KR100759812B1 - Tapered waveguide Bragg grating device - Google Patents

Abstract

Disclosed is a Bragg grating device in which the group delay spectrum in the reflected wavelength band has the form of a linear function with respect to the wavelength. The grating element includes a tapered waveguide region having a tapered structure and a Bragg grating formed in the tapered waveguide region as a part of the waveguide so as to implement a shape of w (z) below. Where w (z) = w ₀ -αln (1 + z / L), where w is the width of the waveguide, z is the waveguide lengthwise position, and w ₀ is the position at which the taper starts (z = 0) Is the characteristic value that indicates the effect of the width (w) of the waveguide on the effective refractive index of the waveguide propagation mode, L is the value determined by the position at which the taper ends, the waveguide width at this position, and the value of α to be. Also disclosed are variable means capable of effectively modulating the slope of the linear group delay spectrum by the grating element.

Bragg grating element, waveguide, taper

Description

Tapered waveguide Bragg grating device

1 is a plan view schematically showing an example of a linear waveguide Bragg grating device having a conventional uniform period.

2 is a plan view schematically showing a chirped waveguide Bragg grating device which is another example of a conventional waveguide Bragg grating device.

3A is a plan view schematically illustrating a wavelength band variable method by a thermo-optic effect of a conventional planar waveguide Bragg grating device. 3B is a cross-sectional view taken along the line A-A of FIG. 3A.

4 and 5 are plan views schematically showing a tapered waveguide Bragg grating device according to a first embodiment of the present invention. FIG. 5 relates to a tapered waveguide extending in a shape opposite to that of FIG. 4.

FIG. 6A is a graph theoretically predicting group delay spectra with respect to a wavelength of a waveguide Bragg grating device according to a first embodiment of the present invention having a tapered waveguide structure according to w (z).

FIG. 6B is a graph for theoretically predicting group delay spectra of wavelengths for a waveguide Bragg grating device having a linear tapered waveguide structure, which is generally used to prepare for FIG. 6A.

FIG. 7A is a graph illustrating a waveguide Bragg grating device according to a first embodiment of the present invention having a tapered waveguide structure according to w (z) and measuring reflectance and group delay spectrum with respect to wavelength.

FIG. 7B is a graph of a waveguide Bragg grating device having a linear tapered waveguide structure, which is generally used for comparison with FIG. 7A, to measure reflectance and group delay spectrum with respect to wavelength.

FIG. 8A is a schematic plan view of a variable Bragg grating device including a waveguide Bragg grating device according to a twelfth embodiment of the present invention, and FIG. 8B is a cross-sectional view taken along line B-B of FIG. 8A.

FIG. 9 is a graph theoretically predicting modulation characteristics of group delay spectra for a variable waveguide Bragg grating device according to a first exemplary embodiment of the present invention.

10 is a plan view schematically showing a tapered waveguide Bragg grating element according to a second embodiment of the present invention.

* Description of the symbols for the main parts of the drawings *

110; First linear waveguide region 120; Bragg Grid Area

122; Tapered waveguide region 124; Uniform Cycle Bragg Grating

130; Second straight waveguide region 142; Thin film heater

150; Heating or cooling means

The present invention relates to a waveguide Bragg grating device, and more particularly to a waveguide Bragg grating device having a taper structure.

The Bragg grating device exhibits excellent properties for selectively reflecting or diffraction of a narrow wavelength band. Accordingly, Bragg grating devices are manufactured in various shapes and structures, and are utilized in a wide range of filters, resonators, couplers, diffractometers, sensors, optical pulse compressors, dispersion compensators, and the like. In particular, the Bragg grating device is manufactured in the form of a waveguide, and is mainly applied in the optical communication area, and active applications are also expected in the sensor area. To date, the most active studies on the structure and characteristics of Bragg grating devices are devices based on fiber Bragg gratings.

The waveguide Bragg grating device including the optical fiber mainly uses the characteristic that only a narrow band of light is reflected in the reverse direction around a specific wavelength satisfying the Bragg reflection condition λ _B = 2NΛ among the light of various wavelengths traveling through the waveguide. Λ _B is the center wavelength of the reflection band, N is the effective refractive index in the waveguide of the wavelength, and Λ is the period of the Bragg grating.

