阅读说明：本技术 一种纤维集成傅里叶变换微光学系统 (Fiber integrated Fourier transform micro optical system ) 是由 苑立波 孟令知 陈宫傣 于 2020-05-10 设计创作，主要内容包括：本发明提供的是一种纤维集成傅里叶变换微光学系统。其特征是：它由两段经热扩散制备后,折射率分布为圆周对称准高斯分布的光纤连接组成。纤维集成傅里叶变换微光学系统是将光纤放置在恒温场中,经热扩散制备并连接而成,光纤的纤芯掺杂剂扩散后,折射率分布变为圆周对称的准高斯分布,可以等效为微凸透镜。本发明主要提供一种光纤微透镜的构造方法,同时在光纤中构建纤维集成傅里叶变换微光学系统。本发明可用于纤维集成微凸透镜的制备,可广泛应用于基于纤维集成傅里叶变换微光学系统的微型内窥镜、细胞生物光纤成像系统、光纤光镊系统、微型无人机等领域。(The invention provides a fiber integrated Fourier transform micro-optical system. The method is characterized in that: it is formed by connecting two sections of optical fibers which are prepared by thermal diffusion and have circumferentially symmetrical quasi-Gaussian refractive index distribution. The fiber integrated Fourier transform micro-optical system is prepared by placing an optical fiber in a constant temperature field, and performing thermal diffusion preparation and connection, wherein after the fiber core dopant of the optical fiber is diffused, the refractive index distribution is changed into a quasi-Gaussian distribution with circumferential symmetry, and the quasi-Gaussian distribution can be equivalent to a micro-convex lens. The invention mainly provides a construction method of an optical fiber micro lens, and a fiber integrated Fourier transform micro optical system is constructed in an optical fiber. The invention can be used for preparing the fiber integrated micro convex lens, and can be widely applied to the fields of micro endoscopes, cell biological optical fiber imaging systems, optical fiber optical tweezers systems, micro unmanned aerial vehicles and the like based on fiber integrated Fourier transform micro optical systems.)

1. A fiber-integrated Fourier transform micro-optical system. The method is characterized in that: it is formed by connecting two sections of optical fibers which are prepared by thermal diffusion and have circumferentially symmetrical quasi-Gaussian refractive index distribution. The fiber integrated Fourier transform micro-optical system is prepared by placing an optical fiber in a constant temperature field, and performing thermal diffusion preparation and connection, wherein after the fiber core dopant of the optical fiber is diffused, the refractive index distribution is changed into a quasi-Gaussian distribution with circumferential symmetry, and the quasi-Gaussian distribution can be equivalent to a micro-convex lens.

2. The fiber-integrated Fourier transform micro-optical system of claim 1, prepared and connected by placing the optical fiber in a constant temperature field, and performing thermal diffusion. The temperature of the constant temperature field is above 1000 ℃.

3. The fiber-integrated Fourier transform micro-optical system of claim 1, wherein the optical fiber after thermal diffusion is cut to a certain length after being heated and diffused in a constant temperature field for a certain time, so that micro-convex lenses with different focal lengths can be prepared.

4. The fiber-integrated fourier transform micro-optical system of claim 1, wherein different parameters of the optical fiber are selected, including initial refractive index profile, dopant species, numerical aperture, etc. of the optical fiber. The refractive index distribution of the selected optical fiber is in a quasi-Gaussian distribution with circumferential symmetry after the optical fiber is prepared by thermal diffusion.

5. The fiber-integrated Fourier transform micro-optical system according to claim 1, wherein after two microlenses with the same focal length are connected, the sum of the back focal lengths (the distance from the focal point to the second surface) of the two microlenses is equal to zero, so as to form the fiber-integrated 4f Fourier transform micro-optical system.

6. The fiber-integrated fourier transform micro-optical system according to claim 1, wherein after two sections of microlenses with different focal lengths are connected, and the sum of back focal lengths (the distance from the focal point to the second surface) of the two microlenses is equal to zero, the fiber-integrated fourier transform micro-optical system with the beam compression collimation function can be formed.

7. The fiber-integrated Fourier transform micro-optical system according to claim 1, wherein after two sections of micro-lenses are connected, the sum of back focal lengths (distances from focal points to the second surface) of the two micro-lenses is not equal to zero, so that the fiber-integrated Fourier transform micro-optical system with equivalent focal length can be formed.

