Michel Chein

Michel Leclère

Yann Nicolas

R R Lirmm-Graphik

SudocAD: A Knowledge-Based System for Object Identification

Introduction

The problem addressed in this paper is an object identification problem. Since a long time, ([?] is a seminal paper published in 1959) various problems having at their core identification problems have been extensively studied under different names (cf. the bibliography [?]) such as:

• entity resolution, reference reconciliation: identifying multiple references to the same object and distinguishing them from mentions of different objects, finding which records in two different databases represent the same entity

• de-duplication: finding duplicate data (object) then deleting the duplicates (Classical problem: creation of mailing lists)

• merging merging records judged to represent the same world entity

• record linkage, linking records through references to same world entities

• entity alignment this term is issued from analogy with ontology alignment and is used in the context of web of objects ( ?)

• object identification is used in this paper as a generic term to single out, to distinguish, to recognize in a computer system symbols aiming at representing the same individual entity in the world modeled in the system These problems have been considered for many kinds of databases, especially data warehouses where, for instance, it is important to know if two identifiers refer to the same object or to different entities in the exterior world. These problems acquired a new importance due to the web, especially in the so-called web of objects, where, for instance, one wants to gather all available information concerning the same entity. Most solutions of object identification problems are based on classification techniques. In such an approach, an entity is described by a list of attributes; attribute values are simple data types (e.g., strings or numbers) and approximate similarity measures are assigned for each kind of attributes vector; a similarity measure is built for lists of attributes (often it is a weighted combination of the attribute similarities); finally, a decision procedure allows to state when two lists of attributes represent the same entity. Recently, logical approaches using knowledge representation techniques (e.g., Fatiha Saïs, Nathalie Pernelle and M.-C. Rousset consider data sources conforming to the same RDFS schema [?, ?] ...) and combinations of these two kinds of methods have been developed (...).

Our method belongs to this latter type, it combines numerical measures for comparing low level attributes and for building symbolic relations and uses logical rules for processing these qualitative relations. The languages of the semantic web, RDFS and OWL, and knowledge representation techniques have been used for developing the system aiming at solving a specific object identification in a context of bibliographic databases.

The problem and the method described in this article can be sketchily stated as follows.

Having a database containing information about entities E = {E 1 , . . . , E n } of a specific type T , e.g. P erson, and having a (new) piece of information d concerning an entity E of type T , i.e. a P erson, one wants to find if there is E i ∈ E such that E and E i refer to the same person. Our approach consists in computing a qualitative partition of E, whose classes called {StrongLinkage, M ediumLinkage, . . . , ImpossibleLinka are ordered by decreasing relevance with respect to co-reference with E. This result can be used as follows.

If there is only one element E in the class StrongLinkage then the system can automatically conclude that E = E , otherwise the classes can be successively presented to a human operator who will have to choose. In the bibliographic context considered, the database contains (at least) authority databases (one for each type of authority, e.g. Person, Collective entity, Geographical place, ...) containing data about the authorities, and a document database containing metadata about documents and in particular references to the authorities. Thus, E is composed of a base A of authority notices gathering general information concerning a specific type of entities and a base D containing document notices referring to entities in E. If the initial database is not structured in such a way, the method proposed can be nevertheless applied if it is possible to build E and D from it (cf. section 3.2 that can be adapted to do that).

Let us mention some reasons enlightening the importance of object identification problems in document databases. Firstly, all the previous mentioned problems are important in the context of libraries: some of them are induced by the evolution of libraries (e.g., adding notices to a base, merging bibliographic bases, maintenance of the different bases), others concern the quality of the notice bases (e.g., consistency inside and between bases, relevance of the subject). Secondly, a document database is a very rich source of information about the documents themselves and about authorities. International work is done to standardize the metadata (FRBR, CIDOC CRM, RDA, ?), to build shared ontologies. This allows the transformation of a document base into a knowledge base and then knowledge-based techniques can be used to make the most of the information present in the base. Thirdly, whenever the languages of the semantic web are used for solving object identification problems (as it is the case in the system described in this paper) and due to the large size of document bases, the techniques developed are not only interesting per se but also as a testbed for object identification in the context of the web of data.

The paper is organized as follows. In section 2, the bibliographic database context and the goals of the system sudocAD are precisely stated. In particular, how a bibliographic database has been represented as a knowledge base by using the web standards. The hybrid method, combining numerical and logical aspects, is presented in section 3. The results of the evaluation of sudocAD are described in section 5. Specificities of the system sudocAD are presented section 4. Conclusion and further work end the paper. Note that in this paper the term sudocAD is used for the system described section 3 and section 4. The version presented is the one that has been evaluated, the methodology of the evaluation and the results are presented in section 4. Many improvements have been considered during the development of sudocAD and some of them are presented in the last section. We are presently investigating what are the changes and improvements mandatory to make it usable in production ...

The Bibliographic Context

Bibliographic and Authority Notices, sudoc and IdRef

Sudoc is the national bibliographic infrastructure for the French higher education. As such an infrastructure, Sudoc is both:

• a shared database where bibliographic records are created once, but used by all ;

• a network of professional catalogers, with common tools, guidelines and tools.

The core function of this collective endeavour is to create and maintain database records that describe the documents held or licensed by French Universities and other higher education institutions. Sudoc contains more than ten million such records (2012 figure). Documents described by Sudoc are mainly electronic or print books and journals, but also manuscripts, pictures, maps, etc.

A Sudoc record is composed of three kind of information:

• Meta-information

• Descriptive information

• Access points Meta-information is information about the record. It is out of the scope of this paper. Descriptive information is mere transcription of information that is found in the document to be catalogued. By instance, the descriptive field Title contains the very text string that is written on the title page. The same is true for the descriptive field Author: the record has to keep the author's name as it is found in the document, even if the cataloger knows that the title page misspelled this name. This strictly descriptive approach aims to identify without any ambiguity the publication. The transcribed information is to be sufficient in order to distinguish two editions of the same work. But this descriptive approach may make the document harder to find. If the title page, hence the bibliographic record, assumes that the author's name is "Jean Dupond" whereas the actual name is "Jean Dupont", the library users that are only aware of the actual name will fail to find and access the record in the catalog and then to find and access the document in the library. In order to prevent this kind of problem, the cataloguing rules prescribe to add the actual name in the record, not instead of but besides the one found on the title page. This kind of additional non descriptive information is called "access point".

Access points constitute the third kind of information that is to be found in a bibliographic record. An access point is a piece of information that focuses on some aspect of the described document that may be relevant for finding the record in a database and that is not directly observable in the document itself. As we have seen above, it can be the actual author's name. It can also be the author's name written according to a specific convention (e.g. "Dupont, Jean" or "Dupont, Jean (1956-)"). But an access point is not necessarily an alternative textual form of a piece of information that was observed on the described object. It can be the result of the analysis of the content of the document. By instance, an access point can be a keyword expressing the subject of the document (e.g. "cars"). Any bibliographic record is the result of the description of the document and the selection of relevant access points. But when is a bibliographic deemed to be achieved? Theoretically, the description could last forever but cataloguing guidelines fix a finite list of which document properties must or may be described. But regarding access points, when to stop? If access points are there to help the user to find the record, there can be plenty of them. Should the record describing the book by Jean Dupont and about cars have access points mentioning all the variant of Jean Dupont's name and as many access points as there are synonyms for "cars"? And should it be the case for each book by Jean Dupont or about cars? In order not to repeat all the variants of a name or a concept in all the bibliographic records using this name or this concept as an access point, theses variants are grouped in specific records, namely authority records. By instance, the authority record for Jean Dupont will contains his name variants. One of these variants will be distinguished as the preferred form. Some guidelines will help the cataloguers to choose the preferred form. Some guidelines expect the preferred form to be unique. If true, the preferred form will be used as if it was an identifier. The preferred form is the only form to be used an an access point in the bibliographic records. If it is unique, it works like an identifier for the authority record, that contains the rest of the variants: the preferred form used as an access point links the bibliographic record to the authority record. In many recent catalogs, the link from the bibliographic record to the authority record is not the preferred form but the authority number. It is the case in Sudoc. The Sudoc bibliographic record access points are just authority record identifiers. When the record is displayed or exported, the Sudoc system follows the link and substitutes a name or a term to the identifier. Sudoc has more than ten million bibliographic records and two million authority records. An authority record is not an entry in a biographical dictionary. It is supposed to contain nothing but information sufficient to distinguish a person from another one described by another authority record. Authority records for ppeople contain mainly information about their names, their dates and their country. Authority records for concepts contain information about their labels and their relationships to other concepts (broader, narrower, etc).

