**2. Ion exchange in glasses in the presence of an electric field**

In the two-component model of the ion exchange in the glass [33] there are two oppositely directed streams of ions: stream of admixture ions Φ → <sup>A</sup> and stream of modifier ions Φ → <sup>B</sup> (Fig.2). The stream of admixture ions diffusing in the glass in the ion exchange process is the sum of the two components [33] (p.174):

$$\vec{\Phi}\_A = -D\_A \nabla c\_A + \mu\_A c\_A \vec{E}\_0 \ \left( m^{-2} s^{-1} \right) \tag{1}$$

The first one is related to the local concentration gradient of admixture in the glass. The second component expresses the electric drift of admixture ions in the local electric field. This electric field can be the effect of a difference in mobility of exchanged ions. In addition to the ion exchange processes based on a purely thermal diffusion of admixture ions, some processes are also carried out in the presence of an external electric field. In such processes an additional parameter occurs: the intensity of the external electric field E → <sup>e</sup> (Fig.2). These processes are briefly called electrodiffusion. They are characterized by a directed migration of ions intro‐ duced into the glass caused by the effects of an electric field.

**Figure 2.** Ion exchange process in glass.

The local field E → <sup>d</sup> is then a superposition of the diffuse field which is the result of differential mobility of exchanged ions and external field E → e :

$$
\vec{E}\_0 = \vec{E}\_d + \vec{E}\_e \tag{2}
$$

The form of the function describing the distribution of the admixture concentration cA(x), introduced into the glass in the electrodiffusion process is dependent from the interaction between the diffusion component DAcA and the electric migration component μAcAE → 0 of the admixture stream (DA and μA denote, respectively, the diffusion coefficient of the admixture and its electric mobility). In the case of electrodiffusion processes the local electric field takes the form [33] (p.176):

$$
\vec{E}\_0 = \frac{\vec{E}\_e}{1 - \alpha u} + \frac{HkT}{e} \cdot \frac{\alpha}{1 - \alpha u} \nabla u\_\prime \tag{3}
$$

where u(x) = cA(x)/c0, α = 1 - μA(u)/μB(1 - u).

In the above equations, c0 - equilibrium concentration [33] (p.175), H - the correlation coefficient (0 < H < 1) [34], k - the Boltzmann constant, T - the absolute temperature, μA and μB - electro‐ chemical mobilities of admixture ions and modifier ions respectively.

In the electrodiffusion processes the external electric field may have polarization established during the process. Then we talk about the electrodiffusion processes with fixed electric polarization. The polarization of this field can also be changed during the implementation of the ion exchange process. Such processes are called processes with a change of electric polarization.

#### **2.1. Electrodiffusion processes with fixed electric polarization** of the plate the solid electrode is applied. Between the molten salt and the solid electrode a

The first one is related to the local concentration gradient of admixture in the glass. The second component expresses the electric drift of admixture ions in the local electric field. This electric field can be the effect of a difference in mobility of exchanged ions. In addition to the ion exchange processes based on a purely thermal diffusion of admixture ions, some processes are also carried out in the presence of an external electric field. In such processes an additional

briefly called electrodiffusion. They are characterized by a directed migration of ions intro‐

<sup>d</sup> is then a superposition of the diffuse field which is the result of differential

<sup>0</sup> *d e EEE* = + rrr (2)

<sup>r</sup> <sup>r</sup> (3)

→ e :

The form of the function describing the distribution of the admixture concentration cA(x), introduced into the glass in the electrodiffusion process is dependent from the interaction

admixture stream (DA and μA denote, respectively, the diffusion coefficient of the admixture and its electric mobility). In the case of electrodiffusion processes the local electric field takes

a

 a

between the diffusion component DAcA and the electric migration component μAcAE

<sup>0</sup> , 1 1 *<sup>e</sup> <sup>E</sup> HkT E u ue u*

In the above equations, c0 - equilibrium concentration [33] (p.175), H - the correlation coefficient (0 < H < 1) [34], k - the Boltzmann constant, T - the absolute temperature, μA and μB - electro‐

In the electrodiffusion processes the external electric field may have polarization established during the process. Then we talk about the electrodiffusion processes with fixed electric

= +× Ñ - -

a

chemical mobilities of admixture ions and modifier ions respectively.

