution include the relational database (nk.rwb) containing the refractive-index spectra. So use of the ‘nk’ script is optional.
Next: Wedged Databases, Previous: Material Databases, Up: Material Databases [Contents][Index]
The nk.scm file in the distribution functions as a shell script named ‘nk’ on Unix systems; under MS-Windows, the nk icon invokes nk.scm as an interactive command-line shell with the prompt ‘nk’.
Use the nk program to create, manage, and query a refractive-index spectra database. The nk program can read Sopra format files. These files have a ".nk" suffix. A bundle of spectra for over 275 materials is available from: http://www.sopra-sa.com/index2.php?goto=dl&rub=4 (2010-06-14). Some metal spectra included with FreeSnell also have a ".nk" suffix, but with a different format. The zip file http://www.sspectra.com/files/misc/win/SOPRA.EXE contains "README.TXT" identifying the Sopra files. http://luxpop.com/RefractiveIndexList.html has 274 refractive-index files, mostly X-ray spectra. The optional argument [-F path] sets the path to the database file to be accessed or created. If it is not given, then the environment variable "NK_DATABASE_PATH" names the database file if defined, defaulting to "nk.rwb" in the current directory. The name for each spectrum in the database is taken from its filename sans the ".nk" or "ir.nk" suffix. Usage: nk [-F path] Starts the nk shell. Type nk commands without the nk; ^Z to exit. Usage: nk [-F path] --add FILEGLOB.nk ... Add spectra matching FILEGLOB to database. Wildcards must be in the leaf directory only. Usage: nk [-F path] --new FILEGLOB.nk ... Add new or replace spectra matching FILEGLOB to database. Wildcards must be in the leaf directory only. Usage: nk [-F path] --del 'GLOB' ... Delete spectra of names matching GLOB from database. Usage: nk [-F path] --plot 'GLOB' ... Usage: nk [-F path] --lin-lin 'GLOB' ... Usage: nk [-F path] --log-log 'GLOB' ... Usage: nk [-F path] --log-lin 'GLOB' ... Usage: nk [-F path] --lin-log 'GLOB' ... Usage: nk [-F path] --lin-eV 'GLOB' ... Usage: nk [-F path] --log-eV 'GLOB' ... Usage: nk [-F path] --lin-/cm 'GLOB' ... Usage: nk [-F path] --log-/cm 'GLOB' ... Create encapsulated-PostScript (and view with Ghostview) spectra plots from database of names matching GLOB. The first symbol controls the y-axis. Usage: nk [-F path] --list 'GLOB' ... List names of spectra matching GLOB in database. Usage: nk [-F path] --range 'GLOB' ... List names and data ranges of spectra matching GLOB in database. Usage: nk [-F path] --desc 'GLOB' ... List names and descriptions of spectra matching GLOB in database. Usage: nk [-F path] --annotate sopra.txt Add chemical-symbol and description annotations to database. Usage: nk [-F path] NAME NUMBER.UNIT ... Prints NAME's n+k*i values at each NUMBER.UNIT from database. The NUMBER can be fixed or floating point; the UNIT either "eV" (electron-volt) or "m" (meter) with an optional metric prefix or "cm^-1" (wave-number). Usage: nk --help Prints this help and exits.
Next: Creating Databases, Previous: The nk script, Up: Material Databases [Contents][Index]
Although it tries to be careful, if the ‘nk’ script encounters an unexpected condition while the database file (default ‘nk.rwb’) has a table open for writing, then the database file can become unusable from both the ‘nk’ script and design files. This damage will only result from the ‘nk’ script; all simulations should be read-only from database files.
To start afresh, delete these files (with all occurrences of ‘nk.rwb’ replaced by your database name):
If the wedged database was ‘nk.rwb’ from the distribution, then retrieve ‘nk.rwb’ from the distribution. Otherwise rebuild your database (using ‘nk --add’ commands).
