some quick answers:

1) if the electrons move collectively in one direction, this creates an electric dipole moment (center of mass of positive and negative charges are displaced with respect to each other)

a) this creates a restoring force (linear in the displacement to first order) and therefore this is a harmonic oscillator

b) the oscillating electric dipole acts like a dipole (Hertz) antenna

c) as with the Hertz dipole near field and far field don't look exactly the same, see behnam Farid's answer to your previous question

2) Reflection is coherent scattering from a macroscopic surface. This is a condition not fulfilled for NPs (dimension similar or smaller than the wavelength).

Otherwise, absorption and scattering both have their share in what's going on. What dominates depends on the optical properties ofthe material ("complex dielectric function") and particle size (and shape) (-> boundary conditions for the electromagnetic fields).

3) A dipolar field (light) shining on the particle with a frequency reasonable near the plasmon frequency. in order to be a prominent feature, the plasmon oscillation should be sufficiently lon lived, so damping may not be too large. Damping is large in most transition metals due to their high density of states at the Fermi level. Therefore in most transition metal particles, you don't actually see the plasmon. It' very different in the noble metals, as you will know.

4) Bulk plasmons are charge density oscillations (see previous thread of yours). The Plasmon we're talking about here exists due to the finite size of the particle. An analog to this mode exists also in finite size metal plates, with the homogeneous charge density oscillating back and forth along the direction connecting the surfaces. This is sometimes referred to as a surface plasmon. There is no density oscillation involved. Two-dimensional charge desity oscillations also exist, and think that was what Behnam was referring to in his previos answers.

Nevertheless, the surface plasmon I described has a resonance frequency related to charge density just as the bulk plasmon and there is "just" a geometry related proportionality factor between them (could be 1/sqrt(2) for vacuum environment, but I am not totally sure just from memory)

Pick a good solid state physics textbook (I like to recommend Ashcroft & Mermin) and/or any other book or resource we recommended earlier and you will be able to study the plasmon physics from scratch.

some quick answers:

1) if the electrons move collectively in one direction, this creates an electric dipole moment (center of mass of positive and negative charges are displaced with respect to each other)

a) this creates a restoring force (linear in the displacement to first order) and therefore this is a harmonic oscillator

b) the oscillating electric dipole acts like a dipole (Hertz) antenna

c) as with the Hertz dipole near field and far field don't look exactly the same, see behnam Farid's answer to your previous question

2) Reflection is coherent scattering from a macroscopic surface. This is a condition not fulfilled for NPs (dimension similar or smaller than the wavelength).

Otherwise, absorption and scattering both have their share in what's going on. What dominates depends on the optical properties ofthe material ("complex dielectric function") and particle size (and shape) (-> boundary conditions for the electromagnetic fields).

3) A dipolar field (light) shining on the particle with a frequency reasonable near the plasmon frequency. in order to be a prominent feature, the plasmon oscillation should be sufficiently lon lived, so damping may not be too large. Damping is large in most transition metals due to their high density of states at the Fermi level. Therefore in most transition metal particles, you don't actually see the plasmon. It' very different in the noble metals, as you will know.

4) Bulk plasmons are charge density oscillations (see previous thread of yours). The Plasmon we're talking about here exists due to the finite size of the particle. An analog to this mode exists also in finite size metal plates, with the homogeneous charge density oscillating back and forth along the direction connecting the surfaces. This is sometimes referred to as a surface plasmon. There is no density oscillation involved. Two-dimensional charge desity oscillations also exist, and think that was what Behnam was referring to in his previos answers.

Nevertheless, the surface plasmon I described has a resonance frequency related to charge density just as the bulk plasmon and there is "just" a geometry related proportionality factor between them (could be 1/sqrt(2) for vacuum environment, but I am not totally sure just from memory)

Pick a good solid state physics textbook (I like to recommend Ashcroft & Mermin) and/or any other book or resource we recommended earlier and you will be able to study the plasmon physics from scratch.

Kai, could you please mention which portion I need to read in that book to understand plasmonic effects .

Not so easy to tell exactly.

(i) Elliott, "The Physics and Cemistry of Solids" is on a more introductory level than Ashcroft. Here, Chapter 5 would be most relevant. Chapter 5.6.2 is (short and) on plasmons. these are the bulk plasmons (density oscillations).

(ii) Ashcroft. I happen to have the German 2001 edition at hand only. I dont know whether chapters are identical and whether exercises cover the same topic(s) as an edition you might get hold of. In my version Chapters 1 through four are on free electrons in metals. Very, very recommended for any physicist. Later chapters (in the higher tens and twenties) treat metals more profoundly. The exercises to Chapter one in my book contain one on surface plasmons. These are the ones Behnam wrote about in his answer(s).

(iii) The simplest oscillation of a homogeneous charge density in a flat, metallic plate along its surface normal is something you should try (and be able) to do by yourself (find the charges and associated electric field (-> restoring force) as a function of displacement, derive the equation of motion of the corresponding harmonic oscillator and find the resulting resonance frequency. Feel free to send me or post your result).

(iv) For the extension to small particles (i.e. metallic spheres) you will have to recur to the more specialized literature, I guess. We have mentioned the book of Kreibig and Vollmer on Optical properties of metal particles (and a few other titles). On the web you might well find dissertations or other theses which have chapters on the topic. You may also search the scientific literature authored e.g. by U. Kreibig, who has worked a lot on plasmons in the late 1900's.

Edit:

hint: I just did the calculation for (iii) and you should get the same frequency as is usually mentioned in the books for the plasmon: omega_p = sqrt(e^2*n/m epsilon_0),

where e is the elementary charge, n the number density of free electrons, m the electron mass and epsilon_0 the permittivity of the vacuum. This result is thus valid in SI (MKSA) units.

Hi Shamjid, so quick response to the points you raised

i) how free electron oscillations in a metallic NPs generate the localized waves:

The localized surface plasmons  (LSP) are free electrons oscillating in response to an oscillating electric field. The amplitude of such oscillation reaches a maximum when we approach the localized surface plasmon resonance (LSPR).

The LSPR is just like any resonance; it occurs when you have a periodic driving force applied on a system that has a restoring force, i.e. an oscillator. The restoring force arise when you have some curvature in your metal. Also, in order to excite surface plasmons, the nanostructure should be smaller or in the order of the wavelength of the impinging light.

ii) Is there the incident light absorbed , reflected or scattered by the metal NPs.

Since we are dealing with a sub-wavelength particle, the idea of reflection does not exist. You are only left with front and back scattering of light, and because metals are lossy, the scattering is accompanied with optical losses (in the form of absorption). 

iii) what is the minimum requirement to generate plasmon from a metal NP

In addition to having a metal with curvature and that the size is in the order of a wavelength, you should have the metal size smaller than the skin depth of light at the desired frequency, otherwise the oscillation will be over damped and will be lost. 

iv) how metal NP plasmon different from bulk and surface plasmons.

LSPR is different from surface plasmon polaritons, which is a propagating surface wave, not a localized resonance. It is a wave that propagates between a metal dielectric interface under certain conditions. 

Bulk plasmon is a longitudinal wave, basically oscillation of free electrons along the bulk of a metal. Because light is a transverse wave, light cannot excite a bulk plasmon.