CN112379485B - Integrated optical filter structure with ultra-large free spectral range - Google Patents
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- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
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- G02B6/293—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
- G02B6/29331—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by evanescent wave coupling
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Abstract
The invention discloses an integrated optical filter structure with an ultra-large free spectral range, which comprises an edge coupling waveguide formed by sequentially connecting an incident waveguide, a bent waveguide and an emergent waveguide, and a left Bragg waveguide grating, a tapered and graded waveguide grating, a reverse tapered and graded waveguide grating and a right Bragg waveguide grating which are sequentially connected. And the perpendicular line of the lowest point of the curved waveguide passes through the connection point of the tapered waveguide grating and the reverse tapered waveguide grating. The periods of all the waveguide gratings are equal, the forbidden band bandwidth of the Bragg waveguide grating is smaller than twice the free spectral range of the F-P resonant cavity, and the resonant wavelength of the F-P resonant cavity is close to the middle of the forbidden band of the Bragg waveguide grating. The invention combines the waveguide coupler, the Bragg waveguide grating and the F-P resonant cavity, and can realize single longitudinal mode excitation in a full spectrum range by utilizing the limited forbidden band bandwidth of the Bragg grating and the large free spectrum range of the F-P resonant cavity, thereby realizing single-channel signal filtering.
Description
Technical Field
The invention relates to the field of optical filters, in particular to an integrated optical filter structure with an ultra-large free spectral range.
Background
The increasing demand for high-rate data in today's communication networks and computing systems has driven the development of low-cost, high-speed optical links. In optical interconnects, various advanced multiplexing techniques, such as wavelength division multiplexing, polarization multiplexing, and mode multiplexing, have been successively used to increase the throughput optical communication capacity. Among them, wavelength division multiplexing using different wavelengths in shared physical channels is one of the most popular techniques in optical interconnects in recent decades. Such photonic links based on wavelength division multiplexing technology need to have a large number of wavelength channels. Thus, in operation of the filter wavelengths used in wavelength division multiplexing based optical interconnects, a plurality of filters are cascaded to effect multiplexing of a plurality of wavelength channels. The larger the free spectral range means that more independent wavelength channels can be supported without mutual interference between the channels. By utilizing the principle of reversible light path, the filter with large free spectral range can realize the downloading of the input spectrum, thereby realizing the analysis of wide-spectrum signals.
On the other hand, in recent years, the optical sensor is widely applied to the fields of medical treatment, oil and gas, electric power, military industry, urban construction, food safety, geological exploration and the like under the promotion of the scene demand of the internet of things, so that the market of hundreds of millions of scales is promoted. In order to realize multi-site multi-parameter sensing, distributed sensing using wavelength division multiplexing technology is one of the key technologies for constructing a sensing network. The distributed optical detection technology can simultaneously obtain the spatial distribution and time-varying information of the measured field. The filter with a large free spectral range can effectively increase the number of mutually independent sensors on a single sensing link, and realize simultaneous sensing of more sites and parameters.
There are various schemes for implementing filters with large free spectral ranges. The micro-ring resonator can realize a larger free spectral range by selecting an ultra-small radius, and has a compact size, but the free spectral range is difficult to break through 100nm, so that the application of the micro-ring resonator is limited. In order to realize the expanded free spectral range in the micro-ring resonator, a vernier effect or a plurality of series-coupled micro-rings coupled at two points are used, but the scheme is sensitive to the size change of an actual device, has small process tolerance and generally needs thermal regulation to align the resonance peak of the micro-ring. The single-ring upper-level coupler can also realize a wide free spectral range, but in order to obtain a narrower forbidden bandwidth, the groove width of the Bragg waveguide grating in the coupler is required to be extremely small, the process difficulty is high, the industrial production is not facilitated, and the scheme still needs to align the main peak of the Bragg waveguide grating with the micro-ring resonant peak, and the process tolerance is small. An ideal integrated filter should have a large free spectral range, a high rejection ratio, and large process tolerances to avoid precise wavelength alignment.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an integrated optical filter structure with an ultra-large free spectral range, which can realize single-channel signal filtering in a wide spectral range or even a full spectral range.
