Jean-Stéphane Ulmer
email: jeanstephane.ulmer@ensiacet.fr

Jean-Pierre Belaud
email: jeanpierre.belaud@ensiacet.fr

Jean-Marc Le Lann
email: jeanmarc.lelann@ensiacet.fr

Towards a pivotal-based approach for business process alignment

Keywords: user): Alignment, Transformation Business Process Engineering, Metamodeling, Transformation, Alignment. Comment [J2]: IJCIM ref

Towards a pivotal-based approach for Business process alignment

This paper focuses on business process engineering especially on alignment between business analysis and implementation. Through a Business Process Management approach, different transformations interfere with process models in order to make them executable. To keep the consistency of process model from business model to IT model, we propose a pivotal metamodel-centric methodology. It aims at keeping or giving all requisite structural and semantic data needed to perform such transformations without loss of information. Through this we can ensure the alignment between business and IT. This article describes the concept of pivotal metamodel and proposes a methodology using such approach. In addition we present an example and the resulting benefits.

Introduction

Adaptation to an unstable demand, ability to improve efficiency and bringing changes to its value chain are the challenges that companies have to constantly confront. In order to remain competitive, a company must be able to describe and remain reactive to an endogenic or exogenic event. Such flexibility can be obtained by using a process-oriented approach or BPM (Business Process Management). BPM represents the business process engineering of the organization using information technology [START_REF] Malone | Organizing Business Knowledge -The MIT Process Handbook[END_REF], [START_REF] Smith | The Emergence of Business Process Management[END_REF]. It is intended to model, deploy, execute and optimize business processes in an ongoing way. A BPM cycle consists of 3 major steps (Figure 1). The first step is the business process analysis (BPA). During this step, process models including various views (functional, informational, organizational, and resource) are constructed. The second step is intended to deploy and execute business process, the business process implementation (BPI). The third one relies on monitoring processes and analyzing data. It gives scorecards and key performance indicators [START_REF] Alfaro | Business process interoperability and collaborative performance measurement[END_REF]). This step, the Business Activity Monitoring (BAM), is out of the scope for this paper.

The BPM is most often seen and interpreted as a further step and a natural evolution of the workflow management. This could explain the attention given to the functional view and the associated control-flow during the BPA step.

[Figure 1 near here] Figure 1: BPM Cycle [START_REF] Debauche | BPM Business Process Management : pilotage métier de l'entreprise[END_REF] Specialized editors, like ARIS, IBM Telelogic, MEGA, W4 … offer BPMbased services. These BPM tool suites provide some methods that guide the end-user through a BPM cycle. For example, the ARIS editor defines its BPM approach by " ARIS Methodology" which contains 4 phases (BP Strategy, BP Design, BP Implementation and BP Controlling).

This article proposes a methodology 1 which enhances transformations between heterogeneous models, e.g. from analysis models to implementation models and vice versa. This enhancement is obtained thank to a systematic model formalization and the use of a pivotal metamodel. By obtaining this formalization, we allow reverse transformations. The models are synchronized and consistent with each other. This synchronization and this intermodel consistency reduce the gap between business domain and IT domain, which increase the Business-IT alignment.

The following parts of the paper are organized as follows. Section 2 reviews one of the main research areas about heterogeneous model alignment. In Section 3 we highlight the difficulties encountered in not only translating a BPA model to BPI model but also to maintain them structurally or semantically consistent. The use of a 1 We consider a methodology as "a body of methods, rules, and postulates employed by a discipline: a particular procedure or set of procedures" as defined by Merriam-Webster dictionary (http://www.merriam-webster.com/dictionary/methodology). pivotal metamodel-centric approach is justified in Section 4. The Section 5 presents the methodology used to formalize the relationships between models, metamodels and pivotal concepts. Section 6 describes the prototype framework, the standards, technologies and tools used to accomplish this purpose. This framework supports our methodology and reveals how pivotal model and metamodel are used to transform BPA and BPI models. An example illustrating these elements is also detailed in this section. Then the benefits of the approach are discussed in Section 7. Finally conclusions and future outlook are presented in Section 8.

F

Model-Driven Architecture vs. Business Process Management

Several researches areas study on models as a solution for enterprise performance including the Model-Driven Engineering (MDE) [START_REF] Perez | MDE for BPM: A systematic Review[END_REF], [START_REF] Combemale | Ingénierie Dirigée par les Modèles (IDM) --État de l'art[END_REF], and particularly through the Model-Driven Architecture (MDA) approach [START_REF] Kadima | MDA : conception orientée objet guidée par les modèles[END_REF].

MDE aims at generating whole or part of software, based on models and their metamodels, and facilitates the definition of Domain-Specific Modeling Languages (DSMLs). These languages provide a specific formalization to the technical aspects used. MDA focuses on defining Platform Independent Models (PIMs), technicallyindependent from execution platform (J2EE, .Net, PHP…) and enables the automatic generation of a set of Platform Specific Models (PSMs) (Figure 2).

[Figure 2 near here] Figure 2: MDA and BPM, adapted from Model-driven.org 2

We can identify the different components of BPM with those of MDA.

According to (OMG 2003), Computation Independent Models (CIM) are associated The association of CIM and PIM can be identified as the BPA model. PIMs are then "technically enriched" to generate a Platform Specific Model (PSM). The PSM may be related to a system, language, or technology, unlike PIM. This step is critical to the generation of code and therefore the implementation of the target process and it is typically the goal of the BPI's step. So PSM can be identified as an implementation model, the BPI model (Figure 3). However the analogy has some limits [START_REF] Smith | BPM and MDA: Competitors, Alternatives or Complementary[END_REF]. BPM and MDA were not designed to achieve the same objectives. MDA had been designed to help software design and generation while BPM allows process engineering.

Concepts from MDE and the use of MDA provide a multi-domain management with/for models of different abstractions. Nevertheless, MDA is too restricted for the engineering of business process. MDA does not formally describe how business models are defined at a CIM level and how they are associated to PIMs. It becomes necessary to evolve from an MDA-approach to a BPM-approach but concepts from MDE and MDA have to be taken into account.

[Figure 3 near here] Figure 3: MDA and BPM

Problem statement

The main issue encountered in a BPM cycle is the "discontinuity" among business analysis and IT implementation views. For business and IT professionals, the inability to bridge the gap is mainly due to differences in model objectives. The analysis step (BPA) generates informal business process models and mostly interpretable by human beings. This contributes to complicate the implementation step (BPI). The lack of mutual understanding impedes the production of desired results. This is a "Business-IT alignment" problem in the sense that the company is unable to use IT effectively to achieve its business objectives. Several transformations from a BPA model to a BPI model are required. It is necessary to emphasize that models will be modified and implemented processes might evolve. Thereby, synchronization and modelconsistency are imperative.

Another key issue that arises is the use of unique software platforms in integration-based approach which leads to an editor dependency. As processes and theirs models are evolving perpetually, an enterprise might have to change its software platform or adapt to new technologies. Hence the ability to modify modeling tool or integration platform necessitates the use of "loose coupling" between BPA and BPI models. Loose coupling means that these models should remain autonomous to each other and that their environments can be modified although the strong intrinsic interaction between them.

Proposed methodology

We propose a methodology for the business process management integrating concepts from MDE. This methodology allows business analysts to develop conceptual models, generally graphical ones, in accordance with a formalized metamodel. It also guarantees to IT specialist the conversion of a conceptual model to a block-structured one (technical model) in order to ease its implementation on an execution platform.

And from an implementation model, our approach shall fully restore a graphical model, in the spirit of reverse engineering [START_REF] Müller | Reverse Engineering[END_REF]. This synchronization between BPA and BPI models is considered like a necessary condition for model consistency. Our methodology is generic. However specific languages and standards are required for its use.

From bidirectional transformations to the notion of pivot

Consider MM BPA, MM BPI , metamodels and m BPA , m BPI their associated models.

Bidirectional transformations between models help to ensure their maintenance and their consistency. This transformation is a way to algorithmically specify modelconsistency. This transformation can be bijective:

(1)

And we obtain:

(2)

In most of cases, the bijective transformation is too restrictive and is impossible to get if models cardinalities are different [START_REF] Stevens | A Landscape of Bidirectional Model Transformations[END_REF]. But, we consider models that can be heterogeneous and different levels of abstraction. Each model may have information that is not contained in other, in particularly with BPA models and BPI ones. A possible approach is to take one of the models and to modify so it contains all information from other models. The transformation is made subjective without modifying models appearance to the users. Consider τ BPA and τ BPI two transformations and MM Int an intermediary metamodel:

• (3) • (4)
Models and are considered as equivalent if and only if:

(5)

So if we consider that and , we obtain the following relationship:

The bijective transformation can be made subjective, without changing the models appearance perceived by the user, and and remain unchanged.

Our pivotal approach starts with this new equivalence and defines these transformations and as functions of constructive conformity, the built model from these transformations is the pivotal model.

