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# Nonlinear Optics - Science topic

Explore the latest questions and answers in Nonlinear Optics, and find Nonlinear Optics experts.

Questions related to Nonlinear Optics

Generally, all Beta values are given in m/W

Hi there,

I hope you are doing well.

In the lab we have different BBO crystals, however, in the past, they did not mark them so we don't know which crystal is which. I appreciated it if somebody have an idea about how to measure the thickness of BBO crystals.

The second question is, are the BBO crystals sandwiched by two glasses or not? If yes is the measurement become complicated?

Best regards,

Aydin

I manage to saw in both articles where they mention the materials' nonlinear response towards light are difficult to control with simple fabrication process. Unless we are using MBE technique.

Is there any reference article which discuss this in depth and it will be great if you can recommend articles that provide a SA fabrication method which is repeatable.

I tried fabricate quite a number of SA (especially graphene and MoS2) but its not repeatable as mentioned in the artcles. Its more like I have to trial and error until 1 SA can suddenly being used in my laser setup.

Thanks in advance.

How to calculate the nonlinear optical property of bulk material with VASP?

Hello every one,

I am looking for references about the theoretical calculation of nonlinear optical properties of hybrid perovskite quantum wells and how to set the hamiltonian of an electron, in the conduction band, confined in a quantum well.

thank you.

Thermal properties play a powerful role in Engine oils. As Nonlinear Optics in the thermal regime has a correlation with thermal-induced phenomena, so maybe we could investigate the quality of such oils based on NLO. I need some references and precise ideas.

There are two distinct frequency regimes for nonlinear optics in semiconductors which correspond to real and virtual excitation. Real excitations usually result in a reduction of the refractive index at frequencies of interest. In contrast, by exciting optical solids at frequencies much less than the gap, a considerably smaller, but faster, positive nonlinear refractive index n2 due to bound electronic effects are observed.

Why do real excitations result in a reduction of the refractive index while virtual excitations result in an increase? What is the fundamental mechanism behind it?

What could be the applications where the presence and control on the fifth-order nonlinear optical susceptibility could be essential or advantageous?

Thank you.

Dear all,

I am building and aligning mech Zehnder type f-2f interferometer for CEP signal detection. I have a few questions regarding this setup if someone could advise or comment?

- so, I have a collimated supercontinuum beam, is it ok to align the interferometer with this beam or I should use a different laser for alignment?
- Should I first optimize SHG signal and then combine it with the other arm or is it possible to combine both arms of the interferometer on a beam splitter and look for the CEP signal by changing crystal temperature, crystal pump power focus spot etc.
- what are the power requirements to pump SHG crystal? In my case, I have 10 mW over the spectrum from 600-950 nm. Is it enough to generate SHG?
- The literature says, for efficient SHG the following conditions should be met:

- (crystal length / 2 x Z
_{R}) = 2.84 and we can work out the focus spot inside the crystal and focal length of the lens. Since In my case I have low power to use as a pump (10mw), do I need to focus tightly, or follow this condition? (I am using 10mm PPLN crystal)

Thanks in advance!

Hello,

I wanted to enrich my knowledge about nonlinear optics and quantum technologies. Are there any resources to study them?

Thank you.

Hi

i am Dhanya, a research scholar from kerala university.

i am studying non- linear optical properties of a set of compounds using DFT with functional B3LYP and basis set 6311G (d p)using Gaussian 09 software. Upto my knowledge i believed that if a compound having good NLO properties, it has low HOMO - LUMO gap and high hyperpolarizabilities.

i calculated HOMO - LUMO gap and hyperpolarizabilities. But in the case of set of compounds of my study, the decreasing of HOMO - LUMO gap and increasing of hyperpolarizabilities are NOT IN SAME ORDER.

What should i do?

please help me🙏😔

Hello everyone,

I did some research on the internet about analogies between nonlinear optics (NLO) and general relativity (GR), e.g. https://arxiv.org/pdf/0711.4796.pdf. That's already a very nice result, but is it possible to go even futher? It's a stupid idea, but since both GR and NLO are nonlinear field theories, is there any mapping between these two say at least for special solutions to the Einstein field equations? So more generally asking: Is it possible to simulate and study black holes (or other GR scenarios) with nonlinear optical setups in a earth-based laboratory? I'm really excited about this. Thanks a lot!