1 is a plan view schematically showing an example of a linear waveguide Bragg grating device having a conventional uniform period. At this time, the Bragg grating device is a Bragg grating device having a uniform period, and is the most common type of Bragg grating device. In addition, the grating element has a waveguide having a uniform width in the longitudinal direction.

Referring to FIG. 1, the illustrated Bragg grating element includes a Bragg grating region 20 having a Bragg grating 22 having a uniform period and a first linear waveguide region in which reflected light by the Bragg grating 22 travels in the reverse direction. 10) and a second linear waveguide region 30 disposed opposite to the first linear waveguide region 10 with respect to the Bragg grating region 20. As the Bragg grating device with a uniform period has a longer length of the Bragg grating region 20, the bandwidth of the reflected wavelength is reduced and the reflectance is gradually increased without changing the center wavelength. At this time, the group delay spectrum according to the wavelength in the reflected wavelength band maintains a substantially constant value.

 If necessary, in order to remove the multiple reflection effect generated at both ends of the Bragg grating region 20 and to effectively suppress the influence of the side peaks on the reflectance spectrum, the Bragg grating (20) is placed toward both ends of the Bragg grating region 20. Apodization can be applied which gradually reduces the coupling coefficient of 22). This method is widely used in waveguide Bragg grating devices having other structures.

2 is a plan view schematically showing a chirped waveguide Bragg grating device which is another example of a conventional waveguide Bragg grating device. In this case, the chirped Bragg grating device has a form in which the period of the Bragg grating gradually increases or decreases gradually in the longitudinal direction of the device. On the other hand, the lattice element has a waveguide with a uniform width in the longitudinal direction.

The illustrated chirp Bragg grating element comprises a Bragg grating region 20 having a chirp Bragg grating 24 whose width of the grating gradually decreases or increases, and a first linear waveguide in which reflected light from the chirp Bragg grating 24 travels in the reverse direction. A second linear waveguide region 30 is disposed opposite to the first linear waveguide region 10 with respect to the region 10 and the Bragg grating region 20. Since the chirp Bragg grating device reflects light in different wavelength bands according to the position due to the periodic change in the longitudinal direction, it is possible to adjust the reflected wavelength band and the group delay spectrum by using this. In addition, when the thermo-optic effect is applied to the chirp waveguide Bragg grating device, the reflection wavelength band and the group delay spectrum can be modulated in various ways. In recent years, many efforts have been made in applying optical fiber Bragg gratings to devices for compensating for dispersion occurring in high-speed optical communication (Z. Pan et al., J. Lightwave Technol. Vol. 20, p. 2239, 2002).

Recent research results (NQ Ngo et al., J. Lightwave Technol. Vol. 21, p. 1568, 2003) apply thermo-optic effects to optical fiber Bragg grating devices with cladding of straight or curved taper structures. A technique for variably inducing group delay in an optical signal has been disclosed. However, in the above method, since the taper structure is applied to the cladding region instead of the core region, in the case where there is no chirp effect of the lattice period of the optical fiber Bragg grating element itself or the chirp effect induced by external anthropogenic factors, The delay spectrum cannot be obtained in the desired form.

On the other hand, with the rapid development of optical fiber Bragg grating device, based on the polymer material which is more advantageous for optical device integration and the thermo-optic coefficient is much higher than that of silica optical fiber, the fabrication of Bragg grating device with planar waveguide structure and wavelength by thermo-optic effect Techniques such as band varying have been developed gradually (MC Oh et al. , Appl. Phys. Lett. Vol. 73, p. 2543, 1998).

3A is a plan view schematically illustrating a wavelength band variable method by a thermo-optic effect of a conventional planar waveguide Bragg grating device. 3B is a cross-sectional view taken along the line A-A of FIG. 3A. 3 and 4 apply the Bragg grating element to the cladding region.

3A and 3B, the illustrated grating element has a structure in which the waveguide Bragg grating region 20 and the heater 42 are sequentially arranged on the substrate 5. In this case, the waveguide Bragg grating region 20 includes a waveguide core 21 surrounded by the cladding region and a uniform periodic cladding Bragg grating 22 formed on the top of the waveguide core 21.