→

<sup>e</sup> (Fig.2). These processes are

→ 0 of the

parameter occurs: the intensity of the external electric field E

duced into the glass caused by the effects of an electric field.

**Figure 2.** Ion exchange process in glass.

108 Ion Exchange - Studies and Applications

→

mobility of exchanged ions and external field E

where u(x) = cA(x)/c0, α = 1 - μA(u)/μB(1 - u).

The local field E

the form [33] (p.176):

In the case of such electrodiffusion processes implemented with the use of a molten source of admixture, the molten salt (AgNO3) contacts with one side of the glass plate. To the other side of the plate the solid electrode is applied. Between the molten salt and the solid electrode a potential difference is produced. The molten salt is at a positive potential in relation to the glass. With such polarization the silver ions Ag+ in glass drift toward the electric field. At the same time the modifier ions (Na+ ) in the volume of the glass drift toward the negative electrode. There their reduction to the atomic form occurs. As a result, between the glass surface and the negative electrode the metallic sodium is generated. This reduces the adhesion of the electrode to the glass surface. potential difference is produced. The molten salt is at a positive potential in relation to the glass. With such polarization the silver ions Ag+ in glass drift toward the electric field. At the same time the modifier ions (Na<sup>+</sup> ) in the volume of the glass drift toward the negative electrode. There their reduction to the atomic form occurs. As a result, between the glass surface and the negative electrode the metallic sodium is generated. This reduces the adhesion of the electrode to the glass surface. Figure 3a presents the method of implementation of the electrodiffusion process with fixed

Figure 3a presents the method of implementation of the electrodiffusion process with fixed polarization. The role of the solid electrode here is served by electrically conductive glue layer resistant to high temperatures. Figure 3b shows refractive index profiles of planar waveguides produced by the electrodiffusion processes for different values of electric field intensity. The durations of these processes are almost the same. Each process has been carried out at the temperature *T* = 300°C. For comparison the refractive index profile of the waveguide produced in the same conditions (time and temperature) in the diffusion process (E → <sup>e</sup>=0) is presented. The presented refractive index profiles have been determined for the wavelength *λ* = 677 nm. polarization. The role of the solid electrode here is served by electrically conductive glue layer resistant to high temperatures. Figure 3b shows refractive index profiles of planar waveguides produced by the electrodiffusion processes for different values of electric field intensity. The durations of these processes are almost the same. Each process has been carried out at the temperature *T* = 300°C. For comparison the refractive index profile of the waveguide produced in the same conditions (time and temperature) in the diffusion process (E�� � � �) is presented. The

presented refractive index profiles have been determined for the wavelength *λ* = 677 nm.

**Figure 3.** (a) Implementation of electrodiffusion processes with fixed polarization. (b) Refractive index profiles of pla‐ nar waveguides (*λ* = 677 nm) produced in electrodiffusion processes for different values of electric field intensity.

Due to the kinetics of diffusion assisted by an electric field, the electrodiffusion processes can be used as a tool for producing deep waveguide structures in a relatively short time. This is not the only argument in favor of the use of this type of technological processes. Much more

intensity.

Fig.3 (a) Implementation of electrodiffusion processes with fixed polarization. (b) Refractive index profiles of planar waveguides (*λ* = 677 nm) produced in electrodiffusion processes for different values of electric field

can be used as a tool for producing deep waveguide structures in a relatively short time. This is not the only argument in favor of the use of this type of technological processes. Much more important

Due to the kinetics of diffusion assisted by an electric field, the electrodiffusion processes

important are there the opportunities to influence the shape of refractive index profiles of waveguides generated in the electrodiffusion processes through changes in polarization direction of the electric field.

