DETAILED ACTION
Claims 1 – 11 have been presented for examination.
This office action is in response to submission of the amendments on 09/10/2025.
Response to 112 remarks
Applicant’s amendments overcome the 112(b) rejection. Therefore, it is withdrawn. However, a new 112(a) and 112(b) rejection is included in the instant Office Action necessitated by the amendment (see Claim Rejections - 35 USC § 112).
Response to 101 remarks
Applicant’s arguments have been fully considered. However, the Office does not consider them to be persuasive.
Applicant argues: “The claimed invention therefore overcomes all limitations of previous attempts to provide a simple and numerically reliable modal expansion for Maxwell's equations. The claimed method is applicable to a diverse range of practical applications because it applies to the solution of any partial differential equation.”
Applicant appear to argue that the claimed invention has broad applicability and/or is novel and non-obvious. Examiner notes that broadly applying the claimed invention does not amount to a practical application. Further, the novelty or non-obviousness of the claimed invention does not transform it into eligible subject matter.
Applicant argues: “Additionally, the claimed invention performs highly efficient computations based on an unusual modal expansion in terms of (complex) eigen-permittivity normal, which, by definition, cannot be done in the human mind or via pen and paper alone”
Applicant argues that the claimed invention is more efficient, and the computations cannot practically be performed in the mind. Examiner notes that an abstract idea cannot be a practical application of itself (i.e., efficiencies deriving from mathematical concepts). Further, the claimed invention covers mathematical concepts and also mental processes.
Applicant argues: “Additionally, Applicant submits that the method of claim 1 includes, inter alia, a specific innovation of computing the modes of each pair of scatterers using an eigen-permittivity mode hybridization representing interaction of localized electromagnetic modes of individual scatterers to generate new hybrid modes”
As discussed previously, the novelty or non-obviousness of the claimed invention does not transform it into eligible subject matter.
Response to 103 remarks
Applicant’s arguments have been fully considered over Lofgren (Thesis, Modeling), and they are persuasive. However, a new grounds of rejection is included over Bergman, D. ““Generalizing Normal Mode Expansion of Electromagnetic Green’s Tensor to Open Systems” (see Claim Rejections - 35 USC § 103 for the detailed mapping).
Applicant’s arguments have been fully considered over Chen. However, the Office does not consider them to be persuasive.
Applicant argues: “However, Green's tensor calculations pose a major limitation on computationally intense problems such as quantum optical effects on the nanoscale, multi-scale geometries, optimization procedures and real-time calculations for computer graphics and computational vision. In addition, Chen suggests defining modes with permittivity rather than frequency as the eigenvalue. Also, Chen fails to teach or suggest the claimed method, which, at least as amended, is a highly efficient computational method that is based on a new modal expansion in terms of ( complex) eigen-permittivity normal, which can be implemented to a high number of scatters with generic structure.” (emphasis added)
In response to applicant's argument that the references fail to show certain features of the invention, it is noted that the features upon which applicant relies (i.e., quantum optical effects on the nanoscale, multi-scale geometries, optimization procedures and real-time calculations for computer graphics and computational vision) are not recited in the rejected claim(s). Although the claims are interpreted in light of the specification, limitations from the specification are not read into the claims. See In re Van Geuns, 988 F.2d 1181, 26 USPQ2d 1057 (Fed. Cir. 1993). Specifically, the claim merely recites “an arbitrarily complex scatterer geometry”. Chen explicitly teaches solving for the electromagnetic modes of any arbitrary shape (arbitrarily complex scatterer geometry) enclosed by a sphere (defining the background geometry) (Chen Page 3, Left “For example, since quasinormal modes are complete internally, modes of a sphere can generate modes of wedges or any arbitrary shape enclosed by the sphere [46], such as split-ring resonators”). Examiner notes that the claim explicitly recites “eigen-permittivity mode[s]” as contrasted with frequency modes.