On the other hand, US Patent Application Publication No. 2004/0071401 discloses a waveguide Bragg grating device with a uniform period in which the mode effective refractive index is changed linearly with respect to the longitudinal direction in order to obtain a similar effect to the optical fiber Bragg grating device, and a straight line to the waveguide Bragg grating device. And a method for implementing a device for compensating dispersion compensation and dispersion slope by applying a thermo-optic variable electrode having a tapered structure having a quadratic curve shape. However, the patent is only a conceptual reference to the general knowledge in the art that the application of the appropriate taper structure can linearly change the effective refractive index of the mode along the length of the waveguide. In addition, no direct or actionable content is presented that substantially exceeds the level of concepts commonly understood in terms of the composition of the preferred tapered waveguide device. In addition, there is no clear basis and valid composition for the composition of the thermo-optic variable electrode suitable for dispersion compensation and dispersion slope compensation.

Accordingly, an object of the present invention is to provide a Bragg grating device in which the group delay spectrum has a form of a linear function with respect to the wavelength in the reflection wavelength band. Another object of the present invention is to provide a variable means capable of effectively modulating the slope of a group delay spectrum in a Bragg grating device having a linear group delay spectrum.

Bragg grating device according to the present invention for achieving the technical problem is a waveguide in which the incident light can proceed in the forward and reverse direction, as a part of the waveguide tapered structure to implement the form of w (z) It includes a tapered waveguide region having. It also includes a Bragg grating formed in the tapered waveguide region. Where w (z) = w ₀ -αln (1 + z / L), where w is the width of the waveguide, z is the waveguide lengthwise position, and w ₀ is the position at which the taper starts (z = 0) Is the characteristic value that indicates the effect of the width (w) of the waveguide on the effective refractive index of the waveguide propagation mode, L is the value determined by the position at which the taper ends, the waveguide width at this position, and the value of α to be.

The variable Bragg grating device which adds a thermo-optic effect to the Bragg grating device according to the present invention is located on the waveguide on the Bragg grating device to cover the tapered waveguide region while implementing a form of w _h (z) below. It further comprises a variable means. Where w _h (z) = w _h0 / (1 + Az), where w _h0 is the width of the thermally variable means at the position where the taper of the waveguide starts, and A is the position where the taper of the waveguide ends and at this position Is the value determined by the width and the w _h0 value of the thermally variable means.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. The embodiments described below may be modified in various other forms, and the scope of the present invention is not limited to the embodiments described below. Embodiments of the present invention are provided to more fully explain the present invention to those skilled in the art. Like reference numerals denote like elements throughout the embodiments.

An embodiment of the present invention will propose a Bragg grating device in which the group delay spectrum of the reflected wavelength band by the Bragg grating has a linear function form with respect to the wavelength, and which can effectively modulate the slope of the linear group delay spectrum. . Here, the group delay spectrum refers to a spectrum reflected with a delay time that varies depending on the wavelength. Therefore, the group delay spectrum can be used to separate the wavelength of the spectrum over time. The linear group delay spectrum means that the delay time according to the wavelength of the spectrum is linear. Further, embodiments of the present invention will describe embodiments and modifications according to the shape of the tapered waveguide Bragg grating.

(First embodiment)

4 and 5 are plan views schematically showing a tapered waveguide Bragg grating device according to a first embodiment of the present invention. FIG. 5 relates to a tapered waveguide extending in a shape opposite to that of FIG. 4. Here, the tapered waveguide refers to a constant increase or decrease in width along the longitudinal direction of the waveguide, and it is preferable that both sides of the waveguide bring about a change in width to the same extent.

As shown, the width w of the waveguide core has the following relationship depending on the position z in the waveguide longitudinal direction. In other words,

satisfies w (z) = w ₀ -αln (1 + z / L).

Here, w (z) is a taper function indicating the change of the waveguide width according to the waveguide lengthwise position, and w ₀ represents the waveguide width at the position where the taper starts (z = 0). Α is a characteristic value representing the influence of the width w of the waveguide on the effective refractive index of the waveguide propagation mode. The value α may be determined from a material characteristic and a structure of the waveguide through a computer simulation or an experimental method. Further, the value of L is determined by the position where the taper ends and the waveguide width and the value of α at this position. When L has a negative value, the tapered waveguide extending in a shape opposite to that of FIG. You have a structure.