Semantization of Bibliographic Metadata

Reasoners need our records to be expressed in RDF. As RDF is nothing but a generic model, one have to choose one or several RDF vocabularies. This vocabulary had to meet some expectations:

• to be able to express precise bibliographic assertions

• to be minimally stable and maintained by a community

The FRBRoo vocabulary meets these expectations:

• It has been develpped for fine grained bibliographic requirements First, FRBRoo takes it main concepts form FRBR (1998), a prominent model that was developed by the International Federation of Library Associations during the 1990's. FRBRoo keeps core FRBR(1998) concepts but claims to overcome some of its alleged limitations. Second, FRBRoo is built as an extension of another model for cultural objects, namely CRM CIDOC. CRM CIDOC's main scope is material cultural heritage, as curated by art or natural history museums. It is focused on expressing the various events that constitute an object life, before or after its accession to the museum. FRBRoo imports many of its classes and properties from CIDOC CRM, but needs to forge a lot of new ones, to cope with more abstracts entities as texts and works.

• It is well documented • It is
For SudocAD's needs, it was not necessary to convert all UNIMARC fields in FRBRoo. But even for the conversion of the fields needed for the reasoning, we had to extend FRBRoo and forge some new classes and properties. The problem: link an entity E in d, representing an object O in the exterior world, to an authority notice in A, representing the same object O, if such an authority is in A.

The Method

Important tasks of the implemented method can be briefly stated as follows.

• Linkage knowledge: comparison criteria and rules.

A fundamental task consists of building linkage knowledge whose main components are comparison criteria and logical rules.

An elementary comparison criterion is a function c δ that associates, with respect to a specific notion δ, a value to a couple composed of an entity E in d and an authority A in A. In order to precisely define comparison criteria one has to build a " linkage ontology" O L which contains the concepts and the relations needed to express the comparison criteria.

• Working Knowledge Base

Having defining comparison criterion, the next step consists of restricting and transforming the database into a knowledge base that only contains useful information for linking entities in d to authorities in A. A piece of information may be useful for the linkage problem if it is used in a comparison criterion. Let W be this knowledge base which is based on the formal ontology composed of the ontology O B , in which D and A are expressed, and the linkage ontology O L . W should have two main properties: it should contain all the authorities in A which may be linked to entities in d and it should be small enough to do efficiently the computations needed by the linkage problems.

• Authority Enrichment

The links between document notices and authority notices in W are used for enrichment of the authority notices. Enrichment of an authority notice A consists of specializing A. For instance, if an authority A is author of a lot of documents dealing with medicine it is probably relevant to add that medicine is within the competence of A. Applying this rule leads to adding a value to an existing attribute whenever competence is initially in A , otherwise, if competence is a linkage concept in O L which is not in the initial ontology O B it leads to adding a new attribute to A.

• Linkage Computations

For each couple (E, A), where E is an entity in d which may be linked to an authority A, and for each comparison criterion c δ one has to compute, in W, the value c δ (A, E). This computation may use numerical computations but the values are qualitative values (e.g., similar, intermediate, weak, dissimilar) so that can be used as hypotheses in logical rules.

Finally, logical rules, having values of comparison criteria (between A and E) in hypothesis and a value of the global qualitative comparison criterion, link, in conclusion are fired. The result is a partition of the authority candidates ordered by decreasing relevance with respect to the possibility of linking E and A. For instance, if link(E, A) = strong there is strong evidence that E and A can be linked, i.e. that they represent the same in the exterior world.

3.1 Working Base and authority candidates

Principles

In this paper we consider named entities. It means that considered objects have an important discriminant attribute which is their name. In d an entity E is thus identified by a name. It is also assumed that an authority in A has a specific attribute denomination, which is the set of different names used for the object represented by this authority.

The whole data base is very large and a first step is to limit it to useful information for the linkage problem. This working base should ideally contain all the possible candidates and should not be too large in order to be able to process it efficiently. As our problem is to link named entities in d to existing authorities having names in the authority notice base, we start by using a name criterion.

Thus, the first step consists of constructing a graph containing (potentially all) the possible candidates, information useful for the linkage problem and this graph being not too large in order to be able to process it efficiently.

In sudocAD

The working base is built as follows.

1. For each author name in d, the first task is to represent an author name in d in the same way, say name, as denomination in authority notices (this may need an alignment between 'author name' in d and 'denomination' in authority notices).

2. The set A = sim(name) of authorities in A having a denomination, (either restraint or rejected if there is such a discrimination in the base), similar to name is computed.

3. For each authority A in A , the set Bib(A) of bibliographic notices having A as an author or as a significant role is computed. As we only consider named entities of type Author in d, in Bib(A) we only consider documents for which A is a contributor with a role compatible with the role Author (e.g. Scientif icEditor, P hDAdvisor, ...).

4. The working base W(name) is obtained by making the union of the authority notices in A and the document notices Bib(A) for all A in A .

A fundamental assumption is that the function sim is sufficiently robust to author name variations in order that if there is an authority in A corresponding to the author whose name is name in d then this authority is (almost surely) in A . Another assumption is that W (name) contains sufficient contextual knowledge concerning the authorities in order to remove the ambiguities, i.e. to solve the linkage problem. The linkage problem can be now stated as follows: for each name of a named entity in d, compute a set of authority notices in A ordered by decreasing relevance with respect to identity, using W, d, the domain and the linkage ontologies and general knowledge represented by rules (cf. ).

Super-authority

Principles

The aim of this step is to enrich the data concerning an authority A with information that can be used in comparison criteria. For doing that, information concerning documents in which A is a contributor are computed, synthesized and then attached to A.

In sudocAD

In d, which is a notice of a paper in a scientific journal, one has only, besides names of the authors, a publication date, the paper title, the language and a list of scientific domains. For each of this notions one can possibly enrich an authority notice by using information in the document notices, Bib(A), in which A is a contributor. For instance, aggregating all domains of notices in Bib(A) is, generally, more precise than a piece of information concerning the competence in A. In the same way, one can compute, then associate to A, an interval of publication dates. Note that, due to the nature of d (scientific paper), the kinds of contributor considered have been restricted to those having a scientific role, e.g., author, PhD supervisor, scientific editor, preface writer, etc. From now on, for simplicity sake, A denotes the set of super-authorities and a super-authority is simply called an authority.

Comparison Criteria

Principles

Let us call dimension an abstract notion for which information exist both for named entities in d and in authorities. For instance, as seen previously, the time is such a dimension since we have a publication date in d and (possibly) life dates and a publication date interval in authorities. For each dimension δ, a comparison criterion c δ is built that associates to a pair (E, A), where E is a named entity in d which may be linked to A, a qualitative value. These values can be considered as propositional symbols for doing reasonings in the following way. Indeed, let us consider a pair (E, A) and a comparison criterion c δ whose values are the set v 1 , . . . , v k . Let us assume that c δ (E, A) = v i then considered as propositional symbols, v i takes the value true while the others take the value f alse (cf. section 3.4 to see how they are used in rules) .

In sudocAD

The dimensions taken into account in sudocAD are: {denomination, domain, time, language}. The sets of values of their associated criteria contain from 2 to 4 values ordered with respect to the similarity relevance.

• Denomination

The set of values of the 'denomination' criterion is : {sameDenomination, closeDenomination, distantDen Given a name of an author in d and a denomination of an authority A, the sudocAD algorithm has two parameters: a threshold and an algorithm for computing an edition distance. For the evaluated sudocAD system, the threshold is 0.8 and the Levenshtein's algorithm is used.

Split n d , the name of an author E in d, and n A , a denomination of an authority A, into two strings, respectively (n 1 , p 1 ) and (n 2 , p 2 ). The first string is the most discriminant part of the name, in our case it corresponds to the family name, and the second string, less important, is composed of first names or first name initials. The strings n 1 , n 2 , p 1 , p 2 are normalized (transformation of uppercases into lowercases, deletion of accents and of redundant spaces, etc.). Two independent functions compare respectively n 1 , n 2 and p 1 , p 2 . For both, their result is one of the same qualitative value set identical, stronglyCompatible, compatible, distant, dif f erent, they use the same threshold and the same distance edition algorithm, but due to their different nature(e.g., initials in p i 's ) the two functions are rather different. For instance, they differently use the prefix notion.

The results of these two functions then are aggregated as follows.

if (n 1 and n 2 are identical or strongly compatible) then (if p 1 and p 2 are identical or strongly compatible return SAME else if p 1 and p 2 are compatible or distant return CLOSE else return DISTANT) else if(n 1 and n 2 are compatible) then (if p 1 and p 2 are identical or strongly compatible or compatible return CLOSE else if p 1 and p 2 are distant return DISTANT else return DISSIMILAR) else if(n 1 and n 2 are distant) then (if p 1 and p 2 are identical or strongly compatible or compatible or distant return DISTANT else return DISSIMILAR) return DISSIMILAR Finally, as an authority A may have a set of denominations, Denom(A), the value of the denomination criterion c denomination (E, A) is equal to the maximum value over the set of denominations of A, i.e., c denomination (E, A) = max{c denomination (n d , n A )|n A ∈ Denom(A)}, where n d is the name of E.