The purpose of the invention is realized by the following technical scheme:
an integrated optical filter structure with an ultra-large free spectral range comprises an incident waveguide, an emergent waveguide, a curved waveguide, a left Bragg waveguide grating, a right Bragg waveguide grating, a tapered graded waveguide grating and a reverse tapered graded waveguide grating, wherein:
the incident waveguide, the bent waveguide and the emergent waveguide are sequentially connected to form an edge coupling waveguide;
the left Bragg waveguide grating, the tapered graded waveguide grating, the reverse tapered graded waveguide grating and the right Bragg waveguide grating are sequentially connected, and the left Bragg waveguide grating is coaxial with the right Bragg waveguide grating;
the vertical line of the lowest point of the curved waveguide passes through the connection point of the tapered waveguide grating and the reverse tapered waveguide grating;
the incident waveguide, the curved waveguide, the emergent waveguide, the left Bragg waveguide grating, the tapered waveguide grating, the reverse tapered waveguide grating and the right Bragg waveguide grating are all single-mode waveguides;
the left Bragg waveguide grating, the tapered waveguide grating, the reverse tapered waveguide grating and the right Bragg waveguide grating are all periodic structures, and the periods of the four are equal;
the left Bragg waveguide grating and the right Bragg waveguide grating form an F-P resonant cavity;
the curved waveguide and the F-P resonant cavity form a side coupling F-P resonant cavity;
the larger value of the forbidden bandwidth of the left Bragg waveguide grating and the right Bragg waveguide grating is delta lambda sb Free spectral Range FSR of F-P Cavity FP Then the two satisfy the following relation:
Δλ sb ＜2FSR FP
and the resonant wavelength of the F-P resonant cavity is close to the middle of the forbidden bands of the left Bragg waveguide grating and the right Bragg waveguide grating.
Furthermore, the filter structure is a bilateral symmetry structure, and Delta lambda sb ＜FSR FP 。
Furthermore, the filter structure also comprises a single-mode waveguide positioned between the tapered waveguide grating and the reverse tapered waveguide grating, wherein the lowest point tangent of the curved waveguide is parallel to the single-mode waveguide and has a gap to form a side-edge coupling waveguide structure; and the perpendicular from the lowest point of the curved waveguide to the single-mode waveguide passes through the midpoint of the single-mode waveguide.
Further, the free spectral range FSR of the F-P cavity FP The calculation formula of (a) is as follows:
wherein L is pd The penetration depth L of the left and right Bragg waveguide gratings t For the length, n, of a tapered waveguide grating, reverse tapered waveguide grating g1 Representing the group refractive index, n, of a single-mode waveguide g2 Representing the group refractive index, n, of the left and right Bragg waveguide gratings g3 The group refractive index of the tapered waveguide grating and the reverse tapered waveguide grating is represented; n is eff，w And n eff，n The effective refractive index is periodically changed in the left Bragg waveguide grating and the right Bragg waveguide grating; λ is the operating wavelength of the filter structure.
The invention has the following beneficial effects:
the integrated optical filter structure with the ultra-large free spectral range can simultaneously realize the operation of the ultra-large free spectral range, the sub-nanometer optical bandwidth and the large process tolerance. That means that more independent wavelength channels can be supported without interference between the channels. The method has great application value in the field of optical communication and the aspect of distributed sensing.
Drawings
FIG. 1 is a diagram of a filter structure with a very large free spectral range according to a first embodiment of the present invention;
FIG. 2 is a diagram illustrating the operation of a very large free spectral range filter according to a first embodiment of the present invention;
FIG. 3 is a graph showing the transmittance of the filter of the first embodiment in the wavelength range of 1400-1620 nm;
fig. 4 is a diagram showing the simulated electric field distribution of the filter of the first embodiment at 1400, 1521, 1522 and 1620nm, wherein white arrows indicate the direction of injected light.
FIG. 5 is a diagram of a filter structure with an ultra-large free spectral range according to a third embodiment of the present invention;
FIG. 6 is a diagram of a filter structure with a very large free spectral range according to example V of the present invention;
FIG. 7 is a cross-sectional view of the waveguide of the Bragg waveguide grating 104 shown on the left side of FIG. 6;
FIG. 8 is a diagram of a filter structure for ultra-large free spectral range according to a sixth embodiment of the present invention;
FIG. 9 is a cross-sectional view of the waveguide of the Bragg waveguide grating 104 shown on the left side of FIG. 8;
FIG. 10 is a diagram of a very large free spectral range filter structure according to a seventh embodiment of the present invention;
in the first to seventh embodiments, 101 is an incident waveguide, 102 is an exit waveguide, 103 is a curved waveguide, 104 is a left-side bragg waveguide grating, 105 is a right-side bragg waveguide grating, 106 is a tapered waveguide grating, 107 is a reverse tapered waveguide grating, 108 is a single-mode waveguide, 201 is a waveguide core layer, 202 is a waveguide cladding layer, 203 is an etched waveguide cladding layer, 301 is a waveguide core layer, 302 is a waveguide cladding layer, and 303 is a nano-rod.
