Hello Dr. Farber,

I recently was reading up on plasmons myself and found this very nice review.  I think it answers most of your questions. See attached.

Regards,

Sebastian

Hi there.  I have been dealing with "plasmons" for the past 5 years, so I am happy to address this question.  Of course, reading the many review papers on the subject is always a good idea.  But if you are looking for a concise and simple answer, I will do my best. 

The most common form of "plasmon" concerning the past decade of research are "surface plasmon polaritons (SPPs)".  From the vantage point of classical electromagnetics, SPPs are nothing more than TM (transverse magnetic) waves that exist at the interface between a metal and a dielectric.  In the simplest case, the metal and dielectric are assumed semi-infinite, such that only a single interface, and therefore single SPP, exists.  Beyond this, one may consider a thin metal film surrounded by two semi-infinite dielectric, or vise versa.  Then we have SPPs at each interface.  If the middle layer is sufficiently thin, coupling between adjacent SPPs can occur.   Stacking such thin layers indefinitely leads to the creation of a hyperbolic metamaterial (HMM), which in my opinion is the most exciting application of plasmons generally.

In addition to SPPs, other plasmons include localized surface plasmons, which exist in metallic nanoparticles (think of a gold or silver sphere with a radius of ~50nm with the electrons oscillating about it), as well as volume plasmons.

(b)  The most important commercial application to date is in bio-chemical sensors based on resonances of a SPP.  However, I suggest you search recent reviews on HMMs for a wider range of intriguing applications, e.g., hyper-lensing, spontaneous emission engineering.

(c)  Experimental excitation of SPPs requires a prism, grating, or scattering element to achieve momentum conservation between the incident light and the SPP. 

I'd recommend the following books to deepen your knowledge of the subject:

1. Plasmonics: Fundamentals and Applications Hardcover(Springer, 2007) by Stefan Alexander Maier

2. Principles of Nano-Optics (Cambridge University Press; 2 edition, 2012) by Lukas Novotny

Dear Joseph

What are the thickness of thin films of HMM in practice regarding the incident light wavelength?

Dear Dr. Sebastian Requena,

I also seen the review paper which you have attached with this conversation, it is very good for understanding of plasmonics. Thank you very much for providing it.

Hi,

1) solve Maxwell equations in vacuum. You will get two solutions with the spectrum omega=ck and two orthogonal polarizations. The electric field vector E will be perpendicular to the wave vector k for both solutions. These modes are called TRANSVERSE electromagnetic waves.

2) Try to find the solutions of Maxwell equations with the electric field parallel to the wave vector. You will see that such solutions do not exist. So, LONGITUDINAL waves do not exist in vacuum.

3) Consider plasma, e.g. freely moving electrons on a positively charged uniform background. This is a "uniform electron gas" model which is often used in solids. Repeat items 1) and 2) for this model. Describe the plasma using the simplest model current=sigma(omega)*field, where take for the conductivity sigma(omega)=ne^2/(i*m*omega), where n is the electron density (Drude). You will find that (a) there are two TRANSVERSE modes, like in vacuum, with two perpendicular polarizations and with E perpendicular to k. Their spectrum is omega^2=c^2k^2+omega_p^2, where omega_p^2=4*pi*n*e^2/m. (b) there is one more mode which has the spectrum omega(k)=omega_p and which has the electric field vector PARALLEL to the wave vector. This is a LONGITUDINAL mode.

4) This LONGITUDINAL mode is called plasmon. The frequency omega_p is called the plasma frequency. Plasma oscillations are oscillations of the electric field and electric charge. In the transverse modes there are no charge oscillations (only field and current). This is the main difference.

5) The plasmon mode can be found simpler by solving not the full system of Maxwell equations, but only the electrostatic equations div E=4 pi rho, d rho/dt + div j=0 and j=sigma(omega)E.

6) Consider a boundary plasma - vacuum (e.g. metal - vacuum) and find the wave running along the boundary using the same simple model. If you will solve only electrostatic system of equations, you will find the solution omega=omega_p/sqrt(2). This is a surface plasmon. Check how the electric field of this mode look like. You will find that it has not only longitudinal but also transverse components of the electric field (e.g. if the boundary is z=0 and the wave runs in the x-direction, the electric field will have E_x and E_z components).

7) Since this mode has transverse components it must interact with light. Solve the full system of Maxwell equations to find the same mode. You find that the solution omega=omega_p/sqrt(2) is valid only at ck>>omega_p. In the opposite limit this modes has the spectrum omega~ck. So, this mode is a "mixture" of the plasma (charge) oscillations and of light. Such "mixed" modes are called plasmon-polaritons.

