Applied Optics - Science topic

Dear Farhad Vedad ,

sorry, but such laser cexperiments have nothing to do with shadow blister effect.

In the shadow experiments, which are handling with bright white light from extended sources, one only deals with penumbras; diffraction effects cannot be seen due to the very low amount of diffracted light on a huge background.

In your diffraction related videos it is mentioned by yourself, that you have to (i) darken the lab for avoiding any backgroud signal and (ii) that you have to acquire the data over a lot of time...

Best regards

G.M.

1) The diffraction pattern is oscillatory in nature. For monochromatic light, you won't have a sudden dark fringe follow by a sudden bright one. You'll see gradual transitions between both.

2) Those are obviously not monochromatic lights. As such, there is no reason all wavelengths should be extinguished at the same time in dark fringes. One would instead see color variations.

3)Let's do dome rough calculations. In the k-space the diffraction pattern for an aperture or object will be similar to sinc(a*k) where a is the half width of the object.

That means the first 0 will be for k=pi/a.

But that is the tangential component of hhe k vector only, or the sine of its projection.

So, if you want to find the corresponding angle you have

Sin(ang) = pi/a / (k0) = lambda/(2a)

Let's say 2a=3cm and lambda=600nm (yellow), we obtain

sin(ang) = 600e-9 / 3e-2 = 2e-5 ~ang

As such, if you where at 10m from the latter, the corresponding length projected on the sensor of your camera would be roughly

L ~ ang * 10 = 0.2 mm, wich is much smaller than the sensor itself. So we should see the diffraction pattern of it had any actual energy in it.

You did not see diffraction.

Thank you Bikash Kumar Das and Michael Belsley

In remote sensing, GRD is the smallest distance that can be resolved by the sensor. It is influenced by various factors such as atmospheric conditions, sensor resolution, and altitude. GSD, on the other hand, is the distance between the centers of two adjacent pixels on the ground. The sensor resolution and the altitude determine it.

The formula you mentioned, GRD=2kGSD, relates the two parameters, where k is a constant that incorporates all the influences other than the sensor resolution and altitude. This constant can be used to calculate the GRD value for a given GSD.

However, there is no direct formula to calculate k. It is generally determined experimentally by measuring the GRD values for different atmospheric conditions and sensor settings. In practice, k values can range from less than one to several, depending on the atmospheric conditions and sensor characteristics.

One can say that the camera is limit diffracted when k reaches its maximum value, which is typically around 1.5-2. Beyond this value, the sensor performance is limited by atmospheric conditions, and further improvements in the sensor resolution will not lead to a significant increase in the GRD.

Several authors discuss the influence of atmospheric conditions on remote sensing parameters, including GRD and GSD. Some of the useful sources are the books "Remote Sensing and Image Interpretation" by Lillesand and Kiefer and "Introduction to Remote Sensing" by Campbell and Wynne, and the journals "IEEE Transactions on Geoscience and Remote Sensing" and "Remote Sensing of Environment."

Rather than trying to calculate the magnification you could take an image of a stage micrometer and measure it.

Good day! Here I found brief and complex explanation on reflectance and transmittance phenomenons:

Gerhard Martens Thanks! I guess that is my problem solved.... Thanks for your input and suggestions.... :-D

Farhad Vedad,

I suggest you post your experiments and ask this question right at the beginning. If you write out what you are trying to do, that will clarify your own thoughts and ideas. But it will help others to help you.

Variable index of refraction devices are wide spread. Gradient index materials are many. Power intensity (Watts/meter^2) dependent and frequency dependent processes in materials are widely studied - in chemistry, in photonics. If you allow the identical concepts and processes with lattice and acoustic signals, your can find still more useful places to put your time and skills. Acoustic resonance, impulse response functions, 3D imaging, materials processing, laser cutting, laser material interactions - the list is not endless but enough millions of pathways for a single lifetime.

If you say what you want to build, design, understand, accomplish - then others can help.

Your question is too vague and too narrow. Ask BIG questions and then work out the details.