### **2.2. Electrodiffusion processes with a change of the electric polarization**

sources on both sides [35–37].

If a change in direction of the vector of external field E → <sup>e</sup> is made in the equation (3) describing the local electric field E → 0 in the electrodiffusion process, then this can obtain the value of the field E → <sup>0</sup> at which the change occurs in the direction of flow of admixture ions in the glass. This occurs only in situations where admixture ions are supplied on both sides of the glass substrate. It is then that the condition of continuity of ionic current flow through the glass can be satisfied. The electrodiffusion processes with the change in polarization of the external electric field are carried out under conditions of glass substrate being in contact with the liquid admixture sources on both sides [35-37]. This occurs only in situations where admixture ions are supplied on both sides of the glass substrate. It is then that the condition of continuity of ionic current flow through the glass can be satisfied. The electrodiffusion processes with the change in polarization of the external electric field are carried out under conditions of glass substrate being in contact with the liquid admixture

**Figure 4.** The implementation of electrodiffusion processes with a change of the direction of the electric polarization.

Fig.4 The implementation of electrodiffusion processes with a change of the direction of the electric polarization. The idea of using a cyclic change of polarization of the external electric field in the electrodiffusion processes has been described by Houde-Walter and Moore [35]. The authors have indicated there a theoretical ability to influence the final form of the refractive index profile of the The idea of using a cyclic change of polarization of the external electric field in the electrodif‐ fusion processes has been described by Houde-Walter and Moore [35]. The authors have indicated there a theoretical ability to influence the final form of the refractive index profile of the waveguide in the electrodiffusion processes in which a multiple change of polarization of the electric field was applied. Such processes create major possibilities to influence the final form of the admixture distribution in the glass. The factors that determine here the shape of the resulting distribution of admixture in the glass are both the value and the polarization direction of the external electric field, as well as temporal relations between states with opposite polarizations. If a possibility of multiple repetitions of polarization changes of E → <sup>e</sup> field is also taken into consideration, the number of these factors will further increase.

waveguide in the electrodiffusion processes in which a multiple change of polarization of the electric field was applied. Such processes create major possibilities to influence the final form of In the electrodiffusion processes, where a change of the direction of polarization of the external electric field E → e is made, the admixture is introduced into the glass on both sides of the substrate.

possibility of multiple repetitions of polarization changes of E��

consideration, the number of these factors will further increase.

external electric field E��

the admixture distribution in the glass. The factors that determine here the shape of the resulting distribution of admixture in the glass are both the value and the polarization direction of the external electric field, as well as temporal relations between states with opposite polarizations. If a

In the electrodiffusion processes, where a change of the direction of polarization of the

substrate. Therefore the waveguide structures are formed on both sides of the glass plate. In order

� is made, the admixture is introduced into the glass on both sides of the

� field is also taken into

Therefore the waveguide structures are formed on both sides of the glass plate. In order to distinguish between these two structures the following designations are used (Fig.4): wave‐ guide "A" is formed on the side of the substrate, where the initial polarization of the electric field enhanced the process of migrating admixture into the glass, while the waveguide "B" is formed on the opposite side of the substrate, after the reversal of polarization. Figure 4 also indicates the conventionally adopted positive and negative polarization states.

important are there the opportunities to influence the shape of refractive index profiles of waveguides generated in the electrodiffusion processes through changes in polarization

→

<sup>0</sup> at which the change occurs in the direction of flow of admixture ions in the glass. This occurs only in situations where admixture ions are supplied on both sides of the glass substrate. It is then that the condition of continuity of ionic current flow through the glass can be satisfied. The electrodiffusion processes with the change in polarization of the external electric field are carried out under conditions of glass substrate being in contact with the liquid admixture

(a) (b)

**Figure 4.** The implementation of electrodiffusion processes with a change of the direction of the electric polarization.

