Manuel Pozo
email: manuel.pozo@isep.fr

Raja Chiky
email: raja.chiky@isep.fr

Zakia Kazi-Aoul
email: zakia.kazi@isep.fr

Enhancing Collaborative Filtering Using Semantic Relations in Data

Keywords: collaborative filtering, distributed systems, recommender system, semantic web technologies

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The amount of information in the web has greatly increased in the past decade. This phenomenon has promoted the advance of Recommender Systems (RS) research area. The aim of these systems is to provide personalized recommendations. They help users by suggesting useful items to them, usually dealing with enormous amounts of data.

Typically, in order to create a top K items (K most relevant items) that should be presented first to the user, Recommender Systems study the interaction between users and items. For instance, users may rate items (such as films, books, etc.) using a 0-5 stars scale (explicit feedback), or user might just create a navigational path clicking links or purchasing items (implicit feedback). Hence, Recommender Systems exploit these feedbacks to set up recommendations. In the literature, Recommender Systems have been usually classified into two basic types: Content-based CB and Collaborative Filtering CF [1]. The former focus on the characteristics of the items in order to determine similarities between them, and finally recommend similar items to the one the user liked in the past. The latter groups users according to their preferences profile and recommend items that people from the same group have already liked [2]. However, the correct exploitation of the data and the recommendation accuracy are the trend challenges of RS. On the one hand, seeking more relations between users and items may increase the recommendation quality. To this task, the RS might use semantic information about items, which enhance the data representation and help to find out the underlying reasons for which a user may or may not be interested in a particular item [3]. On the other hand, as the quantity and the variety of information constantly increase, the scalability and the domain generality of the system are two important aspects to alleviate the time processing and the heterogeneity of data.

In this paper, we propose a semantic collaborative filtering recommender system in order to improve the recommendations quality and preserve the domain genericity. In addition, we use an easily distributable collaborative filtering technique based on the well known ALS algorithm [4] to ensure the system scalability.

This article is structured as follows: in section 2, we present related work. In section 3, we explain our general approach. In section 4, we expose the experimentation phase and the comparisons. Finally, we discuss in section 5 about the results and the future work.

Related Work

Recommender Systems (RS) use users feedback to predict interest in items. Nowadays, the current challenges for Recommender Systems are to improve their recommendations quality, their items domain genericity (i.e the domain independency) and their scalability. In order to address these issues, a trend topic is the use of semantic knowledge. For instance, [5] and [6] propose Content Based (CB) recommender systems based on items domain descriptions, such as ontologies. The approaches associate items and keywords that characterize them, creating a bag of words for each item. Hence, the items similarity looks for common keywords in bags. Recently, [7] proposed a recommender system architecture that facilitates the integration of heterogeneous data. The system creates a semantic graph representation of data in order to weight the relations between the nodes of the graph. The system explores the graph and chooses the best weights for predictions tasks.

Nevertheless, some authors have already demonstrated the effectiveness of more extended Collaborative Filtering (CF) techniques [2]. For example, [8] proposed a CF method that took the implicit users feedback into account. Authors used Alternating Least Squares (ALS) CF technique that is based on Matrix Factorization techniques. The ALS method can be easily distributed among machines, and thus, enhances the scalability of the system. [9] focus on the relevance of items in the ranking, rather than in the items ratings prediction using a technique similar to ALS. [10] proposes another approach that improves CF techniques using item-item similarity based on items description in Wikipedia. In cases where sparsity is too high, the system guess artificial ratings for new items regarding the last user ratings on similar items.

Differently, but also aiming to improve CF, [11] suggests a three-layer representation for data: users, interests and items. For a user, an interest is a characteristic that an item must have. For an item, an interest is one of its attributes. Thus, authors construct a correlation matrix graph containing users hidden interests. Other approaches encourage the use of multi-criteria feedback to improve recommendations quality [12][13][14]. In order to explain an overall rating in items, authors also analyze these item attributes feedbacks and also predict their rating.

In [15] and [16], authors proposed an approach for reducing dynamically the big number of item features needed for the recommendations. Both approaches construct an items-attributes matrix that they reduce by using SVD algorithm, alleviating sparsity and noise.

However, most of the approaches lack distribution environment and domain genericity [3][17][11]. Thus, we propose a general semantic CF method based on ALS [8][9] and an ontology semantic technology. ALS allows the distribution of the computation among several machines using Matrix Factorization techniques, whereas ontologies add information representation and domain independency to the system.