For more details see Annex.

• Domain

The set of values of the 'domain' criterion is : {domainStrongCorrespondence, domainIntermediateCorr We compare the set of domains of the Journal in which d has been published with the weighted list of domains in the authority A.

More precisely, to each A a domain profile is associated. A domain profile is a set of weighted domain {(d 1 , p 1 ), . . . , (d k , p k )} computed as follows. To a document which is in Bib(A), i.e., for which A is a scientific contributor, is associated a set {(d 1 , q 1 ), . . . , (d m , q m )} where {d 1 , . . . , d m } is the set of domains occurring in the document and a document counts for one, i.e., m i=1 q i = 1 Such a set can be considered as a vector on the set of domains and the domain profile of A is the sum of these vectors. In the same way a domain profile can also be associated with the document d, the weight of a domain of d being equal to 1/#dd, where #dd is the number of domains associated with d. The profile domain of any entity in d is the domain profile of d. -domainStrongCorrespondence whenever 0.8 < sim(P, P ) ≤ 1,

-domainIntermediateCorrespondence whenever 0.5 < sim(P, P ) ≤ 0.8, -domainW eakCorrespondence whenever 0.2 < sim(P, P ) ≤ 0.5, -domainW ithoutCorrespondence whenever 0 ≥ sim(P, P ) ≤ 0.2.

Note that we take c domain (E, A) = c domain (d, A) for any entity in d.

For more details see Annex.

• Date

The set of values of the 'date' criterion is : {dateStrongCorrespondence, dateIntermediateCorrespondenc An overview of the date criterion is as follows. Two booleans are used compatibleP eriod expressing compatibility between the publication date p d of d and the interval of publication dates (beginP eriod, endP eriod) of A and compatibleLif e expressing compatibility between the publication date of d and the life interval (birthDate, deathDate) of A. If the birth date of the death date of A does not exist then they are given the value null. There are three thresholds: T 1 for the age at which a person can publish (set to 20 in sudocAD), T 2 for the length life whenever either the birth date or the death date of an author is unknown (set to 100 in sudocAD) and T 3 (set to 10 in sudocAD) to express that if the publication date of d is within the interval of publication dates plus or minus T 3 then they are compatible. For more details see Annex.

• Language

The set of values of the 'language' criterion is : {languageStrongCorrespondence, languageW ithoutCorre For our experiment the language is not discriminant and we have chosen a simplistic language criterion: if in Bib(A) there is a document written in the same language as d then the value of c language (d, A) is language s trong c orrespondence otherwise it is language w ithout c orrespondence.

Note that, as well as for the domain criterion, the language criterion deals with d and is transferred to each entity E in d.

For more details see Annex.

Linkage

Principles

Let E be an entity in d and A the set of authorities. For any criterion c δ we have the value c δ (E, A) of this criterion for the pair (E, A). These values are used for computing the possibility of linkage between E and A. This possibility is expressed by a (global) comparison criterion called linkage. As well as for the elementary comparison criteria the values of are qualitative values, e.g. strongLinkage or impossibleLinkage and they can be considered as propositional symbols. Let us assume that there is k dimensions δ 1 , . . . , δ k . The hypothesis of a rule is a conjunction of k propositional symbols, H 1 and ... and H k , where for all i H i is a value of c δ i . The conclusion of a rule is a value linkage(E, A) of the linkage criterion for the pair (E, A). For each value of linkage we have a set of rules having this value as conclusion. Here is an example of a rule. If sameDenomination anddateIntermediateCorrespondence and domainStrongCorrespondence and languageStrongCorrespondence then strongLinkage. This rule is used as follows. If for a given pair (E, A) all hypotheses are true then the system concludes that there is a strong evidence that E and A represent the same entity. Said otherwise, the system cannot distinguish E from A. At the opposite, if linkage(E, A) = impossibleLinkage it means that the system considers that there is strong evidence that E and A do not refer to the same exterior object.

The set of rules are used to partition the authorities. If the values of linkage are {v 1 , . . . , v n } then there is at most n classes defined by the value of linkage(E, A), i.e. the i-th class is the set {A ∈ A|linkage(E, A) = v i }.

The results will be used differently depending on whether the system is used in an automatic mode or as an aid to a human operator. The choices made in sudocAD for these two modes are presented in section 4.

Implementation in sudocAD

Seven qualitative values have been considered for the linkage criterion: {strongLinkage, mediumLinkage, weakL

The rules are described below in an array.The lines correspond to rules and the columns correspond to the comparison criteria. The following notations are used. The values of the elementary comparison criteria are represented as follows.

• values of the denomination criterion: +++, ++, +, -(where: +++ stands for sameDenomination, ++ for closeDenomination , + for distantDenomination , -for dissimilarDenomination)

• values of the date criterion: +++, ++, +, ?, -(+++ stands for dateStrongCorrespondence, ++ for dateIntermediateCorrespondence , + for dateW eakCorrespondence, -for dateW ithoutCorrespondence and ? for unknown)

• values of the domain criterion: +++, ++, +, ?, -(+++ stands for domainStrongCorrespondence, ++ for domainIntermediateCorrespondence , + for domainW eakCorrespondence, -for domainW ithoutCo and ? for unknown)

• values of the language criterion: +, ?, -(+ stands for languageStrongCorrespondence, -for languageW ithoutCorrespondence)

The 300 cases are gathered into 7 subsets labeled S, M, W, P, N, U, I correspond respectively to the rules concluding by strongLinkage, mediumLinkage, weakLinkage, poorLinkage, neutralLinkage, unrelatedLink 4 The System SudocAD

(to be finalized)

The system sudocAD has been developed upon COGUI. COGUI is a platform for designing, building and reasoning on conceptual graph knowledge-bases (see [?]) that has been used at each stage of the project. The project is persistently stored in the xml file Xblablabla. We will briefly browse through the project to get an idea of what sorts of functionality are provided. In order to fully understand the capabilities of COGUI one has to read the documentation. • Input Data Input data consist of a part of the sudoc database and of a PERSEE notice. As explained in section 2 the sudoc database have been translated into RDF. A part of it, containing authority notices whose denominations are closed to the name of an author in the PERSEE notice and the bibliographic notices in which these authorities have a scientific role, is imported into cogui through the import RDF/S natural mode tool. The file Xblablabla contains ...

• The scripts The method described in section 3 is implemented through the scripts which use the queries for searching the data graph. We will skim through the "STEP BY STEP" mode which allows to understand how the system works.

-

STEP1 -STEP2 -STEP3 -STEP4 -STEP5
We give here the 24 rules in STEP5 scripts and the way they are actually used in sudocAD. Their semantics is equivalent to the 300 rules previously given. These rules are fired in a specific order and for a given pair (E, A) the value linkage(E, A) is the first value obtained. As soon as a rule is fired for a pair (E, A) the others are not fired. The chosen order, which is important for the result is as follows: LI1, LI2, LU3, LP4, LS1, LS2, LM1, LM2, LM3, LM4, LM5, LW1, LW2, LW3, LW4, LW5, LP1, LP2, LP3 LU1, LU2, Another case. The order on the set of values of a comparison criterion is also used. If the value of a criterion is positive, say p, then it is assumed that it has also all the positive values p ≤ p. Note also that the joker * stands for any value of a criterion as well as the absence of value.

-STEP6 -STEP7

5 Evaluation

Methodology

Given a base D of document notices, a base A of authority notices and an entity E in a document notice d results of sudocAD is essentially a partition of A in classes ordered by decreasing relevance with respect to co-reference. It seems difficult to assess the quality of this partition and even to define what could be the quality of such a partition. Thus, we consider two ways of using this partition which can be evaluated by human experts: an automatic mode and a decision-aided mode. In the automatic mode, the system either proposes an authority A to be linked to E or proposes no link. In the decision-aided mode, the system proposes a list of authorities in a decreasing relevance order until the operator chooses one authority or stops using the system. From the database PERSEE, 150 bibliographic notices, referencing 212 authors, have been chosen at random. For these notices, professional librarians had to do their usual work, that is to try to link authors in PERSEE notices to authorities, and that in their usual work environment. That is to say, librarians had the complete PERSEE notices (even if parts of the notices are not taking into account by sudocAD, for instance the title of the paper) and on-line access to the bases D and A. Librarians had also a limited time, no more than 5 minutes for linking an author, and they also have to respect the usual constraint to not create erroneous links. For an author E in a PERSEE notice a librarian could take one of the following decisions:

• link with certainty E to an authority A

• link with uncertainty E to an authority A and suggest other possible authorities

• refrain for linking with certainty

• refrain for linking with uncertainty nevertheless suggest possible authorities A librarian analyzed the results of this first step. He was not involved in this step and did not work in the usual work environment a librarian has for linking because he could use any sources of information (e.g. the web) and had no limited time. After having modified, if necessary, results of the first step, it is hoped to have the best possible linkages to compare with those obtained by sudocAD.