Detailed Description
The ultra-large free spectral range filter structure of the present invention will now be described in more detail with reference to the accompanying schematic drawings, which show preferred embodiments of the invention, it being understood that a person skilled in the art may modify the invention described herein while still achieving the advantageous effects of the invention. Accordingly, the following description should be construed as broadly as possible to those skilled in the art and not as limiting the invention.
In the description of the present invention, it should be noted that, for the terms of orientation, such as "central", "lateral", "longitudinal", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., indicate orientations and positional relationships based on the orientations or positional relationships shown in the drawings, which are merely for convenience of description and simplification of the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and should not be construed as limiting the specific scope of the present invention.
The invention is described in more detail in the following paragraphs by way of example with reference to the accompanying drawings. The advantages and features of the present invention will become more apparent from the following description. It is to be noted that the drawings are in a very simplified form and are not to precise scale, which is provided for the purpose of facilitating and clearly illustrating embodiments of the present invention.
As shown in fig. 1, the filter structure with an ultra-large free spectral range of the present invention includes an incident waveguide 101, an exit waveguide 102, a curved waveguide 103, a left bragg waveguide grating 104, a right bragg waveguide grating 105, a tapered waveguide grating 106, a reverse tapered waveguide grating 107, and a single mode waveguide 108;
the incident waveguide 101, the curved waveguide 103 and the exit waveguide 102 are connected in sequence to form an edge-coupled waveguide;
the left-side Bragg waveguide grating 104, the tapered and graded waveguide grating 106, the single-mode waveguide 108, the reverse tapered and graded waveguide grating 107 and the right-side Bragg waveguide grating 105 are sequentially connected, and the left-side Bragg waveguide grating 104 is coaxial with the right-side Bragg waveguide grating; a single-mode waveguide 108 is arranged between the left Bragg waveguide grating 104 and the right Bragg waveguide grating 105, and an F-P resonant cavity is formed; the lowest point tangent of the curved waveguide 103 is parallel to the single-mode waveguide 108 with a gap to form a side-coupled waveguide structure; the length of the single mode waveguide 108 may be zero. The perpendicular from the lowest point of the curved waveguide 103 to the single-mode waveguide 108 crosses the midpoint of the single-mode waveguide 108; the curved waveguide 103 and the F-P resonant cavity form a side-coupled F-P resonant cavity.
In addition, the incident waveguide 101, the curved waveguide 103, the exit waveguide 102, the left bragg waveguide grating 104, the tapered waveguide grating 106, the reverse tapered waveguide grating 107 and the right bragg waveguide grating 105 are all single-mode waveguides, and the left bragg waveguide grating 104, the tapered waveguide grating 106, the reverse tapered waveguide grating 107 and the right bragg waveguide grating 105 are all periodic structures, and the periods of the four are equal.
In particular, when the filter is in use, laser light is injected into the filter's incident waveguide 101, which is coupled into the F-P cavity through the curved waveguide 103. The non-resonant wavelength is coupled into the exit waveguide 102 from the F-P cavity, the resonant wavelength is coupled into the F-P cavity and enhanced until the input power, the outcoupled power, and the cavity loss power reach dynamic balance, and the light image is bound by the cavity and cannot be coupled into the exit waveguide 102 from the F-P cavity, thereby realizing the filtering of the light with specific wavelength. By introducing the tapered waveguide grating 106 and the reverse tapered waveguide grating 107 between the left-side bragg grating 104 and the right-side bragg grating 105, the mode mismatch of the left-side bragg grating 104, the right-side bragg grating 105 and the single-mode waveguide 108 is reduced, so that the intra-cavity loss is reduced, the sideband jitter is suppressed, and the quality factor of the resonant cavity is increased. The single-mode waveguide 108 connects the tapered waveguide grating 106 and the reverse tapered waveguide grating 107. The free spectral range of the F-P resonant cavity can be regulated and controlled by controlling the period number of the tapered waveguide grating 106 and the reverse tapered waveguide grating 107 and the length of the single-mode waveguide 108. As shown in fig. 2, a tapered waveguide grating 106 and an inverse tapered waveguide grating are selectedThe number of cycles of the tapered graded waveguide grating 107 and the length of the single-mode waveguide 108 (the length of the single-mode waveguide 108 can be zero) are as small as possible, so that the forbidden band bandwidths of the left-side Bragg waveguide grating 104 and the right-side Bragg waveguide grating 105 are smaller than twice of the free spectral range of the F-P resonant cavity, and the excitation of a single longitudinal mode can be realized, and a filter with a single peak or a single valley in a full spectral range and an ultra-large free spectral range can be realized. Wherein, Δ λ sb Representing the forbidden band width, FSR, of a Bragg waveguide grating FP The free spectral range of the F-P cavity satisfies the following relation:
Δλ sb ＜2FSR FP ；
and the resonance wavelength of the F-P resonant cavity is close to the middle of the forbidden bands of the left Bragg waveguide grating (104) and the right Bragg waveguide grating (105).