General Approach

The proposed architecture includes a collaborative filtering engine that relies on domain knowledge about the items. This knowledge is represented using an ontology that will enhance the recommendation quality. The architecture is represented in figure 1 and is composed of two main modules: a semantic module and a recommendation module.

The semantic module exploits the domain ontology to define the relations between items and their attributes. Because the number of those attributes could be huge, we apply a dimension reduction technique based on Principal Component Analysis (PCA) in order to select the most representative ones (preanalysis phase). The PCA also provides weights for attributes to give them more or less importance in the recommendation process. The recommendation module is based on matrix factorization method. Both modules will be described in the following subsections.

Semantic Module

A user could be interested in an item because of one or more of its attributes. For example, a user might appreciate a set of movies only because they have in common his favorite actor. Therefore, the purpose of this module is to take into account the attributes that compose items to better serve the user. For that, Fig. 1. Global architecture of our approach its relies on a domain ontology (i.e. an ontology that describes the domain for which we want to implement a recommendation system).

To transform traditional ratings into "semantic rating", we focus first on the number of occurrence of attributes that were rated by a user. This occurrence that we call occurrence frequency or coincidence is the number of times the attribute values of the items rated by the user are repeated. The second step is to calculate the semantic value (sv) based on the occurrence frequency. The equation used is presented in (1):

sv = r + E[r] * F i=1 c i * w i N (1)
Where r is the value of the initial rating, E[r] is the average of the user ratings, F is the total number of attributes, c i is the occurrence frequency of the attribute i in the set of items that have been rated by the user, w i is the weight calculated from the PCA phase, and N is the total number of items rated by the user. This equation takes into account positive and/or negative ratings. It can be used at two levels in the Recommendation. On the one hand, we can apply it to all ratings available in the original database, which helps to explain the users interest for particular characteristics of the rated items. On the other hand, we can choose to apply the semantic equation to the output of the recommendation. Indeed, suppose the recommendation module returns the result as top K items for a user, with an estimation of ratings of this top K. These user ratings will be transformed into a semantic rating according to the equation (1) and will be reordered accordingly in top K'. K' can be less than or equal to K.

Matrix Factorization

As its name suggests, the matrix factorization consists on decomposing a matrix into two or several matrices, which results in the same original matrices after their multiplication. This method allows discovering latent or hidden relationships between a user and the items. For instance, we may suppose that two users have highly rated a movie because they like its actors/actress on it, or because it is an action movie, which may be their favorite movie genre. Thus, if we are able to discover these hidden-reasons, we may be capable of predicting the interest on each item, because the associated characteristics of preferences may correspond with the ones that the items contain.

The Matrix Factorization is closely related to Singular Value Decomposition (SVD), which is widely used to identify hidden relation factors in information retrieval. Collaborative Filtering method may adapt this technique in order to work on the typical sparse rating matrix.

The Matrix Factorization models the interaction between users and items by applying a scalar product of two vectors representing the latent features in a space of dimension f. As a consequence, each item i is associated to one vector q i ∈, as well as each user u is associated to a vector p u . The dot product of both vectors represents an estimation of the ratings that the user may give to the item.

r ui = q T i p u
Hence, the challenge is to obtain all these vectors q i and p u ; by solving the equation ( 2)

min q * ,p * u,i⊂K (r ui -q T i p u ) 2 + λ( q i 2 + p u 2 ) ( 2
)
Where K is the set of pairs (u, i) in which the ratings of r u,i are available, and λ is a regularization parameter that allows controlling the learning model [4].

Alternating Least Squares (ALS) To solve equation (2), [18] proposes an approach called Alternating Least Squares (ALS). In this equation, the vectors q i and p u are unknown, and thus the equation is not convergent. However, if we are able to fix one of them, the optimization problem becomes square, and we are able to optimally solve the equation. Thus, the ALS techniques fix in each iteration q i or p u : when p u is fixed, the system computes q i by least squares, and vice versa. This fact allows an optimal convergence in the iteration of the equation. This method is highly interesting because it is easily distributable among multiple machines. In fact, the system computes each q i independently of the other factors, as well as for each p u . 4 Experimentation

Experimental Dataset

In order to implement the semantic module, we need a dataset and an items domain description that defines the elements. We choose MovieLens, a movies dataset, which contains a good number of items (films) and users ratings.