Richard Collins, The Internet Foundation

Dear Yu Yu:

You can benefit from these valuable articles about your topic:

@https://opg.optica.org/oe/fulltext.cfm?uri=oe-29-23-37418&id=462642

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@https://www.lenticularripsoft.com/lenticular-printing/

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I hope it will be helpful ...

Best wishes ....

Supercontinuum generation by short pulse with high power that lead to traction or fusion soliton.

The roundtrip OPD inside the CCR is

1 OPD=2H/cos(theta), where H is the vertical distance from input plane of CCR till the Apex

and theta is angle of incidence and reflection (retroreflective) into and out of CCR.

2 OPD=2H*n/cos(thetan), where H is the physical path from input plane of CCR till the Apex, thetan is

the angle inside the solid (glass) CCR and n is the refractive Index of the glass material. Incident and

retroreflected angle can be found from Snell's Law.

Problem solved : The reel was getting pinched and deflected at the bare fiber adapter to the detector causing a huge drop in power.

Vincent Lecoeuche Thanks for your thoughts as well.

Dear Anatoly Smolovich , in addition to the previous answers, I would like to add probably one of the most popular materials for replication: PDMS, there are several commercial preparations of this silicone, but probably Sylgard184, by Dow, is the more commly used. It normally requires a mild curing temperature (80ºC for two hours or even at room temperature, but requiring longer curing times) and if temperature is an issue they also have some UV-curable PDMS. It has a key advantage over rigid polymers, given that it is an elastomer and that facilitates the demolding process without harming both the original and/or the replica. I also had good experiences with Microresist as pointed by Daniel Stolz , in fact I use to make the replica with PDMS (reverse replica) and the direct replica of the original with Ormocomp by Microresist, with very good results. These resins are solvent free and that is important both for avoiding damage of the original and to minimise the shrinking, so that the grating period is mantained.

Both, PDMS and Ormocomp do not need application of pressure, unlike the case of the PP replicas made for injection molding in the article provided by Przemyslaw Wachulak , (of course you can apply pressure but it is not necessary, just a glass slide or a cover slide will be enough.

About your late question related to the treatment of the original grating surface treatment:

It will depend on the nature of the grating and its surface. If your grating is made of glass or metal (alone) most antiadhesive treatments would work. If it is made of some polymer, you will need to know what polymer to apply some material that does not damage the grating.

If your grating is made of any material and coated with a thin metallic coat, then you should check that the antiadhesion material and the replication resin (or the solvent) are not going to damage the thin metallic film by disturbing the adhesion between the substrate material and the metal coat.

Hope this helps.

Jones matrices are not necessarily normalized. The intensity of the light after a Jones matrix can be less than went in. Take, for example, a polarizer where all the light in one polarization is lost. You can even have the light get brighter. Many laser gain media have polarization dependent gain and the gain is modelled as a Jones matrix.

So, I am curious how your Jones matrix was constructed, and whether or not you are sure that it needs normalized.

However, let's assume you know your Jones matrix represents a set of lossless optics, and let's assume for mathematical convenience or some other reason you have constructed it in a way that it doesn't preserve intensity but is in every other way correct.

You cannot normalize it by elements, and you cannot normalize it for a particular polarization. If the optics are lossless, then the Jones matrix must be lossless for all polarizations. For an arbitrary Jones vector "v" the light after the optics is "u" = Mv. For lossless optics it must be that u*u = v*v. The correct normalization is (v*v)/(u*u). If everything is correct, the parameters of v will cancel and there will be no arbitrary terms in the normalizer.