Wherein, FSR FP The calculation formula of (a) is as follows:
wherein L is pd Lt is the length of the tapered waveguide grating 106 and the reverse tapered waveguide grating 107, n is the penetration depth of the left Bragg waveguide grating 104 and the right Bragg waveguide grating 105 g1 Representing the group index of refraction, n, of the single mode waveguide 108 g2 N represents the group refractive index of the left-side Bragg waveguide grating 104 and the right-side Bragg waveguide grating 105 g3 The group refractive indexes of the tapered waveguide grating 106 and the reverse tapered waveguide grating 107 are shown; n is eff，w And n eff，n Effective refractive indices of periodic variations in the left-side bragg waveguide grating 104 and the right-side bragg waveguide grating 105; λ is the operating wavelength of the filter structure.
A number of embodiments of the filter structure of the invention are given below.
Example one
An integrated ultra-large free spectral range filter is prepared based on a 220nm silicon-on-insulator platform. The width of the incident waveguide 101, the width of the exit waveguide 102, the width of the curved waveguide 103, and the width of the single-mode waveguide 108 were 500nm, the waveguide was a ridge waveguide, the etching depth (waveguide height) was 150nm, and the bending radius of the curved waveguide was 20 μm. The left-side bragg waveguide grating 104 and the right-side bragg waveguide grating 105 are formed by periodically alternating wide waveguides and narrow waveguides, the width of each wide waveguide is 500nm, the width of each narrow waveguide is 300nm, the period number is 150, and the period is 317nm. The tapered graded waveguide grating 106 is formed by periodically alternating wide waveguides and narrow waveguides, the width of the wide waveguides is 500nm, the width is unchanged, the width of the narrow waveguides is linearly widened from 300nm to 500nm, the period number is 5, and the period is 317nm; the reverse tapered graded waveguide grating 107 is formed by periodically alternating wide waveguides and narrow waveguides, the width of the wide waveguides is 500nm, the width is unchanged, the width of the narrow waveguides is linearly changed from 500nm to 300nm, the period number is 5, and the period is 317nm; the single mode waveguide 108 has a zero length and the gap between the curved waveguide 103 and the single mode waveguide 108 is 250nm.
In this embodiment, the filter is in use, swept continuous laser light is injected into the input waveguide 101 of the filter, and the laser light is coupled into the F-P cavity through the edge-coupled waveguide structure. The resonant wavelength 1521nm always oscillates in the resonant cavity and cannot be coupled into the exit waveguide 102 from the resonant cavity, and the non-resonant wavelength (except 1521 nm) is coupled into the exit waveguide 102 from the F-P resonant cavity, so that the 1521nm wavelength laser can be filtered out.
Fig. 3 shows the spectral transmission of the filter of the first embodiment, and it can be seen that only one deep notch at 1521nm is seen in the extra-large wavelength range of 220nm, and the response is flat at the off-resonance wavelength. Figure 4 shows the electric field distribution throughout the structure at operating wavelengths of 1400, 1521, 1522 and 1620 nm. For light with wavelengths 1400 and 1620nm out of the forbidden band, the filter is considered a conventional dual-waveguide coupler. Thus, the light cannot be enhanced in the F-P cavity, but is coupled into the Bragg grating on the right. For wavelengths at 1522nm within the stop band, rather than at resonance, the light is coupled into the cavity, then reflected by the bragg grating, and finally transmitted to the through port. For a resonant wavelength of 1521nm, light is coupled into the cavity, and the power in the cavity is enhanced until a dynamic balance is achieved among the coupled power, the outcoupled power and the loss power. Thus, the light is as if trapped within the cavity, with little power coupling to the through port.