Applicant argues: “However, Tsang's teachings are explicitly limited to low wavenumbers (that is, long wavelengths, low frequency) for which material parameters are typically frequency-independent (non-dispersive), or even correspond to perfect electric conductors (PEC). In addition, the teachings of Tsang are limited to periodic structures. By contrast, the claimed invention is not limited to periodic structures, and can easily handle dispersive material with no difficulty. The method of the present invention is capable of handling many bodies, non-periodic and even multi-scale structures without a prohibitive computational overhead.” (bold emphasis added, italicized emphasis in original)
In response to applicant's argument that the references fail to show certain features of the invention, it is noted that the features upon which applicant relies (i.e., that the claimed invention is applied to non-periodic structures, and that the material properties are frequency dependent) are not recited in the rejected claim(s). Although the claims are interpreted in light of the specification, limitations from the specification are not read into the claims. See In re Van Geuns, 988 F.2d 1181, 26 USPQ2d 1057 (Fed. Cir. 1993). Examiner further notes that Tsang is relied upon merely to teach the recited computer elements of claim 9 (see Claim Rejections - 35 USC § 112). Examiner notes that Tsang is analogous art because it solves the same problem of solving partial differential equations, and because it is in the same field of mathematical algorithms. Further, one of ordinary skill in the art would have been motivated to make this modification in order to solve a desired problem (Tsang (580) Paragraph 33).
Priority
The instant application is a 371 national stage entry of international application number PCT/IL2020/050545 filed on 05/19/2020 (see Petition decision, dated 01/25/2024). Further, there is a foreign priority indicated to US provisional application 62/849909 filed on 05/19/2019 (see Application data sheet, dated 11/17/2021 and 03/29/2022 and 01/17/2024). Comparing the instant claim 1 to the foreign priority document, there does not appear to be explicitly disclosed “if there is more than one scatterer, hybridizing the modes of each pair of scatters”. Therefore, the priority date is 05/19/2020 to the international application. Specifically, both the foreign priority document and international application disclose a hybrid definition of the adjoint for symmetries (see the instant application Page 25 “Several types of symmetry such as continuous rotational symmetry, continuous translational symmetry, and discrete translational symmetry (also known as periodicity) may be considered … This leads to the more familiar case of the adjoint mode being the complex conjugate, … This conflicts with the definition {60), so a hybrid definition of the adjoint becomes necessary for these three symmetries”) (see the foreign priority document Page 14). However, only the international application discloses a hybridization technique in context of more than one scatter (see the instant application Page 48 “At the next step 206, the modes of each pair of scatterers are computed via the hybridization technique described in [Rosolen, Chen, Maes, Sivan, Phys. Rev. B 101, 155401 (2020)].”)
Receipt is acknowledged of certified copies of papers required by 37 CFR 1.55 which perfects the foreign priority.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1 – 11 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
With regard to claim 1, it recites “if there is more than one scatterer, calculating an overlap matrix for each pair of scatterers”. The limitation is unclear since it is not readily known if the limitation is interpreted as a single matrix that covers all the pairs of scatterers (i.e., as the matrix elements), or if it is matrix for each pair of scatters (i.e., multiple matrices). The limitation is interpreted for examination purposes as a single matrix covering all the pairs of scatterers.
With regard to claim 9, there appears to be a copy-paste error since it recites a claim which appear to be from a different application. The claim is interpreted as the version submitting previously dated 11/17/2021, with similar amendments as in claim 1.
With regard to claims 2 – 8 and 10 – 11, they are rejected by virtue of depending from a rejected parent claim, and without reciting additional limitation to overcome the rejection.
The following is a quotation of the first paragraph of 35 U.S.C. 112(a):
(a) IN GENERAL.—The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor or joint inventor of carrying out the invention.
The following is a quotation of the first paragraph of pre-AIA 35 U.S.C. 112:
The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor of carrying out his invention.
Claims 1 – 11 are rejection under 35 U.S.C. 112(a) or 35 U.S.C. 112 (pre-AIA ), first paragraph, as failing to comply with the written description requirement. The claim(s) contains subject matter which was not described in the specification in such a way as to reasonably convey to one skilled in the relevant art that the inventor or a joint inventor, or for applications subject to pre-AIA 35 U.S.C. 112, the inventor(s), at the time the application was filed, had possession of the claimed invention.
