Dr. Vadym Zayets

Important technologies for plasmonic waveguides:

Any plasmonic structure contains a metal, which strongly absorbs light. Reduction of propagation loss is essential for any practical application of a plasmon. There are two technology, which are very effective for reduction of plasmon' propagation loss:

(technology 1) Looser out-of-plane confinement by a double-layer dielectric.

The looser optical confinement makes the optical field of a plasmon more far from the metal. As result, the propagation loss is reduced.

This page describes the details of the technology (1).

(technology 2) Lateral optical confinement out-of-metal edge. Use of wedge, bridge and similar designs of a plasmonic structures.

In this case a huge optical scattering loss at edge of the metal can be avoided.

Details of the technology (2) are described here

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Technology 1 for reduction of plasmon' propagation loss.

Looser out-of-plane confinement by a double-layer dielectric.

The idea was proposed here and it was verified here.

How does it work?

The metal absorbs light. The less light is inside the metal and the less light is inside the dielectric, the smaller plasmon' propagation loss is. For a simplest plasmonic structure, which consists of one dielectric covered by a metal, the ratio between amounts of light inside the dielectric and metal is fixed by the dielectric constants of metal and dielectric. It can not be optimized. In contrast, in a double-dielectric plasmonic structure, the thickness of one dielectric can be optimized so that the amount of light in the metal becomes smaller and the amount of light in the dielectric becomes larger. It makes the smaller plasmon' propagation loss.

 

it is important. Using this technology, metals, which have never been used for the plasmonic before, can be used. The ferromagnetic metals like Fe and Co are the example. (See here and here)

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The story for engineering of plasmonic loss in short:

For around a century, it has been known that certain metals, such as gold, silver, copper, and aluminum, well support plasmons. The distinct yellowish color of gold, for instance, stems from plasmonic absorption. Experimental observation of surface plasmons in these metals is relatively straightforward, and they are traditionally employed in plasmonic devices, with gold being particularly favorable. On the other hand, metals like Co and Fe exhibit substantial absorption of surface plasmons, and, in practice, these plasmons are rarely observed in such metals. These experimental observations align well with theoretical calculations.

The categorization of metals into "plasmonic-friendly" and "plasmonic-unfriendly" is naturally attributed to variations in intrinsic bulk absorption among different metals. This classification is rooted in the fact that metals solely serve as sources of absorption for plasmons, making this rationale both reasonable and unquestionable.

However, our calculations reveal that bulk absorption in metal does not directly correspond to the absorption of surface plasmons. We have found that another critical factor, the penetration depth of the plasmonic field into the metal, plays an even more substantial role in determining plasmonic absorption.

Due to the extremely small penetration depth, plasmonic absorption is over 1000 times smaller than in the bulk of the metal. Since the penetration depth is small, a slight variation in the penetration depth results in a significant difference in plasmonic absorption. That is the reason why the penetration depth of the plasmonic field into the metal is critically important for plasmonic absorption. The penetration depth can be changed in a more complex plasmonic structure. Therefore, the plasmonic loss can be engineered. The ability to control and engineer the penetration depth opens the door to the practical use of 'plasmonic-unfriendly' metals in practical plasmonic devices.

 

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Trade-off between the plasmon-propagation loss and the plasmon confinement.

Different types of plasmons for different applications.

 

Q. The reduction of plasmon' propagation loss occurs only when the plasmon confinement is looser. How "bad" for plasmonic applications is the loose (or weak) confinement of a plasmon?

 

A. Since the refractive index step between a dielectric and a metal is a very large, the optical confinement for a plasmon is very strong and there is a lot of room for the reduction of confinement without any effect on the application.

 

For example, the optical confinement of a plasmon is significantly stronger than the confinement of a waveguide mode in a Si nanowire waveguide. The large difference in confinement could cause the bad coupling between a plasmon and a waveguide mode. Therefore, for the integration plasmonic and dielectric waveguide (See here and here) the reduction of the optical confinement for a plasmon is required.

 

 

However, some focusing applications (for example, thermo- assisted hard disk recording) requires smallest size of a plasmon. In this case a plasmon with the strong and narrow confinement is used.

In data processing applications the smallest loss of a plasmonic device, but not strongest and narrowest confinement, is required.

 

 

 

 

Q. Does the stronger optical confinement means the smaller size of a plasmon?

Yes. The stronger optical confinements generally corresponds to the smaller size of a waveguide mode or a plasmon.

 

Q. What is the optical confinement? Why does it important for a plasmon or a waveguide mode?

In free space the light propagates in all directions and the propagation path is straight. Because of the optical confinement, light propagates along a fiber, a plasmonic or dielectric waveguide. For example, when the fiber bends, light does not go to the free space, but light propagation path bends along the bent fiber.

The stronger the optical confinement, the smaller bending radios is possible. For example, the optical confinement in a Si nanowire waveguide is rather strong and the bending radios as small as 1 um is possible (see here). Light can propagate along such bent waveguide with no loss. In contrast, the optical confinement in a GaAs waveguide is weaker. In 1-um-bended GaAs waveguide, all light goes to the free space and it does not propagate along the waveguide.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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How to control the plasmon confinement?

 

Answer:

The insertion of a thin dielectric layer of a different refractive index between the metal and dielectric makes the plasmon confinement looser. When the insertion layer becomes thicker, the plasmon confinement becomes looser and the amount of light inside metal becomes smaller. As result, the plasmon' propagation loss becomes smaller.

