The present application relates generally to methods and apparatuses for photonic filtering using nonuniform lattice filters.
The field of photonic integrated circuits (PICs) has rapidly expanded over the past four decades. While PICs are widely used in data and communications, they are also used in the fields of healthcare, automotive sensors, and even agriculture. In its most basic form, a PIC is a circuit that detects, generates, transports, and/or processes light. A PIC can be made up of one or more photonic components. One type of component is a waveguide-based photonic filter. In general, a filter allows certain wavelengths, or frequencies, to be efficiently transmitted while blocking or reflecting others. A number of interferometric waveguide filters exist including Mach-Zehnder interferometers, which when combined in series are commonly referred to as lattice filters. In a lattice filter, there are generally two output ports. One output port is designed to pass a certain frequency band while suppressing others. The degree to which the transmission in the “pass” port and the suppression in the “block” port are achieved are critical design parameters for PICs. While conventional filters can suppress unwanted signals, to a degree, it would be beneficial to have lattice filters that can provide even greater suppression over arbitrarily wide optical bandwidths.
One or more the above limitations may be diminished by structures and methods described herein.
In one embodiment, an apparatus for photonic filtering using nonuniform lattice filters is provided. The apparatus includes a plurality of directional coupler-differential delay devices connected in series and an end-stage directional coupler. Each of the directional coupler-differential delay devices includes a directional coupler section and a differential delay section. Each directional coupler section has a corresponding coupling constant. A first of the plurality of directional coupler-differential delay devices is constructed to receive a pump and a signal. The end-stage directional coupler is connected in series to a last of the plurality of directional coupler-differential delay devices and includes an input port, a through port, and a cross port. The end-stage directional coupler is constructed to receive the pump and the signal at the input port. The end-stage directional coupler has another coupling constant, and at least one of a plurality of coupling constants respectively corresponding to a plurality of directional coupler sections and the other coupling constant corresponding to the end-stage directional coupler are different. The signal is output on the through port of the end-stage directional coupler, and the pump is output on the cross port of the end-stage directional coupler.
The teachings claimed and/or described herein are further described in terms of exemplary embodiments. These exemplary embodiments are described in detail with reference to the drawings. These embodiments are non-limiting exemplary embodiments, in which like reference numerals represent similar structures throughout the several views of the drawings, and wherein:
Different ones of the Figures may have at least some reference numerals that are the same in order to identify the same components, although a detailed description of each such component may not be provided below with respect to each Figure.
In accordance with example aspects described herein are methods and apparatuses for photonic filtering using nonuniform lattice filters.
In
In terms of materials, the waveguide core disclosed herein, including waveguide cores 302A and 302B, may be formed of any material which is partially or completely surrounded by a cladding material (or atmosphere) with a lower index of refraction than the waveguide core material. Exemplary waveguide core materials include: silicon nitride, alumina, titania, glass, silicon, gallium arsenide, indium phosphate, germanium, and combinations thereof, so long as those combinations have a higher index of refraction than the cladding material. An exemplary cladding material is silicon dioxide. In
A uniform lattice filter, such as filters 400 and 500, may be formed, in one embodiment, by photolithography. First, the desired waveguide material is deposited on a cladding material 702 layer, which acts as a substrate. Photoresist, either positive or negative, is then applied to the deposited waveguide material. A photomask that defines a pattern for forming the plurality of DC-DD devices comprising the lattice filter is then placed on top of the deposited photoresist and exposed to electromagnetic radiation. If positive photoresist was applied, then the photoresist that was exposed to the electromagnetic radiation, i.e., it was not covered by the photomask, is removed when exposed to a developing solution. If negative photoresist was used, then the opposite occurs; areas that were covered by the photomask are removed by the developer solution. Of course, the type of photoresist (positive or negative) used must correspond to the patterned photomask. After exposure to the developer, a photoresist pattern remains on top of the waveguide material layer. An etch process is then performed whereby areas of the waveguide material layer that are not covered by photoresist are removed to a predetermined thickness by controlling the etch rate and time. Then, the remaining photoresist is chemically stripped leaving waveguides, corresponding to the patterned photomask and lattice filter design, on top of the substrate. If desired, an additional cladding layer of the substrate material or a different material may then be deposited on the formed waveguides and substrate to partially or completely embed the waveguides. The dimensions, shape and position of the waveguides are controlled by the photomask and the deposition and etching processes. In one embodiment, the waveguides designed for visible for near-IR wavelengths are rectangular waveguides with a width between 100 nm and 2000 nm, inclusive, and a thickness between 10 nm and 1000 nm, inclusive.