In addition, we need the relative information about the attributes of the items, which is not provided in the MovieLens dataset. To alleviate this lack, we use an ontology in order to associate automatically the movies with their attributes. Filling a dataset might be a hard work because we have to deal with each item, its properties and its attributes [19]. As a consequence, it may become an obstacle for the experimentation [20]. For this task, we use the IMDb database that represents the relations described in the ontology. Thus, the use of both sources (IMDb and MovieLens) facilitates the integration of the semantic module, which needs items (MovieLens) and their attributes (IMDb). Note that the titles might have different representations, and thus, we needed a clean up phase in order to merge both sources.

Moreover, the ratings dataset in MovieLens and the associated attributes from IMDb are too big and this does not help to apply the semantic equation, which may require important processing time. In order to test our approach, we reduce the number of users to the 100 users who have more rated movies and we focus on only 9 attributes (actor or actress, color, editor, director, genre, language, producer, writer and productions year). Table 1 summaries information about our experimental dataset.

Semantic Recommender System

As far as we know, there is no existing recommender system that handles or facilitates the usage of the web semantic technologies. In addition, such a system might be really complex to implement in order to validate our approach. Thus, we decided to add a semantic layer to an existing recommender system. Moreover, our objective is to implement a collaborative filtering algorithm based on Matrix Factorization in order to be able to analyze huge volume of data. This algorithm is implemented in numerous recommender systems libraries. Hence, we choose a system that better fit our work environment and our constraints: the system has to use a collaborative filtering technique and be easily distributed for handling scalability issues. For our experimentations, we use Myrrix [21]. It is a natural evolution of the widely extended Apache Mahout libraries [22]. We consider Myrrix as a black box: it takes a dataset, analyzes it and executes the recommendation technique. To interact with the ontologies, we use the Jena library [23].

We test the semantic recommender system using two approaches:

-Semantic Top K: In this first approach, we aim to apply the semantic layer on the output data. Typically, recommender systems provide a list of K items ordered by user's preference. In this case, the semantic module reorders these items and gives back a new list in an other relevance order. This approach allows better recommendations in a reduced execution time. -Semantic Dataset: In this second approach, we apply the semantic layer on the input of the system. A pre-analysis is done on the dataset before it goes into the recommender system. This approach allows finding out new items that were not taken into account a priori. However, the semantic module needs to analyze the whole dataset increasing the process time in comparison with the non-semantic analysis.

In the next section, we present how these approaches have modified the recommendations, and the quality of the obtained results.

Results

We tested our approach using the recommender system Mahout/Myrrix and adding the semantic layer either at the input or the output. From the experimental dataset, we chose the user who has rated more items (the user with id 13 and 636 ratings). Then, we took out 60 ratings of this user (all of them have been rated with a 5 over 5). Next, we ask to the system a list of 60 items for this concrete user. The table 2 presents the top 10 items (over the 60 items) with the higher prediction scores in the three approaches (non-semantic, semantic dataset and semantic top K).

Semantic Output: Semantic Top K The semantic top K approach works over the 60 films asked to Mahout/Myrrix. The semantic algorithm re-evaluates the predictions associated to each film and gives them back in a new order. The table 2 shows up the modification in the top K. In concrete, we can see that the film 121 is now in the most preferable, when before it was the third one. The film 237 has gone from the 10th place to the 3rd one. Moreover, note that the half of items in the semantic top K items is absent in the non-semantic top 10; yet, they are still in the list of 60 extracted films.

Semantic Input: Semantic Dataset In this approach, the semantic layer is applied on to the whole dataset before Mahout/Myrrix analyzes it. The results in the table 2 present some small differences against the non-semantic recommendations. The similarities are more important than semantic Top K, in particular the first top 7 recommended films are the same but in different order. However, we also see the emergence of new films (202 film in position 9). In order to study in more details the impact of the semantic layer on the results, we performed some statistical comparison techniques. We use 3 evaluation methods, all of them are implemented in the Mahout/Myrrix libraries.

-The Area Under Curve (AUC) represents the probability to give a higher rating to a relevant random item than an irrelevant item. In this measure, the higher value is the better one. -The Precision and Recall (PAR) measures the relevance of the items in the top K recommended list. It combines the fraction of all recommended items that are relevant (precision) and the fraction of all relevant items that were recommended (recall). In this case, the higher value is the better one. -Estimated Strength (ES) measures the quality and reliability of the results.

