Photonic Crystals - Science topic

Michael Rüsing

Actually, I have the material I was looking for. Now my problem is with the design. I have designed a crystal photonic based SR-flip flop for 420 nm light. Based on band structure diagram, I considered a/lambda =0.38 and the waveguiding is just fine. But I don't know the physics(photonic crystal based) of ring resonators. Therefore the output is not rational. Would you kindly help me with that Sir?

The electrolyte used in the previous question is hydrofluoric acid with a 3:1 ratio of ethanol.

I have a Chinese website describing how to calculate Chern number using COMSOL, but I'am not sure whether you can understand Chinese.

I can not speak English

Two years ago, I asked this question here.

I'm excited to share that this initial curiosity led me on a journey of research and discovery, resulting in the publication of the first book on metalenses in the world. The book is titled "Introduction to Metalens Optics" and has been published by the Institute of Physics in the UK.

It’s amazing to think that what started as a simple question has now led to this book, which provides a detailed look at the fundamental characteristics of metalenses.

For those interested, you can find more information about the book here: .

Hi

if you want obtain the band gap graph for 2D-photonic crystal, there is an example in COMSOL's library.

In addition this video maybe can guide you

Maple

The most important thing is that you determine the input and output signals. In the case of our rare earth doped crystals, the input signal or control signal is a laser. By changing the experimental conditions, such as laser power, temperature, etc. We can just get some output signals. This opens up the possibility of designing devices.

Kırıcılık indisi ile frekans doğru orantılı.

InGaAsP katmanına zarar vermeden SİO2 maskesini çıkarmak için katmanlar arasına InP, GaAs, GaP gibi çözücüler enjekte edilmeli.

Photonic crystals have regular periodic structures, and the periodic change of refractive index makes it produce photonic bandgap, which can prohibit the propagation of electromagnetic waves due to the regulation of Bragg's diffraction in all directions.

Kristal kafesin geometrik şekli dalga kılavuzunun oluşumunu etkiler.

Kristal kafesin geometrik şekli onun kararlılığını belirler. Bu yüzden dalga kılavuzunun verimliliğini etkiler.

Seal lifleri ile dalga kılavuzu oluşturulabilir.

My suggestion is to use the Lumerical Software...Can try 30 days trials..Tqs

I'm working with linear optics and I want to study the transmission spectrum at the output of the four ports of the projected photonic device.

Thank you, Sulaf Waiss for your valuable suggestions.

Thank you for your comprehensive explanation. It helped me a lot. Thank you again.

It is possible by CVD but this will not represent the graphene properties. You can say thin graphite.

abaqus里即使能做Floquet边界，也需要另写程序进行参数化扫描，何必呢。

hye. how you open MPB from ubuntu? any guidance cause i already install it but dont know how to access

X eksenine ve Y eksenine göre band aralığını doğru yazmışsın. Enerji bandları :iletim bandı, yasak bölge,değerlik bandı olmak üzere comsol kirişte üç bölgeye ayrılır.

Dear Rachel Darthy ,

I've exactly same problem now.do you find any answer or approach to solve that problem?

tnx

Dear Abinash

You can place two regular 1D PC separated by some finite distance to study defect and place some sample in between with finite length. The effect of defect can be investigated the comparative analysis between experimental and theoretical data with different frequency or wavelength regime.

Here is a link that may be helpful to you.

Maybe it can change the intensity of transmitted optical mode (loss), but it has no effect on displacement of the transmitted optical mode wavelength. The Transmitted wavelength depends on the defects of the photonic crystal structure and also the refractive index of the environment around the structure (due to the change of effective refractive index).

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

When considering the material losses, the absorption of 1D PhC will be induced. Therefore, both the transitivity and reflectivity of 1D PhC will decrease. However, if the extinction coefficient of the material (i.e., the imaginary part of the refractive index of the material) is small (on the order of 10^(-4)), the decrease of the transitivity and reflectivity of 1D PhC will be extremely small.

Then I answer your second question. When considering the material losses (not too large), both the transitivity and reflectivity of 1D PhC will decrease. However, the wavelength position of the transitivity peak or dip will be almost unchanged while the full width of half maximum (FWHM) will slightly increase. If the sensor is based on the wavelength position of the transitivity peak or dip, the sensitivity of the sensor will almost not be affected while the figure of merit (FOM) of the sensor will slightly increase. Only when a large extinction coefficient of the material is considered, the transitivity peak or dip will disappear and cannot be used to design a sensor.

Feng Wu

I am humbly suggest video below on how to fit using Origin 2019

The following research article is related to this thread:

Best Regards.

nice answer dear

Dear Gustavo,

You could see these papers:

Best,

Fran

What is confinement loss?

