# Negative index of refraction transmission

• Matej Kurtulik

#### Matej Kurtulik

Hi guys,
I have slab of negative index of refraction material, inside the material the evanescence field is amplified. I want to calculate transmission of this slab for evanescence waves, so I used fresnel equations with multiply reflection inside of slab. I found this method in some papers. First question is, how is possible that I can use geometric series of reflection inside the material, I have evanescence field, which doesn't propagate, so what is it reflected? If I use Fresnel equation for transmitted field I get for epsilon=-(1+delta) and mu=epsilon. How is possible that I get more than one, is that means that it is like superpossition of bounded surface mode and evanescence field which is transmitted? if I use epsilon=-(1+i*delta) and mu=epsilon, the peak disappear, so basicaly I introduce small absorption with imaginary epsilon what is the principle which cause this abrupt change(I think that I have evanescence wave, so it means that my wave vector in z-direction is choosen to be real, so if I introduce imaginary epsilon I will get imaginary part of kz which means that I have propagation wave not absorption.)

It is not clear to my how is possible that if I have slab of metal with negative only epsilon, and I want to excite the plasmon wave the energy will transfer from one interface to another(Kretchman configuration). Evanescence wave doesn't carry energy, so how can this happen?

Please, if you can suggest some advice or some reading to understand these things I will appreciate it so much

.

Dear forum member,

Thank you for your question regarding the transmission of evanescent waves through a slab of negative index material. I can understand your confusion as this is a complex and highly debated topic in the field of optics.

Firstly, let me clarify that the use of geometric series of reflection inside the material is a mathematical tool that is commonly used in theoretical analysis to simplify the calculations. It does not mean that there is actual reflection happening within the material. The evanescent field is not reflected, rather it is amplified due to the negative index of refraction.

To answer your second question, when you use the Fresnel equation for transmitted field, you are essentially calculating the transmission coefficient of the evanescent wave through the slab. The result of greater than one indicates that there is an enhancement of the evanescent wave within the material, which is due to the amplification of the evanescent field.

In the case of introducing a small absorption with imaginary epsilon, it results in the disappearance of the peak because the imaginary part of epsilon causes a decrease in the intensity of the evanescent wave. This is due to the fact that the imaginary part of the wavevector in the z-direction is related to the absorption of the wave.

Now, coming to your third question about the transfer of energy in the Kretschmann configuration, it is important to note that the evanescent wave does carry energy, although it is not a propagating wave. In the case of a negative index material, the evanescent wave is amplified and can transfer energy from one interface to another, resulting in the excitation of plasmon waves.

I would suggest reading more about the concept of negative index materials and their properties, as well as the theory of surface plasmon polaritons to gain a better understanding of these phenomena. Additionally, consulting with experts in the field and discussing your questions with them can also be helpful in clarifying any doubts.

I hope this helps in your understanding of the topic. Do not hesitate to reach out if you have any further questions.

Best regards,

## 1. What is a negative index of refraction transmission?

A negative index of refraction transmission is a phenomenon where light travels through a material with a negative index of refraction, causing the light to bend in the opposite direction as it would in traditional materials with a positive index of refraction.

## 2. How is a negative index of refraction transmission different from traditional materials?

In traditional materials, such as air, water, and glass, light travels in a straight line and bends towards the normal as it passes through the material. In materials with a negative index of refraction, the light bends away from the normal, resulting in unique optical properties and potential applications.

## 3. What are some potential applications of negative index of refraction transmission?

Some potential applications of negative index of refraction transmission include creating superlenses with the ability to resolve smaller details than traditional lenses, developing invisibility cloaks, and designing more efficient solar cells and optical fibers.

## 4. How do scientists create materials with a negative index of refraction?

Scientists can create materials with a negative index of refraction using metamaterials, which are artificial materials designed with specific structures to manipulate the behavior of light. These materials can be made from various substances, such as metals, semiconductors, and dielectrics.

## 5. Are there any challenges or limitations to utilizing negative index of refraction transmission?

There are still challenges and limitations to utilizing negative index of refraction transmission, such as the difficulty in creating materials with a negative index of refraction at visible wavelengths and the high cost of producing these materials. Additionally, the practical applications of these materials are still being explored and developed.