In this measure, the lower value is the better one.

The table 3 presents the obtained results using or not the semantic layer in the Top-K, and thus it may compare the approaches. The non-semantic dataset contains 0-5 scaled ratings whereas the semantic dataset ratings are between 0 and 10. In the row Semantic (0-5), the ratings have been scaled to 0-5 for a quick comparison with the non-semantic dataset. From this table, we can say that:

-Concerning semantic Dataset (0-10), we got good results for the AUC and the ES measures in comparison to the non-semantic approach. -Semantic Dataset (0-5): In this case, we observe good results in the AUC and PAR measures. Moreover, the ES values in both semantic and non-semantic approach are very close.

Finally, note that these results are preliminary, and can be improved. Indeed, a closer analysis of the data set would improve the weightings applied to the semantic equation (equation ( 1)). Further, adding attributes and more users and feedbacks will improve the semantic equation, and therefore the quality of recommendations.

Conclusion

Recommender systems face a substantial challenge when dealing with huge amount of data. In this paper, our main goal was to help solving this problem by describing an easy development of a distributed recommender system. This was possible by using a powerful algorithm of Collaborative Filtering called ALS which can be easily distributed among several machines. In addition, we propose a semantic equation that allows to reorder the top K suggested items to the user according to his preferences (based on underlying reasons for which a user may or may not be interested in a particular item). The proposed approach in this paper has demonstrated an efficiency on the recommendation of films by using the MovieLens dataset and a film ontology, which was filled from IMDb data source. We decided to choose this domain because the MovieLens dataset is public and highly available.

Nevertheless, the design of the approach is very independent of the application domain. Our system may be used as a black box, where we can connect a database to introduce ratings as well as the application domain ontology. Our future work will focus on two main aspects: (1) To reproduce similar experimentation in different domain datasets in order to prove the genericity of our system, (2) To improve the semantic-layer in order to get better recommendation results and to reduce the time execution of the system.

Table 1 .

 1 Experimentation: Dataset

	Users Films Ratings Features
	100 1232 11019	9

Table 2 .

 2 Experimentation: Top-10 results for a request of the user 13 of MovieLens

	Non-Sem.	Sem.Ratings	Sem.Top K
	ID Prediction ID Prediction ID Prediction
	56	0.720	127	0.74	121	1.12
	127 0.690	56	0.73	56	1.06
	121 0.610	121	0.63	237 1.049
	135 0.600	100	0.60	202	1.03
	100 0.570	135	0.58	127	1.00
	50	0.560	50	0.579	13	0.91
	234 0.550	234 0.572	423 0.902
	204 0.519	237	0.53	993	0.90
	181 0.517	202 0.518	161 0.894
	237 0.500	181 0.514	50	0.883

Table 3 .

 3 Comparisons: different scale datasets.

	Dataset	AUC PAR	ES
	Non-Semantic (0-5 ratings) 0.6233 0.0692 0.929
	Semantic (0-5 ratings) 0.6448 0.0728 0.937
	Semantic (0-10 ratings) 0.7945 0.0329 0.1651


Naman Jain
email: namanjain2009@vit.ac.in

Manuel Pozo

Zakia Kazi-Aoul
email: zakia.kazi@isep.fr

Sampling Semantic Data Stream: Resolving Overload and Limited Storage Issues

Keywords: Big Data, Linked data-stream, Processing time, Sampling 1367501887000 1367501889000

The Semantic Web technologies are being increasingly used for exploiting relations between data. In addition, new tendencies of realtime systems, such as social networks, sensors, cameras or weather information, are continuously generating data. This implies that the data and the links between them are becoming extremely vast. Such huge quantity of data needs to be analyzed, processed, as well as stored, if necessary. In this paper, we propose sampling operators that allow us to drop RDF Triples from the incoming data. Thereby, helping us to reduce the load on existing engines like CQELS, C-SPARQL, which are able to deal with big and linked data. Hence, the processing efforts, time as well as required storage space will reduce remarkably. We have proposed Uniform Random Sampling, Reservoir Sampling and Chain Sampling operators which may be implemented depending on the application.

