Nonlinear Optics - Science topic

In Linear optics, the study and manipulation of light in a linear and deterministic manner. The response of optical element is proportional to the amplitude of the incident light wave. Nonlinear optics is the study of the interaction of intense laser light with matter. The nonlinear susceptibility is a quantity that determines the nonlinear polarization of a material medium in terms of the strength of the applied electric field. There are many nonlinear optical processes like second harmonic generation, sum and difference frequency generation, optical parametric oscillations, Third harmonic generation, intensity dependent refractive index, saturable absorption, two-photon absorption. The electro optical effect is the phenomenon that the refractive index of a material is modified with an electric field. The linear electro-optic effect is the Pockels effect where the refractive index change is proportional to the electric field strength. Only non-centrosymmetric materials exhibit the linear electro-optic effect e.g. LiNbO3, KTP, BBO etc. On the other hand, all centrosymmetric media exhibit the quadratic electro-optic effect i.e. Kerr effect.

Wow! Not much optical path length in that crystal!

I think your plan with the UV cure adhesive sounds fine. We more often use a thermally cured epoxy like Ablebond or Minbond, but we’ve had good luck with UV cured adhesive in less challenging uses.

There are just a couple things to consider. It doesn’t stick until the UV light hits it, so you’ll want perform the mounting in an orientation where gravity helps keep it in place until you cure the glue. A similar point: it doesn’t stick unless UV light gets to it. It doesn’t look like an issue here: it’s just a thin plate and BBO is transparent to the curing light. But, the point is, you want to be sure the curing light gets to the glue.

The one think that concerns me: why did it debond in the first place? Glued at the corners, there is little thermal conductivity. Do you think there might have been enough absorption in the BBO to cause any differential thermal expansion? This looks like a simple arrangement where that isn’t an issue, and SHG in BBO generally doesn’t deposit much heat. Nevertheless, it might have come unglued for a reason.

Thanks Kirill Brekhov

II I Sc, Bangalore

Dear Maxim,

LGS and LGSe crystal can be purchased today from only one supplier. :)

There are also many new very interesting nonlinear materials with high laser damage and large nonlinearity coefficients.

Sincerely,

Dmitry.

I'm looking for a team.

Dear Sumeet Sonvane

In the nonlinear optics literature beta can be used for different physical quantities. The most common is the nonlinear (two photon) absorption coefficient that is a generalization of Beer's law I (z) = I_0*exp(-Beta*I_0*z), assuming small absorption. The conversion from SI units (m/W) to esu units (the cgs system) is a factor of 10^-9. See the Wikipedia article

Hope this helps

Best regards

Michael

Thank you Bikash Kumar Das and Michael Belsley

Here are some info I have found. Below are the statements in the articles.

As an important part of modern optics and photonics, nonlinear optics is of great significance for photonic applications such as optical harmonic generation [1,2], ultrafast light switching [3], optical imaging [4] and optical data storage applications [5,6]. Yet, the inherent nonlinear response of materials is usually weak and difficult to control. The existing nonlinear optical crystals improve the nonlinear conversion efficiency by increasing the length of the interaction. Researchers have also taken a series of methods to improve the nonlinear properties of materials, but the designs are often more complex and less effective. It is urgent to look for materials with high stability and huge nonlinear optical (NLO) response. https://doi.org/10.1016/j.optmat.2021.110841

Another example: if the optical properties of nonlinear oxides are repeatable, this high level of accuracy would be unnecessary. It is shown that MBE affords unique advantages, particularly in the crucial areas of stoichiometry control and deposition uniformity, while offering significant challenges in areas such as growth rate and, in limited cases, interfacial chemistry control. https://doi.org/10.1116/1.1926294

