and updates it. Thus it is not editable by a user. Since updating of the library on the actual machine can only be accomplished whenever a patch is applied an online version of the library is also maintained. Pro-vided the machine has access to the Internet the li-

brary can be searched with the Browse Online Mate-rials Library... Command, and the online version of the library can, of course, be updated more frequently than the onboard version.

Different samples of a pure crystalline material will generally exhibit the same optical constant values at the same wavelength and that is a principal reason for the designation of constant. However this is not nec-essarily the case with thin film materials. Their micro-structure, for example, tends to vary with deposition conditions, impacting their optical constants. As a

result many of the materials in the Materials Library have multiple entries showing sub-tle differences in their corre-sponding values.

There are many different sources of loss in a material, but almost all depend on the square of the electric field amplitude and thus can be lumped together, and charac-terized by a single extinction

coefficient, k. The irradiance of a wave along its physical

propagation distance z, varies

as exp(-4πkz/λ), z and λ hav-

(Continued on page 2)

Materials in the Essential Macleod

The Tools menu in the Essential Macleod includes

the items Browse Materials Library... and Browse Online Materials Library... that give access to the extensive library of materials data provided with both the Essential and the Concise Macleod. The optical constants of materials, that is their refractive index,

n, and extinction coefficient, k, are of vital impor-tance in optical coating design and performance cal-culation. Refractive index is the ratio of the velocity of light in free space to that in the material while ex-tinction coefficient is a measure of the exponential reduction in amplitude as the wave traverses the ma-terial. Both vary with the wavelength of the light, a phenomenon known as dispersion.

The Materials Library is provided by Thin Film Center as a reference. Thin Film Center maintains it

Macleod Medium December 2015 Volume 23 Number 4

Thin Film Center Inc, 2745 E. Via Rotunda, Tucson, AZ 85716-5227, USA

Figure 1. Searching the library for RG610 has found the data for this glass in the Schott collection. A material and a substrate document are available.

ing the same units. The expression applies to any value

of z, even to long distances and certainly to passage through a substrate. However, there is a problem. For any light to pass through a thickness of several milli-metres of material, the extinction coefficient must be vanishingly small. Such miniscule extinction coeffi-cients have almost no effect on the transmission of light through a thin film and so variations in their mag-nitudes have almost no influence on the properties of a thin film but do considerably affect the transmittance of a slab of several millimetres of material. If we are accurately to calculate transmittance of such thick ma-

terials, we need very precise values of k that have been

measured on appropriate slabs of material. In fact, k is not often used for such purposes unless it is known to

(Continued from page 1)

Page 2 Macleod Medium

be completely reliable. Absorption coefficient, α,

given by 4πk/λ, expressed usually in inverse centi-metres is a much more useful quantity. The loss as light propagates can be expressed as

d being the distance propagated, I is the irradiance

at distance d and I0 at d = 0. Thus α is what we nor-mally use in our calculations involving thick slabs of material. Unfortunately publication of direct meas-

urements of α is rare and normal practice is to give

a value of I/I0 at a particular value of d, a quantity known as Internal Transmittance and usually stated

in percent. Of course, knowing d, we can immedi-

ately derive the corresponding value of α. To keep matters simple for the user, then, we store this in-

formation in the Materials Library as internal transmit-tance of the given thickness of material and the pro-gram calculates the necessary absorption coefficient. Refractive index and extinction coefficient are then used for the surface properties while absorption coeffi-cient is used for transmittance through the substrate.

Where do the data originate? We try to keep track of

that in the Notes tab of the documents. The bulk of the data is extracted from publications. A few common materials date back to the original DOS version that did not include the source. Rather than guess, we sim-ply then state that the source is unknown.

Our practice is to avoid any editing of the published figures - we leave that to the user - and since manufac-turers seldom publish internal transmittance figures at values of wavelength identical to those for refractive

index, n and k information and internal transmittance must be maintained sepa-rately, each with its own set of wavelength values.