Notion of pivot

The concept of pivot has already been used, designed for example in Database Thus fulfilling the "pivotal approach" commonly used in system interoperability [START_REF] Meinadier | Le métier d'intégration de systèmes[END_REF], we consider that a pivotal metamodel eases transformations between models and a pivotal model is necessary to reduce issues of syntaxical heterogeneity issues. The pivot's role is to maintain a semantic equivalence between BPA and BPI models. For our approach, we are expanding its scope by adding the following:

• Since information gaps exist for implementing BPA models and for analyzing BPI model , a pivotal metamodel must be able to strengthen them by adding necessary information, to preserve the information integrity and its consistency during the BPA-BPI transition (and vice versa). • It must also allow autonomy between the target model and the initial model (e.g. be able to modify the BPA model without taking in consideration the BPI one) in order to have a loose-coupling between BPA and BPI models. • This intermediate format (the model from the pivotal metamodel) becomes necessary to store and exchange information between the modeling and integration environments (Figure 4). Each metamodel focuses on different aspects of the same process, hence considering their relationships allow for a more in-depth comprehension of the process model [START_REF] Saidani | Towards Situational Business Process Meta-Modelling[END_REF]. In our case the relationships are established by the pivotal element.

These relationships between these two metamodels are determined according to the business domain. This involves the consideration of structural and semantic features of modeled processes. However during a BPM approach, BPA and BPI metamodels are not always explicit and formalized. Thus transformation rules between BPA and BPI models are not really flexible. According to our approach, the specification of the metamodels relies on the pivotal metamodel. In this way we systematically provide formalized metamodels and ease mappings between them.

[Figure 4 near here] Figure 4: BPA, BPI and Pivotal metamodels

In a classic BPM-approach context, an enterprise has two main actors:

business analyst and IT expert. According to [START_REF] Various | A Guide to the Business Analysis Body of Knowledge (BABOK guide)[END_REF] a business analyst seeks new ways to improve business efficiency. This improvement can be done by increasing coordination between working teams changing tools or processes. The IT expert then addresses these business requirements and converts them into IT requirements. Due to the several issues as discussed before (section 3), a third role is needed, the role of a process architect (figure 5).

[Figure 5 near here] with their default values used by the output model (here m BPI ). Then these data are manipulated by the correct actor (here the IT expert). During the second transformation, the pivotal model is able to store data specific to the input model and to restitute data stored at the previous transformation. We obtain a complete output model without any data loss.

[Figure 6 near here] Figure 6: BPA to BPI with our pivot

Genericity concept

Adaptability to all types of models, standard or specific languages, would make our pivotal metamodel complex, difficult to implement and to maintain, and in most cases infeasible to resolve. In order to reach a complete genericity, our pivot will become a "monster". We must seek a compromise between absolute genericity and agility. In our case, the approach is restricted to "relative genericity", i.e., our pivot is relative to:

• a business domain (banking, physico-chemical process...),

• a context of study and • a desired level of abstraction.

Nevertheless, the overall methodology to build our pivot is generic and independent of business domain and selected technologies.

Scope of our methodology

The enterprise modeling consists of several views showed in figure 7: functional view, informational view, organizational view and resource view [START_REF] Vernadat | Enterprise Modeling and Integration: Principles and Applications[END_REF].

Thus our methodology focuses on the functional view and especially on the concept of activity/process as shown in [START_REF] Vernadat | Techniques de Modélisation en Entreprise: Applications aux Processus Opérationnels[END_REF]).

[Figure 7 near here] The concepts inherent to the other views may intervene, depending on modeling languages used or on the process architect modeling requirements. The pivotal metamodel can be given elements from other views than the functional one and that are considered necessary by the process architect. For example, a standard language such as BPMN focuses on the functional view but also allows:

• To model input/output documents/data (informational view);

• To define actions involved in products/information networks (resource view).

In the same way, our current pivotal metamodel contains the swimlane elements pool and lane, related to the organizational view, in order to describe the actor's roles performing the modeled process.

Methodology

In this section, we formally describe how our methodology can guarantee consistency links between its different elements. Then the various steps constituting our framework are defined. A partially implemented case study on the proposed framework is discussed at the end of this section.

Consistency between model, metamodel and pivotal metamodel

We formally define a BPA metamodel, , by two elements. The first element is constituted by a representation standard or language, MM rep , which is generally a business user-friendly graphical language. The second element is a set of business rules setting a business repository, RefMet. This repository can be obtained by using constraints or business rules as OCL (Object Constraint Language) or SBVR (Semantic Business Vocabulary and Business Rules).

The MM BPA is specified as follows (µ):

In a same way, the BPA model, m BPA has to conform to ( χ ) MM rep and RefMet (Figure 8). Thus we obtain the following relation:

We can explain by analogy the different links existing between m BPI and

MM
In a general way, with i for BPA or BPI:

(11)

We obtain a link between BPA and BPI and their respective models m BPA and m BPI , which can be considered as "equivalent" (Figure 8). However, if we have , we should keep in mind that ≠ .

[Figure 8 near here] Figure 8: Relationships between models, metamodels and pivotal metamodel

Pivotal Metamodel and Semantic equivalences

The functions of conformity allow producing a pivotal model equivalent to a BPA model ( 4) or a BPI one (5). In this article we focus particularly on the conformity of the elements modeled in the control flow.

Elements of the pivotal metamodel

In this section, we define the elements used in the different metamodels.

As a first step, our study is restricted to use only 17 objects (Table 1) at the stage of modeling. This reduces the expressiveness of the language by limiting the number of elements [START_REF] Ulmer | Analyse de l'expressivité des langages de modélisation de processus par les patterns[END_REF], in order to reduce the scope of our study and to ensure a model transformation from one kind of language (like a graphical one) to another one (like implementation language) unambiguously.

[table 1 We extend this definition to our study, in which a BPI tool can import and understand a BPA model and in the same way a BPA tool a BPI model. Each of these models must stay in accordance with our pivotal metamodel. We notice that even if the item "pool" is present, this approach does not take in consideration, for now, the choreography of collaborative processes. In the same way, in order to ease metamodel transformations and manipulations, we limited our diagram hierarchy to three levels:

Process -Subprocess -Activity.

Our metamodel, inspired by the XPDL specification (WfMC 2008) and [START_REF] Morley | Processus métiers et S.I. -Evaluation, modélisation[END_REF]) is activity-centric and is expressive-enough to represent most of business processes (Figure 9).

Semantic equivalences

To identify the semantic relationships between the elements of two models, we will handle the definitions of semantic equivalences of (Rizopoulos and Mçbrien 2005) :

• Thanks to these relationships we can identify the semantic links between our pivotal metamodel and the BPA and BPI metamodels.

[Figure 9 near here] Figure 9: Pivotal metamodel

Methodology implementation

The previous section proposed a model compliance methodology by analyzing its elements. After formally defining our approach, we now apply it on a triplet {analysis environment, pivot environment, implementation environment}.

A "prototype software" framework is being developed that instantiated the methodology. It is based on the Eclipse platform, especially on EMF (Eclipse Modeling Framework). The metamodeling part is realized by using Ecore tools. If the mapping between metamodels is determined by the process architect, it is assisted by the Kermeta (Kernel Metamodeling) language [START_REF] Muller | Weaving Executability into Object-Oriented Meta-Languages[END_REF]. After a detailed presentation of the framework development, the section 6.2 presents a short demonstration of the software framework.

Framework development

Developed by the Triskell team, the Kermeta language is an extension of the EMOF (Essential Meta-Object Facilities) language. Languages like EMOF or Eclipse can only model structures with concepts like classes, attributes, associations. Kermeta enables the possibility to describe the semantic and the behavior of these structures helped with its imperative action language. Kermeta also allows the writing of model transformation and model constraints. Business rules will be written according to the SBVR standard (Semantic Business Vocabulary and Business Rules).

Figure 12 illustrates the passage from a BPA diagram to an implementation model and its code (transformations t1-t2-t3-t4), and vice versa (transformations t4-t5-t6-t1). In order to realize these transformations, we must first do mapping between MM BPA , MM BPI and MM Pivot (m1, m2, m3, m4).

From BPA to Pivot

To illustrate our approach, we describe the transformation from an organizational model m BPA to the pivotal model m pivot . Foremost the respective metamodels are constituted. Elements of our metamodel shown in figure 9 are identified with those of XPDL standard. Thus we obtain our pivotal MM rep , an altered form of the XPDL process definition metamodel. As we wish to highlight efforts to perform the mappings and transformations, we consider in this paper the metamodel shown in figure 10 in Ecore diagram format as our BPA MM rep , SimpleCompany. The company model used is a generic one, in order to ease its representation and The next step in our approach is to realize the mapping (m1) between the two metamodels. We decide to use Kermeta as an aspects-weaver adapted to Ecore metamodels which is able to manipulate them without modification [START_REF] Mosser | Réflexions autour de la construction dirigée par les modèles d'un atelier de composition d'orchestrations[END_REF]. Hence, defining a transformation using Kermeta is equivalent to implementing one (or more) visitor(s), within the meaning of Visitor design pattern [START_REF] Gamma | Design Patterns -Catalogue de modèles de conception réutilisables[END_REF]. The visitor design pattern is applied as follows (figure 13): each element to be visited has an accept() method (a) that takes " visitorEntreprise" as an argument. The accept() method calls back the visitElementName() with the visited element as argument (b). Thus, a visitor may be aware the reference of the element and calls its methods. Using this pattern is particularly advantageous as it facilitates the addition of new operations that may be required during transformations. Indeed, a new operation on a metamodel is translated by adding a new visitor. Conversely, the addition of new elements is difficult: for each element a new operation in the visitor has to be made. Nevertheless, if a certain level of maturity is reached by the process architect, we assume that within our approach, we more often modify/add/remove operations performed on metamodels than change these metamodels.

