Metal type Effect on Plasmonic Fiber Properties

In this study, the properties of plasmonic fiber have been studied, in which the core is one of the noble metals (Au,Ag,Cu,Al). The modes and the effective refractive index associated with each wavelength were derived using the COMSOL MULTIPHYSICS based on the Finite Element Method. The electrical permetivity was studied using the relationship Lorentz derode to determine the real part for the refractive index and the imaginary part responsible for the attenuation coefficient. Where a frequency range was chosen to hold negative values for the real part. The results show that when drawing the relationship between (εr ) or (εi ) a function of the wavelength that gold has the highest value and then silver, copper and then aluminum, but in the case of (nr ) or (ni ) we notice that aluminum has the highest elements. (neff ) has also drawn as a function of the wavelength, the four metals, and different of the core radius (a=100, 200, 300, 400, 500) for the three modes (LP 01,LP 11,LP 21) and the metal used. It is observed that increasing the mode index increases the lobes where the mode (LP 01) is one spot and the mode (LP11) is two spot and the mode (LP 21) is four spot, where the power index increase is the increase in red and yellow color, and this applies to all modes. In other words, by controlling the radius of the core and wavelength, we can balance the ratio of power that propagation forward and backward. The refractive index (neff) has the highest value at small wavelengths and then begins to decrease with increasing wavelength, and has the highest value in the case of gold, then silver, then copper. Then aluminum, which is less than the rest of the elements.


Introduction
Plasmons are collective oscillations of electron densities that can be generated by a free electron gas interacting with ( ) waves [1]. These special plasmons are then called plasma polaritons. The most prominent material group exhibiting such interactions are metals. Plasmonic vibrations inside a bulk volume of metal possess a special, material-

Basic Formalism and Software
To describ light in a waveguide, we solve a wave equation in each region (core and cladding) for both the electric field and the magnetic field. We are interested in traveling plane-wave solutions, As the permittivity of the core are complex functions, so too is the A surface Plasmon polariton ( ) wave is a guided wave along the interface of a metal film or a metal substrate and a surrounding dielectric material [5]. This type of wave is formed by the coupling of an electromagnetic wave to oscillating free electrons at the surface

Results and Discussion
The results include four types of (plasmonic fiber) where noble metals ( , , , ) were used to calculate electrical permittivity (ε) and for each element the equation (1) and the values in the table (1) were used and the coefficient of Refraction is calculated from ( = √∈) considering that the material is not magnetic ( = 1). After that, in order to calculate the modes, a COMSOL program was used.
COMSOL MULTIPHYSICS (4.5) is a commercial application which depending on the Finite Element Method ( ) [7]. This software includes many physical models and a design window using Computer Aided Draw ( ) for structured design, mesh generator, internal matrix assembler, various numerical solvers for matrics, and several post-processing features [8].
( ) is a method to solve differential or partial equations numerically involve depending on dividing the physical systems, such as structures, solid or fluid continua, into small sub regions or elements [9]. Each element is an essentially simple unit, the behavior of which can be readily analyzed. The complexities of the overall systems are accommodated by using large numbers of elements, rather than by resorting to the sophisticated mathematics required by many analytical solutions. One of the main attractions of finite element methods is the ease with which they can be applied to problems involving geometrically complicated systems. The price that must be paid for flexibility and simplicity of individual elements is in the amount of numerical computation required. Very large sets of simultaneous algebraic equations have to be solved, and this can only be done economically with the aid of digital computers [10].   (1): parameter values for the Drude-Lorentz model [11]. ) is drawn. The plasmonic property is related to ( ), and we see from the figure that gold has the highest value, followed by silver, copper, and aluminum. In general, we see that ( ) decreases with increasing wavelength, and that the aluminum component is far away from its properties by other properties. We know that the attenuation factor correlates with the imaginary section ( ) and we see from the figure ( as a function to ), the most valuable metal is aluminum and the least copper is in gold and silver are identical in the values of (λ < 0.5) but at the values of (λ > 0.5) we notice the superiority Gold on the elements, then copper, then silver, and finally aluminum, we see here a difference in this behavior. Figure   followed by copper, noting that gold is higher than silver at (λ< 0.5), and they agree roughly at the values of (0.5 < λ < 1). The values of mµ (λ > 1) are silver and copper agree, then gold.   where the mode ( 01 ) is one spot and the mode ( 11 ) is two-spot and the mode ( 21 ) is four spot. The difference here when using a normal fiber is that the core does not show details  6 of the mode and this is why it is used (metal core). It can be seen that the ratio of energy outside (core) increases with increasing (λ). As the energy increase indicator is red and yellow. This applies to all modes. In other words, controlling the radius of the core and the wavelength we can balance the ratio of the power that propagates forward and backward, and even stopping the light can be achieved. From the observation of Figure (     Figures (9) to (13) represent ( ) as a function of (λ) using the three modes 01 , 11 , 21 and various elements ( , , , ) for the radii (100, 200, 300, 400, 500) In order. Figure (9) shows the relationship in the case of the radius core (a = 500) nm, where we notice from the figure in the case of the mode ( 01 ) that the refractive index ( ) has the highest value at small wavelengths and then begins to decrease with increasing wavelength, and has a higher a value in the case of the element of gold, then silver, then copper, and aluminum, the least of which is at a wavelength (λ > 1400). We note that silver and copper are almost identical. We also notice that ( ) is one less than the rest of the elements. This is the same thing in the case of the mode ( 11 ) and the mode ( 21 ), but in the case of the mode ( 11 ), we note the match of gold, silver, and copper at (λ > 1200) and

Core Radius Effects
in the case of the mode ( 21 ) then we notice in this case that the refractive index ( ) Gold, silver, and copper are almost identical from the beginning, and ( ) in the three types of patterns remains aloof, and the lowest of them is in the mode state ( 01 ) . ( ) has the highest value of all elements in the case of mode ( 01 ), then the mode follows ( 11 ) and then ( 21 ).
As for Figure (10), the relationship is shown in the case of the radius core of (a = 400) nm, as it is similar to Figure (9). Figure (11) shows the relationship in the case of the radius core (a = 300) nm as it is similar to the figure (9). However, in the case of the mode  Figure   (13) shows the relationship at the radius core (a = 100) nm, where we also notice a similar shape to (9), but in the case of the pattern ( 21 ), the refractive index ( ) of all elements is exactly the same from the beginning, and we notice a wavelength. (λ > 1800) The deviation of the curves from its primitive path and ( ) of ( ) is less than one of the elements. ) as a function of (λ) using the three modes ( 01 , 11 , 21 ) and various elements ( , , , ) for the radii (a= 100).

Conclusions
As a conclusion: the plasmonic property is related to ( ), and it was noted that gold possesses the highest value and hence silver, copper and aluminum, and that ( ), decreases with increasing wavelength. The attenuation factor is related to ( ), and it is noted that aluminum has the highest value and that copper has the lowest value. The true portion of the refractive index of gold and silver has the highest value at small wavelengths, while the imaginary part of aluminum has the highest value. Controlling the radius of the heart and the wavelength, we can balance the ratio of the power that propagates forward and backward, that is, the difference (a) means different control conditions with the type of propagation.