At the present time these data are kept in completely sepa-rate files with the designation

Material for the n and k data, and Substrate for the internal transmittance. Not all materi-als have a corresponding sub-strate file but, in the library, if

(Continued on page 3)

Figure 3. Raw imported material data exhibiting variation that gives quite sharp corners with linear interpolation.

0 exp -I I d (1)

Figure 2. The new style of the mate-rial document soon to be released.

Macleod Medium Page 3

internal transmittance. This new form of the material document is completely compatible with, and can be used along with, the existing two documents. Conver-sion to the new form can be a completely gradual process.

Now we return to the n and k values. Although we avoid editing the data we provide lots of editing tools for the user. To illustrate some of these tools we set up an admittedly contrived example, Figure 3.

Interpolation of data in the software is linear because linear interpolation contains no surprises. However, it is possible to use cubic spline interpolation in the ma-terial document itself, when we are able visually to check the result. To activate cubic spline interpolation simply edit the material document by inserting enough points through the document. The added points will interpolate the wavelengths linearly but instead of val-

ues of n and k, asterisks will appear. When a plot is selected in the Edit menu for the document, these points will be replaced by values interpolated by a cu-bic spline. Figure 4 shows the result of applying this process to our example, where we have inserted three points in between each existing point. More points would yield still smoother curves. Note that in interpo-lation, the resulting curves pass exactly through the existing points, also shown.

Smoothing is an alternative form of manipulation using a model with parameters varied to give best fit. The smoothed results do not necessarily pass through existing points. The available models are intended for dielectric materials and treat refractive index and ex-tinction coefficient separately. Cauchy and Sellmeier models are available for refractive index and Cauchy and exponential for extinction coefficient.

Note that in Cauchy and Sellmeier, following com-mon practice, wavelength is expressed in micron with

(Continued on page 4)

both exist then they are given the same name so that any substrate file that exists will open along with the material. You will find that substrate files accompany all glasses and most material that could be used as sub-strates but thin-film materials are generally represented by material files only.

Having the same name for material and substrate has allowed us to use a single reference to designate both in a medium in a design. The success of this approach has prompted us to extend the idea still further. Very soon we will be introducing a new version of the mate-rial document that we are currently testing. This will contain both data sets in one single document. Figure 2 shows the proposed arrangement. There are no changes in the data themselves but they will be con-tained within one document rather than two. This gives us the opportunity to extend the range of choices available for internal transmittance and the extra field, Internal Transmittance Model, has four alternatives. Un-defined means exactly what it suggests, and, if a sub-strate field is available, then whatever is entered there will define what should be used in calculations. Loss-less, as usual, implies 100% internal transmittance. Ta-ble indicates use of the contained table of internal transmittance. Use k is a completely new concept and

accepts that the k of the given material is accurate enough to be used in the derivation of the necessary

(Continued from page 2)

Figure 4. Insertion of four points between each of those in Figure 3, followed by cubic spline interpolation, rounds the sharp corners

but note the drop in the k values between 900nm and 1000nm clamped at zero.

1 20 2 4

2 2

1 2

2 2

1 2

or

1

exp

A An k A

A An

B B

Bk A

Cauchy:

Sellmeier:

Exponential:

(3)

Page 4 Macleod Medium

Essential Features

We are constantly working on the Essential Macleod. This involves extensions and improvements but also, we admit, the occasional bug fix. So that our users can take advantage of this activity we publish frequently patch files on our web site. These patch files can be

accessed through the Check for Updates command in the program or directly from the Support page of our web site. They should not be mistaken for installation programs. They replace only part of the installation and cannot operate unless a correct corresponding ver-sion of the program is already installed. The system is explained fully on the Support page. A full installation requires an installation program, not a patch, and we have to supply a URL for that.●

Figure 5. Cauchy smoothing has been used for both n and k val-ues in the data of Figure 2.

Figure 6. The results of Sellmeier smoothing of the n and expo-

nential of the k values of Figure 2.

consistent units for the constants. The exponential model uses nanometre.

Parameters can either be entered, when the material editor will use them to calculate the correct values, or the tool can find values to give the best fit as illustrated in Figures 5 and 6.