Next: Listing the Database, Previous: Wedged Databases, Up: Material Databases [Contents][Index]
FreeSnell comes with a database of refractive-index spectra for several hundred materials. If you want to add spectra of your own, it is probably better to create a separate database for them using the ‘-F’ option to the ‘nk’ script.
nk -F mynk.rwb --add *.nk "sicrir" ==> "sicr" "sio2ir" ==> "sio2" ag.nk: ev n k R(th=0) ; Silver al.nk: ev n k R(th=0) ; Aluminium au.nk: ev n k R(th=0) ; Gold, electropolished, Au (110) cr.nk: ev n k R(th=0) ; Chromium cu.nk: ev n k R(th=0) ; Copper fe.nk: ev n k R(th=0) ; Iron ge.nk: ev n k R(th=0) ; Germanium, single crystal li.nk: ev n k R(th=0) ; Lithium ni.nk: ev n k R(th=0) ; Nickel ta.nk: ev n k R(th=0) ; Tantalum ti.nk: ev n k R(th=0) ; Titanium (Polycrystalline) v.nk: ev n k R(th=0) ; Vanadium w.nk: ev n k R(th=0) ; Tungsten zn-e.nk: ev n k R(th=0) ; Zinc, E || to c^28 zn.nk: ev n k R(th=0) ; Zinc, E _|_ to c^28 zr.nk: ev n k R(th=0) ; Zirconium (Polycrystalline)
Your new databse can be accessed from design files thus:
(define mynk (open-database "mynk.rwb" 'rwb-isam)) (define Ag (interpolate-from-table (open-table mynk 'Ag) 2))
Next: Querying the Database, Previous: Creating Databases, Up: Material Databases [Contents][Index]
nk --list 7059 a-al2o3 a-c a-sih ag againp0 againp1 againp10 againp3 againp6 againp7 al al2o3 al2o3-e alas alas028t alas052t alas072t alas098t alas125t alas152t alas178t alas204t alas228t alas305t alas331t alas361t alas390t alas421t alas445t alas469t alas499t alas527t alas552t alas578t alas602t alas626t alcu algaas0 algaas1 algaas10 algaas2 algaas3 algaas4 algaas5 algaas6 algaas7 algaas8 algaas9 alon alsb alsi alsiti arachi asi au baf2 be beo bk7 bk7_abs caf2 carbam ccl4 cdse cdte co co_2 cor7059 cosi2-4 cr cr3si cr5si3 crsi2el2 csi cu cu2o cuo d-c fe fesi2el1 fesi2el2 fesi2epi gaas gaas031t gaas041t gaas060t gaas081t gaas100 gaas103t gaas111 gaas126t gaas150t gaas175t gaas199t gaas224t gaas249t gaas273t gaas297t gaas320t gaas344t gaas367t gaas391t gaas415t gaas443t gaas465t gaas488t gaas515t gaas546t gaas579t gaas603t gaas634t gaaso gaasox gan-tit gan01 gan02 gan03 gan60 gan70 gap gap100 gapox gasb gasbox ge ge100 h2o h2o-ice hdpe hfo2 hfsi2 hg hgcdte0 hgcdte2 hgcdte3 hgte inas inasox ingaas ingasb0 ingasb1 ingasb10 ingasb3 ingasb5 ingasb7 ingasb9 inp inpox insb insbox ir ir3si5e ir3si5p ito2 k kbr kcl lasf9 li lif mgf2 mgo mo mosi2 mosi2-e na nacl nb nbsi nbsi-e ni ni2si ni3si nisi os p_sias p_siud pbs pbse pd pd2si pd2si-e pe pt resi1-75 resige0 resige1 resige22 resige39 resige51 resige64 resige75 resige83 resige91 rh ringas0 ringas10 ringas20 ringas24 se se-e sf11 si si-t02 si-t10 si-t15 si-t20 si-t25 si-t30 si-t35 si-t40 si-t45 si100_2 si110 si111 si11ge89 si20ge80 si28ge72 si3n4 si65ge35 si85ge15 si98ge02 siam1 siam2 sic sige_ge sige_si sin_bf5 singas0 singas10 singas20 singas24 sio sio2 sion0 sion20 sion40 sion60 sion80 siop sipoly sipoly10 sipoly20 sipoly30 sipoly40 sipoly50 sipoly60 sipoly70 sipoly80 sipoly90 sipore snte stsg0 stsg064 stsg123 stsg169 stsg229 ta taox1 taox2 tasi2 tasi2-e te te-e thf4 ti tic tin tini tio2 tio2-e tisi-e v vc vn vsi2 vsi2-e w wsi2 wsi2-e y2o3 zn zn-e zncdte0 zncdte1 zncdte10 zncdte3 zncdte5 zncdte7 zncdte9 zns znse znsete0 znsete1 znsete10 znsete3 znsete5 znsete7 znsete9 zr zro2 zrsi2
Previous: Listing the Database, Up: Material Databases [Contents][Index]
Refractive index data can be retrieved at specified wavelengths, energies and wavenumbers.