Now, without loss of generalization v can be written (e^(i phi), e^(-i phi)). Taking your matrix to be ((A, B),(C,D)) where I am not going to write out the complex components as you did, you will find the normalizer calculated as indicated above is (A*A + B*B + C*C + D*D) + (AB* + CD*)e^(i 2 phi) + (A*B + C*D)e^(-i 2 phi)

This must not depend on phi, so those last two terms had better be zero. This puts a constraint on your Jones matrix. If it preserves energy for all polarizations then it must be antisymmetric. Also, if it preserves energy and is antisymmetric, the normalization you want is (A*A + B*B + C*C + D*D)

I think your premise is flawed. There isn’t going to be “an answer” because tailoring this parameter and trading it against other properties you might like is the crux of coating design and the answer might be anything over a wide range depending on what was designed under what set of constraints. For example, your example of a mirror being 4% is at best a rule of thumb and most often completely wrong. Over a fair range of wavelengths bare i coated aluminum happens to be around 4% absorptive. However Silver is only 2% absorptive in that range. Bare Gold may be terribly absorptive at shorter wavelengths. At longer wavelengths it doesn’t reach the 98% of silver, but over much of the IR and aluminum become terribly absorptive and gold is the best. More importantly, mirrors are rarely uncoated and a dielectric coating can raise the reflectivity of metallic mirrors above 99%. See for example Edmunds “ultrafast” enhanced aluminum coating.

And that is just metallic coatings. Metal is useful over a wide wavelength range when you don’t know what a mirror is going to be used for. However, if you know the wavelength (and what acceptance angle you need, and other constraints) you can use a pure dielectric stack. Dielectric mirrors can be made very close to 100% reflective. What’s more, very little light is absorbed, so what little doesn’t reflect transmits.

That brings us to beam splitters. It is not at all difficult to make a dielectric coating where essentially no light is absorbed. It is all either transmitted or reflected. Adding the reflected to the transmitted should yield just about 100% every time. When you found placed where they appeared to add up to higher than 100%, that is just experimental error or round off error, but they probably do add up to almost 100%

NPBS: A matrix which operates on the electric fields at the input (E1, E2) and generates the electric fields at two outputs would be one of the:

[-r, t; t, r], [i*r, t; t, i*r]; or [r, i*t; i*t, r]

where:

t = sqrt(transmission);

r = sqrt(1-transmission);

i = sqrt(-1)

which matrix exactly it is depends on the specific implementation of the beamsplitter, (actually there are more possibilities). However the first one is ok for a plate with AR coating and fused fiber coupler.

PBS: A Jones matrix per port is required:

output port 1: [0, 0; 0, 1],

output port 2: [1, 0; 0, 0],

these matrices would be applied to the polarization vector.

The phase would result from difference in optical path.

You are very welcome, Dr. Marziyeh Mohebbi

Well, first, it’s N+1 obstacles or if you don’t want to count the long walls at either end for some reason, N-1obstacles, but certainly not N obstacles.

It certainly doesn’t matter what you call it. In your picture the two terms are both correct, and not mutually exclusive. It is in, in fact, N+1 obstacles forming N slits.

I don’t think anyone misunderstands that slits are formed by barriers, and if you talk about N slits everyone will instantly picture a barrier with slits in it. However, on a practical note, at optical wavelengths it generally isn’t possible to have free standing barriers like this. Instead the solid wall continues above and below. Generally a transmissive grating looks like a solid barrier with ”slits” cut into it. So the ”slits” term is constructivist. It is indicative of how the structure is created. You cut slits into a foil or similar. That is the dictionary definition of slit: a narrow cut. That is also how this became the standard terminology in optics because in the early experiments that is literally how gratings were made. We’ve greatly improved our “knife”, but fundamentally that is still how subtractive transmission gratings are still made today.

Terminology is for understanding, and often it uses similarity for recognition. No one thinks the arrow slits in a castle wall were literally made by cutting, but they look like cuts. If you call them slits everyone understands what you are talking about. That is the only important cr for terminology.

In optics we always talk about the slits. This is probably because we are focused on the light. Each slit is treated as a source, we propagate on using Huygen’s principle, etc. It doesn’t really matter what the barriers are so long as they exist. However, we have to talk about slit width and slit spacing, so in what an artist might call “negative space” we are inevitably also describing the barrier. Everyone gets that. I don’t think I’ll switch to explicitly talking about the barriers any time soon

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.

I have many advanced books and can send you by e-mail, if you need.