The observation that with increasing particle size SA becomes more pronounced is consistent with earlier measurements on Ag and Au nanoclusters and NPs. (22, 34, 62) This effect is understood in terms of size dependence of the electronic structure of the particles. For very small particles the discrete nature of their electronic states hinders plasmonic excitations, reducing considerably their linear absorption and, thus, corresponding to very high saturation irradiance for the particle’s first excited state. https://doi.org/10.1021/acs.jpcc.7b09017

you can use elk code

thank you so much

Nonlinear optics describes the behavior of light in media with nonlinear response. Its traditional topics cover different types of parametric processes, such as second-harmonic generation, as well as a variety of self-action effects, such as filamentation and solitons, typically observed at high light intensities delivered by pulsed lasers.

there is a direct relationship between the refractive index and the energy gap of the semiconductor

you can check the following: https://www.sciencedirect.com/science/article/abs/pii/0020089181900336

In my experience, there is no need to use another laser for alignment. I also used a Mech Zehnder type f-2f interferometer. I used a grating to spatially disperse and a APD to detect, as shown in the figure. Right in front of the APD, if you see the beam using a white paper, you will see two beams, one is the SC, the other is the SHG beam. In my case, I used 1200 nm -> 600 nm. I didn't measure the power, but I can clearly see the beam spot of SHG after grating. Then I aligned the spatial overlap of the two beams both in near field and far field. Finally I adjusted the delay, CEP signal could be found. I suggest to use a fan type crystal, that gives you a more flexible choice of SHG wavelength. I think 10-mm long is fine. You can check this paper [OE, 25, 10, 11910, 2017].

rp-photonics.com - simple explanation + references for more detailed study

Although it is true that compounds with a narrow HOMO-LUMO gap often display large hyperpolarizabilities (beta) and hence second-order NLO properties, the HOMO-LUMO gap is not directly proportional to hyperpolarizability and therefore it is not expected to follow the same trend.

So if you are interested in NLO you have to calculate beta values, there are no shortcuts. In Gaussian this can be done within a vibrational analysis (freq=Raman). I and my coworkers have published a couple of papers regarding NLO properties of metal complexes. An example is this:

I hope this may help.

A recent overview, ``Optical analogues of black hole horizons", might be useful, too:

you welcome Abbas N..

I think RF Spectrum Analyser is much more suitable and easier for estimating time jitter. The Allan deviation and phase noise could be measured by RF spectrum analyser, and these two parameters are always used to analyze the short/long time period stability of modelocked lasers. I recommend you to read this paper, maybe it will help you.(10 GHz regeneratively mode-locked thulium fiber laser with a stabilized repetition rate)

Hello

by using COMSOL Software Programm

I would suggest to verify the temporal synchronization of the two detectors. For a too narrow coincidence window and different latency of the detectors, the true coincidences might be outside of the coincidence window. Only false (random) coincidences are present. The first step would be to increase the coincidence window to dozens of ns to surely cover any difference in latency. Then you can start decreasing the coincidence window and adding a delay to the fastest detector channel, e.g. using time tagger functionality or simply extending the length of a coaxial cable.

Also, it might be useful to add cut-off filters transmitting the red signal and stopping the blue pump in front of the detectors. Using the filters you make sure that your signal comes from the SPDC process and not from the laser. Filters https://www.semrock.com/filterdetails.aspx?id=blp01-633r-25 are very good but you can use any low-cost alternative.

Dear Prof. Walid Tawfik , I want to convert 1600nm to 800nm using SHG crystal.

Thanks for the link you have provided.

Dear

Many thanks for your response and valuable information.

TOPTICA Photonics has unveiled some commercial THz sources with 0.1-6 THz spectrum in mW range.

Naively, I would say that the intensity simply scales with the cosine of the incidence angle, but one probably has to be a bit more careful here. If you know the complex-valued refractive index of your metamaterial, you can simply apply Fresnel's equations to determine the field strength and intensity inside the material for arbitrary incidence angle.