 The tapered Bragg grating device according to the first embodiment of the present invention includes a Bragg grating region 120. Bragg grating region 120 is a taper waveguide region 122 whose width of the waveguide core satisfies the taper function w (z), and Bragg grating 124 of uniform period formed at or near the tapered waveguide region 122. Is made of. One side of the tapered waveguide region 122 is connected to the first linear waveguide region 110, in which incident light travels in the forward direction and reflected light by the Bragg grating region 120 travels in the reverse direction, to the first linear waveguide region 110. The second linear waveguide region 130 is connected so as to face each other so that the transmitted light by the Bragg grating region 120 travels in the forward direction. In this case, the group delay spectrum appears in the reflected light traveling in the reverse direction.

Although not shown, the taper structure according to w (z) may be applied to the height of the waveguide or simultaneously to the width and height of the waveguide. In addition, the present invention can be applied not only to the width and height of the planar waveguide, but also to optical waveguides having various structures such as the core diameter of the optical fiber. On the other hand, if necessary, the first linear waveguide region 110 may be replaced with an arbitrary tapered structure in order to minimize coupling loss between the optical fiber and other waveguide elements, and mode matching. In some cases, the second linear waveguide may be replaced. Region 130 may be omitted.

FIG. 6A is a graph theoretically predicting group delay spectra of wavelengths for the waveguide Bragg grating device according to the first embodiment of the present invention having a tapered waveguide structure according to w (z), and FIG. 6B is compared with FIG. 6A. In order to theoretically predict the group delay spectrum with respect to the waveguide Bragg grating device having a linear tapered waveguide structure generally used for the purpose.

6A and 6B, the waveguide Bragg grating device according to the first embodiment of the present invention has a waveguide Bragg grating device having a taper structure according to w (z) in the form of a logarithmic function. We maintain a straight line function with respect to. In contrast, the group delay spectrum of a waveguide Bragg grating device having a general linear tapered structure exhibits a curve function out of the linear form.

FIG. 7A is an example of a graph in which a waveguide Bragg grating device according to a first embodiment of the present invention having a tapered waveguide structure according to w (z) is fabricated to measure reflectance and group delay spectrum with respect to wavelength, and FIG. FIG. 7A illustrates an example of a graph in which a waveguide Bragg grating device having a linear tapered waveguide structure, which is generally used, is manufactured to measure reflectance and group delay spectrum with respect to wavelength. In this case, the ripple of the group delay is considerably large due to the limitation in the pilot manufacturing to which the apodization is not applied.

Referring to FIGS. 7A and 7B, it is possible to clearly distinguish the difference in the overall change pattern of the group delay spectrum. In FIG. 7A and FIG. 7B, the results obtained by fitting the group delay spectrum of the reflected wavelength band based on the mode analysis in order to exclude the effect of the group delay ripple that can be suppressed through the application of apodization are shown in bold dotted lines. FIG. 7A In the case of Figure 6a it can be seen that the group delay spectrum well maintained as in the theoretically predicted results. On the other hand, in the result of FIG. 7B in which a general straight tapered waveguide structure is applied, the group delay spectrum has a curved shape that is impossible to fit in a straight line and shows a change pattern similar to that of FIG. 6B. From this, it can be seen that the waveguide Bragg grating device according to the first embodiment of the present invention provides an effective means for obtaining a group delay spectrum in the form of a linear function.

(2nd Example)

FIG. 8A is a schematic plan view of a variable Bragg grating device according to a second embodiment of the present invention. FIG. 8A illustrates a change in the slope of the waveguide Bragg grating device and the linear group delay spectrum obtained therefrom according to the first embodiment of the present invention. It includes a variable means for. FIG. 8B is a cross-sectional view taken along line B-B of FIG. 8A.

8A and 8B, the variable Bragg grating element according to the second embodiment of the present invention includes all the components of the waveguide Bragg grating element described with reference to FIGS. 4 and 5, and is disposed on the grating element. Thermal variable means, for example, further includes a thin film heater 142 and the electrode 140. At this time, the heater 142 is preferably manufactured in a thin film form, the width (w _h ) of the thin film heater 142 has the following relationship. In other words,

satisfies w _h (z) = w _h0 / (1 + Az).

Here, w _h0 represents the width of the thin film heater at the position where the taper of the waveguide starts (z = 0), and the value of A is the position where the taper of the waveguide ends and the width of the thin film heater at this position and the value of w _h0 . Is determined by For example, FIG. 8A shows a taper structure when A has a positive value, but when A has a negative value, the direction in which the taper extends is opposite to that of FIG. 8A. Although not shown, the tapered heater structure according to w _h (z) may be applied to the height of the heater, or may be simultaneously applied to the width and the height of the heater.