[Figure 12 near here] Figure 12: Implementation of the approach [Figure 13 near here] Figure 13 [Figure 14 near here] Figure 14: Extract from the "enterprise to pivot" transformation code

The transformation t2 of m BPA is shown in figure 15. Therefore at the current state of our framework prototype development, we succeed to execute the mappings m1 and m2, and the transformations t1, t2 and t6.

[Figure 15 near here] Figure 15: Extract from the m Pivot (in .xmi)

Unlike an usual analysis-implementation transformation [START_REF] Grangel | Transformation of decision models into UML: application to GRAI grids[END_REF]), the pivotal model obtained, m Pivot , contains all data belonging to the analysis model m BPA . It also contains elements necessary to establish complete and comprehensive implementation model m BPI . Future works will demonstrate how modifications from a m BPI to a m BPA , or vice versa, are propagated. Integrity of information being provided and modifications being propagated during transformations, our approach enables synchronization and a semantic equivalence between models. We consider that these conditions improve the alignment between business and IT domains.

Pivotal-based approach's benefits

Architecture and business modeling software use several operations to transform a BPA model to a BPI one and vice versa. These tools and their underlying metamodels to other editors. Furthermore consistency, inter-model compliance and alignment between models and metamodels are difficult to ensure.

For example ARIS contains various techniques for business process modeling.

Every aspect of the modeled process is described by a metamodel. However, there is not any global metamodel ensuring consistency and a good visibility between these metamodels [START_REF] Leist | Evaluation of Current Architecture Frameworks[END_REF]. In the "good BPM architecture" proposed by [START_REF] Havey | Essential Business Process Modeling[END_REF], there is no feedback to the analysis models studied before.

Several issues arise if these models are neither enhanced nor updated:

• models become 'contemplative",

• their relative documentation is difficult to use,

• and this result in a lag between BPI models and business process executed.

In order to resolve these issues, we explained the importance of a rigorous and semantic centered methodology. Our proposal for a pivotal approach guaranties a loose coupling between BPA and BPI, and consistency between models and metamodels. The methodology remains generic because of its language independency. It may use enterprise-specific or standard languages. Then we apply conformity and semantic equivalence rules to confirm intermodel consistency and bidirectional transformation.

However, using a pivotal metamodel complicates the transformation rules definition. We have to consider transformation problems between BPA, BPI and pivotal metamodels and not only between BPA and BPI ones. But as result of this approach, we ease transformations between models and obtain a better consistency between them, as explained in section 4.

By providing a true "communication" between analysis and IT models, this approach increases the business/IT alignment. Besides we get semantically strong models, independent to modeling and integrating environments. Furthermore, we

Conclusion and outlook

During a process-lifecycle, consistency is difficult to maintain between models from different environments. The successive developments and changes made by different stakeholders lead to the development of inconsistencies between models. A discontinuity between business perspective and IT perspective appears.

In this article we have proposed a semantic oriented solution based on the concept of a pivotal metamodel, an essential element of our approach in business process engineering. Then we have defined how to formally establish relations of conformity between models and their metamodels as well as rules of semantic conformities between elements. The establishment of this pivot creates a loose coupling between process analysis and process integration.

Our generic approach was partially illustrated using the proposed framework through a simple example. Future research will allow us to validate and refine this approach. From these generic concepts, the prototype will therefore ensure the portability and validity of the analysis model, models "interoperability" and models consistency. Another possible perspective of our work is to consider our approach in a Service-Oriented Architecture context. Therefore, the pivot's role would be to divide the BPA model according to defined patterns associated with web-services. The relevance of such an approach is under study. In the near future an industrial process from a SME will be studied in accordance with our approach, the target integration platform being an ERP software.

Figure 5 :

 5 Roles, data and environments Concretely the role of a process architect is to determine what data from the BPA model are used into the associated BPI model (a) (e.g. control-flow data). The process architect must be able to provide the necessary information in order to complete the BPI model (b) (e.g. details on roles and methods). Finally, he guarantees the preservation of the information model integrity from a BPA model to the resulting BPI one (c) (e.g. graphical information, unspecific or irrelevant annotation...). The reverse operation (a BPI model to a BPA model) is achieved in a similar way and requires a similar involvement of the process architect. Indeed a process architect is responsible of the technical strategy of the organization; who must keep a global and complete vision of the BPM methodology. The figure 6 shows how the pivotal step provides an additional file containing information-type (b) through a BPM cycle. During the first transformation, the m Pivot stores specific data form the input model (here m BPA ). The m Pivot also provides data

Figure 7 :

 7 Methodology coverage and enterprise-model spaces (from[START_REF] Touzi | Aide à la Conception de Système d'Information Collaboratif Support de l'Intéropérabilité des Entreprises[END_REF]

  Equivalence: the concepts of models A and B are equivalent, A S = B, • Subsumption : A is a subsumption of B, B S ⊂ A, • Intersection: the concepts of A intersect the B ones, A S ∩ B, • Disjunction: A and B are disjointed if and only if A S ∩ / B.

  instantiated model m BPA is partially shown in figure 11. We do not consider, in this example, the business rules and the graphical aspects.[Figure10near here] Figure 10: Studied metamodel, SimpleCompany [Figure 11 near here] Figure 11: Extract from the SimpleCompany instantiated model

  : Extract from the enterprise visitor code (in Kermeta language) can use and manipulate concepts of the BPA metamodel under consideration (figure14) and realize the mapping m1 from the Enterprise_Simple to the MM Pivot (c) as the transformation t2 from an Enterprise_Simple model to a m Pivot (d) (Builder/linker method).

(

  when they exist) are usually opaque and slightly open. Thus the result is frequently a unilateral change where the process model cannot be converted to other languages or

  of implementation files among different implementation engines (m BPI1 m Pivot m BPI2 ).

  Figure 1.

  Figure 2.

  Figure 3.

  Figure 4.

  Figure 6.

  Figure 7.

  Figure 9.

  Figure 10.

  Figure 12.

  Figure 13.

  with system requirements and / or a business domain. A CIM describes the environment, business processes and other specific requirements of the system. It supports the definition of business rules and vocabulary and represents the organizational aspect of the system. So a CIM can be associated with a business model obtained during the BPA step. But this business model remains incomplete without the control-flow description of business processes. This information can be provided by Platform Independent Models (PIM). According to[START_REF] Panetto | Towards a classification framework for interoperability of enterprise applications[END_REF]) PIM represents business functionalities and the system behavior without worrying about technical details. The PIM is a conceptual model independent of any considerations related to the target platform, its language or used technologies. It captures the logical aspect of the business process and respects rules set by the CIM.

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  BPI using their own MM rep and RefMet. The relations of compliance between

	model and meta-model being established, we can specify the rules of transformations
	allowing converting a model	or	to a pivotal model m

Pivot . To ensure the consistency of models used in these transformations, we define functions of constructive conformity

[START_REF] Favre | L'ingénierie dirigée par les modèles : au-delà du MDA[END_REF]

fc BPA et fc BPI respectively defined from MM BPA and MM BPI to MM Pivot . Let us consider that m BPA belongs to the space of models conforming to MM BPA as for m BPI and MM BPI : • ; • We obtain the following: s ≡

Table 1 .

 1

	ecore

URL: http://mc.manuscriptcentral.com/tandf/tcim Email:ijcim@bath.ac.ukInternational Journal of Computer Integrated Manufacturing

RNTL FAROS project (a composition environment for reliable service-oriented architectures) : http://www.lifl.fr/faros


Johan Boullet

David Sabourdy

Agnès Desfarges-Berthelemot

Vincent Kermène

Dominique Pagnoux

Philippe Roy

Bernard Dussardier

Wilfried Blanc

Coherent combining in an Yb doped double core fiber laser

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Thanks to their compactness, good heat dissipation, high conversion efficiency, and high beam quality, fiber lasers are very attractive sources especially for free space communications, range finding, or manufacturing applications. However, to ensure fundamental mode laser emission, the transverse dimension of the fiber core is limited to a few micrometers, involving high spatio temporal confinement of the signal wave. The consequence is that, due to the non linear effects, the spatial and spectral qualities of the laser beam may be dramatically damaged. To increase the non linear effect threshold, several solutions have already been experimented: Large Mode Area (LMA) fiber lasers [START_REF] Jeong | Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power[END_REF][START_REF] Limpert | High power air-clad large-mode-area photonic crystal fiber laser[END_REF][START_REF] Glas | Cladding-pumped large mode area Nd-doped holey fiber laser[END_REF], taper performing modal filtering [START_REF] Alvarez-Chavez | Mode selection in high power cladding pumped fiber lasers with tapered section[END_REF], beam clean up by wave mixing in non linear materials [START_REF] Lombard | Diffraction limited polarized emission from a multimode Yb-doped fiber amplifier after nonlinear beam cleanup[END_REF]. An other attractive way consists in designing clad pumped multicore fiber lasers [START_REF] Wrage | Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide[END_REF][START_REF] Cheo | Recent advances in high power and high energy multicore fiber laser[END_REF]. Because of a large overlap between doped cores and pump radiation, high pump absorption is achieved with these fiber lasers. Moreover, the distribution of the power density in several cores leads to a significant reduction of non linear effects. Up to now, in this kind of composite structures, the emission occurs on a supermode with a large M compared to the fundamental Gaussian beam.