8. The method for manufacturing a fiber-integrated fourier transform micro optical system as claimed in claim 1, comprising the steps of:

1) selecting initial parameters of the optical fiber

The optical fiber is prepared by thermal diffusion, and the refractive index distribution of the optical fiber is quasi-Gaussian distribution with circumferential symmetry.

2) Performing thermal diffusion treatment on the optical fiber

And (3) putting the optical fiber in a constant temperature field for thermal diffusion treatment, and after heating for a certain time, gradually changing the refractive index distribution of the optical fiber into stable, circumferentially symmetrical quasi-Gaussian distribution.

3) Cutting the optical fiber after thermal diffusion

The optical fiber after thermal diffusion is cut in a fixed length, and optical fiber micro convex lenses with different focal lengths can be prepared.

4) And welding the two sections of optical fibers after thermal diffusion

And welding the two sections of optical fibers cut to a certain length to form the fiber integrated Fourier transform micro-optical system.

(I) technical field

The invention relates to a fiber integrated Fourier transform micro-optical system, which can be used for preparing a fiber integrated micro-convex lens, can be widely applied to the fields of a micro endoscope, a cell biology optical fiber imaging system, an optical fiber tweezers system, a micro unmanned aerial vehicle and the like based on the fiber integrated Fourier transform micro-optical system, and belongs to the technical field of fiber integration.

(II) background of the invention

The fiber-integrated micro-optical element has the advantages of small volume, light weight, flexible design and manufacture, low manufacturing cost, easy realization of arraying and batch production and the like, can realize the function which is difficult to realize by a common optical element, and has important application value in the fields of optical fiber communication, information processing, aerospace, biomedicine, laser technology, optical calculation and the like.

In general, the optical fiber micro-lenses are divided into three types, and the optical fiber micro-lenses which are originally appeared and are most easily conceived are like the traditional geometric lenses, and the change of the curvature of the end face of the optical fiber is realized by polishing and grinding of the end face of the optical fiber, corrosion, surface tension forming in a high-temperature molten state and the like. The second is to realize the micro-lens effect by the modulation of the refractive index inside the optical fiber, such as the welding or adhering of a segment of self-focusing optical fiber or self-focusing lens on the end of the common optical fiber. The third is the recent production of fiber microlenses by printing polymer lenses directly on the end faces of optical fibers using high precision 3D printing technology, which enables the production of microlenses and microlens arrays with high precision and high freedom of design, but the required equipment is very expensive and difficult to obtain, and the polymer materials have limited application range.

In recent decades, the position of microlenses in photonic integrated devices and optical fibers has become more and more important. Current lens systems are limited in size, shape, and dimensions by the manufacturing process. Since a conventional lens geometry lens only changes the trajectory of light at the input and output surfaces, while the inside of the lens travels straight, it is difficult to construct an ideal fiber-integrated fourier transform micro-optical system as desired.

Graded index (GRIN) lenses represent another approach to lens design, and instead of relying on a uniform material surface to manipulate light, the refractive index can be varied throughout the lens body to enable greater manipulation of the light ray trajectory. Although GRIN lenses have significant potential advantages over conventional lenses, they are far from common in practical applications because the process of achieving large refractive index gradients in a controlled manner makes it quite difficult to fabricate the lenses.

The thermal diffusion technology provides a potential gradient refractive index design scheme for people, on one hand, the difficulty in the preparation process of the gradient refractive index material is avoided, on the other hand, the refractive index distribution in the material can be reshaped in a flexible mode, and finally smooth gradient refractive index change is presented, even a three-dimensional gradient refractive index structure is constructed.

Meanwhile, the thermal diffusion processing technology has the advantages of easiness in implementation, low cost, simplicity in operation and the like, and has great application potential in micro-electro-mechanical systems, optical integrated devices, optical communication and optical fiber sensing. The optical fiber is subjected to thermal diffusion treatment, so that smooth gradual change of the refractive index can be formed in a thermal diffusion processing area, and the smooth gradual change refractive index area has the effect of a micro lens.

The initial parameters of the optical fiber are reasonably selected, and the optical fiber is subjected to thermal diffusion processing, so that the micro-lenses with different focal lengths can be prepared. When the refractive index distribution of the optical fiber after the thermal diffusion treatment is circularly symmetric quasi-Gaussian distribution, the optical fiber can be equivalent to a micro convex lens, and the prepared micro lenses with different focal lengths are connected, so that a fiber integrated Fourier transform micro optical system can be constructed in the optical fiber.