Having described how waveguides 302 and 304 may be formed to create a lattice filter, attention will now be directed to constructing an n-stage nonuniform lattice filter. The difference between an n-stage uniform lattice filter and an n-stage nonuniform lattice filter is that in an n-stage uniform lattice the coupling constants respectively corresponding to the plurality of directional coupler sections are the same whereas in an n-stage nonuniform lattice filter at least one of the coupling constants corresponding to one of the directional coupler sections is different from the other coupling constants respectively corresponding to the other directional coupler sections. A nonuniform lattice filter could also be made from differential delay sections of different delays, i.e., the path length may be varied for each delay section. To provide a roadmap for the remaining of the specification, attention will first be directed to determining a coupling constant for an n-stage uniform lattice filter at a wavelength of a pump (laser), hereinafter κ0. That coupling constant, κ0, will then be used to generate n+1 coupling constants (κ1 . . . κn+1) for an n-stage nonuniform lattice filter. The materials and processes used to form the n-stage nonuniform lattice filter are generally the same as those described above for the uniform lattice filter, but a discussion of how an n-stage nonuniform lattice filter may be designed will be provided without duplicating information provided above. Then, the performance of an n-stage uniform lattice filter will be compared to the performance of an n-stage nonuniform lattice filter formed as described below. Finally, an exemplary PIC using an n-stage nonuniform lattice filter will be shown and described with reference to
To begin, attention will be directed to deriving the coupling constant κ0 for an n-stage uniform lattice filter 400. To derive the coupling constant κ0 for an n-stage uniform lattice filter 400, we begin by considering how the DC sections and DD sections that constitute the n-stage uniform lattice filter 400 are modeled. A DC device 100, with a coupling constant κ can be modeled using a transfer matrix approach in which a 2×2 matrix relates the optical fields at the input ports 104A and 104B to the output ports 106A and 106B, each represented by 2×1 column vectors. The transfer matrix for a DC device 100 is given by:
where |τt|2=|τb|2=|τ|2 is the “through” power coupling coefficient, |κ|2 is the “cross” power coupling coefficient with |κ|2=1−|τ|2. These complex coupling coefficients depend strongly on the physical properties of DC device 100 and contain phase information that may be different between waveguide 102A and waveguide 102B due to different optical path lengths within the DC device 100.
In a similar manner, the DD device 200 can be modeled using another transfer matrix given by:
where ΔL is the differential path length of the DD device 200 and β=2πneff/λ is the waveguide propagation constant for the design mode. As one of ordinary skill will appreciate, this describes the phase of the light as it propagates down the waveguide. Since light is in both the core and cladding as it propagates the effective refractive index (neff) is a combination of the two for the mode. In Equation 2, A is the free space wavelength, and neff is the effective index of the waveguide mode. The transfer matrix for an n-stage uniform lattice filter formed by connecting n DC-DD devices 300 in series, followed by a DC device 100 in series, may be found by multiplying the matrices for each component, which is given by (Equation 3):
Exemplary performance is achieved by coordinating the DC coupling and DD differential phase shift for maximum extinction on the through port (output port 408A in
where θ=arctan(√{square root over (1−|τ|2/|τ|)}). Optimal coupling for light entering a single input port (e.g., port 406A) of the uniform lattice filter is then given by setting the diagonal elements of Equation 4 to zero, giving (Equation 5):
cos[(n+1)arctan(√{square root over (1−|τ|2/|τ|)})]=0
Using Equation 5, one can solve for |τ|2 for any value of n. With |τ|2 in hand, one can then determine κ0 for that same value of n using |κ0|2=1−|τ|2. Thus, for a 4-stage uniform lattice the solution of Equation 5 yields |τ|2=0.905 and |κ0|2=0.095 and for an 8-stage uniform lattice filter, |τ|2=0.970 and |κ0|2=0.03.
Having shown and described an n-stage uniform lattice filter where the coupling constant is the same for the n+1 directional coupler stages, attention will now be directed to designing an n-stage nonuniform lattice filter where each DC stage has a unique coupling constant.
The nonuniform lattice filter 800 includes two input ports 806A and 806B and two output ports 808A (also known as the through port) and the 808B (also known as the cross port). Using nonuniform coupling constants for the DC sections 802-1A . . . 802-nA, allows for improved signal blocking in the cross port (808B) without sacrificing transmission of the pump (or laser) in the cross port 808B. Since complete, or substantially complete, transmission of the laser in the cross requires only perfect, or nearly perfect, destructive interference in the final through port (i.e., output 808A), each stage 802-1 . . . 802-n of the filter 800 can have a different coupling constant. Or, as described above, the coupling constants may have a symmetrical distribution. As long as the net phase of the pump (or laser) wavelength after all of the stages results in perfect, or near perfect, interference, efficient laser transmission in the cross port 808B can still be achieved. Also, by using nonuniform coupling constants, the ripple in the signal blockband (which can be present in a similar uniform lattice filter) can be suppressed, but at the expense of the laser passband bandwidth. The ripple in the signal blockband is due to the phase accumulation in the n-DD sections of an n-stage uniform lattice filter such that an n-stage lattice filter can appear to have a net delay of nΔL. This would appear to reduce the FSR by a factor of n, creating constructive interference in the through port every FSR/n, though with poor efficiency due to improper couplings. Nevertheless, this ripple fundamentally limits the signal block in the cross port of a uniform lattice filter. However, unequal coupling constants suppress this ripple by broadening the wavelengths over which destructive interference occurs, at the expense of the inter-ripple extinction. The coupling constants for an n-stage nonuniform lattice filter are, in one embodiment, given by (Equation 6):