With regard to claim 1, it recites “if there is more than one scatterer, calculating an overlap matrix for each pair of scatterers”. Looking to the disclosure, it is explicitly disclosed that the overlap matrix is for each scatter with respect pairs of modes, as contrasted with pairs of scatterers (see the instant application Page 48, Top “At the next step 205, the overlap matrix (Eq. (20) or equivalently, (22)) is calculated for each scatterer and the resulting eigenvalue equation is solved for each scatterer”, using the base transverse modes that have been calculated for each embedding geometry and the longitudinal modes that have been calculated for each scatterer.”). Examiner notes that there is a “for each pair” disclosure for other features (see the instant application Page 6 “hybridizing the modes of each pair of scatterers”).
With regard to claim 9, there appears to be a copy-paste error since it recites a claim which appear to be from a different application. The claim is interpreted as the version submitting previously dated 11/17/2021, with similar amendments as in claim 1. Therefore, it would have the same deficiency as claim 1.
With regard to claims 2 – 8 and 10 – 11, they are rejected by virtue of depending from a rejected parent claim, and without reciting additional limitation to overcome the rejection.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1 – 11 are rejected under 35 U.S.C. 101 because the claimed invention is directed to a judicial exception (i.e., an abstract idea) without significantly more.
Independent claim 1 recites at Step 1 a statutory category (i.e. a process) numerical method for providing fast and efficient solution of partial differential equations to calculate generalized electromagnetic modes being the permittivity modes of an arbitrarily complex scatterer geometry using a modal expansion for Maxwell’s equations, comprising: a) defining the background geometry and the scatterer's geometry; b) embedding each scatterer in a simpler geometry; c) calculating the base transverse modes for each embedding geometry; d) for each scatterer: calculating the longitudinal modes; if there is more than one scatterer, calculating an overlap matrix for each pair of scatterers; solving a resulting eigenvalue equation, using the base transverse modes that have been calculated for each embedding geometry and the longitudinal modes that have been calculated for the each scatterer; e) if there is more than one scatterer, hybridizing the modes of each pair of scatterers using an eigen-permittivity mode hybridization representing interaction of localized electromagnetic modes of individual scatterers to generate new hybrid modes, f) solving a resulting eigenvalue equation for the complete structure; g) projecting a source is on target modes; and h) substituting a result is in a final equation. At Step 2A, Prong I the recited limitations in part, alone or in combination, amount to steps that, under its broadest reasonable interpretation, cover performance of the limitations in the mind in combination with using a pen and paper (see MPEP 2106.04(a)(2)(I)). For example, the “defining” and “embedding” and “hybridizing” and “projecting” cover modeling actions which require no more than mental judgements and evaluation. At Step 2A, Prong I the recited limitations in part, alone or in combination, amount to steps that, under its broadest reasonable interpretation, cover mathematical concepts (see MPEP 2106.04(a)(2)(III)). For example, the “calculating” and “solving” recite performing specific computations using mathematical elements. Accordingly, the claim recites an abstract idea.
At Step 2A, Prong II this judicial exception is not integrated into a practical application since there are no further recited limitations. The claim is directed to an abstract idea.
At Step 2B the claim does not recite additional elements that, alone or in an ordered combination, are sufficient to amount to significantly more than the judicial exception since there are no further recited limitations. For at least these reasons, the claim is not patent eligible.
Dependent claim 2 - 8 recite(s) at Step 1 the same statutory category as the parent claim(s), and further recite(s): Claim 2 wherein a limited set of overlap integrals between the modes of an embedding simple shape are computed, for allowing solving a smaller eigenvalue equation for the modes; Claim 3 wherein the modes of an arbitrarily complex scatterer embedded inside a bigger scatterer of a simple shape are expanded, using the completeness of the permittivity modes inside the bigger scatterer the completeness representing a requirement that a set of electromagnetic modes, which incorporate permittivity variations, must form a complete basis to accurately represent any arbitrary electromagnetic field or scattered wave.; Claim 4 wherein the eigenvalues of the simpler shapes are computed using an algebraic equation; Claim 5 wherein the entries in the eigenvalue equation are overlap integrals of the known modes over the domain of an arbitrary scatterer; Claim 6 wherein the calculation of modes incorporates the mode discontinuity at the scatterer boundary, for minimizing the size of the eigenvalue problem that has to be solved; Claim 7 wherein the overlap integrals are evaluated by replacing the volume integrals by surface integrals and the surface integrals by line integrals; Claim 8 wherein modes of the target geometry are expanded based on the modes of a simpler geometry. At Step 2A, Prong I the recited limitations in part, alone or in combination, amount to steps that, under its broadest reasonable interpretation, cover performance of the limitations in the mind in combination with using a pen and paper (see MPEP 2106.04(a)(2)(I)). For example, the “are expanded” cover modeling actions which require no more than mental judgements and evaluation. At Step 2A, Prong I the recited limitations in part, alone or in combination, amount to steps that, under its broadest reasonable interpretation, cover mathematical concepts (see MPEP 2106.04(a)(2)(III)). For example, the “are computed” and “are overlap integrals” and “are evaluated” and “calculation of modes incorporates” recite performing specific computations using mathematical elements. Accordingly, the claim(s) recite(s) an abstract idea.