Example two
The second embodiment is different from the first embodiment only in that the ridge waveguide in the first embodiment is changed into a strip waveguide.
EXAMPLE III
The third embodiment is different from the first embodiment only in that the left-side bragg waveguide grating 104, the right-side bragg waveguide grating 105, the tapered waveguide grating 106 and the reverse tapered waveguide grating 107 in the first embodiment are changed from a scheme in which wide waveguides and narrow waveguides alternate to a scheme in which small holes are etched in the waveguides. As shown in fig. 5, the left-side bragg waveguide grating 104 and the right-side bragg waveguide grating 105 are each formed by periodically alternating a normal single-mode waveguide and a perforated single-mode waveguide; the tapered graded waveguide grating 106 is formed by periodically alternating a single-mode waveguide and a perforated single-mode waveguide, the width of the single-mode waveguide is unchanged, and the radius of the circular hole is gradually reduced; the reverse tapered waveguide grating 107 is formed by periodically alternating single-mode waveguides and perforated single-mode waveguides, the width of the single-mode waveguides is unchanged, and the radius of the circular hole is gradually increased.
Example four
The fourth embodiment is different from the third embodiment only in that the circular holes of the left-side bragg waveguide grating 104, the right-side bragg waveguide grating 105, the tapered waveguide grating 106 and the reverse tapered waveguide grating 107 in the third embodiment are replaced with non-circular holes, such as rectangular holes, square holes, elliptical holes and the like.
EXAMPLE five
The fifth embodiment is different from the first embodiment only in that the left-side bragg waveguide grating 104, the right-side bragg waveguide grating 105, the tapered waveguide grating 106, and the reverse tapered waveguide grating 107 in the first embodiment are changed from a scheme in which a wide waveguide and a narrow waveguide are alternated to a scheme in which a waveguide cladding is etched. As shown in fig. 6, the left-side and right-side bragg waveguide gratings 104 and 105, the tapered waveguide grating 106, and the reverse tapered waveguide grating 107 are each composed of a normal single-mode waveguide and a periodically etched cladding. Fig. 7 is a cross-sectional view of the waveguide of the bragg waveguide grating 104 shown on the left side of fig. 6. 201 is a waveguide core layer, 202 is a waveguide cladding layer, and 203 is an etched waveguide cladding layer.
Example six
The sixth embodiment is different from the fifth embodiment only in that the left-side bragg waveguide grating 104, the right-side bragg waveguide grating 105, the tapered waveguide grating 106 and the reverse tapered waveguide grating 107 of the fifth embodiment are changed from a scheme of etching the waveguide cladding to etching the nano-pillars beside the waveguide. As shown in fig. 8, the left-side and right-side bragg waveguide gratings 104 and 105, the tapered waveguide grating 106, and the reverse tapered waveguide grating 107 are each composed of a common single-mode waveguide and periodically etched nano-pillars. Fig. 9 is a cross-sectional view of the waveguide of the bragg waveguide grating 104 on the left side of fig. 8. 601 is waveguide core layer, 302 is waveguide cladding layer, 303 is nano-column. The nano-pillars 303 may be rectangular pillars, square pillars, cylindrical pillars, elliptical pillars.
EXAMPLE seven
The seventh embodiment is different from the first embodiment only in that the left-side bragg waveguide grating 104, the right-side bragg waveguide grating 105, the tapered waveguide grating 106, the reverse tapered waveguide grating 107, and the single-mode waveguide 108 of the first embodiment are changed from a common waveguide to a slit waveguide, as shown in fig. 10.
In addition, for those skilled in the art, on the premise of not departing from the principle of the present invention, several improvements and decorations can be made, and other integrated optical platforms, such as a silicon-on-insulator platform, an inorganic chalcogenide glass platform, a titanium oxide platform, a silicon nitride platform, a lithium niobate platform on an insulator layer, an indium phosphide III-V group platform, and the like, can be adopted; different optical operating bands are used, such as ultraviolet band, visible band, near infrared waveguide, mid-infrared waveguide, and far infrared band.