The table can be edited to reflect the model values if necessary. Derive Table... In the Edit menu replaces the table with values calculated from the model. However this is not a necessary prelude to the use of the model in calculation as explained later.

There are useful tricks that help to achieve the most

suitable values. The table of n and k may not exhibit a constant interval in wavelength, resulting in less weight afforded to certain spectral regions in the fitting. It is useful to select a suitable small wavelength interval in the calculation parameters. Corresponding points are linearly interpolated before the fitting process. For the

(Continued from page 3)

exponential fitting, the Minimum k parameter can be

very helpful. Small values of k are quite difficult to measure in a thin film and frequently have quite large proportional errors. Since the absolute values are small, such errors have little effect on calculated perform-

ance. The larger values of k at shorter wavelengths will usually be much more reliable. By setting the minimum

k value as a larger number, the greater values of k are treated as the significant ones and the fit to these larger numbers will be improved.

Once a set of model parameters has been created, the calculations in the Essential Macleod can be arranged to use the model rather than the table by setting Re-fractive Index Model and Extinction Coefficient Model at the head of the material document appropriately, and saving the document with that setting. No data are lost in this operation and it is always possible to return to the table of values rather than the model, provided the table has not been changed by the Derive Table... com-mand.●

Macleod Medium Page 5

James and a Plasmon Problem

The student was hoping that James could help her with a problem.

"I am working on a project involving the behavior of a suspension of small particles in oil. The quite thick oil we are using has a refractive index of 1.50 and it contains dispersed magnesium fluoride powder with a refractive index of 1.38. My interest is particularly in the settling and sedimentation of the dispersed parti-cles. I thought a useful way of following the buildup of sediment without disturbing it would be to use a sur-face plasmon detector. This would consist of a prism carrying on its hypotenuse a silver layer of the appro-priate thickness with its outer surface facing upwards so as to collect the sediment. The displacement of the p-polarized resonance would be easy to measure and would give me real time information about the pro-gress of the sedimentation without causing the slightest disturbance to the sediment. I have already been in-volved in a study of atmospheric contamination where I used a similar technique. The contaminant was essen-tially dielectric and as its thickness increased the reso-nance moved to greater angles of incidence. I was able to measure thickness changes of a fraction of a nano-

metre. The prism in that case was made of crown glass. For this sedimentation experiment of course I have to use a high-index flint"

"Your ideas sound perfectly feasible," said James. "Now tell me what is the problem."

"When I did the contamination experiment in air," explained the student, "it didn't matter what the refrac-tive index of the contaminant turned out to be, the resonance always moved to greater angles of incidence with increasing contaminant thickness. This morning I ran some calculations on the magnesium fluoride sedi-mentation assuming a prism of N-LAK14 with an in-dex of just under 1.7 and to my surprise, the resonance moves towards smaller angles of incidence with in-creasing thickness. That astonished me and so I re-peated my calculations several times. I am convinced that the effect is correct but I just cannot see why it should happen. Can you help me?"

"You are absolutely correct in your calculations," be-gan James, "but you are missing something very impor-tant. Let me explain."

James then explained why the resonance moved in what the student thought was the wrong direction.

What was James's explanation?●

Please turn to Page 7 column 1 for the answer

Figure 8. Calculation of the surface Plasmon resonance with no added layer (right) and with 10nm of magnesium fluoride (left) showing the shift to smaller angles.

Figure 7. Sketch of the arrangement of the student’s experiment. The measurement system is completely isolated from the experi-mental chamber and so does not interfere with the progress of the sedimentation.

Page 6 Macleod Medium

The central rôle of the Essential Macleod is, of course, the design and analysis of optical coatings but its set of powerful tools can be used for much more. It is a very useful and general tool for data manipulation, calculation and display. And its capabilities are ex-tended enormously if Function is available.

Before the program can be used in this manner, the data must be imported into it, and there are lots of ways to accomplish this. The principal requirement is that the data should already exist somewhere in a con-sistent columnar format. The simplest and most direct way is to copy the data to the Clipboard and paste it into a table. This, of course, implies that the applica-tion hosting the data should fully support the Clip-board. Also, text files can mostly be read directly into the program and there are also some special formats, such as the Hitachi .uds format, that can also be im-ported.