This is not so mysterious. This is an interference phenomenon. The easiest illustration is probably an etalon. Suppose you have an etalon where each surface has 50% transmission. A beam with intensity I is incident. In the first pass through the material the intensity is I/2. Half of that reflects at the second surface and bounces back to the first surface. There half of that bounces again and continues in the original direction. The intensity of this second pass is I/8. Each subsequent pass is 4X smaller. So, the whole sequence is

I/2 + I/8 + I/32 + etc. However, remember that the field strength is the square root of the intensity. So, the fields add up as sqrt(1/2) + sqrt(1/8) + sqrt(1/32) etc. Adding up those first three terms, you see that the electric field is now up to 1.23! So, if you have a nonlinear phenomenon which is proportional to E^2 or higher, you actually can get enhancement in some parts of the interference pattern. In the case of the etalon the place where you get the enhancement is only inside the etalon. As for being at a degenerate band edge, they are talking about the places where the waves interfere constructively. In the example of an etalon, this happens only if the etalon is the right thickness: t = N * lambda/(2*n) where n is the index of refraction. It's a degenerate band edge in that you can see the behavior repeats at any integer multiple lambda/2. All those choices are degenerate, i.e., do the same thing, and in between you have a repeating range of behaviors (a band) that culminates at the places where the behavior starts over (the edge of the band)

This sort of behavior is very common in all sorts of interference phenomena. Different paths add up in constructive interference and you get a crest with amplitude higher than the contributing pieces. The enhancement isn't magic in that the enhancement comes from adding up pieces that come from somewhere. In the case of the etalon you are adding up parts of the beam that are distinct in time. In other constructive interference you might be adding up pieces of the incoming beam that were distinct in space and laying them over each other. Every bright spot comes with a similarly dark spot because you can't get something for nothing. However, in the case of non-linear optics where you care about the field strength rather than the intensity, clever design can produce dramatic enhancement.

I am not going to argue what is the absolute best or most efficient, but I think for somebody just getting started the finite-difference frequency-domain (FDFD) method is awesome. Of all the methods, I think it is the easiest to learn and implement and can be used to simulate a huge variety of devices and configurations. Here is a new book that teaches FDFD in MATLAB for the complete beginner. The book includes multiple photonic crystal simulations with complete MATLAB codes provided and explained.

if you mean the noise from using the photonic crystal as a guide.

there are many things to think about: the thicknesses of the layers can vary upon fabrication, backscattering due to lattice imperfections, attenuation from layers absorption coefficients, etc.

Dear Natraj Athreya a S many thanks for posting this very interesting technical question. In addition to the relevant article suggested by Sofyan Taya please also have a look at the following useful references which might help you in your analysis:

Unfortunately this article has not yet been posted by the author as public full text on RG. Perhaps you can access the full text through your institution. Since it has been published very recently (2020) you could also try to request the full text directly from the author via RG. Fortunately the author has an RG account (https://www.researchgate.net/profile/Lazhar-Kassa-Baghdouche).

Also please have a look at the following PhD thesis entitled:

(see attached pdf file)

I hope this helps. Good luck wth your research and best wishes, Frank Edelmann

Put simply, Photonic Crystal structures allow one to manipulate the local density of states of the radiation field. Depending on whether the modes are enhanced or diminished this can lead to an increase or decrease in the rate of excitation as can be easily seen via Fermi's Golden rule.

Dear Alfredo De Rossi Thank you for your information.

Yes! Photonic crystals are actually good candidates for supercontinuum generation. There are two factors to achieve a wide spectrum exploiting self-phase modulation, field confinement, and material nonlinearity. Photonic crystals are very good at achieving very good field confinement , resulting in large effective nonlinearity coefficients. For short waveguides (1 mm-1 cm) dispersion is not important, the only remaining factor is the material from which the photonic crystal is made, through its nonlinear refractive index

use the program ImageJ

many applications have been written to it. find what you need

In all numerical analysis software, power is increased from minimum to maximum. But in the same conditions we can not minimize the power from the maximum value.

Please know how to do this process.

Thanks for sharing this discussion to me. However, my research area is one-dimensional photonic crystals. So I don't know too much about three-dimensional photonic crystals. I try to answer this question below.

For two-dimensional case (the height of the dielectric rod is infinite), you can obtain photonic band gap by calculating or simulating the band structure. As the height of the dielectric rod becomes finite, the photonic crystal actually becomes photonic crystal slab (with finite height). Therefore, the photonic crystal slab also possesses guided mode. Compared with two-dimensional photonic crystal with infinite height, the band structure of photonic crystal slab with finite height will become quite complex. You can refer the book about photonic crystal by John.

lumerical FDTD solutions

can any one tell me how to add new rod with with new radius in BandSolve

Did you used physical controlled mesh? As far as my experience tell me, the physical controlled mesh does note cope well with periodic boundaries, if you get something very close to a periodic boundary the mesh on that boundary will not adapt to the decreased distance and remain coarse. If you are working with square lattice I suggest use PEC and PMC to cut your model into 1/4, but for hex lattice you can try create your own mesh rather than automatic mesh.