Philip

I want to generate second harmonic using the long-wavelength (1600nm) part of the supercontinuum as pump. How to decide on choosing the right focal length lens for SHG. I am using 10mm-long MgO-PPLN. The average power at the output of supercontinuum is ~100mw and ~40mw for SHG (after long-pass dichroic mirror). Since the temporal profile of the signal after SC is not known (specifically for the 1600nm part ), is it suitable to treat that signal as continuous-wave for SHG pump. For CW pump, the literature suggests that the ratio of crystal length to the confocal parameter (2*Rayleigh range) should be 2.84 for optimal SHG. From where we may calculate the right focal length of the lens to focus light into the SHG crystal.

I am wondering if it is possible to measure mode-locked laser stability (timing jitter, Noise) with an oscilloscope if the pulse duration is in the femtoseconds regime (lets say 150fs). If so, what type of measurement on an oscilloscope would quantify laser stability. What should be the bandwidth of the photodetector and oscilloscope?

Where could I find some numerical results of the P(beta) (power vs effective index) characteristic related to a single layer nonlinear optical waveguide with lambda=0.515 microns, df=1micron, nc=1.55, nf=1.57 and ns=1.55 with nonlinear (Kerr) cladding coefficient n2c=1e-9 or other ? I simply need numerical data for comparison with my method.

Could anyone suggest a suitable and affordable phase noise analyzer to characterize pulsed laser sources with rep rates around 200MHz.

Thanks

I am using the experimental scheme presented in the image below. It seems that no matter what I do, I cannot obtain coincidence counting higher than 350/s, although the single count at each detector is about 500000/s. The crystal used is a 2 cm long 10 um period PPKT collinear type II crystal.

I have generated an octave-spanning supercontinuum (750-1700nm) using 140fs pulses. I want to frequency double longer wavelength (1600nm) using PPLN crystal. Since, I don't know what's the pulse duration/shape, peak power, or energy in that specific bandwidth (around 1600nm), how should I choose SHG crystal (PPLN) for SHG. Specifically, how to determine crystal length and acceptance bandwidth for optimal SHG at 800nm.

Thanks in advance.

Does anybody know what is the maximum power of laser sources (QCL, VECSEL, and so on) in THz regime?

I'm trying to realize a nonlinear effect in THz regime using a THz source without using DFG or SFG. I need 200 mw or more for my device. Is it doable? is there any source to generate that power?

For example, I would like to simulate nonlinear response from the linear response simulation for plane wave incidence at an angle. I know that using Lorentz reciprocity, we can obtain it and there are papers for normal incidence case. One such case is described by DOI: 10.1038/NMAT4214. But this method is only described for normal incidence case. What and how should we modify it for the off-normal incidence case.

I would like to explain experimental SHG results of periodic metasurface for angled illuminations.

In general, it is not possible to observe simultaneously all nonlinear effects described by the nonlinear polarizations, because usually only one nonlinear process is

*phase-matched*.In

*nonlinear nano-optics*, since the wave phase-matching between interacting optical fields does not affect the nonlinear optical interactions, is it necessary to achieve*phase-matching*?I have been trying to understand the second and third-order nonlinear processes (specifically SHG and two-photon absorption). I am still unable to understand how the order of these nonlinear processes is determined. I was unable to find adequate information about this in the Nonlinear optics by Robert Boyd. Please help me understand this, or suggest me a source to study more about it.

Can anyone tell what is the reason of these sharp frequency modulation in SPM broadened power spectrum. This is the spectrum of mode-locked laser with 0.4nm initial bandwidth at 1064nm. After amplification to 400mW (in YDF) and propagating through 6m length of PM-980, such spectrum appeared. I am wondering how to get rid of these modulations to enable efficient pulse compression.

Pls see the attached picture.

What would be the pulse compression limit for initial pulses from fibre laser with average power 4mw, 4.5ps duration and 0.4nm fwhm bandwidth.After amplification to 450mw and propagating through a length of SMF (different lengths can be chosen 5m,10m etc..and hence different amount of spectral broadening) , I want to understand on choosing optimal length of SMF to achieve maximum pulse compression (pulse compression limit using spectral broadening in SMF). How would the length of SMF affect the subsequent pulse compression stage?

Thanks in advance!

how to do f-2f interferometry from an octave spanning supercontinnum with frequency spacing 120MHz. Which would be the most suitable optical filter in this range for filtering f and 2f components from supercontinnum, to detect carrier envelope offset frequency of a mode-locked laser.

Thanks in advance!