The idea of using a cyclic change of polarization of the external electric field in the electrodif‐ fusion processes has been described by Houde-Walter and Moore [35]. The authors have indicated there a theoretical ability to influence the final form of the refractive index profile of the waveguide in the electrodiffusion processes in which a multiple change of polarization of the electric field was applied. Such processes create major possibilities to influence the final form of the admixture distribution in the glass. The factors that determine here the shape of the resulting distribution of admixture in the glass are both the value and the polarization direction of the external electric field, as well as temporal relations between states with opposite polarizations. If a possibility of multiple repetitions of polarization changes of E

possibility of multiple repetitions of polarization changes of E��

In the electrodiffusion processes, where a change of the direction of polarization of the external

e is made, the admixture is introduced into the glass on both sides of the substrate.

consideration, the number of these factors will further increase.

is also taken into consideration, the number of these factors will further increase.

0 in the electrodiffusion process, then this can obtain the value of the

This occurs only in situations where admixture ions are supplied on both sides of the glass substrate. It is then that the condition of continuity of ionic current flow through the glass can be satisfied. The electrodiffusion processes with the change in polarization of the external electric field are carried out under conditions of glass substrate being in contact with the liquid admixture

Fig.4 The implementation of electrodiffusion processes with a change of the direction of the electric

The idea of using a cyclic change of polarization of the external electric field in the

In the electrodiffusion processes, where a change of the direction of polarization of the

substrate. Therefore the waveguide structures are formed on both sides of the glass plate. In order

� is made, the admixture is introduced into the glass on both sides of the

� field is also taken into

→ <sup>e</sup> field

electrodiffusion processes has been described by Houde-Walter and Moore [35]. The authors have indicated there a theoretical ability to influence the final form of the refractive index profile of the waveguide in the electrodiffusion processes in which a multiple change of polarization of the electric field was applied. Such processes create major possibilities to influence the final form of the admixture distribution in the glass. The factors that determine here the shape of the resulting distribution of admixture in the glass are both the value and the polarization direction of the external electric field, as well as temporal relations between states with opposite polarizations. If a

<sup>e</sup> is made in the equation (3) describing

**2.2. Electrodiffusion processes with a change of the electric polarization**

If a change in direction of the vector of external field E

sources on both sides [35–37].

→

direction of the electric field.

110 Ion Exchange - Studies and Applications

the local electric field E

sources on both sides [35-37].

polarization.

electric field E

→

external electric field E��

field E →


**Table 1.** Electrodiffusion processes with a change of direction of the electric polarization.

the polarization t+

and t-

in which the adequate waveguides were formed.

Significant differences in the shapes of refractive index profiles that arise in the case of changes in the polarization direction of the electric field during the process can be explained by considering the situation where the polarization of the applied electric field is changed only once. During such a process, with a positive polarization (Fig.4a), the admixture ions enter the glass substrate form the waveguide "A". On the other side of the glass plate (despite its contact with the source of admixture) a waveguide is not formed, because the glass ions pass into the liquid phase due to the current i+ flowing through the substrate.

After the change of polarization (Fig.4b), the situation is reversed. Through the glass substrate the current i- now flows in the opposite direction. Waveguide "B" starts forming on the other side of the glass, while the opposite stream of admixture ions previously introduced into the glass with the glass modifiers ions changes the distribution of the introduced admixture in the positive polarization. Consequently, the shapes of the refractive index profile of waveguide "A" changes.

processes with a predetermined value of electric field intensity for the positive value E+ = 18.2 V/mm and E‐ = ‐9.1 V/mm for the negative value, for various durations of "+" and "‐" polarization. **Figure 5.** Comparison of refractive index profiles of waveguides produced in the electrodiffusion processes with a pre‐ determined value of electric field intensity for the positive value E+ = 18.2 V/mm and E- = -9.1 V/mm for the negative value, for various durations of "+" and "-" polarization. Waveguides produced on the first side of the substrate (a) and on the other side of the substrate (b).