Expert Results Number

Automatic Linkage

We considered four different ways for automatic linkage listed as follows for the most restrictive to the less restrictive. For the comparison between the expert choice and one of these methods we consider that the answer given by the method is a

• Good decision either when the expert links with certainty E to A as well as the method or when the expert does not link with certainty E and the method does not propose a link

• Acceptable decision either when the expert links with uncertainty E to A and the method links E to A or when the expert does not link with certainty E and the method proposes a link to a doubtful candidate

• Bad decision either when the expert links with certainty E to A and the method links E to A = A or when the expert does not link with certainty E and the method proposes a link

• Prudent decision when the expert links with or without certainty and the method does not propose a link

The means of these parameters for the 212 authors occurring in the 150 PERSEE bibliographic notices are as follows. 86.79% 0.94% 6.6% 5.66%

Method Good decision Acceptable decision

Decision-Aided

In a decision-aided mode the system presents to a human operator an ordered list of the candidate authorities. This list is presented in the decreasing order of relevance strongLinkage, mediumLinkage, weakLinkage, etc. until the operator chooses one authority to be linked to E or stops the unfolding of the candidate authorities and concludes that there is no authority which can be linked to E. Three classical parameters in Information Retrieval have been considered for evaluating the use of our system in a decision-aided mode. They use the following sets of authorities:

• Candidates is the set of authority candidates in the working base • Impossible is the set of authorities related by impossibleLinkage to E

• Selected is the union of the authority linked to E by the operator and, when there is uncertainty, the set of possible authorities proposed by the operator

The parameters are then defined as follows.

  maintained and still developed by an active community• It is connected to other major modelling iniatives.

  In a very general setting one has: The data: a base D of document notices, a base A of authority notices and a (new) document notice d. The bases are represented in a knowledge representation language based on a formal ontology O B .

  The similarity measure between two domain profiles P = {(d 1 , p 1 ), . . . , (d m , p m )} and P = {(d 1 , p 1 ), . . . , (d n , p n )} that have been used in sudocAD issim(P, P ) = m i=1 n j=1 p i p j σ(d i , d j )/ In this formula, σ(d, d ) ∈ [0, 1]is a similarity between domains satisfying, σ(d, d ) = 1 means that d = d or that d and d are synonyms, σ(d, d ) = 0 means that it is quite impossible that a given person can have a scientific role in a document about d and a document about d . The qualitative values for the domain criterion are defined as follows, c domain (d, A) is equal to:

  For instance, a period criterion can use the publication date of d and, if A is a person authority, the life dates of A. For computing the value of a period criterion between an author E of d, and an authority, one can use knowledge such as "if the publication date of d is t then E cannot be identical to a person authority A whose birth date is posterior to t." The set of values of a comparison criterion is a totally ordered set of qualitative values representing the similarity between E and A with respect to the notion δ (typically: similar, intermediate, weak, dissimilar).The (global) comparison between an entity E and an authorityA is also express as a qualitative value (e.g. strong or medium , ..., or impossible) which is the conclusion of a logical rule having values of elementary comparison criterion as hypotheses (e.g. "if the value of the date criterion is impossible then the global comparison has impossible for value".) Note that computing values of criteria may need an alignment step between data in d and data in the A s .

  compatiblePeriod= (beginP eriod ≤ dateP ubli) and (endP eriod ≥ dateP ubli); if (birthDate = null and deathDate = null) then deathDate = birthDate + T 2 ; if (deathDate = null and birthDate = null) then birthDate = birthDate -T 2 ; if(birthDate = null and p d ≥ birthDate+20 and p d ≤ deathDate) then compatibleLif e = true;

if(birthDate = null and birthDate + 20 > p d ) then return dateW ithoutCorrespondence; if(compatiblePeriod and compatibleVie) then return dateStronCcorrespondence; if(compatiblePeriod or compatibleVie) then return dateIntermediateCorrespondence; compatibleP eriod = (beginP eriod ≤ p d ) and (endP eriod + 10 ≥ dateP ubli); if(compatiblePeriod and (birthDate = null or birthDate+20 ≤ p d )) then return dateW eakCorrespondence if((birthDate = null) or birthDate + 20 ≤ dateP ubli ) then return dateW eakCorrespondence;

•

  The Ontology First thing to do is to store on disk the project file then download COGUI and open the file. By clicking on the vocabulary tab on the vertical left panel it is possible to see the ontology used. It contains a hierarchy of (313) concept types and a hierarchy of (1179) relation types (nesting types and modules are not used in sudocAD). A tree view is presented in the left vertical panel and a graphical view in the top right panel (the cycles are due to the existence of synonyms between notions in the standards cidoc-crm and frbr). An entity may have several types and banned types (bottom left panel) express incoherences, for instance there can not exist an entity which would be a P hysicalT hing and a ConceptualObject. The relation types are also hierarchically organized. Note that in sudocAD there are only binary relations but relations with any arity can be used in COGUI. The root of the linkage relations is emphliage : binding vocabulary relation (Resource,Resource) at the bottom of the relation types panel. A relation has a signature which indicates its arity and the maximal types an attribute can have (for instance the two attributes of the relation emphliage : liageAuthority (Person,Person) have to be of type (less than or equal to) Person. Patterns and Prototypes are not used in sudocAD.

  • AL 1 If the best class, i.e. strongLinkage, contains only one authority then E is linked to this authority • AL 2 If the union of the two best classes, i.e. strongLinkage and mediumLinkage, contains only one authority then E is linked to this authority • AL 3 If the union of the three best classes, i.e. strongLinkage and mediumLinkage and weakLinkage, contains only one authority then E is linked to this authority • AL 4 If the union of the four best classes, i.e. strongLinkage and mediumLinkage and weakLinkage and poorLinkage, contains only one authority then E is linked to this authority

There are two different situations: the operator can decide either to link or not to link E to an authority . If he decides to link the recall is not relevant, because in this case the recall is equal to 1 unless Selected ∩ Impossible = ∅ which is unlikely. If he decides not to link Selected is empty. In this case another parameter could be |Impossible|/|Candidates| if Candidates is not empty, this is generally the case since the construction of Candidates is based on the denomination.

The means of these parameters for the 212 authors occurring in the 150 PERSEE bibliographic notices are as follows. Note that this is only a shallow evaluation that should be deepened. Indeed, the measure of performance of a decision-aided system is the gain obtained when the operator uses the system compare to not using the system. But, the linkage problem cannot be solved without a system (unless proposing at random candidate authorities ...). So, for a significant evaluation one should make an experiment comparing two systems. This is a further work that is planned for a decision-aided use of our system but also for an automatic mode. .

Expert choice Recall Precision Relevance

Conclusion and further work

(to be finalized) SudocAD deals with authors but can be used for other authorities as well, e.g. collective entities. The algorithms used in SudocAD assume that the bases are correct. If each notice, either document notices or authority notice, can be assumed to be correct links between them can be erroneous. Further work will take into account the quality of the considered bases.


Tryfon Antonakakis

Fadi Baïda

Abderrahmane Belkhir

Kirill Cherednichenko

Shane Cooper

Richard Craster

Guillaume Demesy

John Desanto

Gérard Granet

Editor Evgeny Popov
email: e.popov@fresnel.fr

Boris Gralak

Sébastien Guenneau

Daniel Maystre

André Nicolet

Brian Stout

Gérard Tayeb

Fréderic Zolla

Benjamin Vial

GratinGs: theory and numeric applications

Periodic systems play an important role in science and technology. Moreover, desire for order in Nature and human society has accompanied development of philosophy. Simple periodical oscillation is referenced as 'harmonic' in mechanics, optics, music, etc., the name deriving from the Greek ἁρμονία (harmonía), meaning "joint, agreement, concord" [1.1]. It is not our purpose here to study harmony in general, nor harmony in physics. We are aiming to much more modest target: rigorous methods of modeling light propagation and diffraction by periodic media.

The methods presented in the book have already shown their validity and use from x-ray domain to MW region, for nonmagnetic and magnetic materials, metals and dielectrics, linear and nonlinear optical effects. The existing variety of these methods is due not only to historical reasons, but mainly to the absence of The Method, a universal approach that could solve all diffraction problems. Some of the approaches cover greater domain of problems, but more specialized ones are generally more efficient. The other reason of the great number of methods is the complexity and variety of their objects and applications.