In summary, in the filter structure with an ultra-large free spectral range provided in this embodiment, the waveguide coupler, the bragg waveguide grating, and the F-P resonant cavity are combined, and the characteristics of the limited forbidden band bandwidth of the bragg grating and the large free spectral range of the F-P resonant cavity are utilized to control the cavity length of the F-P resonant cavity so that the forbidden band bandwidth of the bragg waveguide grating is smaller than twice the free spectral range of the F-P resonant cavity, so that excitation of a single longitudinal mode can be achieved, and thus a filter with a single peak or a single valley and an ultra-large free spectral range in a full spectral range is achieved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and although the invention has been described in detail with reference to the foregoing examples, it will be apparent to those skilled in the art that various changes in the form and details of the embodiments may be made and equivalents may be substituted for elements thereof. All modifications, equivalents and the like which come within the spirit and principle of the invention are intended to be included within the scope of the invention.
Claims (3)
1. An integrated optical filter structure with ultra-large free spectral range, comprising an entrance waveguide (101), an exit waveguide (102), a curved waveguide (103), a left-side bragg waveguide grating (104), a right-side bragg waveguide grating (105), a tapered waveguide grating (106), and a reverse tapered waveguide grating (107), wherein:
the incident waveguide (101), the bent waveguide (103) and the emergent waveguide (102) are sequentially connected to form an edge coupling waveguide;
the left Bragg waveguide grating (104), the tapered and graded waveguide grating (106), the reverse tapered and graded waveguide grating (107) and the right Bragg waveguide grating (105) are sequentially connected, and the left Bragg waveguide grating (104) and the right Bragg waveguide grating are coaxial;
the perpendicular line of the lowest point of the curved waveguide (103) passes through the connection point of the tapered waveguide grating (106) and the reverse tapered waveguide grating (107);
the light source comprises an incident waveguide (101), a curved waveguide (103), an exit waveguide (102), a left Bragg waveguide grating (104), a tapered waveguide grating (106), a reverse tapered waveguide grating (107) and a right Bragg waveguide grating (105), which are all single-mode waveguides;
the left Bragg waveguide grating (104), the tapered and graded waveguide grating (106), the reverse tapered and graded waveguide grating (107) and the right Bragg waveguide grating (105) are all periodic structures, and the periods of the four are equal;
the left Bragg waveguide grating (104) and the right Bragg waveguide grating (105) form an F-P resonant cavity;
the curved waveguide (103) and the F-P resonant cavity form a side coupling F-P resonant cavity;
the larger value of the forbidden band bandwidths of the left-side Bragg waveguide grating (104) and the right-side Bragg waveguide grating (105) is Delta lambda sb Free spectral Range FSR of F-P Cavity FP Then the two satisfy the following relation:
Δλ sb ＜2FSR FP
the resonance wavelength of the F-P resonant cavity is close to the middle of the forbidden bands of the left Bragg waveguide grating (104) and the right Bragg waveguide grating (105);
free spectral Range FSR of the F-P cavity FP The calculation formula of (c) is as follows:
wherein L is pd Is the penetration depth, L, of the left-side Bragg waveguide grating (104) and the right-side Bragg waveguide grating (105) t The length n of the tapered waveguide grating (106) and the reverse tapered waveguide grating (107) g1 Representing the group refractive index, n, of a single mode waveguide (108) g2 Represents the group refractive index, n, of the left-side Bragg waveguide grating (104) and the right-side Bragg waveguide grating (105) g3 Showing the said broachGroup refractive indexes of the graded waveguide grating (106) and the reverse tapered graded waveguide grating (107); n is eff,w And n eff,n Is the effective refractive index of the periodic variation in the left-side Bragg waveguide grating (104) and the right-side Bragg waveguide grating (105); λ is the operating wavelength of the filter structure.
2. The integrated optical filter structure of claim 1, wherein the filter structure is left-right symmetric and Δ λ sb ＜FSR FP 。
3. The integrated optical filter structure with ultra-large free spectral range according to claim 1 or 2, further comprising a single mode waveguide (108) between the tapered waveguide grating (106) and the reverse tapered waveguide grating (107), wherein a lowest point tangent of the curved waveguide (103) is parallel to the single mode waveguide (108) with a gap to form a side-coupled waveguide structure; and the perpendicular from the lowest point of the curved waveguide (103) to the single-mode waveguide (108) passes through the midpoint of the single-mode waveguide (108)
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