Let us take as an example, data that is present in an Excel sheet, Figure 9. We select the data, including the headers, and copy it to the Clipboard. Next, we open a new table in the Essential Macleod. This can have the default of two columns. The necessary number will be

chosen later automatically. Use Paste in the Edit menu or Ctrl+V to paste in the Excel data. The window of the Import Data tool appears, Figure 10, that allows us to flag unwanted entries, choose column separators, headers, and those columns we wish to import. The result is a table containing the data. In the Core Mod-ule we can immediately plot the data, Figure 11, and use the Statistics Tool to extract parameters such as maximum and minimum values and width at a given

(Continued on page 7)

Data from

Elsewhere

Figure 9. Data in Excel showing measured weekly milk yield from dairy cows.

Figure 10. Pasting the data into a table.

Figure 11. The plot of column 2 of the table. The statistics tool can be used to produce the analysis reported in the label.

Macleod Medium Page 7

James (continued from page 5 Column 2)

"There is no problem," explained James. "It is all quite well understood. The first thing to notice is that, at the incident angle corresponding to the resonance, the propagation in the emergent medium of oil is be-yond critical. Since the magnesium fluoride has still lower refractive index than the oil, it too will have a propagation angle beyond critical.

"The light is p-polarized and a dielectric material be-yond critical behaves in a rather special way. Its phase thickness becomes negative imaginary, so that there is the expected exponential decay in amplitude of the resulting evanescent wave as it penetrates the material, but the tilted admittance becomes positive imaginary. This should not be confused with the appearance of gain. It implies that the admittance locus, which looks like that of a perfect metal, is described counterclock-wise with increasing thickness rather than the usual clockwise. It's eventual termination, therefore, is the

admittance point on the positive imaginary axis, not the negative as with the perfect metal.

"The modified tilted p-admittance is infinite imagi-nary at the critical angle and then slides down the posi-tive limb of the imaginary axis to reach the origin at grazing incidence. Because the index of the magnesium fluoride is less than that of the emergent medium it moves down before it so that it is always less. Remem-ber that this is also the termination point towards which the p-admittance locus moves. Thus the effect of the magnesium fluoride coating is to displace the admittance presented by the oil, also on the imaginary axis, downwards towards the origin. This implies that as the angle of incidence increases the surface plasmon condition will be met sooner than in the absence of the magnesium fluoride. In other words the resonance will move to smaller angles.

"You can surely understand that any material with index higher than that of the oil, regardless of whether or not it is beyond critical will exhibit an increase in resonant angle as it is added to the silver surface."●

level. With Function, there are almost limitless possi-bilities. As an example we create a bar chart of the data shown in Figure 12. The important fragment of the code is shown in Figure 13. The constants used to specify the plot type and color are defined in the in-cluded file PlotConstants.bas.

(Continued from page 6)

Figure 12. A bar chart of the data can readily be produced with a script in Function.

Figure 14. It is straightforward to analyze the results in the table to produce statistical parameters. Here we have the mean yield and its standard deviation.

Then, finally, a pair of statistical parameters are calculated. Once the data has been read into the two arrays Xvals and Yvals it requires quite simple code to perform the calculations the results of which are shown in Figure 14 and displayed using a Message Box statement.●

Figure 13. The part of the code that creates and plots the bar chart. The table values are in the arrays Xvals and Yvals.

The course, given by Angus Macleod, covers thin-film funda-mentals and lasts around five hours. It is available on DVD so that it can be played on a computer. The set is accompanied by a pdf file summarizing the content. There are seven lectures with titles and durations:

1

2

3

4

5

6

7

Complex numbers

Complex waves

Optical admittance

Admittance transformers

Applications

Matrix method

Oblique incidence

31 mins

20 mins

37 mins

29 mins

59 mins

71 mins

60 mins

The price for the complete set is $600 (US) plus shipping.