Patent CN01144937.3 discloses an optical fiber having a lens function and a method for manufacturing the same, which is effective for an optical fiber having an abrupt refractive index by using a graded-index optical fiber having a period length indicating lens function. The method can collimate a single mode fiber, but the graded index fiber cannot be obtained at low cost and is designed according to the requirement.

Patent CN201210011571.6 discloses a single mode fiber connector with large mode area and a manufacturing method thereof, which is to perform thermal diffusion of core doping elements on a step multimode fiber to form a graded index lens with a refractive index decreasing outward in the radial direction, and is mainly used for connecting a single mode fiber with large mode area.

Patent CN201721647567.3 discloses a laser fiber collimation focusing lens, which is characterized in that an optical fiber is connected to one end of a glass tube, and the other end is connected with a lens. Since the light beam is collimated by using the microlens, the case of inserting connection or the like cannot be applied, the range of use is limited, and the manufacturing is difficult.

Patent CN201910359143.4 discloses a method for manufacturing a microlens, which is characterized in that a pressure-controlled micro nozzle is used to form a raised ultraviolet curing glue drop shape, and then the drop is transferred to the end face of an optical fiber or the surface of other substrate by contact, and the drop on the end face of the optical fiber or the surface of other substrate naturally forms a spherical lens shape due to the action of surface tension, and then the microlens is obtained by curing, which has substantial difference with the method of the invention.

Patent CN200420023915.6 discloses a thermal expansion core diameter micro-lens multimode optical fiber, which is characterized in that the end part of the multimode optical fiber is provided with a thermal expansion core diameter, and the end of the thermal expansion core diameter part is provided with a wedge-shaped optical fiber end face and a cylindrical optical fiber micro-lens with an arc surface tangent to the wedge-shaped optical fiber end face. The fiber end cannot be effectively used for constructing a fiber-integrated micro optical fiber system in an optical fiber after being ground.

Patent US4269648A discloses a method of mounting a microsphere coupling lens onto an optical fiber, where the microsphere coupling lens can be mounted onto the end of the optical fiber using an adhesive. A method of manufacturing a microlens at an optical fiber end is disclosed, but the method is complicated in manufacturing process.

Patent US7013678B2 discloses a method for manufacturing a graded index fiber lens, which is an important component in a fiber optic communication system and can be used as a lens, but the method is relatively complex in process and high in production cost.

Patent US7228033B2 discloses an optical waveguide lens and method of making the same by fusion splicing a uniform glass lens blank to the distal end of an optical fiber, heating and stretching the lens blank to separate it into two segments, and attaching the segments to the optical fiber defining a tapered end, and then heating the lens blank above its softening point to form a spherical lens. The optical waveguide lens can be used for collimating or focusing light beams, but the lens manufactured by the method is complex in process and high in production cost.

The invention discloses a fiber integrated Fourier transform micro-optical system, mainly provides a preparation method of a fiber micro-lens, and simultaneously constructs the fiber integrated Fourier transform micro-optical system in an optical fiber, so that the fiber integrated Fourier transform micro-optical system can be used for preparing a fiber integrated micro-convex lens, and can be widely applied to the fields of a micro endoscope, a cell biology optical fiber imaging system, a fiber optical tweezers system, a micro unmanned aerial vehicle and the like based on the fiber integrated Fourier transform micro-optical system. The fiber is subjected to thermal diffusion treatment in a constant temperature field by adopting a thermal diffusion technology, a circumferentially symmetrical refractive index gradient region with quasi-Gaussian distribution is formed in the thermal diffusion region, the thermally diffused fiber is cut in a fixed length manner, so that the fiber microlenses with different focal lengths can be prepared, and the two fiber microlenses are connected to construct the fiber integrated Fourier transform micro-optical system. Compared with the prior art, the fiber integrated Fourier transform micro-optical system can be constructed in the optical fiber due to the adoption of the thermal diffusion technology, and can be prepared in batches at low cost and high efficiency.

Disclosure of the invention

The invention aims to provide a fiber integrated Fourier transform micro-optical system which is simple to manufacture, low in cost and capable of being produced in batches.