Recently, we have developed a very efficient combining method of single mode fiber lasers using a multi-arm resonator [START_REF] Sabourdy | Power scaling of fiber laser with all fiber interferometric cavity[END_REF]. Several groups have studied this configuration for different operating regimes and for a large number of arms [START_REF] Sabourdy | Power scaling of fiber laser with all fiber interferometric cavity[END_REF][START_REF] Sabourdy | Efficient coherent combining of widely tunable fiber laser[END_REF][START_REF] Sabourdy | coherent combining of Q-switched fibre laser[END_REF][START_REF] Shirakawa | coherent addition of fiber lasers by use of a fiber coupler[END_REF][START_REF] Simpson | Extraction characteristics of a dual fiber compound cavity[END_REF]. In this paper, we propose an evolution of this method to realize an original fiber laser architecture, based on a clad pumped fiber with two Yb doped cores. The targeted goal is to combine the radiations from the two cores into the fundamental gaussian mode at the fiber laser output.

Power combining principle

The principle of the coherent combining method is based on laser self organization properties ensuring emission of modes of lowest loss, and on the use of an interferometric resonator configuration [START_REF] Sabourdy | Efficient coherent combining of widely tunable fiber laser[END_REF]. To coherently combine two independent fiber lasers, we spliced two fiber amplifiers, each one ended by a high reflectivity mirror, to the input arms of a 2X2 3dB fiber coupler for building a Michelson interferometer. One output end of the coupler is perpendicularly cleaved for providing the light feedback (4% Fresnel reflection), whereas the opposite one is angle cleaved to prevent any feedback. The coherent coupling of the fields propagating into the two amplifier arms is performed by the coupler: only the frequencies leading to constructive interferences on the shared arm can oscillate. In other words, the reflectivity transfer function of such a passive interferometer can be written: R()=sin 2 (.L/c) where is the pulsation of the optical wave, c is the light velocity, and L the difference in effective length between the two arms of the interferometer. Assuming an equal gain on each arm, the interferometer acts as a spectral filter which period is =c/(2.L) and the gain profile provided by the set up is modulated by R(), with a maximum modulation depth. Owing to the self organisation property of the laser, only the longitudinal modes with minimum loss in the shared arm can oscillate in the cavity. We have shown [START_REF] Sabourdy | Efficient coherent combining of widely tunable fiber laser[END_REF] that this kind of laser based on an interferometric configuration, allowed to obtain a 3dB gain in power with regard to a single arm fiber laser. This high combining efficiency is obtained provided that the two beams interfering onto the coupler have the same polarization state. This is the reason why a polarization controller (PC) is set in one arm of the interferometer. Moreover, since an optical path difference This combining method still operates with two amplifying guides embedded into the same component. Fig. 1 shows a double core fiber for which coupling is locally ensured by a few millimetre long fused biconical coupler, located near one end of the fiber. At this end, a differential feedback is applied to the two cores, whereas a high reflectivity mirror reflects light towards both cores at the opposite end.

Efficient power combining may be achieved by controlling the polarization state within the laser, thanks to the use of a two core birefringent fiber. In these conditions, the laser oscillates on the two polarization eigenmodes, and the compactness of the structure is preserved. For a laser bandwidth B, the propagation constant difference between the modes of the two cores must verify the following relation:

B L 2 0 2 0 0 >
for providing a large enough optical path difference between the two arms of the interferometer. 0 is the average propagation constant of the fundamental mode in both cores. L 0 represents the average optical length of the resonator arms.

In our experiment (Yb amplifying media) where B ~ 20 nm, 0 ~ 1075 nm, L 0 ~ 7 m, the minimal propagation constant difference is 4.10 6 .0. The very low required discrepancy is simply obtained thanks to the unavoidable slight differences between the optogeometrical characteristics of the two cores induced along the manufacturing process. Then, it is not necessary to draw a fiber with specific different cores.

Experiments and results:

We have designed and manufactured a fiber with two parallel Yb doped cores which axes are spaced by a distance d=20m sufficient to prevent any coupling between the two cores. The arrangement of the two cores in the fiber is shown in the inset of fig. 1. Both cores are similar and elliptical, their major and minor axes being respectively a=5m and b=3.7m; their numerical aperture is 0.13. The fiber was coated with a low refractive index polymer providing an inner cladding numerical aperture of about 0.4 with a diameter of 70 m.

The experimental setup is shown on the figure 1. A10 mm long coupler was performed near one end of the two core fiber to achieve a power exchange of about 50% at 1075 nm. The fiber end near the coupler was cleaved with an angle of about 15°, in order to prevent any Fresnel reflection. The laser was closed by a 5% output mirror M 2 that can be oriented to perform a selective feedback towards only one core of the fiber (core 1 on Fig. 1). At the opposite end, the 5.3m long Yb doped double core fiber was end pumped through a dichroïc mirror M 1 set in contact with the end of the fiber (Tmax@980nm; Rmax@1064nm) for achieving light feedback towards both cores.

With identical light feedback at the laser output, two beams of equal power were emitted (Fig. 2a). When mirror M 2 performed a differential feedback, a large part of the beam power was transferred from the core with no feedback to the other one (Fig. 2b and2c). At the same time, we have verified that two beams of equal power level were emitted at the opposite end of the two core fiber through M 1 . The performances of the two core fiber laser in terms of energy are reported on figure 3: 96% of the total output power is emitted from the core where the feedback is performed with a slope efficiency higher than 70% (core 1 in the configuration of the fig. 1) . Only 4% is measured at the output of the other core (core 2). These results show that efficient coherent combining is achieved at the laser output. As expected, we have observed stable output power emission despite the interferometric behaviour of the device because the modulation period is lower than the laser bandwidth.

As in previously published experiments [START_REF] Sabourdy | Power scaling of fiber laser with all fiber interferometric cavity[END_REF][START_REF] Sabourdy | Coherent combining of two Nd:YAG lasers in a Vernier-Michelson-type cavity[END_REF], the interferometric architecture of the two core fiber laser leads to a spectral modulation of the combined output beam so that the modulation depth is 1 (Fig. 4). We observed such a spectral behaviour with the two core fiber configuration. Recorded spectra of Fig. 4 exhibit a modulation period close to 0.51 nm corresponding to L/L 0 ~ 0.22 .10 -3 and / 0 ~ 4.10 -4 . Fig. 4a shows that the spectra of the radiations simultaneously emitted by cores 1 and 2 exhibit identical modulations when the power combining is achieved. By switching the feedback from one core to the other, the emitted spectrum is shifted by a half period (Fig. 4b) due to the Michelson geometry of the resonator.

When power combining was performed with two distinct fiber lasers [START_REF] Sabourdy | Efficient coherent combining of widely tunable fiber laser[END_REF], a random shift of the spectral modulation inside the laser bandwidth was observed due to fluctuations of the optical path difference L between the two arms of the active interferometer, induced by environmental perturbations. In the two core fiber laser, both guides suffer nearly the same external perturbations, as they are embedded in the same cladding and the position of the spectral modulation remains stable.

In a previously published work [START_REF] Sabourdy | Coherent combining of two Nd:YAG lasers in a Vernier-Michelson-type cavity[END_REF], we have shown that the use of polarization dependent coupler for realizing the coherent combining of light makes any active control of the polarization unnecessary. The beam splitter used to coherently combine two Nd:YAG bulk lasers allowed only linearly polarized modes to oscillate in a 3-mirror cavity. In the two core fiber laser, the two elliptical cores are birefringent with a beat length close to 20 mm. Moreover, we have experimentally verified that the coupling ratio of the coupler was significantly polarization dependent. Then, as in [START_REF] Sabourdy | Coherent combining of two Nd:YAG lasers in a Vernier-Michelson-type cavity[END_REF], only eigenmodes with lowest loss can oscillate in the cavity and efficient power combining is achieved without any additional control of the polarization.

Conclusion:

We have experimentally demonstrated coherent combining in an Yb doped double core fiber laser. Up to 96% of the total output power is combined into the fundamental mode of one of the two cores, with a slope efficiency higher than 70%. This high efficiency could be still improved by orienting the main axis of the two cores in the same direction [START_REF] Abebe | Reproducible fabrication method for polarization preserving single mode fiber coupler[END_REF]. This efficient power combining is confirmed by the expected modulated spectrum of the emitted radiation. In such a configuration, the power is distributed over in a large area that significantly increases the nonlinear threshold, as well as it decreases the pump absorption length.

. In order to extend this combining method for obtaining higher power emission, fibers with larger cores and lower numerical aperture should be used. Moreover, as the method was already applied to efficiently couple 8 distinct lasers [START_REF] Shirakawa | Power summation and bandwidth narrowing in coherently coupled fiber-laser array[END_REF], it should be extended to a fiber with a large number of active cores. High efficiency coherent combining should be obtained in this case provided that the two following conditions are fulfilled: on the one hand, the distance between neighbouring cores should be sufficient for forbidding any light exchange upstream and downstream the coupler and on the other hand a minimum difference should exist between the propagation constants in each core. In these conditions, high power single mode emission should be achieved with such a multicore fiber. 3. Output power versus absorbed pump power.

4. Output spectrum from: a) core 1 and 2 when coherent combining is performed on core 1, b) core 1 when coherent combining is performed on core 1, and core 2 when coherent combining is performed on core 2.

  central wavelength, B: laser bandwidth), the laser undergoes no power fluctuations despite the interferometric configuration.