At nano-scale, the phase-matching can be replaced by the overlap between the resonances for the interacting wavelengths (both material resonances and resonances due to the geometry of any present nano-structures). Have a look at this paper: https://www.nature.com/articles/s41467-018-04944-9

The order of an optical process is determined by the number of waves that take part in that process. A process involving (n+1) waves will be an n-th order process. An by the waves involved, both the incoming and outgoing waves have to be considered. For eg, in linear absorption, one wave is absorbed and one wave is emitted later, i.e, it's a process involving 2 waves; so it's a 1st order process. SHG involves 2 incoming waves and gives out 1 wave of double the frequency; it involves 3 waves and therefore is a 2nd order process. Now, the mechanism of 2-photon absorption is that 2 photons are absorbed, and while emitting, it emits 2 waves, a signal wave of high eney and an idler wave of low energy, making it a 4 wave process, and therefore it is a 3rd order process. Similarly, you can determine the order of an optical process from the number of waves involved in the process.

As far as I can see, you are showing the spectrum on a log scale, but these oscillations are essentially a hallmark of the SPM, and you can estimate the total accumulated nonlinear phase from the number of the spectral oscillations. This was observed for the first time by Roger Stolen in the 1970s:

Self-phase-modulation in silica optical fibers

R. H. Stolen and Chinlon Lin

Phys. Rev. A 17, 1448 – Published 1 April 1978

A more detailed discussion can be found in the textbook by Govind Agrawal, Nonlinear Fiber Optics. I would estimate the total nonlinear phase in your fiber as about 3.5 \pi.

The famous equation is: \tau_compressed [ps] = 0.05 \sqrt( \tau_in[ps] )

Dianov et al. Efficient compression of high-energy pulses, IEEE J. Quantum Electron. 25, 828 (1989).

Another good reference is: W. J. Tomlinson and W. H. Knox, Limits of fiber-grating

optical pulse compression, J. Opt. Soc. Am. B 4, 1404 (1987).

So you can expect best compression to about 100 fs, and this may already prove to be quite a challenge.

The optical filter has to be matched to the phase-matching bandwidth of your SHG crystal. For Ti:sapphire based combs, one typically uses some off-the-shelf PPLN crystals, e.g., for 532 nm wavelength. You can find matching interference filters from Thorlabs or Edmund Optics. You can also use a simple diffraction grating instead. Details on a suitable setup are here: https://www.nature.com/articles/nphoton.2010.91

Hi Paul,

thank you for that, yes agreed.

I'm happy that SPDC signal and idler are entangled, so now 'all' that is needed now is some mathematical proof to show that OPA signal and idler photons are entangled or not.

The absorption coefficient of a material showing RSA will increase when the input optical fluence is increased. However, the processes underlying RSA (mostly excited state absorption in organic molecules) do not result in the absorption of more light than what is fed into it. Therefore, the scenario you envisage will not happen.

The reliability of data transmission characterizes the probability of getting a distortion for the transmitted data bit. This indicator is often referred to as the Bit Error Rate (BER). The BER value for communication channels without additional means of error protection is 10-4 — 10-6, in optical fiber — 10-9. A ber value of 10-4 indicates that on average, one bit is distorted out of 10,000 bits. The q-factor of the receiving system Q is determined from the expression:

Q = GA/TC,

or, in logarithmic form:

Q[dB] = GA[dB] - 10lgTC[x].

It is the q-factor of the receiving system that determines the signal-to-noise ratio (C/N) at the output of the low-noise Converter (LNC or LNB). It is important to note that the final C/N value does not depend on the LNC gain.

Ok, is the local probability of two photons to undertake SFG and DFG in a quadratic system always the same (from the nonlinear coefficient expansion in the nonlinear quandratic hamonic oscillato)? My question mostly points to if a system in which significant SFG is taking place always requires significant simultanous ongoing DFG (off course I am not referring to the phase matching role in selecting a process)

Here you are,

Dear Prof. Samit Kumar Gupta,

In superconductors, a PT symmetry invariance broken state could be the main manifestation of anionic superconductivity. There are not agreements so far on the subject.