The purpose of the invention is realized as follows:

the fiber integrated Fourier transform micro-optical system is formed by connecting two sections of optical fibers which are prepared by thermal diffusion and have circumferentially symmetrical quasi-Gaussian refractive index distribution. The fiber integrated Fourier transform micro-optical system is prepared by placing an optical fiber in a constant temperature field, and performing thermal diffusion preparation and connection, wherein after the fiber core dopant of the optical fiber is diffused, the refractive index distribution is changed into a quasi-Gaussian distribution with circumferential symmetry, and the quasi-Gaussian distribution can be equivalent to a micro-convex lens.

Thermal diffusion techniques are commonly used for expansion of the fundamental mode field, which enables the dopant profile in the fiber to be graded into a stable, circumferentially symmetric, quasi-gaussian profile. The optical fiber is placed in a constant temperature field for heating, the dopant distribution in the optical fiber is gradually changed into stable quasi-Gaussian distribution, and the normalization frequency of the optical fiber is not changed in the heating process. The quasi-Gaussian distribution of the dopant makes the initial refractive index distribution of the optical fiber gradually change into the quasi-Gaussian distribution, and the optical fiber is bent towards a region with higher refractive index in the process of light beam propagation, so that the optical fiber after thermal diffusion can be equivalent to a micro-convex lens.

During thermal diffusion, the local doping concentration C can be expressed as:

d in formula (1) is the dopant diffusion coefficient; t is the heating time. D depends mainly on the type of different dopants, the host material and the local heating temperature. In most cases, considering the diffusion of germanium in the core of an optical fiber, the heating temperature of the fiber is almost uniformly constant with respect to the radial position r on its axisymmetric geometry, and the diffusion coefficient D is assumed to be constant with respect to the radial position r. In practice, neglecting the diffusion of dopants in the axial direction, the simplified diffusion equation (1) in cylindrical coordinates is:

the doping concentration C of the dopant is a function of the radial distance r and the heating time t. The diffusion coefficient D is also affected by the heating temperature and is expressed as:

t (z) in the formula (3) represents the heating temperature in K, which is related to the longitudinal position of the optical fiber in the furnace; r-8.3145 (J/K/mol) is an ideal gas constant; parameter D₀And Q can be obtained from experimental data. Consider the initial boundary conditions:

where a is a constant and represents the diameter of the optical fiber.

The dopant local doping concentration profile C can be expressed as:

in the formula (5), f (r) is an initial concentration distribution, and the concentration at the fiber boundary surface r ═ a is 0. J. the design is a square₀Is a first class zero order Bessel function with characteristic value α_nIs the root of it

J₀(aα_n)＝0 (6)

Assuming that the refractive index profile of the optical fiber over the thermal diffusion region is proportional to the dopant profile, the refractive index profile of the optical fiber after thermal diffusion can be expressed as:

n in formula (7)_clAnd n_coThe refractive indices of the fiber cladding and the core, respectively. The refractive index profile of the fiber changes with heating time t at a heating temperature field of 1600 c, as shown in fig. 2. FIG. 2a shows the refractive index profile of a step-index multimode optical fiber having a core diameter of 62.5 μm, as a function of heating time t, where curves 21, 22, and 23 are the refractive index profiles of the step-index multimode optical fiber in the radial direction of the optical fiber after heating for 0h, 1h, and 1.7h, respectively; after 1.7h of thermal diffusion treatment, the refractive index profile of the step-multimode fiber tended to be a more stable quasi-gaussian profile, as shown in fig. 2 b. FIG. 2c is a graph showing the refractive index profile of a step-index multimode optical fiber having a core diameter of 50 μm, as a function of heating time t, where curves 24, 25, and 26 are the refractive index profiles of the step-index multimode optical fiber in the radial direction of the optical fiber after heating for 0h, 0.5h, and 1.1h, respectively; after 1.1h of thermal diffusion treatment, the refractive index profile of the step-multimode fiber tended to be a more stable quasi-gaussian profile, as shown in fig. 2 d.