The problem is similar to the analysis of slab waveguide and cylindrical fiber. We sometimes use a layer of metal, semiconductor, superconductor or left-handed material of simultaneously negative permittivity and permeability, as one of the waveguide constitutes. The aim of this is seeking new features of wave guidance in these structures. When we treat a metal-dielectric photonic crystal, we seek new properties of wave propagation.

Without knowing the details of the crystal structure you are referring to, as a rule of thumb photonic band gaps increase with the refractive index difference. Metals have large (often negative) permittivities relating to a large refractive index. On increasing its thickness you probably increase the relative gradient in the refractive indices of the components of your structure.

Raymond Rumpf I would like to estimate the decay length of a surface plasmon at 300 nm wavelength. Also, using Drude model, plot c*Re(B)/wp vs (w/wp), on y and x axis, respectively. How would you do this?

Sebastian A Schulz

Yes, you are right the group index can be calculated using band structure. It is slope of band structure.

My quasi D-Shaped fiber is this according to the paper i follow for its design but i need this kind of result which i attached in the second screen shot. Please, some one help me in troubleshooting the problem?

This depends. I assume you are talking about FDTD simulations here. In these, a pulse is launched and then propagated through your structure. So if your simulation time is sufficiently long, then the pulse will have gone through your structure completely and no energy will be left inside it at the end of the simulation. In this case, increasing the simulation time does not change the results. However, if you simulation time is electromagnetic to short, then at the end of the simulation there will still be electromagnetic energy inside the structure. Now the amount of energy remaining inside might be frequency-dependent and therefore your results will now change as you increase or decrease the simulation time.

To be clear unless you have a very good reason for not doing so, you should always be in the first case, where all the energy has left your structure and your results become independent of the simulation time.

The only way to ensure this is to run a convergence test. I.e. run your simulation with different times until your results become independent of the simulation time. Then, to safe computational resources, you normally want to pick one of the shortest times that gives the converged results.

Alternatively, some commercial implementations of FDTD have an auto shut-off function, i.e. you can specify a long (maximum simulation time), but if the electromagnetic energy reaches zero before that time, then the software will realize that the calculation is finished and stop. Therefore you do not pay a prize anymore for using a long simulation time.

Following

2D modelling is what you do to get fast results so that you can understand most of the important things about your problem. A few 3D runs will then get you the accurate answer you need, especially because you know from the 2D work what to do to correct the change caused by going 3D. It may also be that the shift you get with 3D can be approximated well with a simple formula based on the actual height.

Do the same procedure that I already answer your question. If you need any help more then contact me.

In 1D PC the optical path difference, d between the transmitted and the reflected can be expressed as

d = 2 (n1 x a + n2 x b)

the condition for a standing wave is if d = m lamda where m is a positive integer. An optical bandgap will be formed centered at the Bragg frequency.

Now if there is a defect layer, say n3 then there will be a bandpass line inside this bandgap. Changes in the bandpass profile can be calculated from the dispersion relation. Changing the refractive index of this defect layer will change the bandpass profile. For unknown liquid defect layer the refractive index is determined by comparing the bandpass profile with existing reference, e.g. measuring the passband characteristics for known liquids whose index is already known. See our paper below for references:

The three main criteria are normally:

1. You want the right refractive index and absorption values at the target wavelength.

2. Fabrication suitability, i.e. what can you fabrication partner deposit in their facilities and how easy is it t layer the two materials.

3. Any application speapplication-specificcific material designs, e.g. gain, process compatibility, ...

Have a look at : https://www.mathworks.com/matlabcentral/fileexchange/21810-one-dimensional-photonic-crystal-dispersion-relations?focused=5104560&tab=function

https://www.nature.com/articles/s41598-019-43440-y

Good Luck

follow

For core diameters of around 2 microns, you need a microscope objective , either a 40x or a 60x an a micropositioning system, since the tolerances are really stringent, more than for a single mode fiber

MPD has a function to output the group velocity for the bands. Run that and then if you want the GVD, perform a numerical differentiation of the group velocity curve.

Thank you Raid Daoud

Hi,@ Vadapalli Durga Rama Pavan

you can use the effective index mode solver in this website to calculate the effective refractive index .

https://www.computational-photonics.eu/eims.html

you can also find explanation here:

https://www.computational-photonics.eu/eimsinout.html#LIMITS

Good luck

MPB is designed o calculate the bandstructures, not the transmission. As mentioned above, this can be done in MEEP (or any other Fintie Difference Time Domain solver (FDTD)). However, FDTD will only present one implementation of te PhC with a disorder corresponding to the mismatch between your periodicity and the Fdtd mesh. I.e. if your mesh is 10nm in size and your period is not a multiple of 10, then the PhC holes will appear to have an error in the position, which leads to optical losses. There is an add-on script for MPB that can be used to calculate the propagation loss (not transmission specturm) from a single run. In the end the exact transmission spectrum is almost impossible to predict, as it will depend on the exact disorder realization, ther fabrication tools and methods used and the quality of those.spectrumband structures.