Please see this external reference:

Selected Topics in Superconductivity by L. C. Gupta, M. S. Multani

what is the effect of the increases of the number of rings

Hi, you can using this research

Hi, Ban A. Naser! I hope that you and your family are well.

Although others seem to comprehend what you are doing and what materials might be best, I empathize with the the question asked by Ali Hussain. To me, the best "non-linear material" I could find has been the freshest of the course-grained rock samples that I collected from the Island of Maui, Hawai'i. The non-linearity of refractive indices (RIs) displayed by a powder from that sample can be appreciated by accessing and studying at least these three (3) files

Preprint: https://tinyurl.com/ycrnpcj7

Raw data: https://tinyurl.com/v9u4hkf

Video: https://tinyurl.com/uajcnxx

from folder https://tinyurl.com/to8tsbt

I hope that you will enjoy the attached art, which was created during study of the above-referenced video.

With all best wishes! :-) -Steve- gambist@gmail.com

Abbas N. regarding your 3 points:

1) There is no need for the lens NA to equal that of the fibre. Usually, coupling will be more efficient if the lens NA exceeds that of the fibre, provided the lens aperture (entrance pupil) is sufficiently large to avoid vignetting the input beam.

2) Coupling is optimised when the beam is focussed to a spot whose field profile matches the field distribution of the fibre mode. Typically, both launch spot and mode profile are approximately Gaussian, and the matching criterion is for the launch spot diameter to equal the mode field diameter.

3) Launching the collimated input beam parallel to the optical axis of the lens which in turn is coincident with the optical axis of the fibre will minimise mode mismatch due to tilt errors and lens aberrations.

More specifically, you specify a beam quality factor M² = 1, so the beam is close to an ideal Gaussian beam. When focussed by a lens, the radius of the beam waist at 1/e² intensity, w₀, is related to the wavelength, λ, and the divergence half-angle, θ, also at 1/e² intensity by: θ = M² λ / π w₀

Your collimated input beam width is W=0.65 mm. If the focal length of the lens is f, the radius of the beam at the lens principal plane is W = θ f = f λ / π w₀

provided the lens NA > sin θ. https://www.newport.com/n/gaussian-beam-optics

The fibre mode field diameter will be comparable to the fibre core diameter, but need not be identical. The relationship depends on wavelength, and the extent to which the evanescent field extends into the cladding.

If we assume that the beam spot radius is equal to the fibre radius, w₀ = a = 1 μm, then we require a lens focal length f = π W w₀ / λ = 1.98 mm.

A larger mode field diameter will require a proportionately larger focal length. A 2.8 μm mode field diameter will require a focal length of approximately 2.8 mm. The exact value is not too critical. If the mode field radius is r₀, the coupling efficiency (assuming Gaussian profile for both fibre mode and excitation) is:

η = 4 w_0² r_0² / (w_0² + r_0²)²

A 40% mismatch between launch spot diameter and mode field diameter degrades the theoretical coupling efficiency by only 11% (to 89%).

Regarding the choice between microscope objective and aspheric lens, both are capable of diffraction-limited performance for a monochromatic beam aligned with the optical axis. The microscope objective will be more complex, because it must deliver high resolution imaging over a relatively wide field of view, with illumination comprising a broad range of wavelengths.

The exact focal length of microscope objectives is not always stated. Magnification depends on the distance between objective and eyepiece. Tube lengths of order 160 mm are common, so a crude estimate for high power objectives is focal length f = 160 mm / magnification.

The 60x objective suggested by Suchita Yadav. would have a focal length around 2.7 mm, and would be a reasonable choice, especially if the fibre MFD is larger than 2 μm, but an 80x objective may be better. A 40x objective with 4 mm focal length is probably be too long.

If the microscope objective is optimised for visible wavelengths, there may be some additional losses due to surface reflections at infra-red wavelengths.

Note that a weak supplementary lens can be used to modify the diameter of the beam as it enters the focussing lens, and adjust the spot size for optimum coupling.

Hope this helps.