Diffraction property of periodic media

The most important property of diffraction grating to create diffraction orders has been documented by Rittenhause for the first time in 1786 [1.2] due to the observation made by Francis Hopkinson through a silk handkerchief. The appearance of diffraction orders rather than the specularly reflected and transmitted beams was studied experimentally by Young in 1803 [1.3] with his discovery of the sine rule. A detailed presentation of the analytic properties of gratings can be found in Chapter 2.

Secondary-school pupils are supposed nowadays to know the Snell-Descartes law, which undergraduate students in universities are supposed to be able to demonstrate: singleray diffraction on a plane interface results in a single transmitted and single reflected rays. The critical advantage of periodic perturbation of the interface (variation of the refractive index or surface corrugation) changes the impulsion ( If the interface lies in the xy-plane and the periodicity is along the x-axis (Fig. 1.1), and the incidence lies in a plane perpendicular to the grooves, the equation in reflection takes the form of the so-called grating equation: where λ is the wavelength of light. The case of conical (off-plane) diffraction by a plane grating having one-dimensional periodicity can also be described by eq.(1.1), preserving the wavevector component parallel to the groove direction:

y,m y,i x,m x,i 2 2 2 z,m x,m y,i k k k k mK k k k k = = + = - - (1.3)
where k is the wavenumber in the cladding. As a result, the diffracted beams lie on a cone, thus the name conical diffraction. Two-dimensional periodicity (having grating vectors 1 K  and 2 K  ) imposed on the optogeometrical properties of the plane interface creates two sets of diffraction orders together with their spatial combinations, subjected to the same rule formulated just before eq.(1.1):

S,mn S,i 1 2 k k mK nK = + +     (1.4)
Pure three-dimensional (3D) periodicity appears in crystallography and photonic crystals, if the substance is assumed to fill the entire space. The third-direction periodicity imposes additional condition to the wavenumber (said more precisely, to z,m k , which is already defined by the wave equation as given in the third equation of (1.3)), which leads to creation of discrete modes propagating in 3D periodic structures. This also leads to the appearance of propagating and forbidden zones structure.

Classical gratings in spectroscopy

The most common application of diffraction gratings is due to the fact that outside of the specular order (m = 0), the diffraction order direction depends on the wavelength, as stated in eq.(1.2). The result is that the grating acts as a dispersive optical component, with several advantages when compared to the prisms:

order 0 c x 1.
The grating can be a plane device, while the prism is a bulk one that requires larger volumes of optically pure glass (to add the difficulties of weight and temperature expansion constrains). 2. Provided a suitable reflecting material, the grating can work in spectral regions, where there is no transparent 'glass' with sufficient dispersion. 3. Grating dispersion can be varied, as it depends on the groove period, while prism dispersion depends on the material choice and groove angle, which gives quite limited choices. Since the first works of Young, followed by Fraunhofer's quite serious attention to diffraction gratings use and properties [1.4], there is rarely more important device in spectroscopy achievements that lay the basis of modern physics. An interested reader can find some important aspects of their history, properties, and application in [1.5]. Despite the above-listed advantages compared to prisms, the diffraction gratings never have sufficient performance for their spectroscopy customers:

1. There is no enough diffraction efficiency, defined as the ratio of the incident light diffracted in the order used by the application. This is probably the problem that has been mostly treated by rigorous grating methods, because they are the only ones to provide feasible results on the energy distribution, while the other characteristics (spectral resolution, scatter, dispersion, order overlap, etc.) can be obtained by simpler approaches.

Fig.1.2. Diffraction efficiency of aluminum-made sinusoidal grating with period d = 0.5 µm as a function of the wavelength. Littrow mount (-1 st order diffracted in the direction of the incident beam) for the two fundamental polarizations (transverse electric TE and transverse magnetic TM).

A typical spectral dependence of the diffraction efficiency (defined more precisely as the ratio between the energy flow in the corresponding order and the energy flow in the incident order in z-direction) of a surface-relief sinusoidal grating made of aluminum and working in the -1 st Littrow mount1 is presented in Fig. 1.2. As observed, the problems of spectral variation of efficiency adds to its polarization dependence.

2. There is no enough resolution, defined as the ratio between the working wavelength and the smallest distinguishable (as usual, defined using the Rayleigh criterion) spectral interval:

R λ = ∆λ (1.5)
Classical diffraction theories show that the spectral resolution is proportional to the number of grooves illuminated by the incident beam, and inversely proportional to cos(θ i ), if we consider 1D periodicity in non-conical diffraction (speaking more precisely, the inverse proportionality implies to the sum of the cosines of the incident and the diffracted angles). The latter dependence gives advantages to grazing incidence for higher spectral resolution applications, namely astronomy.

3. The efficiency depends on the polarization. Laser resonators usually use Brewster windows, so that the requirements are for high-efficient grating working in TM (transverse magnetic) polarization. However, spectroscopic applications do not like this at all. In astronomy, this property can be quite costly, because the loss of a half of the incident light intensity requires twice the exposer time. Low polarization dependent losses (PDL) are one of the most important criterions in optical communications, in general, and in grating applications for wavelength demultiplexing, in particular, necessary for multichannel optical connections. Fortunately, contrary to stellar spectroscopy, gratings used in optical communications work in only very small spectral interval, and are used in quite smaller sizes, so that there exist several solutions that provide high efficiency in unpolarized light over a limited spectral region. The idea is to shift the maxima in the spectral dependence of the two polarizations in Fig. 1.2 in order to make them overlap at some required wavelength. One solution is to use a grating having two-dimensional (2D) periodicity, as shown further on in Fig. 7.1. The period in the perpendicular direction is sufficiently small as not to introduce additional diffraction orders, and this additional corrugation can shift the position of the TE maximum to longer wavelengths [1.6].

Fig.1.3. SEM picture of the profile of a grating etched in Si wafer and used for wavelength demutiplexing (after [1.7], with the publisher's permission)

Another more conventional solution is to use a classical grating with a 1D periodicity, but having a deformed profile in order to perform the same shift of the TE maximum [1. [START_REF] Popov | Diffraction-grating based wavelength demultimlexer[END_REF][START_REF] Hoose | Grating device with high diffraction efficiency[END_REF]. This can be achieved by introducing a flat region at the bottom of the grooves and "sharpening" the groove triangle, which needs a sharper apex angle. While this is quite difficult to be made with grating ruling or holographic recording, etching in crystalline silicon naturally produces grooves with 70.5° apex angle, as observed in Fig. 1.3. A flat region on the top is made if the etching is not complete. When covered with gold, such grating can be used from the silicon side, which is transparent at wavelengths around 1.55 µm. Unpolarized Si Au efficiency greater than 80% can be kept over the communication interval of 50-60 nm, as observed in Fig. 1.4.

There is an overlap of diffraction orders.

As stated by the grating equation, if the period is chosen to provide diffraction orders inside a large spectral interval, the second diffracted order has the same direction of propagation as the first one for wavelength of light twice shorter. This problem is avoided in many spectroscopic devices by three different methods: additional spectral filtering of undesired orders; interchange of grating having different spatial frequency (period); adding cross-dispersion grating for echelle applications.

In addition, there is a contradiction between some requirements as, for example, free spectral range (spectrum covered by the grating), dispersion and overlap of orders. In some cases, the only compromise is to use interchangeable gratings in order to cover larger spectral range without order overlap and maintaining higher dispersion. Some spectrographs are designed having multiple channels with splitting of the incident beam between them, however reducing the illumination power in each channel.

Echelle gratings in astronomy

In astronomy, measurements of very low signals coming from far cosmic objects require large periods of time, so that the loss of energy due to low efficiency or/and strong polarization dependence leads to a further growth of costs. When efficiency constraints are added to the independence of the polarization, the only known solution is the echelle grating (high grooveangle triangular groove profile used in grazing incidence, Fig. 1.5) that has the advantages of almost equal and high efficiency in both fundamental polarizations [1.9]. The high efficiency in unpolarized light is obtained when the diffraction is made as if light is reflected by the working facet in its normal direction. Of course, it is necessary that the reflections at consecutive facets are in phase. The problem is that the efficiency varies rapidly with the wavelength, and the maxima switch between consecutive orders (Fig. 1.6). The separation of orders is usually made using another shorter-period grating with grooves perpendicular to the echelle (called cross-dispersion), so that the different orders are separated in direction perpendicular to the echelle dispersion direction. Echelle gratings are also used in transmission, glued to the hypotenuse face of a prism that has a role to deviate back the beam diffracted by the grating, so that the principal diffracted order of the device propagates almost in the same direction as the incident beam for a chosen central wavelength. The device is known as a Carpenter prism or GRISM and gives the possibility to convert an imaging device (camera) into a long slit spectrograph [1.10], commonly used in airborne or space borne scientific missions.