Here are links to some of the software and one of my papers that can serve as a starting point@

Stephen Hughes and Philippe Lalanne have both written some excellent papers on the theory of the transmission of light through PhCs.

Dear Tamer S. Mostafa

you can use AMPS-1D ( Analysis of Microelectronic and Photonic Structures )

simulator or Silvaco TCAD for photonic structure solar cells.

please see:

http://www.ampsmodeling.org/default.htm

and attached file

MIT Photonic Bands (MPB) or Meep are free and widely used for the calculation of Photonic Crystals. You can find plenty of tutorials on the webpages (calculating band structures, defect states etc.)

Hi Ritesh,

Do you know how to sort the order of effective mode indices when sweeping with a range of wavelengths? For example from 400nm-500nm, the refractive index decreases but from 501-700nm, the refractive index increases. It is more obvious when I analyze with more than 2 modes. Thanks!

As an update to the wonderful white paper that Mohammad Albooyeh shared above, there are a few typos in his pdf worth mentioning. In equation 3 the cos(kai*k*L) term in the numerator should be deleted, as should the sin(kai*k*L) term in the numerator of equation 4. Fig 1 should also be updated, and I have attached a corrected version. Note that this is amplitude, not intensity, and S31/S41 are the simulated results. This particular figure was done with a mesh of lambda/10, but I was able to achieve comparable results with a mesh as coarse as lambda/5.

hi,

is "non symmetric results " means the different color of the field magnitude?

if you mean that, i think it's just because different color bar on the right ,adjust

the color bar same,then the field magnitude will be symmetric.

Mr. Kibrisli's question is, "is it possible to make a yellow laser ...". If we interpret the question as asking to make a laser that emits the spectral color yellow accompanied by a spectrum with a single spike at about 575nm, then using a red laser with wavelength at about 670nm and a green laser with wavelength at about 540nm would not work. The two lasers would show a spectrum with two peaks and would not possess the coherence of a true yellow laser. However, the human vision system would interpret the color as yellow in much the same way it interprets light combined from a red and green LED as yellow. So YES to your 'high powered yellow flashlight' characterization. Another view: your red + green = yellow laser would not excite a linear medium with a yellow resonance. Maybe that is a good test criterion for producing a yellow laser.

Hi.

As the number of layers increase, narrower FWHM could be achieved. However there is a trade-off between the device's reflection peak and FWHM, so number of layers can’t be increased indefinitely. You may start from say 5 layers and gradually increase the number of layers until you get the desired response.

what the value of the clad in optical fiber@

You can use meep.

A typical Fano resonance is obtained when a totally reflecting prism is coupled to a planar waveguide. When the guided wave is not lossy, with an incident gaussian beam, the reflected Fresnel field exhibits a dark line followed by an interference pattern. The light is coupled in the waveguide and after a small path decoupled in the reflected field. Interferences occur between this decoupled field (resonance) and the field directly reflected on the prism base (continuum). The prism coupler is very sensitive to the optical properties of the planar waveguide and can then be used as a sensor.

Hopefully, you have your answer from Dr. Kamran's response above.

To push a bit further, here is an interesting question: Can you determine the shape of a drum from its resonances? In other words, can you hear the shape of a drum? This question was addressed by Mark Kac in The American Mathematical Monthly back in 1966 as an answer to a question asked earlier by mathematician Hermann Weyl. The sad answer is no, you cannot. In other words, two differently shaped drums can have the same set of resonances or eigen-frequencies.

How does this relate to your question about a square drum? To find the resonances of any drum requires solving the Helmholtz equation with appropriate boundary conditions. This is what you are doing as you go from the round drum to the square. More complex shapes might not have closed-form solutions but they are all solvable. Their sounds are what make percussion instruments so compelling to listen to -- almost all cultures have their own drums with their own sounds.

In a practical direction, another question asks if you can tell the shape of a room from its resonances, pushing the original drum question from 2 to 3 dimensions. When a blind person taps her cane on the floor of a new room, she can sense its shape from the acoustic response of the air in the room to the impulses of the cane. But is the room shape (in 3D) unique from this impulse or equivalent frequency-domain analysis? I don't know. Kac (1966) would suggest the answer is no. But maybe 3D is different from 2D. So, you question is interesting from a basic physics/math point of view but also interesting enough to keep mathematicians and physicists awake all night thinking about it.

Thank you