Introduction

The semantic web handles many systems, such us Twitter, Facebook or Google, which generate increasing volumes of semantic data everyday. The problem of "too much (streaming) data but not enough (tools to gain and derive) knowledge" was tackled by [START_REF] Sheth | Semantic sensor web[END_REF]. They envisioned a Semantic Sensor Web (SSW), in which sensor data are annotated with semantic metadata to increase interoperability and provide contextual information essential for situational knowledge. CQELS [START_REF] Le-Phuoc | A native and adaptive approach for unified processing of linked streams and linked data[END_REF], SPARKWAVE [START_REF] Komazec | Sparkwave: continuous schema-enhanced pattern matching over rdf data streams[END_REF], C-SPARQL [START_REF] Barbieri | C-sparql: Sparql for continuous querying[END_REF] etc. are existing technologies to exploit these semantic and streaming (continuous and infinite) data, and are based on recommended standard RDF, as the format of representation.

CQELS [START_REF] Le-Phuoc | A native and adaptive approach for unified processing of linked streams and linked data[END_REF] is a native approach in an RDF environment based on 'whiteboxes'. It provides its own processing model and its own operators to deal with streams, for example, window operators or query semantic operators. C-SPARQL [START_REF] Barbieri | C-sparql: Sparql for continuous querying[END_REF] on the other hand, uses a 'black-box' approach which delegates the processing to other engines such as stream/event processing engines and SPARQL query processors by translating to their provided languages.

Although almost all the engines are based on the SPARQL Language, there are only a few systems which are able to process big quantity of data on the fly. Moreover, these engines do not feature any tool that would allow them to reduce the processing efforts and improve the processing time. For many applications, we must obtain compact summaries of the stream. These summaries could allow accurate answering of queries with estimates, which approximate the true answers over the original stream [START_REF] Cohen | Structure-aware sampling on data streams[END_REF].

Thus, we propose the implementation of such sampling operators that could be used in conjunction with other existing real-time engines. These sampling operators will allow us to deal with the requested population by applying heuristic methods. Uniform Random Sampling, Reservoir Sampling and Chain Sampling were implemented on the data streams and were then compared with the error percentage, storage requirements and the load suffered by the engine. Thus, these sampling methods will help reduce processing time and the required memory space.

Extension to Existing Systems

We propose to extend existing semantic data stream querying engines by creating an external abstraction of the sampling operator. The extension acts as follows:

First, we recognize the different operators of the language and split the initial query according to them. This will allow us to use the same operator at different levels of the query: in the input, for sampling static data or streaming data and in the output to sample the result of the query, or both simultaneously. After splitting the query, we make syntax correction. If we identify any errors in our operator, we stop the execution of the query. Hence, if everything is correct, we create a key-value map where we store all the resources and all the requested sampling actions. Thus, we can apply the sampling operator independently by creating a thread for each of them.

RDF Static

RDF Stream

Black Box Engine Result

We start the abstraction of the operator by taking out all the sampling instances in the query. This will allow us to avoid the correction of the rest of operators and leave the task to the specific engine itself.

When we send this query to the engine, as shown in Figure 1, it will run all the threads in charge of each source. By adapting those threads, we apply the sampling method just before the data comes to the engine, thus discharging the processing tasks. In a similar way, we adapt the output of the engines, so as to apply sampling methods at the output and lighten storage space.

Sampling Methods

The query would contain the information of sampling type and the sampling percentage for each unique stream. We apply the appropriate sampling method for each stream in different threads. We used Uniform Random Sampling, Reservoir Sampling and Chain Sampling to compare their advantages and disadvantages. We may choose an appropriate sampling method depending on the application used for.

We have implemented our sampling operators with CQELS [START_REF] Le-Phuoc | A native and adaptive approach for unified processing of linked streams and linked data[END_REF] and C-SPARQL [START_REF] Barbieri | C-sparql: Sparql for continuous querying[END_REF] engine. Example below shows simple type of sampling at 50% i.e. taking one triple and dropping the next one, using CQELS as: As shown in Figure 1, the output of the engine goes through this operator and is given as final result only if the operator permits. Normal sampling algorithm has been used for this i.e. if %80 is specified, then only 4 out of 5 results are termed as final results. If Output Sampling operator is not specified, then the percentage is assumed to be 100 and no result is left out after the processing is done by the engine.