Hello Avijit Prakash,

Based on my knowledge, the radiation pattern of your light source has a significant effect on your results. Therefore, I strongly agree with Dr. Sascha

Regards. - Hossien

i fuly agree with Mike is right that cost is definitely a major factor

The mixing rules for the real part of the index of refraction hold for the complex quanitity and thus for the imaginary part as well (or as bad). The problem is that this is a very complex problem without a clear solution. The names that are connected with this problem are Gladstone-Dale (Arago-Biot), Newton-Lagrange, Lorentz-Lorenz (Clausius-Mossotti), Maxwell-Garnett, Bruggeman, Loyenga... and there are nearly as many different models as names. If you want an overview I suggest

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

Thanks for the good solutions. I know what to choose now. Thanks

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!:)

It depends on the thermal part of incident energy, which in turn rising the charge carriers from valence to conduction band

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.

Dear Sreeprasad

If you are not worried about relative phases and can tolerate a number of very weak secondary beams, perhaps the simplest way is to insert a tilted parallel glass plate into the beam you want to translate. The translation of the main transmitted beam will be Theta*T*(n-1)/n, where n is the refractive index of the glass plate, T is its thickness and Theta is the tilt of the plate's normal relative to the beam propagation direction (in radians). A 1 mm thick glass slide at 5 degrees will result in a shift on order of 50 microns. The main drawback from this method is that more than one beam is transmitted due to the multiple reflections at the glass surface, however the main transmitted beam will be several hundred times more intense than the strongest secondary beam.

Good luck

I f you want to measure the intensity of the incident laser pulse you can use a suitable photo detector which is fast enough to respond for the time variation s of the pulse. Knowing the external quantum efficiency ETAe one can can get the photo flux pulse assuming that the photocurrent Iph= qETAe phi

where q is the electron charge, phi is the the indecent photonflux in photons/ sec.

If you have a pulse then you have to integrate its flux with with time along the duration of the pulse and also you integrate the photocurrent along the same time.

Best wishes

For the general case of refraction in a prism spectrometer, the angle of deflection depends on the refractive index of the prism, the vertex angle of the prism, and the orientation of the prism with respect to the incident beam.

The angle of deviation is a minimum when the prism is aligned symmetrically with respect to incident and refracted output beam directions. In this orientation the deviation depends only weakly on the rotation of the prism. To calculate the refractive index, we need only the deviation angle φ, and the prism vertex angle, θ.

n = sin( (θ+φ)/2 ) / sin(θ/2)

A small error, ε, in the prism orientation gives rise to a much smaller error in the deflection angle, proportional to the square of the orientation error ε². In practice, with reasonably careful adjustment, this error can be neglected.

I don't see how the minimum deviation angle could be made more sensitive to prism rotation, but if this were possible, it would increase the errors arising from measurements of the prism alignment.

The deviation angle does become extremely sensitive to incident angle when the internal refracted ray approaches the critical angle at either the entrance or exit face of the prism. The deviation angle is a maximum at the critical angle, where the beam will mostly be reflected rather than refracted through the prism.

One more thing: In all this, mathematics is totally neutral. People often confuse "mathematical models" (sothing that a natural scientist does) with mathematics (which mathematicians do). Mathematics is not concerned with "truth" at all. All math theorems say "if A than B", but they NEVER tell you whether A is true or not. Math creates pre-fabricated logic containers, it is not concerned with the truth values of their "inputs".

Hence, you should re-formualate you question as "Do mathematical models present solutions for understanding the reality of the universe?". The answer is then obvious: some do, some don't. And often several model lead to the same conclusion. That's all, folks :-)

As John explained, it is not possible from a 200µm/25° light source to get a collimated beam from 100µm to 1000µm. The beam parameter product of your source (diameter×divergence) is a constant. You can then expect 100µm/50° or 1000µm/5° spots. Now if you want spots ranging continuously from 100µm to 1000µm, I would look first for a 10× zoom lens (5-50mm for instance). I would then collimate the output of my fiber with a FOC with twice the shortest focal length of my objective (here 10mm). The collimated beam passing through the zoom will give you at the image plane spot sizes ranging from 100µm to 1000µm . However, the equivalent aperture of your source is F/2.2. It means that the aperture of your zoom have to be greater than F/1.1 for your 100µm spot if you do not want to lost energy and it will be hard for 10× zoom lens. If you can deal with a 30% loss at 100µm, it should work. Good luck.