UV excimer lasers used in photolithography at 193.3 nm wavelength can be equipped with an echelle grating for narrowing the spectral line. While in lasers working in the visible and IR, the resonators are equipped with diffraction gratings with symmetrical grooves working in -1 st order than easily can be made holographically or lithographically, a grating working in the lowest order at 193.3 nm must have more than 9 000 gr/mm, very difficult for fabrication and impossible for replication. Echelles take longer to be made and are more expensive as they require mechanical ruling engines with temperature control and clean environment, but have large periods and can be replicated from the ruled masters and submasters to become available at acceptable prices.

Gratings as optical filters

Spectroscopic applications of gratings use one or more diffraction orders that differ from the specular reflected and transmitted ones, because of the required spectral dependence. There exist, however, several applications that use the zero order(s), even with corrugation of the surface or modulation of the refractive index in the grating region. These are devices having refractive or reflection properties in the zeroth order that are modified by the grating surface.

Zero-order diffraction (ZOD) imaging

One of the applications uses the diffraction in higher orders to change the spectral dependency in the zero order, as light that is diffracted in the higher order(s) is absent in the zero order. The structure known as zero-order diffraction (ZOD) microimage [1.11] represents a transmission grating (usually with a rectangular or triangular groove form that can be replicated by relief printing in plastic sheet. Appropriately choosing the groove depth, one obtains broad-band color filters in transmission by using non-absorbing materials without colorants that can bleach. Another type of gratings have periods, smaller than the wavelength in the substrate and the cladding, chosen to avoid the propagation of other that the zero orders. Such structures are known as subwavelength gratings, and they play important role in integrated optical devices and recently in plasmonics to transfer energy from one to another guided mode in dielectric or metallic waveguides, or to change the mode direction, or to focus guided light (see Section 1.5).

Surface/guided mode excitation

A subwavelength grating can serve to couple the incident light to surface or cavity resonances that can exist in the grating structure. The absence of higher orders means only that they are evanescent rather than propagating in the cladding or in the substrate. The horizontal component of their propagation constant (say, k x ) is larger than the wavenumber in the surrounding media, and thus it can excite a surface or waveguide mode that is subjected to the same requirement in order to stay confined to the surface. The grating action is the same as in the coupling between the incident wave and one of the diffraction orders, only that now x, 1 k - is equal to the real part of the mode propagation constant k g :

g x,i Re(k ) k K = - (1.6)
To fail to see the quite small difference between k g and k 0 in the case of surface plasmons on highly conducting metal surfaces is one of the rare failures of Lord Rayleigh [1.12] when trying to explain Wood's anomalies [1.13]. The case when x,m 0 k k = represents a transition of the m-th diffracted order between a propagating and an evanescent type, as follows from eq.(1.3). This transition leads to a redistribution of energy between the propagating orders, observed in efficiency behavior as a phenomenon called cut-off anomaly.

Lord Rayleigh attributed Wood's anomalies to the cut-off of higher orders, whereas the true explanation is that Wood anomaly is due to surface plasmon excitation. It is easy to judge nowadays, but the difference in the spectral and angular positions of the cut-off and surface plasmon anomaly sometimes is smaller than the experimental error, or more important, the error in the knowledge of the grating period. The resonant nature of the surface-plasmon anomaly has much more pronounced features than the cut-off anomaly, a fact first noticed by Fano [1.14] and further developed by Hessel and Oliner [1.15]. The form of the so-called Fano-type anomaly can easily be derived from the interference with a non-resonant contribution (for example, non-resonant reflection by the grating layer) and a resonant effect (for example, excitation by the incident wave of a surface mode that is diffracted back into the direction of the non-resonant wave), as sketched in Fig. 1.7. Here, by mode, we mean a surface or guided wave that represents an eigen (proper) solution of the homogeneous diffraction problem (assuming non-zero diffracted field without incident wave). The latter effect is commonly described in physics as having a Lorentzian character (e.g. electric circuit dipole oscillator). For example, the wavelength dependence of the total reflectivity r will be the sum of the non-resonant and the resonant Lorentzian contributions: k k c r = representing a zero of the reflectivity. The formula implies that for each resonance, there exist an associated zero, that is expressed as a minimum of the anomaly. In reality, the pole has always non-zero imaginary part due to the interaction between the incident and the surface/guided wave. The zero takes, in general, complex values, but there are several important practically cases when the zero could become (and remains) real, i.e., the reflectivity can become zero. The imaginary part of the pole determines the quality factor (width) of the resonant maximum.

The same reasoning applies in transmission (and in any other existing propagating order), with the same pole (same resonance), but different zeros. Depending on the imaginary parts of the pole and the zero, sometimes the resonant anomaly can show itself as a Lorentzian maximum, sometimes as a pure minimum on otherwise highly-reflecting background, sometimes both maximum and minimum can manifest themselves. The important cases when the zeros are almost real are used in surface plasmon absorption detectors and in resonant dielectric grating filters (see the next two subsections).

Surface plasmon absorption detector

Wood anomaly can sometimes lead to a total absorption of light by shallow metallic gratings with groove depth that does not exceed 10% of the wavelength. This phenomenon was called Brewster effect in metallic gratings [1.16] The position of the anomaly depends on the propagation constant of the plasmon surface wave that is quite sensible to the variation of the refractive index of the surrounding dielectric, thus the determination of the position of the anomaly brings information about the composition of the surrounding medium, i.e., serves as an optical detector (Fig. 1.8). Introduction of the second Fourier component of the profile function increases the direct interaction between the plasmon surface waves propagating in opposite directions (the grating vector of the second harmonic is twice longer that of the first one), interaction that increases the sensitivity of the device.

Resonant dielectric filters

There is a particular case when the maximum in the reflectivity due to the resonant waveguide mode excitation stays theoretically at 100% on a low-reflective non-resonant background value. This is the case of corrugated dielectric waveguides having symmetrical grooves. If, in addition, the substrate is identical to the cladding, the zero in reflection remains real whatever the other parameters, i.e. a 100% maximum is accompanied by a 0 value minimum in the reflectivity (Fig. 1.9). This peculiarity was accidentally found in 1983 [1. [START_REF] Mashev | Zero Order Anomaly of Dielectric Coated Grating[END_REF][START_REF] Golubenko | Diffraction Characteristics of Planar Corrugated Waveguides[END_REF] followed by a theoretical explication in 1984 [1.21]. The effect has been independently rediscovered in 1989 by Magnusson [1.22], who has done a lot for its analysis, and quite important practically, for its extension in transmission [1.23]. The advantage of the device is that the quality factor increases with the decrease of the groove depth, i.e. very narrow-line spectral filters can be obtained using shallow gratings, at least theoretically. However, as usual, the advantage is paid back somewhere, namely in the tight angular tolerances: when eq.(1.6) results in high spectral sensibility, it also is responsible for strong angular sensibility. Sentenac and Fehrembach [1.24] proposed to introduce a direct coupling between the waveguide modes propagating in the opposite direction (as was done in Fig. 1.8), but this time aiming to a significant reduction of the angular sensibility of the effect. The idea was based on the flattening of the angular dependence of the guided wave propagation constant on the boundaries of the forbidden gaps, created by the direct mode coupling due to the structure periodicity, one of the basic properties of photonic (and electronic) crystals. These peaks were identified as resulting from surface plasmon excitation on the upper, or the lower surface. Many theoretical and experimental works appeared as a result of this discovery, which revived the interest to surface plasmons and grating structure, leading to a new name of the plasmon studies called now plasmonics.

Enhanced transmission through hole arrays in metallic screens

It seems nowadays that the explanation of the enhanced transmission observed in Fig. 1.11 lies in the common action of two phenomena [1.26]. The first one is the surface plasmon excitation that enhances the electromagnetic field intensity near the entrance apertures, as represented schematically in Fig. 1.10b. The second phenomenon is the tunneling of the mode in the vertical hollow waveguides inside the holes. Although for small holes even the lowest mode is evanescent (contrary to 1D lamellar gratings, where TEM mode exists without cut-off), it gives the possibility of energy transfer from the upper to the lower interface, much more efficiently than the tunneling through the non-perforated screen [1.27].

One unexpected consequence of the observation of Ebbesen et al. came in fluorescence single-molecule microscopy and in the biomembrane studies. Both require small measuring volumes in order to study only a very small number of molecules or a small portion of the membrane surface. However, small measuring volumes mean week signals. Here comes the role of the surface plasmon enhanced field and evanescent mode inside the aperture. When the mode is close to its cut-off, the real part of its propagation constant along the axis of the hole tends to zero, which leads to a compression of the electromagnetic field at the entrance aperture, increasing even more the field density and thus the measured signal. In addition, as the field is evanescent inside the hole, the effective measuring volume does not extend to the entire hole depth (see Fig. 1.12). The small cross-section of the holes reduces further on the measuring volume to much smaller values than permitted by the diffraction limit, in several cases volumes of the order of several attolitres have been reported.