Figure captions 1 .

 1 Figure captions

Figure Figure 1 :

 1 Figure

Figure 2 .

 2 Figure 2.

Figure 3

 3 Figure 3.

Figure 4

 4 Figure 4.


Preparation and characterization of highly thulium-and alumina-doped optical fibers for single-frequency fiber lasers

Keywords: thulium-doped fibers, thulium-doped fiber lasers, single-frequency master oscillators

Thulium-doped fibers suitable for core-pumped single-frequency lasers were fabricated by the modified chemical vapor deposition (MCVD) method. Refractive index profile, doping profile and spectral absorption was measured. High doping concentration of thulium ions should be achieved to allow for high absorption of light at a pump wavelength while the thulium ions clustering should be avoided to prevent the cooperative upconversion and quenching processes. The fabricated fibers featured pump absorption up to 70dB/m at a pump wavelength of 1611nm. The single-frequency master oscillator with a resonator composed of a pair of fiber Bragg gratings and a thuliumdoped fiber was demonstrated with predominantly single ended operation. We achieved a slope efficiency of 22% and a threshold of 22mW at a lasing wavelength of 1944nm.

INTRODUCTION

Thulium ions have the widest emission cross-section of any rare-earth ions allowing for operation of continuous and pulse thulium-doped fiber lasers in a wavelength range of 1720-2180nm.1 Numerous applications like remote sensing, material processing, optical coherence tomography can be foreseen.2 While double-clad thulium-doped fibers pumped by multimode high power laser diodes at a wavelength of 793nm are suitable for high power thulium-doped fiber amplifiers, for stable, single-frequency master oscillators, core-pumped fibers with a high concentration of thulium ions are preferable to keep the laser resonator as short as possible to support one mode only. Clustering of the thulium ions should be avoided to prevent the cooperative upconversion and quenching processes.

A single-frequency distributed-feedback thulium-doped silica fiber laser emitting at a wavelength of 1735 nm was demonstrated by Agger et al. [START_REF] Agger | Single-frequency thulium-doped distributedfeedbackfiber laser[END_REF] The laser was pumped from the Ti:sapphire laser at 793 nm and its efficiency was limited by working wavelength to 0.2%. A single-frequency master oscillator (SFMO) made of germanate glass fiber pumped by single-mode laser diode at 805 nm was reported which had a pump threshold of 30 mW, and a slope efficiency of 35%.4 SFMO made of a short piece of a double-clad fiber made of multicomponent glass was demonstrated by Geng et al. [START_REF] Geng | Single-frequency narrowlinewidth tm-doped fiber laser using silicate glass fiber[END_REF] The multimode pumping together with a short fiber length and a pump wavelength far away from the absorption peak of thulium ions lead to a low slope and a high threshold of this laser. The laser had excellent spectral characteristic with a laser linewidth of 3 kHz.

We present results of preparation and characterization of special silica fibers designed for single frequency master oscillators. The fibers were fabricated by the modified chemical vapor deposition (MCVD) method6 with a thulium concentration in a range 600-2000ppm, a numerical aperture (NA) of 0.15-0.21, and a core diameter of 8-12um. The refractive index profile, doping profile and spectral attenuation were measured for the fabricated samples. The fibers featured the pump absorption up to 70dB/m at a wavelength of 1611nm. The single-frequency master oscillator with a resonator composed of a pair of fiber Bragg gratings and the thulium-doped fiber was demonstrated with predominantly single-ended operation. The active fiber was core-pumped at 1611nm. We achieved a slope efficiency of 22% and a threshold of 22mW at a lasing wavelength of 1944nm.

FIBER DESIGN, FABRICATION AND CHARACTERIZATION

We fabricated fibers heavily doped by Tm3+ ions. The preforms were prepared by MCVD method. The process started with deposition of porous silica soot layer maintaining suitable deposition temperature inside high quality waveguide silica tube using a standard MCVD setup (Special Gas Controls, GB). Dopant ions namely Al and Tm were introduced in the core-glass matrix employing conventional solution doping technique, where ethanolic solution containing chloride salts of dopant ions (i.e. AlCl3 and TmCl3) was used and soaked for a span of 1 hour. The soaked soot layer was then oxidised, sintered and collapsed to obtain the final perform from which UV-curable acrylated polymer coated fibers of diameter 125±0.5 m were drawn at a fiber drawing tower. A good solubility of the thulium ions in a glass matrix was achieved by strong doping of the core region with aluminum oxide. The concentration of Al2O3 in the preform core is typically 6-8 mol %.

The geometry of the preforms and fibers is summarized in Table 1. The fibers could principally support a few modes at 2000 nm band. No signs of higher order modes was observed when the input end was carefully spliced with the SMF28 fiber and the fiber was cleaved at the distant end to visualize the far field with a pyroelectric camera (Pyrocam III) at a wavelength of 1945nm. In the laser experiment, the higher order modes do not have sufficient gain to get above the lasing threshold. The mode field diameter (MFD) was estimated based on the divergence measurement using the pyroelectric camera and a linear stage. The 4-beam diameter were measured in several slices along the beam path and the MFD was acquired based on the formula

(1)
where is the full divergence angle measured in radians. The MFD measurement method was verified with the SMF28 fiber at 1550 nm, where we measured MFD 10.8 m that is within the uncertainty limits specified by Corning (10.4±0.8 m).

The spectral absorption of the fibers is shown in Figure 1. Since the fibers are intended to be pumped in-band, using an L-band communication laser and amplifier, we are interested in the absorption peak above the 1600nm. The position of the absorption peak maximum of the fiber SG1155 is 1657.3nm. All other fibers have narrower absorption peaks with maxima shifted to longer wavelengths then that of SG1155. This indicates lower disorder in the glass matrix. Some characteristics of the absorption peak for the prepared fibers are summarized in the Table 2. For the pumping of the laser we selected a wavelength of 1611 nm. This is a standard communication wavelength in coarse wavelength division multiplexed (CWDM) systems, where CWDM couplers are commercially available. Moreover, the performance of L-band high-power amplifiers is excellent at this wavelength.

The gain of the fibers was measured on short (25-45 cm) fibers at a wavelength of 1945nm. The fiber length was such that almost all the pump power was absorbed. The reabsorption of the signal is small at 1945nm for short fiber, as can be seen from Figure 1. Therefore, we can compare the gain of the fibers even when their lengths are not exactly equal. The gain measurement results are shown in Figure 2. The input power was 2.9mW in all the cases. There are no signs of gain saturation in the measurement range. The gain is generally low, indicating a strong non-radiative loss inherent to thulium-doped fiber amplifiers. It does not preclude an efficient operation in a laser with a high finesse resonator, where the strong signal inside the resonator draws the pump energy. The gain is lower then 1 for low pump powers and the loss is attributed to a pair of splices (0.2-0.8dB per a splice pair depending on the particular sample) and to absorption in the active fiber. The lowest splice loss (0.1dB/splice) and the best gain slope was achieved with the fiber SG1151 that has the mode-field diameter well adapted to SMF28 fiber and a better overlap integral between the pump and signal due to the smaller core diameter.

LASER TEST

The scheme of the single-frequency master oscillator (SFMO) is shown in Figure 3. Until now, we have tested only one of our thulium-doped fibers, namely SG1155. Since this fiber is, according to the gain and pump absorption measurements, one of the worst fibers, even better results can be expected for other fibers. The laser resonator was composed of 23cm of the thulium-doped fiber and a pair of fiber Bragg gratings. The high reflectivity FBG with a bandwidth of 0.3nm and reflectivity 0.99 was placed on the pumping end of the SFMO. The low reflectivity narrow-band FBG with a bandwidth of 0.08nm and reflectivity of 0.95 was used at the output port of the SFMO. As a wavelength selective element for pumping and characterization, standard telecommunication coarse wavelength division multiplexers (CWDM) were used. We used four CWDMs with a pass band centered at 1611nm (Opneti). Their reflection coefficient is about 0.5dB at a lasing wavelength of 1944.5nm. While the first CWDM is not necessary for the operation of the master oscillator, it allows its precise characterization cutting out the L-EDFA amplifier's ASE and at the same time protects the CWDM2 that could be easily burned by the ASE dissipated in the package when operated in the shown orientation. CWDM2 is used to measure the signal ratio between the output port and unused port of the SFMO. A pair of CWDMs 3 and 4 is used to get rid of the unabsorbed pump power.

The Figure 4 shows how the power of the laser output signal increases with the pump power. The signal power is measured at the output as well as pump end of the SFMO. The ratio of these signals is 3.7, proving preferably single end operation of the laser. The slope efficiency (measured on output end only) is 22% with respect to absorbed power, the threshold is 25mW.

CONCLUSIONS

We have developed an efficient fibers for use in lasers with short resonators. The fibers can be pumped by L-band communication lasers. Their absorption is 42-53 dB/m at a wavelength of 1611 nm allowing to construct lasers with a resonator length of 15-25 cm. Spectral absorption, mode-field diameter, and gain of the fibers was measured. Performance of one of the fibers was tested in a single-frequency master oscillator at 1944 nm. We have achieved a slope efficiency of 20% and a lasing threshold around 20mW. Phase noise characterization as well as further optimization of the master oscillator is under way.

ACKNOWLEDGEMENT

The work was supported by the Czech Science Foundation project P205-11-1840.