$ nk co .3.um .5.um 1.3.eV co: 1.218+2.11i 300.nm (4.13.eV) (33333.3.cm^-1) co: 2.025+3.72i 500.nm (2.48.eV) (20000.cm^-1) co: 3.85+4.77i (954.nm) 1.3.eV (10485.2.cm^-1) $ nk Al 400.cm^-1 al: 75.77+1.7e+02i (25.0.um) (0.0496.eV) 400.cm^-1
The ‘--plot’ option creates an encapsulated PostScript graph of n and k/n for the material specified.
nk --plot co
http://people.csail.mit.edu/jaffer/FreeSnell/co.png
Next: Program Interface, Previous: Material Databases, Up: FreeSnell [Contents][Index]
Designs are coded in Scheme language files. More than one design can
be specified in a design file, permitting sharing of code. A variety
of design examples are contained in the validation suites
dielectric.scm, metallic.scm, and granular.scm.
The graphs output by these suites are shown and discussed in
http://people.csail.mit.edu/jaffer/FreeSnell/dielectric.html,
http://people.csail.mit.edu/jaffer/FreeSnell/metallic.html, and
http://people.csail.mit.edu/jaffer/FreeSnell/granular.html
Next: Optical Stack, Previous: Specifying Designs, Up: Specifying Designs [Contents][Index]
The index-of-refraction of dielectric materials often varies little with wavelength. In these cases the index-of-refraction can be a number. It is often convenient to give a symbolic name to numbers. For example:
(define ZnS 2.2) (define Ge 4.2)
After these definitions, layers can reference the identifiers:
(optical-stack
(substrate 1)
(layer ZnS 528.64e-9)
(layer Ge 178.96e-9)
(layer ZnS 250.12e-9)
(layer Ge 123.17e-9)
…
Sometimes the index-of-refraction is specified as a formula of wavelength. The Refractive index database at http://refractiveindex.info gives a formula for the refractive-index of the plastic PMMA over the range 0.4358.um to 1.052.um. We can use its formula as a Scheme function:
;; n^2 = C1 + C2*wl^2 + C3*wl^-2 + C4*wl^-4 + C5*wl^-6 + C6*wl^-8
(define PMMA
(let ((C1 2.399964)
(C2 -8.308636E-2)
(C3 -1.919569E-1)
(C4 8.720608E-2)
(C5 -1.666411E-2)
(C6 1.169519E-3))
(lambda (w) ; wavelength in meters
;; wavelength in microns and limited to valid range
(let* ((wl (max 0.4358 (min 1.052 (* w 1e6))))
(wl^-2 (/ 1 wl wl)))
(sqrt (+ C1
(* C2 wl wl)
(* (+ C3 (* (+ C4 (* (+ C5 (* C6
wl^-2))
wl^-2))
wl^-2))
wl^-2)))))))
For more compliated material properties FreeSnell retrieves the wavelength-dependent index-of-refraction by calling functions which interpolate values from the materials database (see Material Databases).