Waveguides produced on the first side of the substrate (a) and on the other side of the substrate (b).

Fig.5 Comparison of refractive index profiles of waveguides produced in the electrodiffusion

The parameters of chosen technological processes with the use of a single change of the direction of the electric field polarization are summarized in Table 1. The soda-lime glass was used as the substrate. As liquid source of admixture on both sides of the substrate the molten silver nitrate (AgNO3) was used. The electrodiffusion processes were realized with the use of the laboratory stand described in [33] (p.164). The temperatures of the processes were within the range: 272301C. The given duration of each process consists of two values relating respectively to the positive and negative polarization. In each glass plate two waveguides ("A" and "B") were produced on the opposite sides. The table shows the total electric charge of admixture ions that were introduced into the glass substrate from both sides. Figure 5a,b shows the refractive index The parameters of chosen technological processes with the use of a single change of the direction of the electric field polarization are summarized in Table 1. The soda-lime glass was used as the substrate. As liquid source of admixture on both sides of the substrate the molten silver nitrate (AgNO3) was used. The electrodiffusion processes were realized with the use of the laboratory stand described in [33] (p.164). The temperatures of the processes were within the range: 272÷301°C. The given duration of each process consists of two values relating respectively to the positive and negative polarization. In each glass plate two waveguides ("A" and "B") were produced on the opposite sides. The table shows the total electric charge of admixture ions that were introduced into the glass substrate from both sides. Figure 5a,b shows the refractive index profiles of waveguides produced in electrodiffusion processes, for which the field intensity for the "+" and "-" polarization have been established according to Fig.4.

profiles of waveguides produced in electrodiffusion processes, for which the field intensity for the "+" and "-" polarization have been established according to Fig.4. Here the ratio of the duration of

same and was *t*tot = 90'. The waveguides of "A" and "B" were formed on opposite sides of the glass plate. The equivalent centric symbols in both the charts (a) and (b) denote the same glass substrate

was a variable. In each case, the duration of the whole process was the

Fig.5 Comparison of refractive index profiles of waveguides produced in the electrodiffusion

The parameters of chosen technological processes with the use of a single change of the

direction of the electric field polarization are summarized in Table 1. The soda-lime glass was used as the substrate. As liquid source of admixture on both sides of the substrate the molten silver nitrate (AgNO3) was used. The electrodiffusion processes were realized with the use of the laboratory stand described in [33] (p.164). The temperatures of the processes were within the range: 272301C. The given duration of each process consists of two values relating respectively to the positive and negative polarization. In each glass plate two waveguides ("A" and "B") were produced on the opposite sides. The table shows the total electric charge of admixture ions that

processes with a predetermined value of electric field intensity for the positive value E+ = 18.2 V/mm and E‐ = ‐9.1 V/mm for the negative value, for various durations of "+" and "‐" polarization. Waveguides produced on the first side of the substrate (a) and on the other side of the substrate (b).

Here the ratio of the duration of the polarization t+ and t- was a variable. In each case, the duration of the whole process was the same and was *t*tot = 90'. The waveguides of "A" and "B" were formed on opposite sides of the glass plate. The equivalent centric symbols in both the charts (a) and (b) denote the same glass substrate in which the adequate waveguides were formed. "+" and "-" polarization have been established according to Fig.4. Here the ratio of the duration of the polarization t+ and t was a variable. In each case, the duration of the whole process was the same and was *t*tot = 90'. The waveguides of "A" and "B" were formed on opposite sides of the glass plate. The equivalent centric symbols in both the charts (a) and (b) denote the same glass substrate

in which the adequate waveguides were formed.

profiles of waveguides produced in electrodiffusion processes, for which the field intensity for the

Significant differences in the shapes of refractive index profiles that arise in the case of changes in the polarization direction of the electric field during the process can be explained by considering the situation where the polarization of the applied electric field is changed only once. During such a process, with a positive polarization (Fig.4a), the admixture ions enter the glass substrate form the waveguide "A". On the other side of the glass plate (despite its contact with the source of admixture) a waveguide is not formed, because the glass ions pass into the

flowing through the substrate.

