8. Conclusions

where explicitly the coefficients are:

In a similar manner, the second IP will be:

And taking expression (67)

Also, by taking Eq. (67):

the two visible light IP:

And explicitly

For the second IP

in which

36

in which

[1–3].

Xn, <sup>1</sup> <sup>¼</sup> <sup>H</sup> <sup>n</sup>

Telecommunication Systems – Principles and Applications of Wireless-Optical Technologies

Xn, <sup>1</sup> ¼ a cos Θ<sup>A</sup>

∞ �∞ Xn, <sup>2</sup>

Xn, <sup>2</sup> <sup>¼</sup> <sup>H</sup> <sup>n</sup>

Xn, <sup>2</sup> ¼ a cos Θ<sup>A</sup>

we have enlarged the scope of the formalism we named vector-matrix or VMF

2ω<sup>2</sup> � �

> n 2ω<sup>2</sup> � � δ

<sup>4</sup><sup>d</sup> þ ω<sup>0</sup> � �<sup>t</sup> � <sup>n</sup> � � � �

� �<sup>t</sup> � <sup>n</sup> � � (74)

� �<sup>t</sup> � <sup>n</sup> � � (76)

þ δ

þ δ

<sup>4</sup><sup>d</sup> þ ω<sup>0</sup>

n 2 <sup>π</sup> <sup>4</sup><sup>d</sup> þ ω<sup>0</sup> � � !

" #

<sup>4</sup><sup>d</sup> þ ω<sup>0</sup> � �<sup>t</sup> � <sup>n</sup> � � � �

<sup>4</sup><sup>d</sup> þ ω<sup>0</sup>

n 2 <sup>3</sup><sup>π</sup> <sup>4</sup><sup>d</sup> þ ω<sup>0</sup> � � !

" #

� �

As we said above, the resonances must come also for the WS. By this procedure,

In order to complete our example, we put explicit values of the resonances for

sin π 2 <sup>π</sup>

π 2 <sup>π</sup>

sin π 2 <sup>3</sup><sup>π</sup>

π 2 <sup>3</sup><sup>π</sup>

H2ðÞ¼ t ∑

H1ðÞ¼ t ∑

H2ðÞ¼ t ∑

∞ �∞ Xn, <sup>1</sup>

Xn, <sup>1</sup> ¼ a cos Θ<sup>A</sup>

∞ �∞ Xn, <sup>2</sup>

Xn, <sup>2</sup> ¼ a cos Θ<sup>A</sup>

2ω<sup>1</sup> � �

> n 2ω<sup>1</sup> � �

� �

sin ½ � πð Þ 2ω2t � n πð Þ 2ω2t � n

þ δ

(69)

(70)

(71)

(72)

(73)

(75)

(77)

In Eqs. (25), (29), (30), (34)–(40), we have shown that it is possible to use an operator language and the properties of the Green function to define the capacity of a channel, the loss of information, and finally, the error in the time-reversal process. Therefore, we can use our results to describe the behavior of LHM interacting with electromagnetic field whether forward or backward in time. Thanks to our interpretation of a resonance in the broadcasting problem with the left-hand material conditions, and the application of the model PSM, we make up a broadcasting system that has the power for distinguishes between signals according to their recording time, and allows to superpose signals in the same frequency range having different recording times with the minor loss because of resonance technology; to this end, we have presented a detailed support and definition of the information packs (IP) and the possibility of application for visible light. In addition, we have enunciated and proved a theorem (theorem III) that establishes: for the TRT and LHM, the normalized error is independent of the particular behavior of the interaction. Summarizing, we give a complete recipe for optimizing communications efficiency.