For a square index distributed radial Graded Index Fiber (GIF), the light ray transmission track inside the core is sinusoidal periodic, and is therefore also referred to as a self-focusing fiber. Light rays emanating from a point will be periodically focused along the fiber, so the GIF can be imaged like a lens. This is the fundamental principle of a gradient index lens rod or a self-focusing lens rod. The function of the radial gradient index of refraction n of the square-rate distribution with respect to the radial position r is generally given by:

n in formula (8)₀Is the index of refraction at the center of the fiber, r is the radial distance from the central axis, and g is the gradient constant. The focal length of the fiber-integrated Fourier transform micro-optical system with the axial length L is

Corresponding, back focal length f_b(distance of focus from second surface) is defined as:

the refractive index of the section of the prepared micro-lens is shown in figure 3a after the step-multimode optical fiber with the core diameter of 62.5 mu m is thermally diffused for 1.7 h; FIG. 3b is a three-dimensional representation of its cross-sectional refractive index. The refractive index of the section of the prepared micro-lens is shown in figure 3c after the step multimode fiber with the core diameter of 50 mu m is thermally diffused for 1.1 h; fig. 3d is a three-dimensional representation of its cross-sectional refractive index. As can be seen, the refractive index of the microlenses is circumferentially symmetric, quasi-gaussian, with the center refractive index being highest and decreasing as the radial distance from the central axis increases.

When the fiber integrated Fourier transform micro-optical system is prepared, optical fibers with different parameters can be selected, wherein the optical fibers comprise the initial refractive index distribution, the dopant type, the numerical aperture and the like of the optical fibers. The refractive index distribution of the selected optical fiber is in a quasi-Gaussian distribution with circumferential symmetry after the optical fiber is prepared by thermal diffusion.

When the fiber integrated Fourier transform micro-optical system is prepared, the fiber is placed in a constant temperature field, and is prepared and connected through thermal diffusion. The temperature of the constant temperature field is above 1000 ℃. The thermal diffusivity of optical fibers with different core dopants is different.

When the fiber integrated Fourier transform micro-optical system is prepared, the fiber is heated and diffused in a constant temperature field for a certain time, and then the fiber after thermal diffusion is cut in a fixed length, so that equivalent micro-convex lenses with different focal lengths can be prepared.

When the fiber integrated Fourier transform micro-optical system is prepared, two sections of micro-lenses with the same focal length are connected, and the sum of the back focal lengths (the distance between the focal points and the second surface) of the two micro-lenses is equal to zero, so that the fiber integrated 4f Fourier transform micro-optical system is formed.

When the fiber integrated Fourier transform micro-optical system is prepared, two micro-lenses with different focal lengths are connected, and the sum of the back focal lengths (the distance between the focal points and the second surface) of the two micro-lenses is equal to zero, the fiber integrated Fourier transform micro-optical system with the light beam compression collimation function can be formed, and the fiber integrated Fourier transform micro-optical system can be equivalent to an all-fiber Keplerian telescope system.

When the fiber integrated Fourier transform micro-optical system is prepared, after the two sections of micro-lenses are connected, the sum of back focal lengths (the distance between a focal point and the second surface) of the two micro-lenses is not equal to zero, and the fiber integrated Fourier transform micro-optical system with the equivalent focal length can be formed.

When the fiber integrated Fourier transform micro-optical system is prepared, after heating and diffusing for a certain time in a constant temperature field, the step multimode optical fiber after heat diffusion is cut at a fixed length, and the optical fiber micro-convex lenses with different focal lengths can be prepared by a formula (9).

The invention discloses a preparation method of a fiber integrated Fourier transform micro-optical system, which is characterized by comprising the following steps of:

first, initial parameters of the fiber are selected. The optical fiber is prepared by thermal diffusion, and the refractive index distribution of the optical fiber is quasi-Gaussian distribution with circumferential symmetry.

And secondly, carrying out thermal diffusion treatment on the optical fiber. And (3) putting the optical fiber in a constant temperature field for thermal diffusion treatment, and after heating for a certain time, gradually changing the refractive index distribution of the optical fiber into stable, circumferentially symmetrical quasi-Gaussian distribution.

And thirdly, cutting the optical fiber subjected to thermal diffusion. The optical fiber after thermal diffusion is cut in a fixed length, and optical fiber micro convex lenses with different focal lengths can be prepared.

And fourthly, welding the two sections of optical fibers subjected to thermal diffusion. And welding the two sections of optical fibers cut to a certain length to form the fiber integrated Fourier transform micro-optical system.