Time duration of laser pulse is needed if one need to calculate the Laser intensity. This can be obtained by dividing the energy density by the time duration of laser. It will have unit of W/cm2.

Thank you dear @Biswas

The Pythagoras theorem works in all Euclidean spaces of dimension D>=2. It can even be been extended to infinite dimensional Hilbert spaces. The notion of cross product can be generalised to every finite-dimensional space, as the wedge operator ^ of Grassmann (exterior) algebra. It can be defined on spaces where no metric is defined, i.e. where the Pythagoras does not make sense. But additional properties, like the * operator, can be defined for metric spaces.

A few came to mind, but none is perfect. You will need to choose based on your application. Each of these below has certain low absorption window in the MIR and FIR, and the optical dispersion (or refractive indices) for some may need to be further characterized.

(1) Acetonitrile

See "Schafer SA et al., Mechanism of Biliary Stone Fragmentation Using the Ho:YAG Laser, IEEE Trans Biomed Eng, vol 41, no 3, 1994."

(2) Glycerol, 1,3-Butylene glycol, trimethylolpropane, Topicare(TM)

See "Viator JA, et al., Spectra from 2.5-15 um of tissue phantom materials, optical clearing agents and ex vivo human skin: implications for depth profiling of human skin, Phys Med Biol, 48 (2003) N15-N24."

Best of luck,

Kin

Following.

When the nonlinear response is dominated by the Kerr effect (nonlinear refractive index change) the asymmetry is easy to understand in the limit of thin media. Essentially the Kerr effect induces a "nonlinear lens" in the material which changes the subsequent propagation of the beam. The example you show in your question would correspond to the case of a negative Kerr effect (n2<0). When the sample is placed before the focal plane of the physical lens, the combined effect of the lens originally used to focus the beam and the negative focal length "lens" induced in the sample is to translate the beam's focal plane further along the z-axis. Thus by the time the beam reaches the aperture it has not diverged as much and the transmission through the aperture is higher. Conversely when the sample is placed behind the focal plane of the physical lens, the induced negative lens leads to an increased divergence and consequently a lower transmission at the aperture. It is not just the phase shift, but difference in curvature of the wavefronts on either side of the focus that gives rise tot he assymmetry. You can find a more detailed explanation in the book "Fundamentals of Nonlinear Optics" by Powers and Haus, chapter 8.

Basically the optics is roughly the same as in the thermal lens case. The main difference is that for an electronic nonlinearity in the absence of absorption, the induced lens is an "instantaneous" response to the transverse profile of the incident beam, whereas in the thermal case it is the radial variation of the adsorbed energy convoluted with thermal diffusion that produced the effective lens induced by the incident beam. Of course the detailed shape of the Z-scan curve will be different, due to the difference in the transverse variation of the induced refractive index change in the two cases. In the "instantaneous" electronic case, this variation will follow the radial variation of the incident beam, in the thermal case the balance between the power deposited by the incident beam and diffusion of the heat within the sample will determine the spatial profile of the induced refractive index change.

I think when nonlinear refraction is dominant, you can extract the nonlinear parameters from the closed z-scan with some confidence. However, there are cases , for example when either NL refraction or absorption are dominant, that you cannot do that without ambiguity, so that is why it is customary to run the open z-scan to get the NL absorption parameters first, and then used them in the closed-aperture results. Experimentally all you need is a beam splitter in the far field, and an extra detector yo obtain both the open and closed-zscan traces at the same time

dear Lucus, thanks a lot for your answer

I really appreciate your help with my project, Prof.Zbigniew Motyka and Prof.Maria Chiara Ubaldi.