Figure 6 shows the distribution of the optical field of a plasmon across Si/SiO2/Co interface. The refractive indexes of SiO2 (n=1.444 at lambda=1.55 um) and Si (n=3.4757) are substantially different. As result, the insertion of the SiO2 layer makes the plasmon confinement weaker.

The decay of optical field inside metal does not depend on the optical confinement and it equals to the skin depth. In contrast, the decay in the dielectric is significantly affected by the SiO2. Without the SiO2 layer the decay is steep and all optical field is very to the metal. In this case the propagation loss is high. When the thickness of SIO2 layer becomes thicker, the decay into the dielectric becomes looser. Therefore, the optical field is pushed away from the metal, inside the metal there is less light and the propagation loss of the plasmon becomes smaller.

 

Q. How much the plasmon' confinement can be reduced? Is there a limit?

A. As can be seen From Fig.6, when the insertion layer becomes thicker, the plasmon confinement becomes looser and looser and eventually is lost. In this case a plasmon can not propagate. This is cut-off condition for a plasmon. Near the cutoff the decay of the optical field is very slow and almost all optical field is inside the dielectric.

In the case when the SiO2 layer is thicker than cutoff thickness, the Si/SiO2/Co does not support any plasmons. It means that when this structures is illuminated by light, all light is reflected and there is no light, which propagates along the interface.

 

The optimized double-dielectric plasmonic structure allows to use the metals in plasmonic applications, which have never been used before!!!

In a simple plasmonic structure, which contains only a single-layer dielectric, the propagation loss significantly depends on a type of a metal. In case of Au or Ag, the propagation loss is small. The 1/e plasmon' propagation distance could be as long as 100-200 um and longer. In contrast, in the case of a ferromagnetic metal (Fe, Co) the plasmon' propagation loss is very high. The 1/e plasmon' propagation distance is shorter than 5 um. Having such a large loss, the plasmon in a ferromagnetic metals have a little chance to be used in practical applications. However, using an optimized double-dielectric plasmonic structure, the the plasmon' propagation loss can be significantly reduced to meet the requirement for a practical application.

 

Q. Often in practical applications of the plasmonic devices are used because of unique optical properties of a metal. For example, the plasmonic isolator profits from a large magneto-optical constants of a ferromagnetic metal. When plasmon confinement is reduced, the amount of light inside the metal is decreasing. As result, the plasmon' plasmon propagation loss is reduced, but the magneto-optical (MO) properties of the plasmons is reduced as well. Is there any profit to reduce the propagation loss when at the same time the important MO properties of a plasmon are reduced???

 

Usually in a magneto-optical materials, there is a trade-off. The increase of MO constants is accompanied by the increase of the optical loss or vice versa. It is the case of magnetic semiconductors (CdMnTe) and oxides (garnets). Often, but not always, it is the case for a plasmon.

It is important. In the case of a surface plasmon near cutoff, both the increase of the MO and decrease of the loss can be done at the same time. It is a unique property of a surface plasmon.

 

 The ability for the simultaneous reduction of optical loss and the enhancement of the magneto-optical response (as well as the electro-optical response and so on) is a unique property of a surface plasmon, which is very important for practical applications of different plasmonic devices.

 

 

 

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Unique properties of a plasmon near cutoff.

Enhancement of the magneto-optical effect near cut off

 

More explanations are here.

Calculated examples:

(1) on Si (lambda=1550 nm) is here

(2) on GaAs (lambda=1550 nm) is here

(2) on GaAs (lambda=800 nm) is here

 

Q. Why MO properties of plasmons are so unique near cut-off? What is special about cut-off?

The cutoff conditions for a plasmon are significantly depend on the dielectric constants of the metal. A tiny change of the dielectric constants of the metal ( for example, due to MO effect) causes a substantial change of the cutoff thickness. Since in the vicinity of the cutoff the propagation loss of a plasmon sharply decreases as the thickness approaches to the cutoff thickness, a tiny change of the dielectric constants causes a substantial change of the plasmon' propagation loss.

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Q. Is it easy to find the cut-off thickness for a double-dielectric plasmonic structure?

It is not easy. For a planar multi-layer plasmonic structure the cutoff thickness can by rather easily calculated by this method (See above examples). However, there are several factors which significantly influence the cutoff thickness, which are

(a) interface roughness

The cut-off conditions are critically sensitive to the interface roughness. Even a tiny roughness makes the decrease of the plasmon' propagation loss near cutoff to be not as sharp as the calculations predict, but slow. Due to the interface roughness, a plasmon can propagate even above the cutoff thickness where it should not propagate.

(b) dielectric constants of the metal

The the dielectric constants of a metal substantially depends on the purity, the deposition method of the metal and post-deposition processing. Prof. Shimizu has found that the dielectric constants of Fe may change as much as two times depending on a Fe deposition method.

The dielectric constants may be significantly different at an interface and deeper into bulk of a metal due to diffusion and oxidation.

The precise knowledge of the dielectric constants of a metal are critically important for the correct prediction of the cutoff and for the optimizing of the plasmonic structure.

(c) in-plane confinement

As it is described here, any realistic plasmonic structure should have an effective in-plane confinement (grove-, wedge- or bridge type plasmonic structure). Such plasmonic structure is not planar. The calculations and optimizations of such 2D structures are difficult (but possible). Of caurse, in the grove-, wedge- or bridge type plasmonic structure the cutoff conditions are different than in the simple planar plasmonic structure

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.Q. A plasmon propagating in a thin metal layer also have a cutoff. Is there any enhancement of the MO effect in this case?

Yes. It is a very similar case and there is an enhancement

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Why it is important?