When the fiber integrated Fourier transform micro-optical system is prepared, after a certain time of thermal diffusion treatment, the initial refractive index distribution of the selected optical fiber tends to be more stable quasi-Gaussian distribution with circumferential symmetry, the refractive index at the center is highest, and the refractive index is reduced along with the increase of the distance from the radial distance to the central axis. After the optical fiber is subjected to thermal diffusion treatment, the dopant forms smooth quasi-Gaussian distribution in a thermal diffusion processing area. The distribution of the dopant is quasi-Gaussian distribution, the refractive index distribution of the optical fiber is also quasi-Gaussian distribution, and the optical fiber is bent towards a region with higher refractive index in the process of light beam propagation, so that the optical fiber after thermal diffusion can be equivalent to a micro convex lens.

As shown in fig. 4, in the micro-convex lens of the present invention, light travels along a sinusoidal curve until reaching the rear surface of the micro-convex lens, and a light beam exits from the fiber end. The length of the light ray that completes a sinusoidal periodic propagation is expressed as a pitch (P). According to the invention, the thermal diffusion optical fiber is cut in a fixed length, the optical fiber micro lenses with different focal lengths are prepared, and the two sections of optical fiber micro lenses are connected, so that the fiber integrated Fourier transform micro optical system with different equivalent focal lengths can be constructed.

When the optical fiber is selected by the invention, the dopant of the fiber core can be one or more different doped dopants according to the requirement. When the optical fiber is selected to prepare the optical fiber micro lens, the optical fiber micro lens with larger mode field diameter can be prepared by designing larger fiber core and cladding diameter or increasing heating time and heating temperature. The use of one or more different dopants doped does not affect the performance of the fiber microlens function. The initial refractive index profile, the numerical aperture of the initial fiber, and the heating temperature and heating time of the thermal diffusion all affect the gradient constant g and ultimately the focal length of the microlens.

The invention discloses a fiber integrated Fourier transform micro-optical system, mainly provides a preparation method of an optical fiber micro-lens, and simultaneously constructs the fiber integrated Fourier transform micro-optical system in an optical fiber. Compared with the prior art, the fiber integrated Fourier transform micro-optical system can be constructed in the optical fiber due to the adoption of the thermal diffusion technology, and can be prepared in batches at low cost and high efficiency.

(IV) description of the drawings

Fig. 1 is a schematic structural diagram of a fiber-integrated fourier transform micro-optical system. 1 is a first micro-convex lens, and 2 is a second micro-convex lens.

FIG. 2a is a graph showing the change of the refractive index profile of a step-mode optical fiber having a core diameter of 62.5 μm according to the change of heating time t in a temperature field of 1600 ℃ and FIG. 2b is a graph showing the refractive index profile after heating for 1.7 h. FIG. 2c is a graph showing the change of the refractive index profile of a step-multimode optical fiber having a core diameter of 50 μm according to the change of the heating time t in a temperature field of 1600 ℃ and FIG. 2d is a graph showing the refractive index profile thereof after heating for 1.1 h.

FIG. 3a is a cross-sectional refractive index profile of a step-multimode optical fiber having a core diameter of 62.5 μm after heating for 1.7h, and FIG. 3b is a three-dimensional representation of the cross-sectional refractive index profile. FIG. 3c is a cross-sectional refractive index profile of a step-multimode optical fiber having a core diameter of 62.5 μm after heating for 1.7h, and FIG. 3d is a three-dimensional representation of the cross-sectional refractive index profile

Fig. 4 is a schematic diagram of light propagating along a sinusoidal curve in a fiber optic lenticular lens.

FIG. 5 is a schematic cross-sectional view of a step-mode optical fiber according to an embodiment. 51 is the cladding of the step-index fiber and 52 is the core of the step-index fiber.

FIG. 6 is a schematic structural diagram of a fiber-integrated Fourier transform micro-optical system according to an embodiment. 61. And 62, microlenses made of different lengths or focal lengths in the embodiments of the present invention.

Fig. 7a shows the light transmission traces of the microlenses 61 in the example. Fig. 7b shows the light transmission trace of the microlens 62 in the embodiment.

Fig. 8a-d show the light transmission traces of the fiber-integrated fourier transform micro-optical system constructed by the micro-lenses 61, 62 in the example.

(V) detailed description of the preferred embodiments

The invention is further illustrated below with reference to specific examples.