Mengjia and Jim, For comparison, I summarized my Ernostar design on OSLO. It works at FOV angle=15degrees, F/4.8. (focal length is 21mm, and wavelength is 0.48,.. 0.656 microns in this case.) Petzval sum is neary the same as Jim's triplet. Shigeo

Thank you very much, Dr. Reza Taheri Ghahrizjani

Dear Prof. Zbigniew Motyka

I appreciate all of your help. Thank you for your presentation.

Your explanation is so good. However, there is another explanation of the Professor Qusay M Ali Hassan as follows:” A pump laser beam with Gaussian intensity distribution is able to stimulate a phase shift, ∆ϕ, in the shape of bell in a nonlinear medium in the transverse direction with respect to the direction of the beam as the one shown in Fig. 1.

On a Gaussian curve, for any point, ρ1, there exists another point, ρ2, having the same slope and wave-vector, their radiation can interfere. Destructive and constructive interferences occurs when the change in phase from the point ρ1, ∆ϕ(ρ1), and the one from the point ρ2, ∆ϕ(ρ2), when the relation ∆ϕ(ρ1)- ∆ϕ(ρ2)= mπ (where m is a constant being odd or even integer for destructive and constructive interferences respectively) is verified.”

I think the diffraction effect does not affect the radius measurement because diffraction only redistributes energy but does not result in energy loss.

I really appreciate your help, Prof.Thomas Mayerhöfer and Prof.Pablo Acebal !

Dear Prof.Zbigniew Motyka and Colleagues,

So what significance do n2.I / n0 ratio have in the third order nonlinear optics? 

 

Thank you very much, Prof.Madhukar Baburao Deshmukh, Uday Saha.

Mechanical property (mechanical strength) of organic material can be lower than that of iorganic material. However, I have read somewhere that organic material has a higher damage threshold. And in this book, author assume that some of the organic materials have much higher damage thresholds than lithium niobate. https://goo.gl/x66fAU

Hi,

This company sells small laser modules that include a collimation system

they also offer a custom service,

Dear Lam Thanh Nguyen:

Thank you for your question, which has introduced me to the Z-Scan technology of which I have previously been completely ignorant. I don't have time to become an expert in your field, but I have just glanced at

My own impression is that as a scientist it is your job to pursue the answers to such questions you have asked by designing your own investigations to achieve the results you seek and to answer for yourself, to your own satisfaction, the questions related to which approaches give you the best information related to the knowledge you seek to gain about nature. Then, to tell others what you've learned and why you believe your work to be useful to others, whether or not your results have confirmed your initial suspicions or taught you some surprising things along the way. 

I have never worried too much about doing things just as others do them routinely. Doing so would make a technologist out of this scientist. Try things out, modify your approaches to fit the need to satisfy your own curiosity, and celebrate the times when you learn something new and think that nobody has done that before.

Your "Why not ...?" makes me think that you may already know the answer to your own question! ;-)

I hope you often enjoy the feeling of success.

Sincerely, -Steve-

It is possible to lock a laser to the side of an etalon resonance using a photodiode to measure the transmitted power.

It is possible to change the laser wavelength by changing the laser pump power.

However, by changing the pump power you mainly change the output power. As a result, the given power transmitted via the FPI is no longer associated with 50% transmission rate. You have coupled two parameters.

Depending on the physical laser design, this concept may still allow for laser locking but with a much lower performance.

If you use a stepper motor you can increase the speed of scan and thus you can eliminate any possible thermal response that appears by overexposure of the sample to the spot laser.

Hi Lam,

I had some experience with optical limiting (OL), and my comments about your question are: (i) nonlinear index (NI) could have important effect for OL if the material/structures have resonant features (micro-cavities, photonics crystal etc.) so that intensity at resonant mode(s) or wavelengths is changed with RI. Good design could make OL based on that. (ii) in general cases, OL effects are mostly from nonlinear absorption (NA) (saturable absorption, two photon absorption etc.). Note that, many optical nonlinear materials have both NA and NI. 

Hope that would help. By the way, I will visit HCM city on December, if you have time we can meet there. 