Pavel Peterka

Ivan Kasik

Anirban Dhar

Bernard Dussardier

Wilfried Blanc

Thulium-doped silica fibers with enhanced 3H4 level lifetime: modelling the devices for 800-820 nm band

Keywords: thulium, fiber lasers, fiber amplifiers, optical fibers

come

INTRODUCTION

Fiber lasers are one of the most spectacular achievements of contemporary optoelectronics and photonics. Variety of fiber lasers were demonstrated ranging from mighty continuous-wave (cw) systems with multi-kilowatt output powers to elegant femtosecond-pulse or tunable-narrow-line sources. Recently, high power fiber lasers have attained growing interest as they may potentially replace conventional "bulk" solid-state lasers in many applications [START_REF] Tünnermann | Fiber lasers and amplifiers: an ultrafast performance evolution[END_REF]. The geometry of fiber lasers provides several advantages over the conventional solid-state lasers such as inherently excellent output beam quality and thermal management. Construction of fiber lasers may profit also from the fact that a variety of fiber optic components are readily available as they were developed for optical communications. Since kilometers of optical fiber can be drawn from a single preform, fiber lasers have potential of cheap mass production. With the cladding-pump technique, fiber lasers and amplifiers have proven to be remarkably efficient at converting the high-power, lowbrightness output of diode lasers into high-power, high-brightness laser beams. The most important multi-watt fiber lasers were reported using double-clad (DC) fibers doped with ytterbium (1030-1100 nm), erbium and ytterbium (1540-1600 nm) and thulium (1860-2090 nm) [START_REF] Nilsson | High-power wavelength-tunable cladding-pumped rare-earth-doped silica fiber lasers[END_REF]. In the field of thulium-doped fiber lasers (TDFLs), significant progress has been achieved in optimization of cross-relaxation process in the TDF in which one 790 nm pump photon can initiate generation of two lasing photons at ~2 µm. Power conversion efficiency of 65 % was reported using such a two-for-one process [START_REF] Moulton | Tmdoped fiber lasers: Fundamentals and power scaling[END_REF].

The amplification and lasing at 800 nm band has been already investigated using fluoride-based TDFs and output power of up to 2 W and 37% slope efficiency was achieved [START_REF] Dennis | High power upconversion lasing at 810 nm in Tm:ZBLAN fibre[END_REF]. The output power was limited by the pump damage threshold of the fluoride fiber. The low-phonon-energy, fluoride-based fibers are known to provide high quantum efficiency of thulium laser transitions in contrast to high phonon energy silica fibers. However, usage of fluoride fibers results in difficulties with fabrication, hygroscopicity and aging of the host material and low pump power damage threshold. Furthermore, the fusion splicing to conventional silica-based fibers is impossible. This necessitates the use of mechanical butt-splices that are comparatively lossy and prone to damage under high power. High price of fluoride fibers is also an issue for many applications. These limitations are the main cause for which devices based on fluoride fibers are relatively rarely seen in practical applications despite numerous laboratory demonstrations, e.g., lasing with fluoride TDFs was reported at wavelengths around 455, 480, 810, 1470, 1900 and 2250 nm [START_REF] Digonnet | Rare earth doped fiber lasers and amplifiers[END_REF]. Thulium wide emission at ~1470 nm can be used for amplification in the telecommunication S-band (1460-1530 nm). It was primarily the application of thulium-doped fiber amplifiers (TDFAs) in S-band that recently spurred the development of alternative host materials with reduced phonon energy that possess long-term reliability. TDFAs based on soft tellurite [START_REF] Taylor | Thulium-doped tellurite fiber amplifier[END_REF] and antimony-silicate [START_REF] Samson | Thulium doped silicate fiber amplifier at 1460-1520 nm[END_REF] glasses were demonstrated. Later, ways of increasing the TDFA gain and efficiency were investigated by modifying the environment of thulium ions only locally, e.g., by codoping the fiber core with oxides of bismuth [START_REF] Ohara | Bi 2 O 3 -based glass for S-band amplification[END_REF], aluminium [START_REF] Blanc | Thulium environment in a silica doped optical fibre[END_REF][START_REF] Faure | Improvement of the Tm 3+ : 3 H 4 level lifetime in silica optical fibers by lowering the local phonon energy[END_REF] and gallium or germanium [START_REF] Cole | S-band amplification in a thulium doped silicate fiber[END_REF][START_REF] Watekar | A Novel 800 nm Double-Clad Optical Fiber Amplifier with 980 nm Pumping[END_REF].

Recently, we have analyzed a compact thulium-doped silica-based fiber laser at around 810 nm, especially the effect of host materials (standard silica, highly alumina doped silica and ZBLAN) on the laser performance [START_REF] Peterka | Theoretical analysis of fiber lasers emitting around 810 nm based on thulium-doped silica fibers with enhanced 3 H 4 level lifetime[END_REF]. Single-and dualwavelength pumping scheme were also discussed in terms of mitigating the possible photodarkening that might happen and inhibit the lasing action under upconversion pumping around 1060 nm. Although lasing action at 803 nm was observed in silica based fibers studied for amplification in the telecommunication S-band [START_REF] Dennis | Amplification device utilizing thulium doped modified silicate optical fiber[END_REF], the details about the actual output power characteristics were not reported. To our knowledge, silica-based thulium-doped fibers (TDFs) have not been used in high-power fiber lasers at ~ 800 nm and neither have they been theoretically analyzed before the Ref. [START_REF] Peterka | Theoretical analysis of fiber lasers emitting around 810 nm based on thulium-doped silica fibers with enhanced 3 H 4 level lifetime[END_REF]. In this contribution we present detailed optimization of the thulium-doped fiber and laser cavity parameters and also potential applications of the developed host material in amplifiers and broadband sources.

The silica-based fiber lasers around 800 nm would extend the spectral range covered by high-power fiber lasers. The single-transversal mode, high-power laser source in the 800 nm spectral band is of interest for a variety of applications. The laser can be used for fiber sensors, instrument testing and for pumping of special types of lasers and amplifiers, e.g. the bismuth-doped lasers and TDFAs. Bismuth-doped fibers pumped around 800 nm may shift their gain to 1300 nm telecommunication band [START_REF] Dianov | Bi-doped fibre lasers and amplifiers emitting in a spectral region of 1.3 m[END_REF][START_REF] Bufetov | Bi-doped fiber lasers[END_REF], where highly reliable silica-based fiber amplifiers are still unavailable. An efficient fiber laser in 800 nm spectral region could potentially be used as a replacement for titanium sapphire laser in some applications. A high-power amplifier in the 800 nm band would be useful in the optical fiber communications and shorthaul free-space communications. Although the laser diodes at this wavelength have been available for a long time, to our knowledge, commercially available single-mode laser diodes are limited to about 200 mW of output power in diffraction limited beam. It should not be confused with, e.g., laser diode stacks of ~kW output power, that are highly multimode with very high M 2 >1000 factor.

FIBER LASER SETUP AND PUMPING SCHEME

The proposed laser utilizes upconversion pumping scheme shown in Fig. 1 and has a compact all-fiber setup, example of which is shown in Fig. 2. Pumping at single wavelength in the range 1020-1090 nm would lead to second step of excited state absorption (ESA) to the 1 G 4 level. This ESA is useless in our case. The upconversion pumping at single wavelength in the mentioned spectral range is studied as first choice because the high-power ytterbium-doped fiber lasers are readily available at these wavelengths. For pump wavelengths at the short-wavelength edge of the ytterbium emission spectrum one can use long-period fiber gratings in ytterbium-doped fibers to enhance power conversion efficiency of the pump laser as we have proposed recently [START_REF] Peterka | Long-period fiber grating as wavelength selective element in double-clad Yb-doped fiber-ring lasers[END_REF][START_REF] Peterka | Extension of the double-clad Yb-doped fiber laser oscillation range thanks to longperiod fiber grating filters[END_REF]. For experimental optimization of the pump wavelength within the range 1020-1090 nm the pump and signal combiner [START_REF] Peterka | Experimental demonstration of novel endpumping method for double-clad fiber devices[END_REF] can be used to facilitate changing the fiber Bragg gratings (FBG) that define the pump laser wavelength. The laser wavelength of the TDFL is selected by the two FBGs that have the wavelength of reflection at 810 nm. Overall cavity losses caused, e.g., by splice losses and insertion losses of FBGs, are estimated in the model to be 1 dB.