Non-resonant filters

Resonant filtering has its advantages, when narrow spectral bands are aimed, but in some important applications it is necessary to have wider bands, accompanied by angular and polarization invariance with respect to the incident wave. Such are the requirements for color filters used to separate the RGB colors on each pixel of the CCD cameras. A promising example [1.29] contains a small subwavelength grating consisting of circular metallic bumps with different diameters and heighst (Fig. 1.13a) that can filter light in different spectral regions, depending on their geometrical parameters, (Fig. 1.13b).

Flying natural gratings: butterflies, cicadas

The observation of Hopkinson (see Sec.1.1) of the diffraction on a handkerchief is far the less exotic grating that exists. As always, Nature had all the time to surpass humanity. A striking realization has been developed during the million-year long evolution of butterfly wings that

(a) Transmission electron microscope image showing the cross-section through a single Morpho rhetenor scale (after [1.30] with the publisher's permission). (b) Modeled structure; the two red lines define a grating layer, the optical index of white regions is 1 (after [1.31] with the publisher's permission).

Fig.1.16. Spectral dependence of the reflection of the butterfly scale (after [1.31], with the publisher's permission).

Another "application" is used by the cicadas (quite common in the southern Europe, see Fig.

Gratings in Integrated optics and plasmonic devices

Gratings are used in integrated optical devices to deviate the direction of propagation of waveguide modes and surface waves, for their focusing inside or outside the guide, or for energy transfer between different modes. Let us consider the case with one-dimensional periodicity. The grating equation can be applied not only to free-space waves, but to the waveguides modes. If the period is suitably chosen, it is possible to couple one mode to another:

g,1 g,2 Re(k ) Re(k ) K = - (1.9)
where g,1 k and g,2 k are the propagation constants of the modes. It is possible to couple the mode propagating in a given direction to the same but contrapropagative mode. This is the case of the so-called Bragg gratings that act as a distributed mirror forming a forbidden zone for the mode propagation, in which the mode field decreases exponentially without being radiated in the cladding and in the substrate. The result is that it is rejected back into a contra-propagative direction (Fig. 1.18). Due to the limit size of the grating region, a small part of the incident mode 1 is transmitted to the right, thus the reflected mode 2 carries smaller amount of energy. The grating grooves can be made curvilinear in order to focus the mode. The same effect can be obtained by replacing the 1D structure by 2D periodicity having also a period in the transversal y-direction (see Section 1.8).

Beam-splitting applications

The fact that the periodicity creates diffraction orders can be used to create multiple beams from a single laser beam. The most-commonly used device is symmetrical groove transmission gratings used as beam splitters for optical disk readers, where the wavelength of the laser source is constant. As a rule, the zero order beam reads the track and the two first order beams read adjacent tracks to keep the head both centered and focused. By controlling the groove depth, the ratio of zero to first orders transmission can be varied over a factor of 10, and a high degree of symmetry is inherent.

A special type of transmission grating can be used to generate an entire family of orders with a groove shape designed to make their intensities as equal as possible. This gives us multiple beam splitters, which may have 5 or even 20 orders on both sides of zero. A top view of such gratings under working conditions (with a laser input) gives rise to the term of "fanout gratings". Applications are found in scanning reference planes for construction use, optical computing, and others [1. [START_REF] Loewen | Diffraction Gratings and Applications[END_REF][START_REF] Boivin | Multiple imaging using various types of simple phase gratings[END_REF]. Such gratings tend to have large groove spacings (10 to 100 µm) and low depth modulations. The difficulty in making such gratings lies in achieving a groove shape that leads to a sufficient degree of efficiency uniformity among orders, especially if they are to function over a finite wavelength range. Two obvious candidates are cylindrical sections or an approximation of this shape in the form of a wide angle V with several segments of different angles. The choice may vary with the availability of the corresponding diamond tools. They have also been made by holographic methods, which are able to produce the parabolic groove form that gives the best energy uniformity mode amplitude between the diffracted orders [1. [START_REF] Langlois | Phase relief gratings with conic section profile in the production of multiple beams[END_REF][START_REF] Shin | Diffraction of surface relief gratings with conic crosssectional gratings shapes[END_REF]. Applications of fan-out gratings are found in scanning reference planes for construction use, in biophysics for simultaneous treatment of great number of samples, etc.

By combining two such grating at right angles to each other, an accurately defined 2D array of laser beams is generated to be used for calibrating the image field distortion of large precision lenses, in robotic vision systems, or in parallel optical computing. Instead of using two 1D periodical grating, it is possible to use a single large-period 2D crossed grating with specially optimized pattern inside each period [1.36].

Subwavelength gratings for photovoltaic applications

As explained in Sec.1.4, resonant excitation in metallic gratings can lead to a total absorption of incident light, effect necessary for the efficient work of photovoltaic devices. The problem with surface plasmon excitation and the accompanying light absorption is that its wave is not localized, thus it is characterized by a well-determined value of propagation constant along the surface, because non-local effects in the real space are localized in the inverse space. This is why the surface plasmon anomalies have very narrow angular and spectral width, an advantage in detector construction, but failing in photovoltaics. Evidently, effects that are less localized in the inverse space will be more localized in the real space. This leads us to cavity resonances, volume plasmonic excitation, and surface plasmons that propagate in the vertical direction but are localized in x-y direction. Cavity resonances in deep grooves or in closed cavities, like embedded dielectric spheres or cylinders inside a metallic sheet can absorb light within relatively large angular region (20-30 deg) [1. [START_REF] Bonod | Total light absorption in a wide range of incidence by nanostructured metals without plasmons[END_REF][START_REF] Popov | Lamellar metallic grating anomalies[END_REF][START_REF] Popov | Comparison of plasmon surface wave on shallow and deep 1D and 2D gratings[END_REF][START_REF] Popov | Total absorption of unpolarized light by crossed gratings[END_REF]. However, the problem of cavity resonances is that they are strongly wavelengthsensitive. An alternative approach consists of using metamaterial behavior of small-feature structures. By mixing metallic and dielectric materials one can, in general, obtain strongly absorbing alloys with effective refractive index that does not exist for known materials. In addition, the equivalent metamaterial layer has a uniaxial anisotropy with axis perpendicular to the grating plane. Thus inside the xOy plane it has isotropic properties and its response is polarizationally independent, at least close to normal incidence.

For example, a crossed channel grating as presented in Fig. 1.19 and made of silver bumps on a silver substrate. It can strongly absorb the incident light in much larger spectral However, the use of such structures for practical applications requires not only a larger spectrum of strong absorption, but also needs that the absorbed light is not immediately transformed into heat and that it is kept inside the photovoltaic layer that transforms light into electricity. The simple structure represented in Fig. 1.19 is not sufficient to efficiently fulfill these purposes. It has to be complicated by a structuring in the depth of the device (Fig. 1.22). Light is incident from the top of the device. Its entering part (in blue) is designed to act as an antireflector, and absorbs most of the blue part of the spectrum. The green part is absorbed in the middle of the rods, while the back-side part (in red) absorbs the longer wavelengths, and serves as a reflector to prevent the unabsorbed part to be lost in the substrate [1.43].

Photonic crystals

Periodic structures in optics can serve for the photons in the same manner as semiconductor crystals for electrons. This common feature led in the '90s to call such structures photonic crystals. As discovered by Yablonovich [1. [START_REF] Yablonovitch | Inhibited spontaneous emission in solid-state physics and electronics[END_REF][START_REF] Yablonovitch | Photonic crystals[END_REF], they present band-gaps that forbid propagation and thus guaranteeing 100% reflection inside the band. While this property is widely known and largely used in multilayer dielectric mirrors (Fig. 1.23a), the band gap of 1D photonic crystals is limited in relatively smaller angular interval. Some other structures that have 2D periodicity combined with a nanostructuring in the third dimensions can be found in Figs.1.15, 17, and 22. A typical band-gap structure of a 2D photonic crystal presented in Fig. 1.23b, but its surface cut at an angle of 45° with respect to the vertical direction, is given in Fig. 1.24 for a system having period d = 1.414 µm in both directions, and consists of circular cylindrical rods with radius equal to 0.35 µm and optical index of 2.9833 in air as a matrix. The figure presents the values of the smallest imaginary part of k z . As can be seen, a forbidden gap in both TE and TM polarization exists for [1.97, 2.33 m] λ ∈ µ [1. [START_REF] Popov | Almost perfect blazing by photonic crystal rod gratings[END_REF][START_REF] Popov | Differential method applied for photonic crystals[END_REF]. Inside the band gap electromagnetic field intensity diminishes exponentially and the entire incident light is reflected back. However, the choice of the ratio of the wavelength and the period allows for the propagation of the -1 st order in reflection. This gives the possibility to guide the entire incident light into this order, thus perfect blazing in the -1 st diffracted order can be obtained in both polarizations, a property that is strongly desirable in many applications. And indeed, Fig. 1.25 presents the diffraction efficiency of the system having cylinders with radii of 350 nm (a) and 150 nm (b). A well-defined spectral region with almost 100% efficiency in unpolarized light can be observed. The property of totally reflecting the incident light whatever the direction, can be of great importance for light guiding and manipulation. Light confinement and guiding in a single dimension is ensured by using planar waveguides. Channel waveguides and optical fibers confine light in two dimensions, but they suffer from two important limitations: dispersion and bending losses. High bending angles damage the guiding properties and lead to radiation losses. A waveguide constructed with photonic crystal walls can ensure bending, Fig. 1.26, without losses even at 90°, as predicted numerically [1.48].