At Step 2A, Prong II this judicial exception is not integrated into a practical application since there are no further recited limitations. The claim is directed to an abstract idea.
At Step 2B the claim does not recite additional elements that, alone or in an ordered combination, are sufficient to amount to significantly more than the judicial exception since there are no further recited limitations. For at least these reasons, the claim is not patent eligible.
Independent claim 9 (see Claim Rejections - 35 USC § 112) recites at Step 1 a statutory category (i.e. a machine) system for providing fast and efficient solution of partial differential equations to calculate generalized electromagnetic modes being the permittivity modes of an arbitrarily complex scatterer geometry using a modal expansion for Maxwell’s equations, adapted to: a) define the background geometry and the scatterer's geometry; b) embed each scatterer in a simpler geometry; c) calculate the base transverse modes for each embedding geometry; d) for each scatterer: calculate the longitudinal modes; if there is more than one scatterer, calculate an overlap matrix for each pair of scatterers; solve a resulting eigenvalue equation, using the base transverse modes that have been calculated for each embedding geometry and the longitudinal modes that have been calculated for the scatterer; e) hybridize the modes of each pair of scatterers if there is more than one scatterer using an eigen-permittivity mode hybridization representing interaction of localized electromagnetic modes of individual scatterers to generate new hybrid modes, f) solve a resulting eigenvalue equation for the complete structure; g) project a source is on target modes; and h) substitute a result is in a final equation. At Step 2A, Prong I the recited limitations in part, alone or in combination, amount to steps that, under its broadest reasonable interpretation, cover mathematical concepts (see MPEP 2106.04(a)(2)(I)). For example, the “define” and “embed” and “hybridize” and “project” cover modeling actions which require no more than mental judgements and evaluation. At Step 2A, Prong I the recited limitations in part, alone or in combination, amount to steps that, under its broadest reasonable interpretation, cover performance of the limitations in the mind in combination with using a pen and paper (see MPEP 2106.04(a)(2)(III)). For example, the “calculate” and “solve” recite performing specific computations using mathematical elements. Accordingly, the claim recites an abstract idea.
At Step 2A, Prong II this judicial exception is not integrated into a practical application since the claimed invention further claims: comprising at least one processor. The “processor” are recited at a high-level of generality such that they amount to no more than mere application of the judicial exception using generic computer components which does not amount to an improvement in computer functionality (see MPEP 2106.04(a)(I)). The claim is directed to an abstract idea.
At Step 2B the claim does not recite additional elements that, alone or in an ordered combination, are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to the integration of the abstract idea into a practical application, the recited “processor” amount to no more than mere instructions to apply the judicial exception using generic computer components. The additional elements do not amount to a particular machine (see MPEP 2106.05(b)(I)). Mere instructions to apply an exception using a generic computer component cannot provide an inventive concept. For at least these reasons, the claim is not patent eligible.