I have been using Degenerate Four-wave mixing technique to measure the third-order nonlinear susceptibility. In this technique, I isolate the signal and then measure the signal power with a sensitive photodiode sensor. I calculate back chi(3) using this measured signal power along with my input powers which has been divided into two pumps and a probe. Raul Rangel-Rojo Kaleem Ullah

Hi Abbas

I have the same question! I am trying to fabricate SMF-GIMF-SMF structure for sensor application. I tried many times to splice the fibres. I manipulated with different splicer parameters as prefusion time, overlap, arc power and so on, but almost always I got splice with a black vertical line (fig. 1).

Once I got good splice. It happened when I accidentally broke the bad splice and respliced it again. Unfortunately, I could never repeat it.

At fig.2 you can see two spectrums. The blue one corresponds to SMF-GIMF-SMF with both bad splices. The red one corrensponds to SMF-GIMF-SMF that have one good splice. The second spectrum had a much better contrast then the first one. This is due to the fact that the modes in GIMF fibre are more equally coupled to the SMF fiber. Thus, there is a difference between coupling coefficients of modes in GIFM to SMF fibre for the "bad" and "good" splice.

P.S. Abbas, please, let me know if you will find a method, how to splice it without bubbles and black curves!:)

Dear Nguyen, I beg You pardon, please read with attention my above given advice.. or at least tell us for what task You are going to apply TPA excitation then it would be possible to figure out correctly what laser beam intensity W/mm² You was needed...

Nguyen, It seems reasonable that the greater the absorption efficiency the greater the release of ROS. This applies to both exogenous photosensitizers and endogenous porphyrins. We are preparing a paper describing the absorption spectra of intact, live planktonic pathogens, both bacteria and fungi, collected with diffuse reflection spectroscopy. (Please see our papers: "The Black Bug Myth" and "Selective Photoantisepsis" posted on RG). I propose that these absorption spectra, if obtained in vivo, will mirror the action spectrum (clinical efficacy VS WL) of the clinical application.

Hello Hari,

Just to add another link: Probably the laser with the highest peak power, which by the way does NOT rely on beam combination is the ELI - NP laser in Romania. That is a a system having roughly 10 Peta Watt of power and should deliver about 1E23 W/cm2 at the focus.

There is a very similar system in China which name I forgot.

Best Regards

Marcus

Hi Tomasz,

In chapter three, the part on the list of examples of the document below, I can not open the entire file in .m format. And I have a question, in the "list of examples" , where you plot the power as a function of time, is the red curve the input function and the blue the output function? http://ufs.edu.pl/index.php?article=hussar&lang=en

The current version with a few bug fixes and several new features. (manual for version 1.3) .

Hussar 1.3 software manualTomasz M. Karda ́sJuly 26, 2018.

Thank you.

I guess the cited N. Bloembergen math relation pinpoint that that intensity in nonlinear processes (like SHG) will increase non-linearly with incident intensity but without violation the energy conservation law. You could know, for example, that under self-focusing output intensity exceeds multiply the incident one. As for SHG in the phase matching conditions increasing number of mode are followed by decreasing of efficiency because to growth of beam divergence and spectral width (one by one or both).

Dear Hegde, the query is nice. As you know, dielectric properties are well connected to refractive indices. Apart from this, permittivity is directly related to refractive index. Hence, if we have an understanding about these properties with respect to NLO, we can tune them according to our choice.

As a result, we can find their application in Drug delivery, molecular sensing, luminescence etc.

The equation for calculating magnitude of second hyperpolarizability (γ) can be found in Section 3.200.7 of latest version of Multiwfn manual. The latest version of Multiwfn is able to directly calculate this quantity based on output file of polar=gamma task of Gaussian, an example is given in Section 4.200.7 of the manual. Multiwfn code and its manual are freely available at http://sobereva.com/multiwfn.

Melek Hajji Thank you for your guidance ya.

Are you interested in theoretical aspects? If yes, decouple your system in the form of a dinNPDE. Apply preferably numerical simulations to see the wave amplitude behaviours, and so forth. Have a needful comparison with the latest reports on it.