(require 'FreeSnell)
(require 'databases)
(require 'database-interpolate)
(define nk (open-database (or (getenv "NK_DATABASE_PATH") "nk.rwb")
'rwb-isam))
(define ge (interpolate-from-table (open-table nk 'ge) 2))
(define zns (interpolate-from-table (open-table nk 'zns) 2))
…
In this example ge and zns can be passed as arguments to
layer and substrate.
For dielectric films embedded with spherical metal granules much smaller than the thickness of the film and the wavelengths under consideration, Maxwell Garnett Theory provides a means to calculate the effective n and k. The thickness of the granular film must be several times the granule size; otherwise the more complicated machinations of [Granfilm] are required.
The ir and ir0 arguments specify the indexes of refraction for the metallic and matrix materials respectively. Each can be either a (complex) number or function of one real argument returning a (complex) number. The real number q is the fractional volume occupied by the metal.
granular-IR returns a complex index-of-refraction (or
function returning a complex index-of-refraction) for the composite
layer.
If Au is a spectral function, the following three definitions are equivalent:
(define ruby-glass (granular-IR Au 8.0e-6 1.5)) (define (ruby-glass w) (granular-IR (Au w) 8.0e-6 1.5)) (define ruby-glass (lambda (w) (granular-IR (Au w) 8.0e-6 1.5)))
Next: Plot-response, Previous: Specifying Materials, Up: Specifying Designs [Contents][Index]
Returns a data structure combining its layer arguments. Each
layer is returned from a call to layer or substrate.
Substrate arguments must be first or last and default to having an
index-of-refraction of 1. A substrate has arbitrarily large
thickness, and is the source or sink of test inputs (radiation).
Returns a layer having the specified index-of-refraction and thickness.
If ir is a number, then the index-of-refraction is ir at
all wavelengths. If ir is a procedure then the
index-of-refraction at wavelength w is (ir
w).
If the number thick is smaller than 1/50, then it is taken as the actual thickness. Note that the effective optical thickness will be larger than the actual thickness because light is slowed by the index-of-refraction.
If the number thick is larger than 1/50, then the thickness is
thick times nominal divided by the real-part of the
index-of-refraction at nominal, where nominal is either
the third argument nom or the value set by the nominal
function. This is a convenient notation for the fractional optical
wavelengths often used to specify filter elements.
Layers specified by layer model the interference effects of
reflections of reflections. This is correct for thin layers or if the
modeled optical system will be illuminated by coherent light. But
layers thicker than several wavelengths have variations extremely
sensitive to incident angle.
Incoherent illumination will average over the wiggles. For these layers FreeSnell computes the transmitted and reflected power ratios, rather than E-fields.
Returns an incoherent layer having the specified index-of-refraction and thickness.
Returns a substrate having the specified index-of-refraction.
If ir is a number then the index-of-refraction is ir at
all wavelengths. If ir is a procedure then the
index-of-refraction at wavelength w is (ir
w).
If substrates are not specified, then their index-of-refraction defaults to 1 (vacuum).
To place a substrate between two sets of layers, use layer*
instead.
Sets the default nominal thickness to nom. Multiple
nominal commands are allowed interspersed with layer
commands. The arguments to optical-stack are considered in
order from the first to the last.
Inserts j copies of the sequence layer1, layer2, … into the stack.
Previous: Optical Stack, Up: Specifying Designs [Contents][Index]
One or more of arg1, arg2, … should be an optical
stack returned by optical-stack, or a value returned by a call
to IR. The other arguments should be values returned by the
functions in sections Ranges and Units, Traces, and
Other Outputs.
Plot-response creates a graph, data file, or color patches as
directed by its arguments. If more than one optical stack is given,
the same quantities are computed for each optical stack; but all are
plotted to a single graph.
Each color1, … should be a string naming a Resene color, a
saturate color, or a number between 0 and 100. If supplied, there
should be one color for each optical-stack. color1, …
default to black (0). If stack-colors is called more than
once, then its color arguments are appended together.
stack-colors causes the traces from each optical stack to be
drawn in its corresponding color.