Is there a simple proof that the signal and idler photons created by spontaneous parametric down-conversion (SPDC) are entangled, whereas those that are created by optical parametric amplification (OPA) are not? SPDC has been used in the optical band to create entangled photons. A view of this is that the SPDC just amplifies the vacuum (zero-point energy) photon to create a signal photon, whilst an idler photon is created to preserve conservation of energy when the pump photon annihilates. In the OPA process a seed photon is parametrically amplified likewise to create a signal photon and idler photon, whilst the pump photon annihilates. What is the proof therefore that the signal and idler photon pair from OPA are not entangled?

I am working on crystal growth of nonlinear optical materials. So I would like to carry out second harmonic generation (SHG) measurements by kurtz and parry powder method. So please suggest any institute or SIFE where this facility is available in India and abroad also.

Dear Colleagues,

I'm studying the optical limiting effect in organic material due to reverse saturation absorption. As we know, in reverse saturation absorption, the transmission coefficient decreases as the intensity increases, or the absorption coefficient increases as the intensity increases, resulting in power loss. So, when we increase the laser power to a threshold P0, there are two competing processes: the increase in input power and the power loss due to reverse saturation absorption. If these two processes are in equilibrium, the optical limit curve is horizontal (as in the attached pictures.) However, if the amount of lost power is greater than the increase in input power, the curve must go down at P0. Why in the paper on optical limiting don’t we see such cases?

Thank you and hoping for your insightful response.

In absence of phase matching constraints (in a microscopic framework), are the quadratic SFG and DFG processes bonded together ? (Assuming you illuminate with two frequencies) is there an ultimate relative efficiency limit?

Hi,

I am studying effects of Spin orbit interaction in nonlinear optical responces espesially SHG.

I want to find relationship between spin-orbit effects and the second harmonic generation(SHG) response in nonlinear optical crystals.

any one who can guide me?

In recent research perspective this is very important field. Parity operation is reversal of co-ordinate (x->-x, p->-p)and time reversal operation is reversal of time (x->x,p->-p, i->-i).

But talking about this combined PT-symmetry in any field of science and engineering, what it implies?

Dear colleagues,

I am investigating the dependence of the number of diffraction rings on the concentration in third order non-linear organic dyes (due to nonlinear refraction and nonlinear absorption). Prof. Pramodini [1] claims that the number of diffraction rings depends linearly on the concentration. However, Prof. Hussain A Badran [2] assume that the number of rings increases exponentially with respect to the concentration. Our experimental curves on aniline blue and Acid blue 29 showed a linear relationship. However, for Oil Red O, experimental curve is not the straight line and the exponential curve. So, is this relationship linear or exponential?

Thank you and hoping for your insightful response.

1.S. Pramodini, P. Poornesh, Effect of conjugation length on nonlinear optical parameters of anthraquinone dyes investigated using He –Ne laser operating in CW mode, Optics & Laser Technology

2. Badran, Hussain A.; Ali Hassan, Qusay Mohammed; Imran, Abdulameer, A Quantitative Study of the Laser-Induced Ring Pattern and optical limiting From 4-Chloro-3-methoxynitrobenzene solution, Basrah Journal of Agricultural Sciences . 2015, Vol. 41 Issue 2, p51-57. 7p.

+1

How to calculate two photon absorption cross section and two photon emission cross section of dyes?

As far as I know, the phenomenon of lasing is considered in nonlinear optics whereas the emission is considered in linear optics. But I don't know why. Can anyone guide me on this?

I am trying to couple light from Laser with M^2=1, wavelength = 1030nm and beam diameter = 1.3mm. Please suggest a lens for efficient coupling into PCF (say 2um core). As far as I know, I have two options, either to use Aspheric lens or Microscope objective, however, I am not really sure which one would be a best choice. As I understood (Please advice if right or wrong)

For efficient coupling, these points should be considered.

1) N.A of lens should be equal or close to that of fibre (PCF)

2) Lens focus diameter should be equal to core size of the fibre (PCF)

3) Input beam should be parallel to Optical axis (Collimated)

Please advice.

Thanks

Hello dear researchers,

I want to measure the value of the third-order nonlinear susceptibility (Chi3). I have only the third harmonic generation (THG) spectra in photon counts and I know the input power at the sample to be probed. In literature, people used some materials whose Chi3 is already known and after comparison, they gave a rough estimation of chi 3. The other way in the literature was used is the utilization of an additional laser to calibrate the power.

I would like to ask is there any other way to measure the output power or chi 3 value? any simpler way if you know the input power and output intensity in photon counts???

how to spliced different different core size (MFD) fibres ( single mode to graded index multimode). I am trying to splice SMF to GIMF, to fabricate SMF-GIMF-SMF saturable absorber.