The parameters of chosen technological processes with the use of a single change of the

= 18.2 V/mm and E- = -9.1 V/mm for the negative

was a variable. In each case, the duration of the whole process was the

direction of the electric field polarization are summarized in Table 1. The soda-lime glass was used as the substrate. As liquid source of admixture on both sides of the substrate the molten silver nitrate (AgNO3) was used. The electrodiffusion processes were realized with the use of the laboratory stand described in [33] (p.164). The temperatures of the processes were within the range: 272301C. The given duration of each process consists of two values relating respectively to the positive and negative polarization. In each glass plate two waveguides ("A" and "B") were produced on the opposite sides. The table shows the total electric charge of admixture ions that were introduced into the glass substrate from both sides. Figure 5a,b shows the refractive index profiles of waveguides produced in electrodiffusion processes, for which the field intensity for the "+" and "-" polarization have been established according to Fig.4. Here the ratio of the duration of

The parameters of chosen technological processes with the use of a single change of the direction of the electric field polarization are summarized in Table 1. The soda-lime glass was used as the substrate. As liquid source of admixture on both sides of the substrate the molten silver nitrate (AgNO3) was used. The electrodiffusion processes were realized with the use of the laboratory stand described in [33] (p.164). The temperatures of the processes were within the range: 272÷301°C. The given duration of each process consists of two values relating respectively to the positive and negative polarization. In each glass plate two waveguides ("A" and "B") were produced on the opposite sides. The table shows the total electric charge of admixture ions that were introduced into the glass substrate from both sides. Figure 5a,b shows the refractive index profiles of waveguides produced in electrodiffusion processes, for which the field intensity for the "+" and "-" polarization have been established according to Fig.4.

(a) (b) Fig.5 Comparison of refractive index profiles of waveguides produced in the electrodiffusion processes with a predetermined value of electric field intensity for the positive value E+ = 18.2 V/mm and E‐ = ‐9.1 V/mm for the negative value, for various durations of "+" and "‐" polarization. Waveguides produced on the first side of the substrate (a) and on the other side of the substrate (b).

**Figure 5.** Comparison of refractive index profiles of waveguides produced in the electrodiffusion processes with a pre‐

value, for various durations of "+" and "-" polarization. Waveguides produced on the first side of the substrate (a) and

same and was *t*tot = 90'. The waveguides of "A" and "B" were formed on opposite sides of the glass plate. The equivalent centric symbols in both the charts (a) and (b) denote the same glass substrate

After the change of polarization (Fig.4b), the situation is reversed. Through the glass substrate the current i- now flows in the opposite direction. Waveguide "B" starts forming on the other side of the glass, while the opposite stream of admixture ions previously introduced into the glass with the glass modifiers ions changes the distribution of the introduced admixture in the positive polarization. Consequently, the shapes of the refractive index profile of waveguide

liquid phase due to the current i+

112 Ion Exchange - Studies and Applications

"A" changes.

the polarization t+

and t-

in which the adequate waveguides were formed.

determined value of electric field intensity for the positive value E+

on the other side of the substrate (b).

**Figure 6.** Comparison of refractive index profiles of waveguides produced by electrodiffusion processes with fixed po‐ larization durations t+ = 45' and t- = 45', for different values of electric field intensity for polarization "+" and "-". Wave‐ guides produced on the first side of the substrate (a) and the other side of the substrate (b).