Dependent claim 10 – 11 recite(s) at Step 1 the same statutory category as the parent claim(s), and further recite(s): Claim 10 in which modes of the target geometry are expanded based on the modes of a simpler geometry; Claim 11 in which the calculation of modes incorporates the mode discontinuity at the scatterer boundary being boundary-adapted modes, for minimizing the size of the eigenvalue problem that has to be solved. At Step 2A, Prong I the recited limitations in part, alone or in combination, amount to steps that, under its broadest reasonable interpretation, cover performance of the limitations in the mind in combination with using a pen and paper (see MPEP 2106.04(a)(2)(I)). For example, the “are expanded” cover modeling actions which require no more than mental judgements and evaluation. At Step 2A, Prong I the recited limitations in part, alone or in combination, amount to steps that, under its broadest reasonable interpretation, cover mathematical concepts (see MPEP 2106.04(a)(2)(III)). For example, the “calculation of modes incorporates” recite performing specific computations using mathematical elements. Accordingly, the claim(s) recite(s) an abstract idea.
At Step 2A, Prong II this judicial exception is not integrated into a practical application since there are no further recited limitations. The claim is directed to an abstract idea.
At Step 2B the claim does not recite additional elements that, alone or in an ordered combination, are sufficient to amount to significantly more than the judicial exception since there are no further recited limitations. For at least these reasons, the claim is not patent eligible.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries set forth in Graham v. John Deere Co., 383 U.S. 1, 148 USPQ 459 (1966), that are applied for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
Determining the scope and contents of the prior art.
Ascertaining the differences between the prior art and the claims at issue.
Resolving the level of ordinary skill in the pertinent art.
Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claims 1 - 8 are rejected under 35 U.S.C. 103 as being unpatentable over Chen et al. “Generalizing Normal Mode Expansion of Electromagnetic Green’s Tensor to Open Systems” (henceforth “Chen”) in view of Bergman, D. “The dielectric constant of a simple cubic array of identical spheres” (henceforth “Bergman”). Chen and Berman are analogous art because they solve the same problem of solving partial differential equations, and because they are in the same field of mathematical algorithms.
With regard to claim 1, Chen teaches a numerical method for providing fast and efficient solution of partial differential equations to calculate generalized electromagnetic modes being the permittivity modes of an arbitrarily complex scatterer geometry using a modal expansion for Maxwell’s equations, comprising: (Page 4, Left “Instead of solving Eq. (7) directly, we first find its stationary or self-sustaining solutions, corresponding exactly to the eigen-permittivity modes of the inclusion.”., and Abstract “We bypass all implementation and completeness issues associated with the alternative quasinormal eigenmode methods by defining modes with permittivity rather than frequency as the eigenvalue”)
defining the background geometry and the scatterer's geometry; embedding each scatterer in a simpler geometry; (Page 3, Left “For example, since quasinormal modes are complete internally, modes of a sphere can generate modes of wedges or any arbitrary shape enclosed by the sphere [46], such as split-ring resonators”)
calculating the base transverse modes for each embedding geometry; (Chen Page 6, Right expanding transverse modes
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for each scatterer: (Page 3, Left clusters and arrays of nanostructures can be analyzed using the modes providing an approximate hybridization approach “A compelling benefit of GENOME over quasinormal modes is that the modes of clusters and arrays of nanostructures can be obtained from known modes of the constituents without further numerical simulation, for example, obtaining dimer modes from monomer modes [29,30]. This constitutes a generalization of the celebrated theory of linear combination of molecular orbitals to electromagnetic structures [47,48], and provides a rigorous generalization of an approximate hybridization approach developed in the context of nanoplasmonics [49].”)