The tapered structure of the thin film heater 142 plays an important role in order to effectively tilt the modulation of the group delay spectrum of the linear function type provided through the variable waveguide Bragg grating device of the present invention. In this case, the thin film heater 142 preferably covers the tapered waveguide region 120 along the w (z).

Meanwhile, the electrode 140 is connected to both sides of the thin film heater 142 to provide the thin film heater 142 with a voltage generated from an external power source. In some cases, in order to shift the reflected wavelength band of the variable waveguide Bragg grating device to the entire neighboring wavelength band, heating or cooling means 150 may be included in contact with the bottom of the substrate 100 to adjust the temperature of the entire device. .

FIG. 9 is a graph theoretically predicting modulation characteristics of group delay spectra for a variable waveguide Bragg grating device according to a second exemplary embodiment of the present invention.

9, the slope of the group delay spectrum in the form of a linear function is effectively modulated by the influence of the local temperature distribution formed by the thin film heater 142 having the tapered structure of w _h (z). In this graph, ΔT (0) represents the magnitude of the temperature change at the position (z = 0) at which the taper of the waveguide starts.

(Third Embodiment)

The tapered waveguide Bragg grating element along w (z), which is the log function form according to the first embodiment, may be applied in various forms within the allowable range required in the application area.

10 is a plan view schematically showing a tapered waveguide Bragg grating element according to a third embodiment of the present invention.

Referring to FIG. 10, a similar group delay spectrum can be obtained through the arrangement 226 of linear tapered waveguides over a plurality of sections instead of the tapered waveguide along the log function w (z) of the first embodiment. That is, by arranging linear tapered waveguides having different slopes for each section, w (z) which is effectively a logarithmic function can be implemented. On the other hand, in addition to the arrangement of the straight tapered waveguide shown 226, the taper characteristic of w (z) can be similarly implemented through the arrangement of a plurality of sections configured using a monotonic reduction (or monotonic increase) function having any shape. . In addition, a slight level of modulation that does not cause a large change in the group delay spectrum can be applied to the log function w (z) type taper within an acceptable range of application. Anyone skilled in the art can readily appreciate that various modification methods including the above examples correspond to the modified application of the technology provided by the present invention. Therefore, various modifications within the log function w (z) form and the necessary allowance for the application based thereon will be collectively referred to as an effective log function.

In the case of the tapered waveguide along the logarithmic function w (z), various modifications are possible, and the thin film heater 142 of FIG. 8A along the inverse function _wh (z) may also be variously modified. Can be. However, it is apparent that minor variations of the intended modifications within the acceptable limits of the application which can be easily understood by those skilled in the art cannot ultimately violate the scope of the present invention. It will be collectively referred to as an effective inverse function, including variants. The thin film heater 142 having a taper having an effective inverse function has a linear waveguide structure having a constant width or other tapered structure or superposition characteristics regardless of the waveguide Bragg grating element according to the first or third embodiment. It can be effectively applied to Bragg grating elements.

Meanwhile, the above-described embodiments of the present invention mainly deal with the case where the Bragg grating of a uniform period is applied to the waveguide element of the channel structure, and the taper waveguide and the thin film heater are applied to the width of the waveguide core and the thin film heater. All. However, in the practical implementation of the present invention, the waveguides mentioned in the present invention may include planar waveguides and optical fiber waveguides of various structures commonly known in the art. Materials used in the implementation of the present invention is also not limited to organic and inorganic materials or organic-inorganic composites, etc., it is possible to apply generally known waveguide materials.

In addition, the taper structure for the waveguide or the thermally variable means may be applied to only one wall of the waveguide, the height, not the width, or the taper for the width and the height may be used at the same time to change the cross-sectional area. It is included in the scope of the present invention. In addition, the Bragg grating referred to in the present invention is a region close to which the mode of light in contact with the waveguide core or the light mode traveling through the waveguide may be sufficiently combined in at least one of various positions such as the upper or lower portion, the side surface, or the intermediate layer of the waveguide core. And a surface sublattice formed in the structure, a bulk grating formed in the waveguide region, a grating limited in some regions of the waveguide, and various modified or expanded grating forms of the gratings. Furthermore, the properties of Bragg gratings include the application of uniform periodic Bragg gratings or linear chirped Bragg gratings, as well as various apodizations regardless of period. On the other hand, at the position of the thermally variable means, at the top or bottom of the core region or at a similar height, regardless of the degree of deviation from the centerline of the core, outside or inside the cladding, the bragg grating element is not directly in contact with the core region. As long as it does not depart from the scope of the present invention.