Best,

Dan

Thank you for your positive comments, Prof.Raul Rangel-Rojo.

dear Lam

in my experience the main source of error in z-scan measurement is the uncertainty in the laser beam fluence measurements, or in other words in the beam shape. As a matter of fact the laser beam is often assumed to be a TEM 00 which is not always realistic. I think this fact can explain the reported differences in the published values and add large uncertainty in the results.

Following Rajeev Gandhi reply, I think it is worth to stress here that measurements using cw sources cannot be compared to pulsed ones since in the first case only the thermo-optical properties are probed. In  fact in this case the signal is originated by the thermo-optical coefficient dn/dT which is not a true third order nonlinear coefficient.

Finally, other techniques for third-order nonlinear characterization may probe other components of the chi^3 tensor, so that the measurements results may be not directly comparable to z-scan results.

Michael's response is more than adequate for the focus location of an incoherent ray bundle. The answer for the coherent field propagation is a bit more complicated than that. The optical field that is converging to the focus in air has a spherical wavefront. For a Gaussian beam, the minimum spot location is not at the center of curvature of the spherical wave. It's actual location depends on both the radius of curvature and the size of the distribution at the location that spherical wave is considered.

The dielectric interface between the media of propagation (considered here to be flat with no curvature) will affect the radius of curvature of the wavefront (this change is consistent with Michael's treatment). Since the radius curvature change, the location of the spot will also change given the same considerations as the location in air before the interface.

Al Siegman gives these considerations a formal treatment for an ideal Gaussian beam distribution that is monochromatic and coherent (originally based on papers from Kogelnik and Li publish by Bell Labs in the 1960s). The problem you have is that these treatments don't pertain well to your problem.

First, the assumption of a Gaussian spatial distribution may not be valid. You did not describe the laser, but if it's based on fiber lasers and fiber gain segments, then the assumption is probably adequate for your purposes.

Second, the field is not monochromatic. The effective bandwidth (wavelength range) of the optical field will increase as the pulse width decreases. Since the dielectric containing your sample is dispersive, the index for each wavelength will be slightly different and hence will the change in the radius of curvature for that field component will change differently. That means the minimum spot location will shift as well. This shift may not be significant but should be considered as it may increase the focus spot size and reduce the field amplitude accordingly.

Third, any absorption in the dielectric medium may produce heat which in turns leads to thermal lensing effects that are often stochastic for media that are gaseous or liquid phase. Random thermal lensing effects give rise to spurious focal power that may not only shift the focus but also move it laterally due to a linear phase component in the random focal power.

Lastly, a femto second laser has a very high peak electric field amplitude. This may introduce nonlinear effects in the material. This is beyond my direct area of expertise but I felt I should mention this for your consideration as well.

If you need to calculate the focus shift with some level of confidence, then the problem is a simple or complicated as you feel it should be to arrive at your level of confidence (for a thesis for example). If you need to maximize nan-particle generation, then an empirical study is probably your best choice. I would start with the numbers you get by assuming a Gaussian distribution and Siegman's ABCD math. You can probably find these equations on the internet somewhere. Be aware that 2 approaches to the ABCD matrix values are in the literature. I prefer the use of matrices that always have a unity determinant because the wavelength that is used to get spot size, radius or curvature, waist size and location are always based on the wavelength in a vacuum. The other approach gives the determinant as the index of the final material, then it is very important to use the wavelength in that material to calculate the results accurately.

fortunately i found the answer.

I am attached the answer below.

Refer to PIV. As the others have mentioned before, use the cylindrical lens. The details of its application can be easily found in the frame of PIV.

      Dear All,

      Minkowski not only introduced the space-time (pseudo-Euclidean) and the imaginary unit in the theory of relativity, but he also introduced the proper time in the frame of reference of observer at rest and related macroscopic bodies (wikipedia/proper-time, wikipedia/собственное-время, Google/proper-time). However, in a multi-dimensional interpretation of the Lorentz transformations, the space-time and the imaginary unit are not in demand: elementary particles move in full space with basic rate (the upper limit of the speed of light) on the Compton distance from the three-dimensional space of the universe. The projection on the extra space of this motion is finite trajectory, allowing macroscopic bodies do not move away from the three-dimensional space, and in it to move freely.