THEORETICAL MODEL AND FIBER CHARACTERISTICS

For theoretical investigation of thulium doped fiber device we used a comprehensive theoretical model of the TDF laser based on the fiber propagation and the laser rate equations. The model is spatially and spectrally resolved and it allows optimization parameters of the fiber laser, i.e., the fiber waveguide parameters, doping concentrations, fiber length, pump wavelength and power and laser cavity. The parameters of the TDF that are subject of optimization are schematically depicted in Fig. 3. The numerical model is based on solution of two sets of equations: differential equations describing the pump, signal and amplified spontaneous emission (ASE) that propagate in the fiber, so called propagation equations, and the set of rate equations describing the population of thulium ions in respective energy levels. Under steady state conditions the rate equations become a set of algebraic equations. The propagation and rate equations are solved simultaneously along the fiber. Since boundary conditions for the backward ASE are not known at the beginning of the fiber, an iterative process must be applied. The numerical model is described in details elsewhere [START_REF] Peterka | Estimation of energy transfer parameters in thulium-and ytterbium-doped silica fibers[END_REF][START_REF] Peterka | Theoretical modelling of S-band thulium-doped silica fibre amplifiers[END_REF]. The fiber preform was fabricated by using the MCVD (Modified Chemical Vapor Deposition) and solution doping methods. From fiber attenuation we determined that the concentration of thulium was 40 ppm mol. The concentrations of GeO 2 and alumina were measured by electron microprobe analysis to be up to 4 and 10 mol %, respectively. The background loss of 0.1 dB/m was measured in spectral region apart from thulium absorption bands at around 1300 nm. The background loss is attributed mainly to relatively high concentration of OH groups of about 7.5 ppm. The fluorescence lifetimes measured in the TDF are shown in Fig. 1 next to the respective energy level. The 3 H 4 lifetime of 58 µs in a highly alumina-codoped fiber represents a significant improvement compared to pure or weakly modified silica glass, where this lifetime is about 14 s [START_REF] Jackson | Theoretical modeling of Tm-doped silica fiber lasers[END_REF]. The fluorescence lifetime of the 3 H 4 level was determined from the measured fluorescence decay. Since the decay curve was not possible to fit with a single exponential, the lifetime was determined as the time interval in which the fluorescence dropped to the 1/e of its peak value. Detailed description of the lifetime measurement and discussion were presented in [START_REF] Blanc | Thulium environment in a silica doped optical fibre[END_REF][START_REF] Faure | Improvement of the Tm 3+ : 3 H 4 level lifetime in silica optical fibers by lowering the local phonon energy[END_REF]. For the numerical modeling, we consider thulium concentration of 1000 ppm mol. With such a concentration, the fiber length can be relatively short while the cooperative quenching of thulium ions excited to the 3 H 4 level can still be neglected [START_REF] Jackson | Theoretical modeling of Tm-doped silica fiber lasers[END_REF]. The measured absorption and emission spectra around 800 nm in the fiber sample can be found in [START_REF] Faure | Improvement of the Tm 3+ : 3 H 4 level lifetime in silica optical fibers by lowering the local phonon energy[END_REF][START_REF] Peterka | Theoretical analysis of fiber lasers emitting around 810 nm based on thulium-doped silica fibers with enhanced 3 H 4 level lifetime[END_REF]. The other spectroscopic parameters are taken from [START_REF] Peterka | Estimation of energy transfer parameters in thulium-and ytterbium-doped silica fibers[END_REF][START_REF] Peterka | Theoretical modelling of S-band thulium-doped silica fibre amplifiers[END_REF].

RESULTS AND DISCUSSION

By means of the numerical model we have optimized the laser cavity shown in Fig. 2 and the TDF parameters. The laser performance was optimized in terms of maximum output power at the optimum fiber length for a given input pump power. It would be more general to investigate the performance in terms of the laser threshold and slope efficiency. However, in the case of the upconversion pumping at around 1060 nm the second ESA to 1 G 4 level leads to laser output rollover with higher pumping. At higher pump, more and more ions are promoted to the 1 G 4 state and these ions do not contribute to the desired lasing transition. Example of the laser output characteristics can be seen in Fig. 4. The TDF parameters in this example were as follows: fiber length 4 m, background loss 0.1 dB/m, core radius 1.7 µm and numerical aperture 0.2. The whole core area was homogenously doped with thulium. Since the laser characteristics are not linear, we can not define unambiguously the slope efficiency and we investigate directly the laser output power. It can be inferred from the Fig. 4 that the output power varies only little for the output FBG reflectivity between 70-90%. Therefore we chose 80% reflectivity of the output FBG in further modeling of the laser. Firstly, we have analyzed the effect of fiber core radius a, numerical aperture NA and then also the radius of thulium doping b. In Fig. 5, the laser output and the corresponding optimum length of the TDF are plotted for a range of fiber core radii and numerical apertures. Three individual graphs stand for three different background losses: (a) the ideal case of zero background losses, (b) the optimistic case of achievable background loss of 0.02 dB/m and (c) the last graph with background loss of 0.1 dB/m, measured in one of the developed fiber samples. The range of relevant core radii is limited to the interval of single-mode regime at the laser wavelength, i.e., where the expected effective cutoff wavelength is smaller than 800 nm. The output power is increasing with increasing NA, but the enhancement become less significant above NA=0.2. Since fabrication of TDF with higher NA may pose fabrication difficulties, we restrict further studies to fibers with NA=0.2 as a compromise. The corresponding optimal core radius is about 1.7 µm.

We have investigated also the influence of the thulium doping radius. In Fig. 6, the laser output and the corresponding optimum length of the TDF is plotted for a range of normalized doping radii B=b/a and numerical apertures. The core radius a=1.7 µm was used in the calculations. Same as in Fig. 5, we investigated three values of background losses: 0, 0.02 and 0.1 dB/m. With small background losses that would allow for long TDF, the output power is slightly increasing for smaller doping area than the fiber core. However, for realistic background losses between 0.02 -0.1 dB/m, the enhancement due to better overlap of the pump and laser signal is lost and the thulium doping in the whole fiber core allows for shorter TDF and consequently higher output powers. Therefore, we assume thulium doping across the whole area of the fiber core in the following calculations.

The laser output power vs. pump wavelength is shown in Fig. 7. In comparison with the TDFA for the telecommunications S-band (1460-1530 nm) with optimal pump wavelength around 1020 nm [START_REF] Peterka | Thuliumdoped silica-based optical fibers for cladding-pumped fiber amplifiers[END_REF] the region of optimal pump wavelengths is shifted towards longer wavelengths because in this case high inversion between 3 H 4 and 3 H 6 levels and high pump absorption from 3 H 6 level is desirable. Although the laser wavelength of 1064 nm is intended to be used in first experiments thanks to its availability, it can be seen from Fig. 7 that the 1064 nm is not the most efficient pump wavelength. The range of optimum wavelengths is between 1070-1120 nm. However, it should be noted that the key parameters for the pump power optimization are the pump ground-and excited-state absorption cross sections that were not measured for the specific fiber sample. Instead, the cross section spectra were taken from literature [START_REF] Peterka | Theoretical modelling of S-band thulium-doped silica fibre amplifiers[END_REF][START_REF] Jackson | Theoretical modeling of Tm-doped silica fiber lasers[END_REF]. Experimental optimization of the optimum pump wavelength would be highly desirable and that is why we propose the laser setup with easily interchangeable FBGs of the pump laser shown in Fig. 2. In order to show potential of the developed TDF core composition in fiber amplifier and broadband source we have studied theoretically performance of these devices. The parameters used in the modeling were the same as in optimized TDF for the fiber laser at 810 nm mentioned above. It should be noted that for both the TDFA and wideband ASE source the optimum parameters might be different but this optimization task is beyond the scope of this contribution. In contrast to the laser setup in Fig. 2, the amplifier uses wavelength division multiplexers to combine the signal and the pump and isolators to prevent laser oscillations. The results of the gain and noise figure calculations are summarized in Fig. 8 for signal input level of 100 µW. In the case of broadband source, the ASE spectra were calculated when no input signal is present, see Fig. 9. Similarly to the laser study described in [START_REF] Peterka | Theoretical analysis of fiber lasers emitting around 810 nm based on thulium-doped silica fibers with enhanced 3 H 4 level lifetime[END_REF], the fiber length is a very important parameter, especially in silica-based TDFs, because for longer TDF the radiation around 800 nm is gradually reabsorbed and the transition 3 F 4 3 H 6 at around 2 µm becomes dominant.

CONCLUSIONS

Using a comprehensive numerical model of the TDF we have optimized the parameters of thulium-doped silica based fiber laser we have recently proposed. We have investigated the fiber length, core radius, numerical aperture, radius of the thulium-doped area, output coupler ratio and pump wavelength. We have shown that efficient lasing at 810 nm can be achieved using silica based Tm-doped fiber with enhanced 3 H 4 lifetime for specific ranges of the fiber and laser cavity parameters. We have also investigated performance of the developed host material in the fiber amplifier and broadband ASE source. More than the 30 dB of gain of the amplifier and more than 500 mW output power of the ASE source with FWHM of 5 nm at 3 W of pump power were predicted.

This work was partially supported by CNRS Office of International Relations project No. PICS 5304 and by the Ministry of Education, Youth and Sports of the Czech Republic, project No. ME10119 "FILA". LPMC is with GIS 'GRIFON' (CNRS, www.unice.fr/GIS ).

Figure 1 .

 1 Figure 1. Thulium energy levels and the pumping scheme. Measured fluorescence lifetimes are shown right to the respective level involved in the model.

Figure 2 .

 2 Figure 2. Setup of the fiber laser.

Figure 3 .

 3 Figure 3. Refractive index profile (RIP) of the TDF with schematic representation of parameters that are subject of optimization: core radius a, numerical aperture NA and thulium doping radius b.

Figure 4 .

 4 Figure 4. Laser output power characteristics vs. input pump power at 1064 nm for various output coupler ratios. The TDF parameters were as follows: length 4 m, background loss 0.1 dB/m, core radius is 1.7 µm and NA 0.2. The laser characteristics are not linear due to gradual population of the upper lying level 1 G 4 .

Figure 5 .