As mentioned above, although the present invention has been described in detail with reference to preferred embodiments, the present invention is not limited to the above embodiments, and various modifications may be made by those skilled in the art within the scope of the technical idea of the present invention. It is possible.

According to the waveguide Bragg grating device according to the present invention described above, by forming a logarithmic or effective logarithmic tapered waveguide region in the waveguide region, Bragg having a group delay spectrum in the form of a linear function with respect to the wavelength in the reflection wavelength band A grid element can be provided.

In addition, by further providing a tapered thin film heater on the waveguide Bragg grating region including the logarithmic tapered waveguide, the effective gradient modulation for the group delay spectrum of the linear function form provided through the waveguide Bragg grating element Can be.

Claims (15)

In a waveguide in which incident light can travel forward and reverse, A tapered waveguide region having a tapered structure so as to form the following w (z) as part of the waveguide; And Tapered waveguide Bragg grating device comprising a Bragg grating formed in the tapered waveguide region. w (z) = w ₀ -αln (1 + z / L), Where w is the width of the waveguide, z is the waveguide lengthwise position, w ₀ is the waveguide width at the point where the taper starts (z = 0), and α is the width of the waveguide (w) to the effective refractive index of the waveguide propagation mode. The characteristic value, L, which represents the effect on the taper, is determined by the position where the taper ends and the waveguide width and α at this position. The tapered waveguide Bragg grating device according to claim 1, wherein the tapered structure according to w (z) is applied to the height of the waveguide. The tapered waveguide Bragg grating device according to claim 1, wherein the tapered structure according to w (z) is simultaneously applied to the width and height of the waveguide. The tapered waveguide Bragg grating device according to claim 1, wherein the waveguide effectively implements the taper structure according to the w (z) within an allowable range of an application area. In a waveguide in which incident light can travel forward and reverse, Bragg grating formed on a portion of the waveguide; And A variable waveguide Bragg grating element comprising a thermal variable means for implementing the form of the following w _h (z) while covering the Bragg grating region on the waveguide. w _h (z) = w _h0 / (1 + Az), Where w _h0 is the width of the thermally variable means at the position where the taper of the waveguide starts (z = 0), A is determined by the position at which the taper of the waveguide ends and the width of the thermally variable means at this position and the value of w _h0 Is a value. 6. The variable waveguide Bragg grating element according to claim 5, wherein the thermal variable means is a thin film heater. 6. The variable tapered waveguide Bragg grating device according to claim 5, wherein the waveguide of the Bragg grating region has a tapered structure. The variable waveguide Bragg grating element according to claim 5, wherein the taper structure according to w _h (z) is applied to the height of the thermally variable means. The variable waveguide Bragg grating element according to claim 5, wherein the taper structure according to w _h (z) is simultaneously applied to the width and the height of the thermally variable means. The variable waveguide Bragg grating device according to claim 5, wherein the waveguide effectively implements the taper structure according to w _h (z) within an allowable range of an application area. 6. The variable waveguide according to claim 5, wherein the Bragg grating is disposed so as to face the thermal variable means with respect to the Bragg grating element, and further includes other thermal variable means to change the temperature of the whole Bragg grating element. Bragg grating element. The waveguide Bragg grating element according to claim 1 or 5, wherein the Bragg grating is formed within a core of the waveguide or within an area where a mode of light traveling through the waveguide can be sufficiently combined. The waveguide Bragg grating device according to claim 1 or 5, wherein the Bragg grating has a uniform period. 6. The waveguide Bragg grating element according to claim 1 or 5, wherein the Bragg grating has a concave shape in which a period increases and decreases along a length direction. The waveguide Bragg grating device according to claim 1 or 5, wherein an at least one side of the Bragg grating is applied with an apodization which gradually reduces the coupling coefficient of the Bragg grating.

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