MDM limitation in general is the modal dispersion and the receiver complexity.

Unfortunately, I have no significant information on BBO. I can only imagine, that the story is similar, i.e. several compounds including LN were competing and BBO stayed persisting due to not only its nonlinear coefficient, but a combination of various practical and technical considerations (Growth, stability, etc.) as well.

Zachariasen was a mineralogist by profession, i.e. he studied geology in Oslo. But his work would from todays perspective probably considered solid state physics. He did systematic x-ray diffraction analysis.

His PhD thesis is called " Untersuchungen über die Kristallstruktur von Sesquioxyden und Verbindungen ABO3", which is in german. Translated it means something like: "Investigation on the crystal structure of sequioxides and compounds of ABO3 type". Sesquioxides are materials of the general chemical compounds A2O3, where A could be things like Al and O is oxides, while ABO3 are things like A=Li and B=Nb etc. His thesis is about x-ray diffraction analysis of as many compounds as possible of these groups to find structural rules etc. The only thing you can find online readily are summaries of his thesis:

As far as I understand it, he did grow (or got someone to grow) LiNbO3, as I am not aware of its natural occurence. Early works on the structure of LiNbO3 point to the early works of Zachariasen as early work on the crystal structure. Compare Abrahams for example:

Anyway, the early works by Zachariasen is only an interesting side-note. Zachariasen never noted the polar structure or ferroelectricity. This was noted by Matthias and Reimeka, who noted this:

by the way: While LN is used for nonlinear devices and not really designed for large nonlinear coefficients, there is work trying to optimize compounds for ultra large second order nonliearities or electro-optic coefficients. This has been done for polymers, because in chemistry and with large molecules, there is more flexibility in designing specific properties.

If you just compare the nonlinear coefficients of these molecules with LN, you will find 100 or 1000 times higher nonlinearities easily. By the way, you may now ask, we we are not using nonlinear polymers. People have built extremely efficient nonlinear frequency converters or electro-optic modulators out of this. But polymers have one big issue, which is stability. Large molecules tend to decompose or change their chemical structure under UV light, heat or ambient chemical enviromements. In contrast to this, LN as a crystal stays stable for years. Even domain structures stay stable for years. LN is relatively resistant to scratches, it melts only a way above 1000°C etc. But again, LN is not without its problems. Just search for research directed to address LNs photorefraction (which I think is also one field, where BBO comes in. It takes more power; This is also one of the reasone, why still alternatives are researched, such as KTP). Another limiting factor of LN are the huge mode sizes in indiffused waveguides in bulk samples. This leads to an ultimate limit in its conversion efficiency or requires huge voltages in modulator. However, the advent of thin film LN has addressed this issue. Just compare these two recent articles:

A further issue is the smallest poling period for quasi-phase matching, which can be achieved. Currently there is a lot of interest to get sub-micron domain periods, which can be used for counter-propagating frequency conversion processes. However, this has not yet been shown in LN, however in KTP. Check the work by Canalias:

I hope, I could help you.

Regards,

Michael

Thanks a lot Prof. Gagik G. Gurzadyan.

All the best

Hi,

I don't know your application however a very good source for the 2nd order nonlinear effects as well crystals is SNLO software (http://www.as-photonics.com/snlo). And its completely free.

Sebastian and Rajib, thanks, those are interesting papers, Cheers, Neil

I think it's worth noting that magnetically induced rotation of linearly polarised light, mentioned by Nikolay, is not chirality. The difference is obvious in the optical isolator, where optically active materials cannot be used.

Mr. Kulichenko,

Static polarizabilities are determined within the framework of the effect of the external electric field. Frequency dependent polarizabilities are the so-called dynamic polarizabilities.

@ Valeriy. Evgenjevitch. Ogluzdin , Thank you for your suggestion.