Although, I could splice with apparently no power loss (shows 0dB loss). However, splicer shows "Bubble Error", even after several attempts.

note:Please have a look at the photos attached

Thanks

Dear professors and colleagues,

I am going to to study effect of the two photons absorption in Safranin O. Safranin O is organic material, so I think that the power needed to activate this effect doesn't need to be too high. However, the two photons absorption is a third-order nonlinear optical effect, so it is usually implemented with high-power pulsed lasers. I cannot afford to buy high-power pulsed lasers. So, can I stimulate effect of two photons absorption in safranin O by continuous wave laser (808 nm or 1064 nm)? And how much is the required power of laser? I hope the colleagues who have experience in this experiment share me useful information.

I look forward to hearing from you. Thanks in advance.

Yours sincerely.

Dear Colleagues,

I am investigating methods to determine the photodynamic activity of photosensitizers for photodynamic therapy. One of the methods being used is absorption spectrometry. A work concludes that significant absorption of light was shown to be prerequisite but not sufficient for high photodynamic activity. My point of view is: When a photosensitizer absorbs more radiation at a certain wavelength, it will produce more Ros (Reactive oxygen species), i.e the absorption maximum will correspond to the wavelength active photodynamic effect best. However, this point of view contradicts the viewpoint in above work.
I look forward colleagues to explain this question.

Thanks in advance.

Nonlinear optics becomes important at higher intensities. I wish to know how large laser powers and intensities have been achieved so far.

I work in the transport of information by optical fiber. I have to draw in 3D in the time domain, and in the spectral domain with the frequency.

First, I want to draw the input signal and the output signal as a function of time. Then take them both out in the same graph to compare them. Secondly, I want to trace the evolution of the pulses as a function of the optical distance z and time on the one hand, and on the other hand, I want to trace the evolution of the pulses as a function of z and the diffraction.

Hi,

this is a question about nonlinear optics.

It was suggested by Bloembergen in 1963 that the number of modes of the fundamental laser N influences the Second-harmonic intensity with a factor (2N-1)/N.

It was then checked experimentally by François 1966, but I still can't understand the reason of this factor which is statistical I guess.

Thank you for your time.

In recent days, many research articles are being produced with studies on dielectric behavior and the third order nonlinear optical properties of the materials. Can anyone explain what can be the possible relevance of dielectric studies for third order nonlinear optical applications?

Hi, I have been working calculating the non linear optical properties of several molecules with Gaussian ('09, revision C), and in the outputs I have some values that represent the non linear parameter (in this case, γ) in several directions (e.g. γxxxx or γxxyy). I have read some papers that present "average values", like <γ>, that are defined with the sum of some of these, but I'm interested in obtaining the magnitude of the tensor, not an average. As the hyperpolarizabilities are tensors the procedure is a little bit more complicated than with vectors, and I have not found an easy way to calculate it with the values printed by Gaussian. Someone can recommend me a paper that explains this, or even tell me the correct procedure to get it?

Thanks.

Because i'm new to the Gaussian user. Thank you.

Rogue waves are an important topic in water waves, plasma physics, nonlinear optics, Bose Einstein condensate and so on

How can we predict a rogue wave?

One of the recent researches suggests to use the optical modes to carry different channels (with different content, modulation). What are the limitation of using such multiplexing technique? I would appreciate any related book or papers.

The synthetic crystals of lithium niobate and beta barium borate (BBO) were designed specifically to have the lowest possible power thresholds for nonlinear effects for use in quantum optics. Was the design strategy for these only to develop a crystal with a unit cell that had the highest possible electric dipole? Of course the crystal needs to be transparent and have suitable refractive indices for phase matching, but were these the only design principles, or were there other metrics and parameters for these crystals that needed to be optimised?

I am looking for the Non linear optical parameters of Calcite and Quartz crystals in the telecom window (1.2 - 1.7 micrometer).

Can anybody please suggest a tool in which non linearity of optical material can be modeled.

If metamaterials could be designed to have non-linear susceptibilities (magnetic or electric) and phase matching properties for the refractive indices in the mm-wave band they might enable novel quantum processes. In naturally occurring dielectrics non-linear susceptibilities arise in non-centrosymmetric crystals. Perhaps something could be synthesized in synthetic materials. There might be magnetic counterparts to this. Scientists working on metamaterials must have considered this, so where is this at the moment? Comments welcome. N

Considering that water molecule is asymmetric , does it show significant optical chirality?