Topics in Optical Coatings

Short Video Course

Japan: Naoji Amano, Shincron Co., Ltd.

Sales Dept. 3-5 Minatomirai 4 Chome,

Nishi-Ku, Yokohama 220-8680, Japan Tel: +81 45 650 2411 Fax: +81 45 650 2448

email: n276amano@shincron.co.jp web: www.shincron.co.jp

Japan: Tsutomu Tsuchiya Sigma Koki Co Ltd

1-19-9 Midori Sumida-ku, Tokyo 130-0021, Japan

Tel: 03 5638 6551 Fax: 03 5638 6550 email: t.tsuchiya@sigma-koki.com

Europe: Len Traub P and T Consulting Ltd

31, Old Perth Road, Milnathort,

Kinross-shire KY13 9YA, UK Tel: 01577 864051

email: sales@PandT.net

Korea: Tae-Woon Kim DigiClassic Ltd

Rm 1309 Hanseo Bldg 11-11 Yoido-dong, Youngdungpo-Ku

Seoul 150-746, Korea Tel: 02 785 3854 Fax: 02 6747 7470

email: webmaster@rf.co.kr

Taiwan: Alan Tuan, Collimage International Co Ltd

4F, No. 232, Sec. 3 Hoping East Road Taipei 106, Taiwan

Tel: 02 8732 8585 Fax: 02 8732 8586 email: sales@collimage.com.tw web: www.collimage.com.tw

India: Jayant Kulkarni , Seagull India Office: “Gloriosa”

Flat No 3 & 5, Plot No 9, Udaybaug B T Kawade Rd, Ghorpadi, Pune 411 013, India

Tel: 02 323 0394 email: seagulloptics@gmail.com

web: www.seagullindia.co.in

Hong Kong: Dr.-Ing. Feng Qian Leyfond Limited

Unit B, 9/F Winner Commercial Building 401-403 Lockhard Road Wan Chai, Hong Kong

Tel: ++852 2575 6688 Fax: ++852 2575 6993 email: qianfeng1964@126.com

web: www.leyfond.net

China: Ms Angie Zhu Infotek Information Science and Technology,

Room 408, Building 7, Yong Deng Business Plaza No. 277, Yongdeng Road

Putuo District Shanghai, 200331, P.R. China

Tel: +86 21-64860708 Fax: +86 21-64860709 email: sales@infotek.com.cn web: www.infotek.com.cn

Singapore: Bryan Khor APP Systems Services Pte Ltd

11 Toh Guan Road East #03-01 APP Enterprise Building

Singapore 608603. Tel: 6668 4605 Mobile: 9147 9007

Fax: 6560 6616 email: bryan.khor@appsystems.com.sg

Write, call, fax, e-mail or visit our web site for more details of videos or courses

is prepared exclusively for members of their Update Service by

Thin Film Center Inc 2745 East Via Rotunda, Tucson, Arizona 85716-5227, USA

Tel: (520) 322 6171 Fax: (520) 917 4395 info@thinfilmcenter.com www.thinfilmcenter.com

Copyright © Thin Film Center Inc 2015 All rights reserved

Macleod Medium

A collection on DVD of short video introductions to various aspects of optical coatings. Each video is essentially a stand-alone presentation that does not rely on the others except that there are certain conventions and definitions that may be assumed. For that reason the Fundamentals video that deals with basic issues and sets the scene for the videos is included, at no extra charge, with any combination of the others. They are formatted as *.mov files intended for use on either a PC or an Apple machine. This new set differs completely from the existing Short Video Course (see column 1) and supplements rather than replaces it.

Fundamentals Included 30 mins

Introduction to Coating Design $125.00 57 mins

Basics of Ultrafast $125.00 32 mins

Basics of Rugates $125.00 35 mins

Topics in n and k Extraction $125.00 35mins

Color in Coatings $125.00 49 mins

The Complete Set $600.00

We run a variety of short courses each year, in Asia, Europe and USA. Please check our web site for more information:

http://www.thinfilmcenter.com/schedule.html

As soon as details become firm they are posted there.●

Short Course News