A useful material is as below:

J. R. Taylor (ed), “Optical Solitons – Theory and Experiment”, Cambridge University Press, Cambridge, UK (1992).

You have posed a very interesting query. Going by your words, the two situations are totally different. If you look minutely, the interchange is not recommendable. However, for your own analysis, you can proceed and compare the results. As I can see, you are more interested in getting variations in frequencies. When the question of replacement comes, you can not rule out the coherence length. In case of fiber lasers, it is different from that of non-linear crystal. Another point is that modulator dimension (NL crystal and fiber ) will also have an impact on the out put. Anyways, best wishes for your endeavor and I will be glad to see them.

Dear Eugene and Furkan

thank you for your comments. Regarding my problem, I know that I've done everything by the book into accounting for the delta_y displacement in the geometry of my oblique diffuse reflectance experiment. What I find strange is that almost no one tells how they handle this displacement in their works. I've mails 4 different authors (some with recent publications) and no one replied back... I find that odd. Or they didn't care about the effect or then they didn't thought about it (which I doubt). Nonetheless I would like to hear from someone that had applied this same kind of experiment to find about tips on how to optimize it.

In principle, and according to the literature, the diffuse approximation should be enough to explain the light behaviour in the kind of turbid samples that I'm probing (biological tissues, milk, etc) so no need to go into specific models. However, I admit that some of samples might not be well explained by assuming isotropic scattering as the diffusion approximations relies on. Some food for thought for sure.

Cheers and thanks

Dário

Have you seen this blog post?

SBS compression can realize this goal. you can see the literature of zhiwei lv or hongjin kong.

Well, it is good to hear from you again, Aleksey! :-) It sounds as though you have done an interesting experiment that relates to the work published in 1957 by R.C. Emmons and R.M. Gates, which you can find at https://tinyurl.com/yd932t29 .

My own work explores the viability of abandoning the instruction "In the determination of the refractive indices of mineral grains by the immersion method, the grains must be in the extinction position, under which condition alone does the transmitted light have the value of one refractive index". Instead, I bring what I call a "fragment" (part of a crushed grain) to NO PARTICULAR ORIENTATION, before comparing its RI to that of the immersion liquid.

One of my primary goals has been ?simply? to discover whether statistically-significant data sets can be created from data derived by assessing whether each fragment encountered during a count is of Lesser, is Equal to, or is Greater than the RI of the immersion liquid (previously calibrated over the visible spectrum and the temperature range of the experiment: about 23°C to 60°C). Results confirm a success in creating statistically-significant data sets, but it is not so easy to say exactly what details are due to displays by any particular mineral/mineraloid/glass phase.

Nonetheless, in 2017 I took first place in the "Data Art" category of this https://www.lpl.arizona.edu/art/ contest, the winning image being available at https://tinyurl.com/yd994zpl . I did not place this year, with any of these https://tinyurl.com/y8h2w3ts entries. "Can't win 'em all." ;-)

In case you do not have it already, by standing permission of GSA I point you to a copy of R.C. Emmons's 1943 Chapter 5, GSA Memoir 8, "Double Variation Procedure for Refractive Index Determination": https://tinyurl.com/yabku63f . A copy of my dissertation can be found (at least for now) at https://tinyurl.com/y9bkao6n .

Work -- more recent than what I entered this year into the abovementioned art exhibition and contest -- has forced me again to seek a way to plot in 4D, after the plans I had to try to do that in 1994, as depicted at https://tinyurl.com/yaxrnzmv . Might you be able to help me with that graphics programming or know somebody who can?

I hope this response is helpful.

Sincerely, -Steve-

For closed aperture Z-scan measurements, one needs to avoid nonlinear absorption and hence the measurements are always performed at low input peak power/intensity. This is the thumb rule.

Even for nonlinear absorption there can be intensity dependent processes (SA at first turning to RSA at higher peak intensities). It depends on the sample and excitation wavelength along with peak intensities used.

In addition to the previous comments, bearing in mind the length of the fiber links and the environmental factors, for fine tuning you can use commercially available devices.

See in the link:

Following.