calculating the longitudinal modes; (Page 6, Right
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calculating overlap integrals and a matrix; (Page 9, Right “The procedure then amounts to evaluating overlap integrals between known modes and diagonalizing a small dense matrix”)
solving a resulting eigenvalue equation, using the base transverse modes that have been calculated for each embedding geometry and the longitudinal modes that have been calculated for the each scatterer; (Abstract eigenmodes of modes are used for solving “We bypass all implementation and completeness issues associated with the alternative quasinormal eigenmode methods by defining modes with permittivity rather than frequency as the eigenvalue”)
if there is more than one scatterer, hybridizing the modes of each pair of scatterers using an eigen-permittivity mode hybridization representing interaction of localized electromagnetic modes of individual scatterers to generate new hybrid modesl; (Page 3, Left clusters and arrays of nanostructures can be analyzed using the modes providing an approximate hybridization approach “A compelling benefit of GENOME over quasinormal modes is that the modes of clusters and arrays of nanostructures can be obtained from known modes of the constituents without further numerical simulation, for example, obtaining dimer modes from monomer modes [29,30]. This constitutes a generalization of the celebrated theory of linear combination of molecular orbitals to electromagnetic structures [47,48], and provides a rigorous generalization of an approximate hybridization approach developed in the context of nanoplasmonics [49].”, and Abstract “We bypass all implementation and completeness issues associated with the alternative quasinormal eigenmode methods by defining modes with permittivity rather than frequency as the eigenvalue”)
solving a resulting eigenvalue equation for the complete structure; (Page 9, Left eigenmodes with related eigenvalues are determined “In practical terms, the key step in using GENOME is finding the eigenmodes and their eigenvalues”)
projecting a source on target modes; and (Page 4, Right “By projecting onto this basis, we obtain an analytic solution of the Lippmann-Schwinger equation (7). We then obtain the desired eigenmode expansion of Eq. (1), which, unlike Eq. (6), may be regarded as the dressed Green’s tensor”, and Page 9, Left the eigenmodes are used as a basis for performing calculations “Finally, Eq. (9) can be efficiently solved for clusters of inclusions using the eigenmodes of its constituents as a basis”)
substituting a result is in a final equation. (Page 9, Right
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Chen does not appear to explicitly disclose: if there is more than one scatterer, calculating an overlap matrix for each pair of scatterers.
However, Berman teaches:
if there is more than one scatterer, calculating an overlap matrix for each pair of scatterers; (Bergman Page 4950, Bottom to Page 4951, Top overlap integrals between different grains indices are used to compute matrix elements between grains
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It would have been obvious to one of ordinary skill in the art to combine the method of using an eigenmode basis for solving an electromagnetic problem disclosed by Chen with the method of using a matrix from overlap integrals of inclusions embedded in a homogeneous host disclosed by Bergman. One of ordinary skill in the art would have been motivated to make this modification in order to solve for desired properties of the composite material (Bergman Abstract).
With regard to claim 2, Chen in view of Bergman teaches all the elements of the parent claim 1, and further teaches: wherein a limited set of overlap integrals between the modes of an embedding simple shape are computed, for allowing solving a smaller eigenvalue equation for the modes. (Chen Page 9, Right “The procedure then amounts to evaluating overlap integrals between known modes and diagonalizing a small dense matrix”)
With regard to claim 3, Chen in view of Bergman teaches all the elements of the parent claim 1, and further teaches:
wherein the modes of an arbitrarily complex scatterer embedded inside a bigger scatterer of a simple shape are expanded, (Chen Page 2, Left
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using the completeness of the permittivity modes inside the bigger scatterer, the completeness representing a requirement that a set of electromagnetic modes, which incorporate permittivity variations, must form a complete basis to accurately represent any arbitrary electromagnetic field or scattered wave. (Chen Abstract “Completeness is achieved both for sources located within the inclusion and the background through use of the Lippmann-Schwinger equation.”, and Page 3, Left to Page 1, Right the eigenmodes together for a complete and accurate representation “Thus, GENOME converges to the correct solution with arbitrary precision as more eigenmodes are considered, regardless of detuning from the inclusion’s resonances and source or detector coordinates”)
With regard to claim 4, Chen in view of Bergman teaches all the elements of the parent claim 1, and further teaches: wherein the eigenvalues of the simpler shapes are computed using an algebraic equation. (Chen Page 4, Left “The Lippmann-Schwinger equation can also be expanded in terms of basis functions, such as the cylindrical harmonic functions, again yielding a linear-algebra problem, but obviating the need for iterative solution [56]”)
With regard to claim 5, Chen in view of Bergman teaches all the elements of the parent claim 1, and further teaches: wherein the entries in the eigenvalue equation are overlap integrals of the known modes over the domain of an arbitrary scatterer. (Chen Page 9, Right “The procedure then amounts to evaluating overlap integrals between known modes and diagonalizing a small dense matrix”)
With regard to claim 6, Chen in view of Bergman teaches all the elements of the parent claim 1, and further teaches: wherein the calculation of modes incorporates the mode discontinuity at the scatterer boundary, for minimizing the size of the eigenvalue problem that has to be solved. (Chen Page 4, Right only eigenmodes of the interior are utilized which would account for any discontinuities between the interior and exterior “The solution is rigorous and valid everywhere even though the eigenmodes form a complete set only in the interior.”)