Next: Traces, Previous: Plot-response, Up: Plot-response [Contents][Index]
Sets title for the run to str. If the string filebase is given, then it is used for the output filename root; otherwise str is used.
According to the symbol sym, sets the disposition of plots to be:
| eps | filebase.eps |
| ps | filebase.ps |
| png | filebase.png |
| jpg | filebase.jpg |
| jpeg | filebase.jpeg |
| filebase.pdf | |
| #t | views filebase.eps using ps:viewer. |
If output-format is not used, then the output-format defaults
to the value of top-level identifier *output-format*, which
defaults to #t.
If a pair of nonnegative exact integers, k1 and k2 follows sym, then the plot will be k1 pixels horizontally and k2 pixels vertically.
The output-format command does not affect the data written by
output-data.
If a string fnt is supplied, then it names the PostScript font
which will be used. The default value is Times.
If a nonnegative real number x follows the fnt, then x is the fontsize.
If two strings follow, then they are used as the templates whose printed representation using fnt is used to size the left and right margins respectively. If not specified, the templates default to ‘-.0123456789’.
If x is not specified and k1 is, then the font height will be k1/33. If neither is specified, then the font height will be 12.
The font command does not affect the data written by
output-data.
If the first character of file is ‘|’, then lines of data are piped to the stdin of the command line in file; otherwise a file of data is written to file.
str1 and str2 are printf format strings for the first number and the rest of the numbers printed on one line. If #f is passed, then the corresponding numbers are written with full Scheme precision and tab delimited.
Sets the ordinate range of the plot to low to high.
Sets the ordinate range of the plot to low to high decibels.
Sets the abscissa range of the plot to be linear from wavelengths 0.75*w to 1.25*w.
Sets the abscissa range of the plot to be linear from wavelengths w1 to w2.
Sets the abscissa range of the plot to be linear from wavelengths w1 to w2 in a graph rectangle from wavelengths g1 to g2.
Sets the abscissa range of the plot to be logarithmic from wavenumbers 0.666*w to 1.5*w.
Sets the abscissa range of the plot to be logarithmic from wavenumbers w1 to w2.
Sets the abscissa range of the plot to be linear from wavenumbers w1 to w2 in a graph rectangle from wavenumbers g1 to g2.
Sets the abscissa range of the plot to be linear from energy 0.666*x to 1.5*x electron Volts.
Sets the abscissa range of the plot to be linear from energy x1 to x2 electron Volts.
Sets the abscissa range of the plot to be linear from energy x1 to x2 electron Volts in a graph rectangle from energies g1 to g2 electron Volts.
Sets the abscissa range of the plot to be logarithmic from wavelengths 0.666*w to 1.5*w.
Sets the abscissa range of the plot to be logarithmic from wavelengths w1 to w2.
Sets the abscissa range of the plot to be logarithmic from wavelengths w1 to w2 in a graph rectangle from wavelengths g1 to g2.
Sets the abscissa range of the plot to be linear from angles 0.75*theta to 1.25*theta.
Sets the abscissa range of the plot to be linear from angles theta1 to theta2.
Places vertical arrows at abscissa coordinates w1, w2,
…. The marker command does not affect the data written
by output-data.
Sets the number of abscissa coordinates to k. The default value is 200.
Sets the number of abscissa coordinates to k. spacing is one of the (single-quoted) symbols ‘eV’, ‘ratio’, ‘wavelength’, or ‘wavenumber’, and determines the spacing of the samples. The default spacing is ‘ratio’ if the endpoint ratio is between 1.5 and 10000; and ‘wavelength’ otherwise.
Note that spacing does not need to match the abscissa scale. To generate 10 samples at evenly spaced wavelengths, do:
(samples 10 'wavelength)
Convolves the traces (before converting values to decibels) with a Gaussian filter having wavelength standard deviation sigma.