The sampling operators can also be implemented on similar systems like Sparkwave [START_REF] Komazec | Sparkwave: continuous schema-enhanced pattern matching over rdf data streams[END_REF], ETALIS [START_REF] Anicic | Stream reasoning and complex event processing in etalis[END_REF] after changing few configurations. In the examples to follow CQELS is used for the experimentation.

For analysing the sampling methods, we computed average of For instance, if the input sampling percentage is set to 60, then we find the probability by dividing 60 with 100 which is 0.6. Then, we randomly generate boolean values with this probability and send the triples to the engine if the boolean value returned is true. Thereby reducing the processing load and time of the engine. This helps to keep number of samples in proportion to total incoming data. The query 4 is of the form

WHERE { STREAM <C:/data-8.stream> [NOW][UNISAMPLING %60] {?location vocab:ozone_8hr_daily_max ?value} }

Figure 2 shows sample size variation and number of triples processed by the engine. They both are same in this type of sampling as there is no removal of elements from the sample. This sampling method is less preferred as the sample size keeps on growing, which may lead to shortage of storage space, and even the outdated data element will be existing.

Reservoir Sampling

The problem of maintaining a sample of specified size 'k' is overcome by Reservoir Sampling [START_REF] Vitter | Random sampling with a reservoir[END_REF]. In this, we add the triple 'i' to the sample with probability k/i and discarding a randomly chosen element from the reservoir or sample to make room for the new element. For instance, here reservoir size of 500 ensures that the number of samples at any point may not exceed 500. Initially, triples are added to the reservoir until it is full. Then incoming triples, with stream number 'i' are added with probability 500/i, after replacing a randomly chosen element from the reservoir. We can also say that chances of adding a triple reduces as the stream number increases. Query 4 is { STREAM <C:/data-8.stream> [NOW][RESSAMPLING 500] {?location vocab:ozone_8hr_daily_max ?value} } Figure 3a shows that the sample size becomes constant after the reservoir is full and Figure 3b shows number of triples processed by the engine over the time. This sampling method helps us to limit the maximum storage space of the samples, but is not favourable when recent data is more important to us, as the sample data may have 'expired'. A significant reduction in load on the engine can also be noted in Figure 3b when compared to Figure 2.

Chain Sampling

In [START_REF] Babcock | Sampling from a moving window over streaming data[END_REF] authors state the Chain Sampling method for sequence based windows. In this method, if the window size is 'n' we add each new element 'i' in the sample with probability min(i,n)/n. As each element is added to the sample we choose an index, in the range (i+1,i+n), of the element that replaces it when it expires. We choose this range as when element 'i' expires the window would be in the range (i+1,i+n). Once the element with that index arrives, we store it and choose the index which replaces it when it expires, thus forming a chain of replacements. STEP operator is used to specify the size of steps that the sequence based window takes. Operator : [CHNSAMPLING{WindowSize} STEP{StepSize}] and the query 4 is of the form WHERE { STREAM <C:/data-8.stream> [CHNSAMPLING 500 STEP 2] {?location vocab:ozone_8hr_daily_max ?value} }

The above query shows that window size 'n' is 500 and window moves in steps of 2. Figure 4a shows that the sample size increases as the window size is increased but Figure 4b shows that number of triples being processed by the engine is lower for higher window sizes. We also note from Figure 3b and Figure 4b that load on the engine is much higher for Chain Sampling.

Chain Sampling ensures to keep sample elements which are present only in the window and eliminates the problem of 'expired element' in the sample. But, the act of storing replacements does not reduce the memory space requirements and load on the engine as effectively as Uniform Random Sampling and Reservoir Sampling. In Chain Sampling percentage of error depends on the elements in the current window and an improvement in sample size is observed in comparison to Uniform Random Sampling but load on the engine is comparatively high as sample replacements are also required to be processed by the engine.

Conclusion

The growing generated data from web applications is becoming a problem for the processing systems, and the relation between data is causing troubles when attempting to exploit data repositories. Therefore, In this paper we have proposed an extension of a real-time request system that allow us to reduce processing tasks and memory space requirements.

Different sampling methods suggested are useful for different applications. For example, if accuracy is required then we may go for Uniform Random Sampling with appropriate sampling percentage, and if memory size is fixed, we should go for Reservoir Sampling. Chain Sampling with suitable window size is favourable only when the samples need to be 'new'. In near future, we will be building the sample according to the importance of incoming data elements, rather than randomly choosing them.