κj=√{square root over (2)}κ0 sin[πj/(n+2)]
where κ0 is the coupling constant determined above for an n-stage uniform lattice filter 400. Thus, for example, for a 6-stage nonuniform lattice filter 900 (shown in
To design an n-stage nonuniform lattice filter, the first step is to determine the difference in path length ΔL for each of the DD sections 802-1B . . . 802-nB. By setting this difference in path length ΔL, the primary laser wavelength, typically the wavelength of the pump, is set along with the FSR. The differential delay sections also determine the wavelengths of the filter maxima (for the cross port) or the filter minima (for the through port). Next, the number of stages in the n-stage nonuniform lattice filter is selected by the filter designer, and then the coupling constant (κ0) for an equivalent n-stage uniform lattice filter is determined (if not determined in advance). Equation 6 is then used, in a preferred embodiment, to determine the (n+1) coupling constants for the n-stage nonuniform lattice filter. The materials for the waveguides and cladding may then be selected, and based on those selections the physical dimensions of the waveguides and cladding layers may be determined. With those dimensions in hand, the n-stage nonuniform lattice filter may be fabricated using, for example, the photolithography technique described above or a fabrication process that is unique to a certain foundry. For example, an n-stage nonuniform lattice filter with silicon nitride waveguides may be constructed using the AIM Photonics Process Design Kit. In regards to selecting the length of a delay section, in one embodiment, the delay is chosen based on Equation 7 below
ΔL=mλ/neff
where is the pump wavelength and m is the order of the lattice filter. A larger order will give a narrower filter passband but a smaller FSR. Equation 7 also assumes a symmetric directional coupler design in which the two paths are identical, or substantially identical. However, an asymmetric design may also be used where the paths are not identical. This design will introduce a delay that will have to be subtracted from the above calculation to get a proper filter wavelength. For a pump (laser) wavelength of 1064 nm and a signal band of approximately 1100 nm to 1300 nm, a nonuniform lattice filter with silicon nitride waveguides of 0.8 microns wide and 0.22 microns thick and surround by silicon dioxide cladding may be constructed. These widths and thicknesses were chosen to give single TM mode operation in this wavelength band for a SiN core. This signal band range lies within the infrared, but as the invention is not so limited. Depending on material selections, the path length ΔL and core width and thickness may be chosen such that the filter wavelength falls within the near-infrared, mid-infrared, far-infrared, visible, or ultraviolet regions. In addition, both modes of light that are predominantly polarized in-plane (quasi-TE) or out-of-plane (quasi TM) can be used for either the pump (laser) or the signal. Waveguides of any size can be used for the n-stage nonuniform lattice filter depending on the core-cladding combination. For each such combination, there exists a range of waveguide thicknesses and widths that permit single-mode operation without adding excessive loss or other deleterious effects. For PICs, typically <1 dB/cm is considered good, and >1 dB/cm is considered not good. But other waveguide thicknesses can also be used such as those that permit multi-mode operation, or extremely large modes with small core widths or thickness. Finally, in an alternate embodiment, the DC sections 802-1A . . . 802-nA could be replaced with other coupling approaches such a multi-mode interference (MMI) couplers, vertical coupling, and y-branch couplers. The transfer matrix shown above would be the same for these other coupling approaches.
Comparing
Described above are methods and apparatuses for photonic filtering using nonuniform lattice filters. These filters allow a narrow wavelength band (referred as the pump or laser above) to be efficiently passed in the filter's cross port, but blocked in the through port, while all other wavelengths (referred to as the signal above) are efficiently passed in the through port, but blocked in the cross port. The nonuniform lattice filters described above can achieve much deeper blocking in a filter stopband than can a uniform lattice filter (where the coupling constants are the same) without sacrificing the blocking performance at the broad filter passband. Deep signal blocking in a single filter allows the use of fewer filters, or few stages in a single filter, to achieve a required filter performance. A photonic circuit with fewer filters, or small filters, is less likely to suffer from fabrication inhomogeneities, takes up less space, and is cheaper to fabricate.
While various example embodiments of the invention have been described above, it should be understood that they have been presented by way of example, and not limitation. It is apparent to persons skilled in the relevant art(s) that various changes in form and detail can be made therein. Thus, the disclosure should not be limited by any of the above described example embodiments, but should be defined only in accordance with the following claims and their equivalents.
In addition, it should be understood that the figures are presented for example purposes only. The architecture of the example embodiments presented herein is sufficiently flexible and configurable, such that it may be utilized and navigated in ways other than that shown in the accompanying figures.
Further, the purpose of the Abstract is to enable the U.S. Patent and Trademark Office and the public generally, and especially the scientists, engineers and practitioners in the art who are not familiar with patent or legal terms or phraseology, to determine quickly from a cursory inspection the nature and essence of the technical disclosure of the application. The Abstract is not intended to be limiting as to the scope of the example embodiments presented herein in any way. It is also to be understood that the procedures recited in the claims need not be performed in the order presented.
This application claims priority to U.S. Provisional Patent Application No. 63/354,537, filed Jun. 22, 2022, the contents of which are incorporated by reference herein in their entirety.
Number | Date | Country | |
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63354537 | Jun 2022 | US |