I'm trying to perform NLO properties calculations with Gaussian and I need to calculate first hyperpolarizability. I faced in literature with static and dynamic ones. Can anyone explain the main difference between them? And which one is more important in such calculations? Thanks in advance!

I have performed an experiment to frequency mix 974 nm LD laser and a C-band ASE laser source in a single period (10.2 um) MgO:PPLN. I however noticed five peaks at 487, 536, 598, 756, and 816 nm wavelengths detected with a fiber spectrometer. Whilst the 487 and 598 nm outputs could be second-order SHG of 974 nm and SFG (974 nm+~1550 nm), respectively, I can't account for the remaining outputs (536, 756, and 816 nm). Can someone kindly shed some light on what processes are likely involved here?. Please see the attached file for the experimental set up and output spectra at two different temperatures.

Frequently in nonlinear optics, to study the dynamics of short optical pulses of femto-second duration one use to adopt multi scale method and derive nonlinear Schrodinger/Gingburg-Landau equation. In many cases, the final equation is obtained keeping terms up to third-order, whereas other cases it is obtained after fourth-order. How to estimate accuracy in both cases?

More explicitely:

If I have a pump laser of a given wavelength and I feed it as a pump into a fiber, does the output contain the pump laser wavelength (minus converted power fraction) and the fiber laser's wavelength at a different wavelength with a fixed phase relationship (not necessarily known).

Or in other words, if I had a nonlinear crystal based optical setup and would not depend on frequency doubling, but only frequency conversion, could I replace the nonlinear crystal by a (laser) fiber?

I'm preparing a spatially-resolved oblique diffuse reflectance experiment with the objective of finding the reduced scattering (mu_s') and absorption (mu_a) coefficients of some turbid samples.

My setup is very similar to that described in Hu et al 2017 (DOI 10.1007/s11694-017-9465-x). I have a couple of technical/practical questions related to this experiment, so if you have never done something alike, you might want to skip this one.

I use an optical fiber to deliver the light at a 45 degree angle at the surface of the sample (liquid) and I'm collecting the reflectance with another fiber that moves in a parallel plane to the incidence plane. This is necessary to avoid collisions between the fibers. The liquid and the fibers are separated by a 0.2 mm cover glass.

The two planes are 2.2 mm apart from one another (delta_y). The main paper describing the theory behind this experimental setup is Lin et al 1997 but the authors (as well as other authors that do similar stuff) do not explain how the shift between incidence and collection planes should be handled in terms of modelling. To me it makes sense that this delta_y enters in the definition of the distances (rho_1 and rho_2) used to compute the theoretical reflectance (R), obtained from the diffusion approximation. However, when I plug in all the values into my code to find \mu_eff by fitting my data, I cannot find a stable solution. I have to "artificially" increase delta_y in order to get \mu_eff values near the expected/theoretical ones. Has anyone experienced such problems?

I've tried small adjustments to delta_x (due to possible errors in the light entry point measurement) and different optical coupling parameters (A), but nothing seems to works. Could it be related with the width of the light beam that enters the sample? In my case the projected beam spot in the surface of the turbid sample is an ellipse of 2.1 x 1.4 mm.

If you have any comment/idea about possible sources of error that I'm might be overlooking, please leave a comment. Also I would like to know your suggestions about the best way to normalize the data before doing the fit procedure for this kind of experiment.

I appreciate any help, advice, reference or person contact that could help me move forward with this. Thanks.

Dário Passos

Hi,

I am attempting to simulate in comsol a nonlinear metamaterial (which by using effective media theory I can approximate as a periodic slab of artificial material).

My process is as follows:

Run a frequency domain study, this contains my model, a propagating wave (from the emw port). I perform the comsol study and place domain point probes at points of interest. I monitor the Ex, Ey, Ez, and normE here.

Next, I find the voltage at a point in my material (at split of my split ring resonator) simply by multiplying a component of the E field at this point by the gap size of the split in the ring.

Next, I couple a time domain study of my model to a circuit model so I can apply a voltage source. I am looking for the second harmonic so I apply V(2w) =1/2 a(Vw)^2 voltage (from an expansion of the voltage in the linear model with 'a' being a nonlinear co-efficient which I will know).

Following this, I have a scattered boundary condition as a source of the field I have saved from my emw.Ey etc run from the frequency domain and I use a polarisation term to couple the incident field chi(2) *(emw.Ey)^2, where chi has been found via an equivalent circuit analysis.