Next: Other Outputs, Previous: Ranges and Units, Up: Plot-response [Contents][Index]
These functions specify whether the plot holds angle constant and
varies wavelength; holds wavelength constant and varies angle; or
plots components of the index-of-refraction of a material. Multiple
invocations of any one of these functions puts all those specified
traces in one plot. To generate separate plots call
plot-response multiple times.
The type of a trace appearing in a plot is specified by a symbol. The first ten in this table are for separate polarizations. The rest average the two polarizations.
| T_s | S-plane transmission |
| R_s | S-plane reflection from top |
| B_s | S-plane reflection from bottom |
| A_s | S-plane absorption from top |
| L_s | S-plane absorption from bottom |
| T_p | P-plane transmission |
| R_p | P-plane reflection from top |
| B_p | P-plane reflection from bottom |
| A_p | P-plane absorption from top |
| L_p | P-plane absorption from bottom |
| T | tranmission |
| R | reflection from top |
| B | reflection from bottom |
| A | absorption from top |
| L | absorption from bottom |
A trace can also be a quoted scheme expression combining numbers and
the symbols listed above with the operators +, -,
*, /, ln, log_10, and average. The
following example computes the reflectivity relative to a substrate
reflectivity of 0.023:
(incident 45 '(/ (- R_p .023) .023))
A plot of trace1, trace2, … versus wavelength will be generated for radiation incident at angle degrees.
The angle argument can also be a list of angles in degrees. In this case the plots of trace1, trace2, … will be averaged over the angles given.
This is useful when profiling materials whose thicknesses are several times wavelengths of interest. Plots at a single angle of incidence can oscillate wildly with wavelength as the reflections go in and out of phase, constructively and destructively interfering.
A plot of trace1, trace2, … versus incident angle will be generated for radiation at wavelength w.
Plots characteristics of procedure substance versus wavelength. Symbols comp1, comp2, … determine the characteristics to be plotted:
n
k
k/n
Normal reflectance from a thick layer.
Previous: Traces, Up: Plot-response [Contents][Index]
Computes the color of trace at angle degrees from normal using CIE illuminant D65.
The following statement will cause plot-response to compute the
reflected color (average of both polarizations) at 30 degrees from the
surface normal.
(color-swatch 30 'R)
If there are any color-swatch statements passed to
plot-response, then a file named
filebase-color.png will be written containing 64x64
pixels color squares, one for each color computed. The squares are
arrayed horizontally in the order they are passed to
plot-response. Vertically, one such row is generated for each
optical stack.
The filebase string is that set by the title command.
For each stack, prints out the results of integrating each trace specified (token1, token2, …) at angle with "Key Centre for Photovoltaic Engineering UNSW - Air Mass 1.5 Global Spectrum" solar irradiance.
Next: About FreeSnell, Previous: Specifying Designs, Up: FreeSnell [Contents][Index]
(require 'fresnel-equations)
layers is a list of lists of index-of-refraction and thickness. The index-of-refraction may be a complex number or a procedure of wavelength (w) in meters returning a complex number.
Layers with negative thickness are modeled as incoherent (with positive thickness); otherwise as coherent (with inteference fringing).
The index-of-refraction of the top and bottom media are given by the first and last layers, which must have thickness 0. w is probe wavelength. th_i is the angle of the incident ray in radians.
Combine-layers returns a list of three non-negative real
numbers:
The transmitted and forward ratios sum to 1.0 if layers are all dielectric (lossless). The transmitted and reverse ratios sum to 1.0 if layers are all dielectric (lossless).
Negative w computes the S-polarization, else the P-polarization.
Complex numbers z1 and z2 are the indexes of refraction of the incident and opposite side of the boundary plane between two materials. th-i is the angle of incidence (from the normal of the boundary plane).
snell-law returns the exit angle (from normal) of an incident
ray impinging at th-i from normal.
If the ray undergoes total internal reflection, then the returned angle will not be real. If z1 and z2 are real, then the real part of the returned value will be pi/2 and represents a quickly decaying evanescent wave. Otherwise, the real part of the return value tends toward pi/2. I don’t know a physical interpretation of the imaginary part.