8) Similarly one can consider electromagnetic waves in a finite-width metallic slab. If the slab thickness tends to zero you will get two modes one of which, the so called two-dimensional (2D) plasmon, has the spectrum omega^2(k)=2*pi*n_s*e^2*q/m, where q is the wave vector along the 2D plane and n_s is the surface density of electrons (per cm^2). This spectrum is valid at large q, at smaller q you will get again omega=cq.

9) Similarly one can find waves running along a cylindrical wire. At large q you will get a spectrum like omega^2(q)=2*n_l*e^2 *q^2*ln(1/qa)/m, where a is the radius of the wire and n_l is the linear electron density (per cm). At q->0 you will get again cq. This is a one-dimensional plasmon polariton.

10) When electromagnetic waves with the frequency 50-60 Hz run to our houses from power stations these are actually plasmon polaritons. This was probably their first application.

11) The electromagnetic waves in different metallic or semiconductor structures (currently fashionable metamaterials, for example) are also mixtures of the charge oscillations in metals and field oscillations around, so these are different types of plasmon polaritons.

One could write much more about plasmons/plasmon-polaritons, but this would then be a book :-). Hope this will help a bit.

in brief,

the simplest words what is that. In addition, I have few questions on this topic:

plasmons are electromagnetic waves that exist only at the metalic/ dielectric interface.

(a)What types of plasmons are exist?

let say that there is two type of plasmonic wave: 1/ loclaized plasmon (mainly in nanoparticales)

2/ deloclaized plasmon (in nanowaveguide and some periodic nanohole array.....) 

(b)What are the practical applications of plasmons?

the main research in plasmonic is still fundamental but there are some commercial applications like pregnancy test (base on plasmonic nanoparticle)....cancer therapy (still in research...using the heat of plasmonic nanoparticle or nanoshell with laser)

(c)What are the plasmon creation conditions?

metal/dielectric interface

additional momentum (to couple light and surface plasmon) by using prism, periodic array,......

Thank you in advance!

Dear Ossama

What are laser properties to induce surface plasmon? wavelength?power? bandwidth? etc

What is the  pre-requisite to generate heat in plasmonic NPs? What about nanostructures such as graphene for cancer therapy? In this case , is it localized or delocalized plasmon?

What is lower and upper bound thickness of the metal/dielectric interface to create the surface plasmon ?

Prism and grating are dispersive elements.How do you create plasmonics using those elements? Which one is more efficient?

1/ you can excite sp even with white light. the sp existe even in the near IR but in the far IR we start talking of the surface wave (no skin depth in the metal). 

2/ I am not expert in the Np and graphene but what I know is:

to generat heat in NP you to excite them with the right wavelength that correspond to their absorption peak (eign mode of localized plasmon) this later depend on size shape medium material ....of your NP. no idea for graphene

3/the thikness of you metal depends of your skin depth the later depends on your material and the wavelength of your light. for example for 632nm the skin depth in your gold film is about 30nm (If I remember well) in this case you have to chose a thicker film than the skin depth like 45nm

4/what you have to know is to excite a sp in general you need to create an evanescent wave(EW). the prism excites sp because you can excite EW  at the angle of total reflexion for example also you excite sp with a metalic sharp tip for the same reason and ......grating excites sp if they respect the condition of bragg diffraction....

all those techniques are  different that we can't campare the efficiency. it will depend on their applications

Dear Parviz and Oussama,

May i add a few points to your questions/comments:

1) You may excite surface plasmon polaritons (SPPs) with a broadband source, but one should bear in mind the dispersion, i.e. the amount of SPPs excited at each wavelength can be quite different. Having said that, it's possible to achieve broadband excitation with the help of some design strategies.

2) The heat is coming from the absorption of the localized plasmon mode in the nanoparticle. The difference arising from graphene or metal depends on how they are utilized and their transport properties.

3) You may use a simple transfer matrix method to calculate the dispersion of the plasmon modes on thin films. Then you will find that (i ) for small thicknesses the dispersion splits into a high and a low energy mode, (ii) for large thicknesses you only find the metal/dielectric half space mode (as Oussama pointed out, the skin depth of the metal has a bearing on the thickness) .

4) The efficiency of the SPP generation depends on many things such as wavelength, aperture size, grating design etc. It may be determined experimentally and also calculated with the mode orthogonality condition for some geometries.

Hope the above helps!