Figure 6a,b shows a comparison of refractive index profiles of waveguides produced by processes in which a division of the duration of each polarization t+ = t- has been set, with the total duration of the process *t*tot = 90'. The values of the electric field intensity were altered for the two polarization states. As mentioned earlier, the waveguides of types "A" and "B" were formed here on the opposite sides of the glass plate. Here again, the same centric symbols in both figures (a and b) indicate the same glass substrates, in which adequate waveguides have been formed. In the case of this sequence of processes, a strong influence of polarization field "-" on the shape of waveguide of type "A" can be seen (Fig.6a). In the extreme case, for the values of electric field intensity: E = +4.5 V/mm and E = -18.2 V/mm, the obtained admixture distribution gives the concave shape of the refractive index profile.

As mentioned earlier, by selecting the duration of a specific state of polarization and electric field intensity, a specified form of the refractive index profile of the waveguide can be deliberately produced. Figure 7 presents the refractive index profiles of two waveguides of type "A" produced in the electrodiffusion processes in which the duration of polarization was t + = t- = 30' and the values of the electric field intensity were E = +18.2 V/mm and E = -9.1 V/mm respectively. The dependencies n(x) are of almost linear nature. The temperatures of both processes were T = 299°C and 272°C respectively. The resulting refractive index profiles vary in depth, which is a result of electric mobility of ions depending on the temperature. In the case of a waveguide produced at a lower temperature, the effect of the diffusion component on the final form of the shape of the refractive index profile in comparison with the electric drift is much smaller.

in either direction are given.

**Figure 7.** Refractive index profiles of produced waveguides with shapes close to linear.

As an illustration of the applicability of the sequence of polarization direction changes of the electric field, Fig.8 shows the refractive index profiles of waveguides produced on both sides of the glass substrate in the electrodiffusion process, in which six different polarization states were applied. The total duration of the process was *ttot* = 60 min. The durations of each of the processes were equal and were t+ = t- = 10'. In the case of waveguide of type "A" (Fig.4a), a 12 modal structure was obtained (TE polarization, *λ* = 677 nm). The shapes of the refractive index profile of this waveguide are similar to that obtained in the electrodiffusion processes with fixed polarization direction of the electric field (compare Fig.3b). For the resulting waveguide of type "B" (10-modal structure) a monotonic course of the refractive index profile with characteristic inflection point at a depth corresponding to the position of the turning point of the mode of 3rd order was obtained (Fig.8b). In both figures the total values of the electric charge that has passed through the substrate in either direction are given. applied. The total duration of the process was *tc* = 60 min. The durations of each of the processes were equal and were t<sup>+</sup> = t- = 10'. In the case of waveguide of type "A" (Fig.4a), a 12-modal structure was obtained (TE polarization, = 677 nm). The shapes of the refractive index profile of this waveguide are similar to that obtained in the electrodiffusion processes with fixed polarization direction of the electric field (compare Fig.3b). For the resulting waveguide of type "B" (10-modal structure) a monotonic course of the refractive index profile with characteristic inflection point at a depth corresponding to the position of the turning point of the mode of 3rd order was obtained (Fig.8b). In both figures the total values of the electric charge that has passed through the substrate

**Figure 8.** The refractive index profiles of the waveguides produced by electrodiffusion processes with a multiple change of the direction of polarization and of the values of the electric field intensity. The waveguide produced on the first side of the substrate (a) and on the other side of the substrate (b).

**waveguide produced on the first side of the substrate (a) and on the other side of the substrate (b).**

refractive index profiles of produced waveguide structures.

**glass**

**Fig.8 The refractive index profiles of the waveguides produced by electrodiffusion processes with a multiple change of the direction of polarization and of the values of the electric field intensity. The** 

The presented measurement results of refractive index profiles of waveguides produced in

the electrodiffusion processes (in which there is a change of polarization direction of the applied electric field) indicate a high possibility of the use of such processes to the intended shaping of

**2. Determination of the equilibrium concentration of modifier ions in the** 

The presented measurement results of refractive index profiles of waveguides produced in the electrodiffusion processes (in which there is a change of polarization direction of the applied electric field) indicate a high possibility of the use of such processes to the intended shaping of refractive index profiles of produced waveguide structures.