(snell-law 2.8 1.3 .1) ⇒ 216.71826868463917e-3 (snell-law 2.8 1.3 .3) ⇒ 689.9583515921762e-3 (snell-law 2.8 1.3 .4) ⇒ 994.9783891781343e-3 (snell-law 2.8 1.3 .5) ⇒ 1.5707963267948965-254.68865153727376e-3i
Next: Index, Previous: Program Interface, Up: FreeSnell [Contents][Index]
Free Software
Fre snel Equations
Snell's Law
=========
FreeSnell
The author can be reached as ‘agj@alum.mit.edu’. The most recent information about FreeSnell can be found on the FreeSnell home page:
http://people.csail.mit.edu/jaffer/FreeSnell
Next: Using FreeSnell, Previous: About FreeSnell, Up: About FreeSnell [Contents][Index]
#! /bin/sh wget http://groups.csail.mit.edu/mac/ftpdir/scm/slib-3c1-1.noarch.rpm wget http://groups.csail.mit.edu/mac/ftpdir/scm/scm-5f4-1.x86_64.rpm wget http://groups.csail.mit.edu/mac/ftpdir/scm/wb-2b4-1.x86_64.rpm rpm -U slib-3c1-1.noarch.rpm scm-5f4-1.x86_64.rpm wb-2b4-1.x86_64.rpm wget http://groups.csail.mit.edu/mac/ftpdir/scm/FreeSnell-1c4.zip unzip FreeSnell-1c4.zip (cd FreeSnell; ./configure --prefix=/usr/local/; make install)
#! /bin/sh wget http://groups.csail.mit.edu/mac/ftpdir/users/jaffer/slib.zip wget http://groups.csail.mit.edu/mac/ftpdir/users/jaffer/scm.zip wget http://groups.csail.mit.edu/mac/ftpdir/users/jaffer/wb.zip wget http://groups.csail.mit.edu/mac/ftpdir/scm/FreeSnell.zip unzip slib.zip unzip scm.zip unzip wb.zip unzip FreeSnell.zip (cd slib; ./configure --prefix=/usr/local/; make install) (cd scm; ./configure --prefix=/usr/local/; make scmlit; make scm5; make mydlls; make wbscm.so; make install) (cd FreeSnell; ./configure --prefix=/usr/local/; make install)
Previous: Installation, Up: About FreeSnell [Contents][Index]
To run FreeSnell from the C:\Program Files\SCM\FreeSnell diretory, click on the FreeSnell desktop icon. In Unix, from the ‘FreeSnell’ directory run ‘scm’.
You can then type expressions to the SCM interpreter. To run FreeSnell’s regression suites type:
(load "dielectric.scm") (dielectric) (load "metallic.scm") (metallic) (load "granular.scm") (granular) (load "coherence.scm") (coherence) (load "polyethylene.scm") (polyethylene)
I set up design directories as peers of ‘FreeSnell’; that is, both are subdirectories of the same directory. I find it useful to put related designs in one directory.
In order to load FreeSnell files, you should create a local SLIB catalog (named usercat) within the design directory or your HOME directory. This catalog translates symbols to the pathnames of FreeSnell files. Here is the usercat included in the FreeSnell distribution, which is suitable to copy to design directories which are peers of FreeSnell:
;;; "usercat": SLIB catalog additions for thin-film optics. -*-scheme-*- ( (fresnel-equations . "fresneleq") (optic-compute . "opticompute") (optic-plot . "optiplot") (optic-color . "opticolr") (video-processing . "video") (optic-solar . "solar-am15") (FreeSnell aggregate optic-compute optic-plot optic-color optic-solar) )
Design files can then load FreeSnell with the expression:
(require 'FreeSnell)
Realize that this usercat file assumes that the FreeSnell directory is named FreeSnell. If your FreeSnell directory is named something else, then substitute its name for FreeSnell in the right hand side of lines in usercat.
Previous: About FreeSnell, Up: FreeSnell [Contents][Index]
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