 5 Figure 5. Laser output power and optimum fiber length vs. core radius for several values of the NA and background loss. Only the relevant core radii where the effective cutoff wavelength of the fiber shall be below 800 nm were taken into account. The doping radius was set to b=1. The light grey curves are the laser output power results from the preceding figure(s), for easy comparison between the three graphs.

Figure 6 .Figure 7 .

 67 Figure 6. The effect of thulium doping area radius b on the laser performance for three values of background loss. The core radius was kept a=1.7 µm.

Figure 8 .

 8 Figure 8. Gain and noise figure of the TDFA for several values of pump power at 1064 nm. Signal input power is 100 µW.

Figure 9 .

 9 Figure 9. Backward ASE spectra for several values of pump power at 1064 nm and TDF length of 4 m.

* peterka@ufe.cz; phone +420 26 773 527; fax +420 284 680 222; www.ufe.cz


Bernard Dussardier
email: bernard.dussardier@unice.fr

Jérôme Maria

Pavel Peterka

PASSIVELY Q-SWITCHED YTTERBIUM AND CHROMIUM ALL-FIBRE LASER

A chromium-doped saturable absorber fibre stabilizes an otherwise spontaneously chaotic ytterbiumdoped fibre laser. This original passively Q-switched all-fibre laser produces sustained and stable trains of smooth pulses at high repetition rate.

INTRODUCTION

development of Q-switched fibre lasers is an alternative to bulk pulsed solid-state lasers operating in the ns-to s-range for many applications such as material processing, medicine, aerial or space communications, remote sensing in free space or in fibre systems. Fibre lasers benefit from the high versatility and reliability of integrated, factoryaligned and fusion spliced fibre devices, relying on fiberized components produced at low cost and having high damage threshold. However Q-switched fibre lasers use externally driven intra-cavity bulk modulators, or bulk passive components such as a bulk polarizer [1], or a semi-conductor saturable absorber mirror [2]. These must be located in a free section of the cavity, causing alignment and reliability problems.

The development of "all-fibre" passively Qswitched (PQS) fibre lasers is interesting because no external electronic driver is needed though some may need additional cheap and slow feedback control systems. Transition metal-doped bulk crystals have been used as saturable absorber (SA) within PQS fibre lasers [3,4], however alignment and optical damage were critical. We have for the first time proposed a core-pumped, low power, all-fibre PQS laser [5] using a newly developed chromium-doped fibre [6] as integrated SA (CrSA). Since, few PQS fiber lasers have implemented alternative SA ions like rare-earth (holmium [7], samarium [START_REF] Fotiadi | CLEO'07[END_REF]) or metals (bismuth [START_REF] Dvoyrin | [END_REF]). However, some of these SA have drawbacks: low saturation intensity, long response time, absorption band narrower or wavelengthshifted relative to the gain medium. These characteristics necessitate additions to the laser cavity rendering the device more complex [7,[START_REF] Dvoyrin | [END_REF]. As for bulk SA, some transition metals from the 3d series, like Cr 4+ ions, are in principle the most attractive SA in silica, because of their high transition strength over broad wavelngth ranges [10] and short response time [11].

fibre laser systems produce self-pulsing in the sub-s domain. Regular self-pulsing in erbium highly-doped fibres were demonstrated, based on energy transfers within the gain medium [12]. However this principle allows only a limited potential for engineering and optimization. More recently, double-clad ytterbium-doped fibre (DCYF) lasers have raised a great interest. However DCYF lasers have the particularity to randomly self-pulse in some cases. In particular, linear cavities with high loss and/or non uniform population inversion induce chaotic pulse generation [13]. The two main operating regimes are the sustained self pulsing (SSP, period longer than cavity round-trip time) and the self mode locking (SML, period equal to cavity round-trip time) [14].

In this paper, we take advantage of the self-pulsing in DCYF lasers and study the effect of a CrSA fibre on the laser dynamics. We show that the DCYF laser alone has a chaotic pulsed behaviour (both SSP and SML) whatever the pump level above threshold, whereas in presence of the Cr-doped fibre SA, relatively stable PQS pulses trains are produced.

EXPERIMENTALS 2.1 Fiber Characteristics

The DCYF and the single-mode CrSA fibre were The diameter and NA of its single-mode core are 7 m and 0.11, respectively. The CrSA was doped with Cr 4+ ions only, having a broadband absorption band across the visible and infrared wavelength range [6] and a composite SA relaxation behaviour [11]. Its core absorption is 3.5 dB/m at 1064 nm and mode-size adapted to the DCYF.

Fiber Laser Setups

Two laser setups were studied. The first used only the DCYF (length 1.2 m, pump absorption < 5 dB). The cavity was formed by a fibre Bragg grating (FBG) with high reflectivity (> 99,5 %) at 1064 nm (bandwidth 0.3 nm) and the perpendicular cleaved end of the DCYF (Fig. 1). The cavity was ~ 6.1 m long. The collimated pump beam was launched into the DCYF cladding using an aspherical lens. The polarization controller (PC) was used to partially control the laser stability. The FBG was limiting the number of longitudinal modes. Note that the pump coupling was not optimized, therefore pumping of the Yb ions populations was not homogeneous, providing favorable conditions for self pulsing (SSP). Also, this cavity was designed to self generate short pulses, therefore a short cavity length, a relatively high loss and high Yb ions inversion factor were chosen. As a consequence, the laser slope efficiency was not optimized. That also increased the stimulated Brillouin scattering threshold far above the achieved output power in this study.

The backward output beam was directed using a dichroic mirror toward a power-meter or a 1 GHz InGaAs detector connected to a fast oscilloscope or an optical spectrum analyser. In the second setup, 0.3 m of CrSA was spliced between the FBG and the PC. (Fig. 1).

Results

The characteristics of both lasers are shown on Fig. 2. Its threshold and efficiency viz. the incident pump power were 0.45 W and 22 %, respectively. The DCYF laser had a chaotic behaviour spontaneously switching between CW and a Qswitched modes over the pumping range. A characteristic time trace of the output is shown on Fig. 3(a), typical of such cavity [3][4][5][7][START_REF] Fotiadi | CLEO'07[END_REF][START_REF] Dvoyrin | [END_REF]11,13]. The few s-long pulse envelops were strongly modulated by short pulses with the period of one cavity returntrip time (Fig. 3(b)). Here we observe a combination of SSP and SML. Using the PC to stabilize the output was quite inefficient, and at best produced a very noisy laser output. The chaotic behaviour was always dominant. Another short section of a commercially available Yb-heavily doped fibre, implemented in the same conditions, produced the same results.

By inserting a piece of CrSA fibre in the cavity, the characteristics of the laser changed drastically : first, the threshold of the laser increased and its efficiency diminished, as usually observed when inserting a SA in a cavity (Fig. 2). The CrSA fibre caused the threshold to increased upto 1.0 W, and the efficency to lower downto 6 %. More importantly, the s-long pulse trains were efficiently stabilized over the whole available pump range. On Fig. 4(a) is shown a typical output at 7.6 times the threshold. The peak RMS fluctuations were less that 10 % at 9.4 times the threshold. The higher the pump, the better stability. Up to the maximum available pump (16 W), the stable passive Q-switching was still present ; no transition to CW operation was observed. The Q-switched envelopes were smoothed compared to the DCYF laser. No submodulation at the return trip period was visible anymore (Fig. 4(b)). The pulse duration and repetition rate versus incident pump power of the DCYF+CrSA laser are shown on Fig. 5, with a 400 ns minimum pulse width, a repetition rate as high as 350 kHz, a 2 J pulse energy and peak power equal to 6.4 W.

DISCUSSION & CONCLUSION

The behaviour of the DCYF+CrSA laser is typical of a PQS mode of operation. It must be noted that this results were obtained with a set of cavity parameters causing self-pulsing or chaotic behaviour in the DCYF laser. Indeed, when CW or relatively stable output beam was set in the DCYF laser (by choosing parameters or setting the PC), then adding the CrSA provided only a quasi-CW regime. It is evident near the threshold of the DCYF+CrSA laser, when the pulse peak power is still too weak to induce the CrSA fibre to saturate : then the behaviour is fully chaotic. It regularly shifts toward a stable Qswitched regime when the pump increases. The capacity of our CrSA to stabilize SSP and cancel out SML in an Yb-doped fibre laser has never been reported, to the best of our knowledge.

In this particular cavity design, the shortest possible pulses were achieved. To further shorten them, a more compact cavity comprising only the active fibres (1.5 m) would produce sub-100-nspulses. Then the pulse peak power would be increased, causing a stronger CrSA saturation, and hence the pulse energy and the slope efficiency would be larger. In order to stay below the non-linear threshold, mode size enlargement will be required by introducing large-mode area fibre technology. MOPA configurations using a power DCYF amplifier could also be considered.

In conclusion, we have shown the potential of a CrSA fibre to produce stable passively Q-switched pulses trains out of a DCYF laser. This is to our knowledge, the first demonstration of such a laser with the active elements Yb and Cr. This laser architecture could be integrated and power upgraded, with great potentials for many applications.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Laser setup. See text.

Fig. 3 :Fig. 4 :

 34 Fig. 3: (a) DCYF laser output, for 1W of pump (2.2 times threshold). (b) zoom on one typical pulse envelop.

Fig. 5 :

 5 Fig. 5: Pulse duration and repetition rate of the passively Qswitch DCYF+CrSA laser.