      Observations show that our three-dimensional universe is isotropic and homogeneous at distances of more than 300 million light-years. This means that on such scale curvature at all points of the three-dimensional universe is the same, and therefore it is a three-dimensional sphere and it can expand, and only in the space of a higher number of spatial dimensions. The scale of the inhomogeneities in the Universe is 100000 times smaller than the characteristic size of Meta-galaxy. 6D-cosmology gives for the radius of Meta-galaxy (a observable part of the universe) value 3980 Mpc. The length of the great circle of Meta-galaxy passing through its borders (particle horizon), can be taken as a characteristic size. Then the size of the irregularities in the Meta-galaxy is 2π 3980/100000 = 0.25 Mpc or 815646 light-years, which is approximately equal to the average distance between galaxies. The curvature of the universe as a three-dimensional sphere is defined as a unit, divided by the square of the radius of the sphere. Today's radius of the universe is equal to 7100 Mpc. As the universe is expanded its curvature relatively rapidly go to zero. Geometric and physical characteristics of three-dimensional universe are given by the cosmological model based on the principle of simplicity, with the fixed parameters of the theory. These parameters are chosen so that the deviations of the compared values from each other were minimal.

     The simplest object in the six-dimensional Euclidean space is a five-dimensional sphere of disturbances in this space. As intersections of the three five-dimensional expanding spheres are expanding three four-dimensional spheres, which consists of three mutual intersections expanding three-dimensional spheres. One of them is our three-dimensional universe.

     If the formulas of Newtonian mechanics refer not to the three-dimensional space, but to the six-dimensional space, then we obtain the formulas of the theory of special relativity and quantum mechanics, provided that the proper time of an elementary particle is proportional to the path traversed by it in the additional space, and velocity of the particle in the whole space is equal to the upper limit the speed of light. In order to the observable interaction of elementary particles could occur, the particles are held in Compton proximity to our three-dimensional Universe by means of cosmological forces perpendicular to our Universe. This is force of the Lorentz type in which the role of the charge played by the mass of the charge particles in a magnetic field oriented along the radius of the universe.

     A simple interpretation of spin and isotopic spin requires at least three additional spatial dimensions. This yields a simple interpretation of the uncertainty relation of Heisenberg, de Broglie waves, Klein– Gordon equation, the intrinsic magnetic moment of the electron, the CPT-symmetry. In the six-dimensional space, the spin and isospin are treated as a projection of the total angular momentum, respectively, on our and additional space to it, and the intrinsic magnetic moment as a result of the rotation of the charge with the speed of light in the additional space in the orbit of the Compton radius.

     The potential energy of a particle is the energy of its motion in extra space.

     A lack of spatial imagination leads to fruitless attempts to replace the physics by philosophy.

     Igor A. Urusovskii

No differenct exept the wavelength. In light we can use geomentic optics. In meters waves we can use too geomtry between Our Sun and Star of Sirius.

Regards, Alexanger

Uygun Vakhidovich Valiev · 30.62 · National University of Uzbekistan

I believe that you can use the following method for the measuring of phase light shift described by Randall D.D.: "A new photoelectrical method for the calibration of retardation plates", JOSA, V. 44, No 8, P. 600-602 (1954).  It is very successful and enough simplest experimental method....

Hope it helps!

2h ago

Thorlabs, Newport, Edmund Optics, Optosigma, Siskiyou, Eksma, Standa and many others. You can use Laser Focus World Buyer`s Guide (Internet)

Thank you Wei for the link to your article. It is very insightful.

Some information on this question may be found, for example, in the work:

E.A.Bondarenko. A laser gyro with a four-mirror square resonator: formulas for simulating the dynamics of the synchronisation zone parameters of the frequencies of counterpropagating waves during the device operation in the self-heating regime. Quantum Electronics 44, 364 (2014).

hope...........is still on the ground