With regard to claim 7, Chen in view of Bergman teaches all the elements of the parent claim 2, and further teaches: wherein the overlap integrals are evaluated by replacing the volume integrals by surface integrals and the surface integrals by line integrals. (Chen Page 8, Left
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With regard to claim 8, Chen in view of Berman teaches all the elements of the parent claim 1, and further teaches: wherein modes of the target geometry are expanded based on the modes of a simpler geometry. (Chen Page 1, Left eigenmodes are used for expansion
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, and Page 3, Left the eigenmodes are based on a simpler geometry such as a sphere “Crucially, modes of analytically insoluble systems can be generated effortlessly and reliably using the modes of a simpler system as a basis”)
Claims 9 – 11 are rejected under 35 U.S.C. 103 as being unpatentable over Chen in view of Bergman, and further in view of Tsang et al. (US 2018/0121580) (henceforth “Tsang (580)”). Chen and Bergman and Tsang (580) are analogous art because they solve the same problem of solving partial differential equations, and because they are in the same field of mathematical algorithms.
With regard to claim 9 (see Claim Rejections - 35 USC § 112), it recites the same steps as in claim 1, which is taught by Chen in view of Bergman.
Chen in view of Bergman does not appear to explicitly disclose: a system comprising at least one processor, adapted to perform the steps.
However, Tsang (580) teaches:
a system for providing for providing fast and efficient solution of partial differential equations, comprising at least one processor (Paragraph 33 a computing system with a processor, and Paragraph 48 solving for modal eigenfunction of a periodic structure comprising scatters)
It would have been obvious to one of ordinary skill in the art to combine the method of using an eigenmode basis for solving an electromagnetic problem disclosed by Chen in view of Bergman with the method of implementing the steps on a computer. One of ordinary skill in the art would have been motivated to make this modification in order to solve a desired problem (Tsang (580) Paragraph 33)
With regard to claim 10, Chen in view of Bergman, and further in view of Tsang (580) teaches all the elements of the parent claim 9, and further teaches: in which modes of the target geometry are expanded based on the modes of a simpler geometry. (Chen Page 1, Left eigenmodes are used for expansion
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, and Page 3, Left the eigenmodes are based on a simpler geometry such as a sphere “Crucially, modes of analytically insoluble systems can be generated effortlessly and reliably using the modes of a simpler system as a basis”)
With regard to claim 11, Chen in view of Bergman, and further in view of Tsang (580) teaches all the elements of the parent claim 9, and further teaches: in which the calculation of modes incorporates the mode discontinuity at the scatterer boundary being boundary-adapted modes, for minimizing the size of the eigenvalue problem that has to be solved. (Chen Page 4, Right only eigenmodes of the interior are utilized which would account for any discontinuities between the interior and exterior “The solution is rigorous and valid everywhere even though the eigenmodes form a complete set only in the interior.”)
Examiner General Comments
With regard to the prior art rejection(s), any cited portion of the relied upon reference(s), either by pointing to specific sections or as quotations, is intended to be interpreted in the context of the reference(s) as a whole as would be understood by one of ordinary skill in the art. Although the specified citations are representative of the teachings in the art and are applied to the specific limitations within the individual claim, other passages and figures may apply as well. It is respectfully requested that, in preparing responses, the applicant fully consider the references in their entirety as potentially teaching all or part of the claimed invention since the entire reference is considered to provide disclosure relating to the cited portions. Further, the claims and only the claims form the metes and bounds of the invention. Office personnel are to give the claims their broadest reasonable interpretation in light of the supporting disclosure. Unclaimed limitations appearing in the specification are not read into the claim. Prior art was referenced using terminology familiar to one of ordinary skill in the art. Such an approach is broad in concept and can be either explicit or implicit in meaning. Examiner's Notes are provided with the cited references to assist the applicant to better understand how the examiner interprets the applied prior art. Such comments are entirely consistent with the intent and spirit of compact prosecution.
Conclusion
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
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/ALFRED H. WECHSELBERGER/ExaminerArt Unit 2187
/BRIAN S COOK/Primary Examiner, Art Unit 2187