It is impossible even only to list here the potential applications of photonic crystal devices, as for example negative refraction, perfect lenses construction, photonic crystal fibers, nonlinear optical applications. The main problem that persists is purely technological: while it is relatively easy to fabricate 3D periodically structures working in the microwave and far-IR domain, scaling down to the visible and the near-IR presents a lot of challenges to optical industry. Fortunately, the process of fiber manufacturing enables literally such mechanical scaling of the dimension, transferring the initial large-diameter preform into a thin fiber by pulling it. If the preform is carefully drilled with macroscopic holes, they are preserved in the final fibers, but scaled to nanodimensions.

  the grating period in a unit-vector direction d .

Fig. 1

 1 Fig.1.1. Lamellar grating working in in-plane regime in TM (transverse magnetic) polarization, together with the coordinate system, incident wavevector.

Fig.1. 4 .

 4 Fig.1.4. Spectral dependence of efficiency in -1 st order for the grating shown in Fig.1.3 (after [1.7] , with the publisher's permission).

Fig.1. 5 .

 5 Fig.1.5. Schematical presentation of echelle grating.

metal 1. 6 Gratings:

 6 Theory and Numeric Applications, 2012

Fig.1. 6 .

 6 Fig.1.6. Diffraction efficiency of an echelle made of aluminum with 31.6 grooves/mm and 64° groove angle of the working facet. Incident angle is equal to 64°. The numbers of the diffraction orders are indicated in the figure.

Fig.1. 7 .

 7 Fig.1.[START_REF] Popov | Diffraction-grating based wavelength demultimlexer[END_REF]. Process of interference between the non-resonant and the resonant reflections (second term in eq.(1.7)) that is created due to the excitation of the surface or guided wave through the -1 st grating order, and then radiated into the cladding through the +1 st diffraction order.

  r n.res. and c res. are slowly varying functions of the incident wave parameters. The pole p x k of the resonant term is equal to the surface/guided wave propagation constant. The Fano-type equation is obtained by taking the common denominator in eq.(1.7

Fig.1. 9 .

 9 Fig.1.9. Reflection by a corrugated dielectric waveguide. Symmetrical triangular profile with groove angle equal to 10°. Substrate and cladding have optical index equal to1, the layer has index 2.3 and its thickness is equal to 69 nm. Incident angle is equal to 26.7°. Excitation of TE waveguide mode leads to a narrow spectral anomaly.

In 1998

 1998 Ebbesen et al. [1.25] reported an interesting effect on metallic screen perforated with circular holes (Fig.1.10a). They were surprised to observe peaks with relatively strong transmission in the spectral dependence (Fig.1.11).

Fig. 1 .

 1 Fig.1.10. (a) Schematical representation and notations of a two-dimensional hole array perforated in a metallic screen deposited on a glass substrate and illuminated from above with linearly polarized incident wave. (b) Surface-plasmon assisted energy flow inside the aperture close to the resonance.

Fig.1. 11 .

 11 Fig.1.11. Spectral dependence of the transmission of the structure presented in Fig.1.10a, with d = 0.9 µm, t = 0.2 µm, and hole diameter of 0.2 µm (after [1.25], with the publisher's permission).

  Fig.1.12. Schematic presentation of (a) single-molecule fluorescence backside microscopy field density, and (b) tiny-portion cell membrane microscopy inside a metallic aperture (after [1.28] with the publisher's permission).

Fig. 1 .

 1 Fig.1.13. (a) Nanostucture consisting of coaxial metallic cylinders, with a subwavelength period equal to 300 nm, external diameter 260 nm, and internal diameter 160 nm. (b) Transmission spectrum of the structure for different metals and cylinder heights, as shown in the inset (after [1.29] with the publisher's permission).

  have so attractive coloring. The so called Morpho rhetenor butterflies have a non-pigment metallic blue color (Fig.1.14) that long has been attributed to multilayer reflection. However, Vukusic et al. [1.30] had the idea (and funds) to use an electron microscope to observe deeper in detail the structure of the scales, as reported in Fig.1.15a, a typical 3D structure that resembles a photonic crystal. The modeling with a 2D grating with a structure given in Fig.1.15b confirms the blue-spectrum reflection of the scales (Fig.1.[START_REF] Hutley | Total absorption of light by a diffraction grating[END_REF]).

Fig.1. 14 .

 14 Fig.1.14. Entire view (to the left) and magnification of the scales (to the right) of a Morpho rhetenor butterfly (after [1.30] with the publisher's permission).

  1.17a) to camouflage themselves on the tree branches. Their wings are covered with an anti-reflection nanostructure, first observed by Xie et al. [1.32] and shown in Fig.1.17b.Anyone that has entered the microwave measuring rooms can identify the cones on the walls that are about 1 million times larger, as scaled to the wavelength.

Fig. 1 .

 1 Fig.1.17. (a) A photo of a cicada, and (b) the nanostructure pattern on its wings (after [1.32] with the publisher's permission).

Fig.1. 18 .

 18 Fig.1.18. Upper part: schematical presentation of Bragg relief type lamellar grating deposited on a waveguide (dielectric or plasmonic) with two propagating modes. Lower part: energy carried by each mode.

Fig.1. 19 .

 19 Fig.1.19. Crossed metallic diffraction grating

  with the surface plasmon excitation effects. As can be observed in Fig.1.20, close to a filling ratio (f = c 2 /d 2 ) equal to 0.7, both the real and the imaginary part of the effective refractive index for small-period structure grow significantly to values that no existing material has in this spectral domain. This increases the effective optical thickness of the system, together with its absorption, so that a very thin grating (h < 10 nm) can totally absorbed incident light[1.41]. Because of the 2D periodicity of the structure, it becomes polarization insensible. Moreover, this effect has no resonant nature and is extended angularly to almost the entire set of angles of incidence, as seen in Fig.1.21. In addition, the spectral domain of absorption stronger than 75% extends to a more than 100 nm interval [1.42].

Fig.1. 21 .

 21 Fig.1.21. Reflectivity of the crossed graing in Fig.1.19 as a function of the wavelength and of the sine of the incident angle. Period d = 3 nm, system thickness h = 6.2 nm, filling factor = 0.7, i.e. c/d = 0.837.

Fig. 1 .

 1 Fig.1.22. Grating rods as optimal photovoltaic absorber (after [1.43], with the publisher's permission)

  Fig.1.[START_REF] Sentenac | Angular tolerant resonant grating filters under oblique incidence[END_REF]. Forbidden bands for the photonic crystalmade of circular cylinders with d = 1.414 µm, r = 0.35 µm (after[1.46] with the publisher's permission).

  0

Fig.1. 25 .

 25 Fig.1.25. Diffraction efficiency in order -1 as a function of the wavelength lying inside the band gap. (a) r = 350 nm, (b) r = 150 nm (after [1.46] with the publisher's permission).

  photonic crystal fiber (Fig.1.27), light is preserved in the central hollow guide by repulsion from the surrounding structure that presents a forbidden gap for the working wavelength.

Fig.1. 26 .

 26 Fig.1.26. Light guiding in a cavity formed by photonic crystal walls consisting of cylindrical objects

  and has found an important application in chemical r n.res. r res. -plasmon grating detectors [1.17]. The effect of total light absorption appears in a narrow spectral and angular interval (Fig.1.8).Fig.1.8. Reflectivity of an optical surface plasmon detector as a function of the incident angle. Wavelength equals 850 nm, TM polarization. Cladding is glass, the substrate index for the two curves is indicated in the figure, and the grating layer is made of silver with thickness of 40 nm. The grating profile function contains two Fourier harmonics:

	0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9 1.0 and biochemical surface60 reflected efficiencies 0.8	65	70	k x p	75	80 n=1.33 n=1.34	85	90
				θ i in degrees
						( 35sin 2 x / d 59 sin 4 x / d ) ( π + π	+ π	/ 2	)

with the depths given in nanometers (after

[1.18]

, with the permission of the publisher).

Littrow mount means retrodiffusion, when the diffracted beams propagates in a direction opposite to the incident beam, i.e. sinθ -1 = -sinθ i