I then export my time domain results to matlab (just for sake of ease as I'm more familiar with matlab) and take the abs(fft(Efield)) to find the frequency content of the output from my model.

I'm aware this method is probably incorrect, but any pointers, or corrections from correct comsol usage to correct method to simulate nonlinear materials, would be greatly appreciated.

Thank you very much

I am looking for a simple and inexpensive method to compress my Nd:YAG nanosecond pulse laser into hundreds picosecond pulse. Please suggest me some if you know or have experience on this pulse compression issue. Thanks!

I'm looking for the source giving quantatively numbers for o- and e-rays refraction indexes in the ice crystal depending on the wavelength.

It is known that graphene and graphene oxide liquid dispersion

(in DMF/NMP) show third order non linear behaviour such as Spatial Self-Phase Modulation (SSPM). Far field diffraction ring pattern due to SSPM is observed even when one attempts to perform z-scan (both with CW and pulsed laser). While open aperture measurement doesn't offer much complication as I only have to focus the transmitted beam onto the detector, I am not very sure how to overcome the ring structure while performing closed aperture z-scan.

Of course, drop casted /spin coated samples don't show SSPM feature, but I am curious about liquid dispersion only.

I'm trying match the phase between different links(all the links has same devices with same parameters). As i know i have to place an exact same length of the fiber between all the links to perfectly match the phase between all the links. I'm unable perform exact calculations to match the phase to over wide bandwidth(around 10 MHz to 3000 MHz). I''m able to match at lower frequencies by cutting the fiber length approximately. Once i over but even by few mm length im going out of phase with the link. I need to have 6 degree phase difference between each link. Can some one give exact calculations to match the phase over wide band.?

Thanks

Surya

Dear Professors,

Can you please send me your paper entitled " A Quantitative Study of the Laser-Induced Ring Pattern and optical limiting From 4-Chloro-3-methoxynitrobenzene solution"

Thank you in advance.

Best regards.

Dear colleagues,

The Z-scan technique is proposed by Sheik-Bahae et al [1]. Theoretically, when there is no nonlinear absorption, the Z-scan curve must be symmetric around the

**origin**of the Z-axis. However, in practice, the Z-scan curve usually has a large asymmetry. I know the reason for this phenomenon for thermal-optic nonlinear mechanisms. For the electronic nonlinear mechanism, what are the reasons for this asymmetric phenomenon? (Except for experimental error). Thank you and hoping for your insightful response.

[1] Sheik-Bahae, Mansoor, et al. "Sensitive measurement of optical nonlinearities using a single beam."

*IEEE journal of quantum electronics*26.4 (1990): 760-769.Dear colleagues,

Without nonlinear absorption, the Z-scan curve corresponding to the pure nonlinear refraction will be symmetric around the origin O. The nonlinear absorption will lead to asymmetry of Z-scan curve. Thus, the closed aperture Z-scan of a material with nonlinear nonlinear absorption and nonlinear refraction give an asymmetric curve. Therefore, we can develop a matlab program to automatically generate nonlinear absorption curves so that these curves multiply with the closed aperture Z-scan curves reproduce a symmetric curve [1]. From this symmetry curve, we can calculate the nonlinear refractive indices, and from the nonlinear absorption curve produced by the matlab program we derive the nonlinear absorption coefficient without the open aperture Z-scan measurement. I have implemented the above idea on closed aperture Z-scan data in works [2] and [3] and found that results perfectly consistent with results in above works. In summary, we can use the matlab program or the numerical methods (fitting curve) generally to determine n2 and beta from the closed- aperture Z-scan data. But why in most works did open aperture Z-scan measurements implement to determine n2 and beta, are this measurements really necessary?

Thank you and hoping for your insightful response.

[1] Beam radius based Z-scan + Matlab method, Link: https://www.researchgate.net/publication/319403552_Beam_radius_based_Z-scan_Matlab_method

[2] Sheik-Bahae, M., Said, A. A., Wei, T. H., Hagan, D. J., & Van Stryland, E. W. (1990). Sensitive measurement of optical nonlinearities using a single beam. IEEE journal of quantum electronics, 26(4), 760-769.

[3] Abrinaei, F. (2017). Nonlinear optical response of Mg/MgO structures prepared by laser ablation method. Journal of the European Optical Society-Rapid Publications, 13(1), 15.

Measuring TPA coefficient (two photon cross section) and non-linear optical refractive index using Z-scan method with pulse or CW lasers is routine. So, is two photon excited PDT by CW laser achievable?