Fig. 1 .

 1 Fig. 1. Block Diagram

  PREFIX lv: <http://deri.org/floorplan/> SELECT ?person ?locName FROM NAMED <C:/floorplan.rdf> WHERE { STREAM <C:/rfid.stream> [NOW] [SAMPLING %50] {?person lv:detectedAt ?loc } GRAPH <C:/floorplan.rdf> {?loc lv:name ?locName } } [OUTSAMPLING %80] We implemented Output Sampling using Operator : [OUTSAMPLING % {Sampling Percentage}]

Fig. 2 .

 2 Fig. 2. Sample size variation/ Number of triples processed by engine in Uniform Random Sampling (During time span of 1 minute)

Fig. 3 .

 3 Fig. 3. Plot of sample size variation and load on engine after using Reservoir Sampling (All plots are for the same time duration of 1 minute)

  8-hour daily maximum ozone concentrations as measured by Clean Air Status and Trends Network (CASTNET) in United States of America. The RDF data contains 2,159,133 triples consisting of 308,380 number of entries. 3 3.1 Uniform Random Sampling In this sampling method, incoming triples are sent to the engine, only if uniform random generation of true/false, with a probability equal to sampling percentage divided by 100, returns true. Operator : [UNISAMPLING %{Sampling Percentage}]

		30000
		25000
	Number of Samples	10000 15000 20000				Sampling 80%
						Sampling 60%
		5000				Sampling 40%
						Sampling 20%
		0	1969740400000000:32	1969740450000000:16	1969740500000000:32	1969740550000000:32	1969740600000000:3
					Time

Table 1 .

 1 Variation of Sample size, Load on engine and Error due to different sampling methods

	Method	Para-Sample Triples	Effective % Triples % of
		meter Size Processed Sampling % Processed Error
	Uniform	20	10034	10034	20.06	20.06	0.1819
	Random	40	19993	19993	39.98	39.98	0.1540
	Sampling	60	29998	29998	59.99	59.99	0.0793
	[Sampling %]	80	40002	40002	80.00	80.00	0.0494
		500	500	2807	1.00	5.61	1.3532
	Reservoir 1000	1000	4925	2.00	9.85	0.8041
	Sampling	2000	2000	8445	4.00	16.89	0.6047
	[Reservoir Size] 5000	5000	16490	10.00	32.98	0.3123
		10000 10229	42589	20.45	85.17	0.4410
	Chain	20000 13183	36332	26.36	72.66	0.5774
	Sampling 30000 14857	31260	29.71	62.52	2.5181
	[Window Size] 40000 16116	27298	32.23	54.59	0.6559

http://data-gov.tw.rpi.edu/wiki/Dataset_8/

Experimentation

The queries in Section 3 were first executed without any sampling, and then after incorporating different sampling operators. After computing 50,000 entries of 8-hour daily maximum ozone concentrations, without any sampling operator, their average was found to be 49.9161. Also, the average of results obtained by 20 iterations (after applying each sampling operator) is demonstrated in Table 1. All results are for 50,000 entries.

We may note that in Uniform Random Sampling probability of error reduces as the sampling percentage is increased while load on the engine is in coalition with the sampling percentage specified. In Reservoir Sampling, we see that the probability of error reduces with increase in reservoir size and a significant reduction in sample size as well as load on the engine is observed.


Abdullah Haskou
email: abdullah.haskou@univ-rennes1.fr

Sylvain Collardey
email: sylvain.collardey@univ-rennes1.fr

Ala Sharaiha
email: ala.sharaiha@univ-rennes1.fr

Small Array Design Using

Keywords: Parasitic Superdirective Antennas ESA, compact, end-fire, broadside, superdirectivity, parasitic element

published or not. The documents may come

I. INTRODUCTION

Electrically Small Antennas (ESAs) are interesting for emerging multi-band wireless technologies. However, these antennas, that are characterized by their narrow bandwidths, low efficiencies and quasi-omnidirectional radiation patterns, cannot be used alone in pointing applications where high directivities as well as compactness are required. In such cases, superdirective ESAs, where the array elements are very closely placed together, may be an attractive solution. There has been a considerable research on the design of superdirective antenna arrays [START_REF] Altshuler | A Monopole Superdirective Array[END_REF]- [START_REF] Haskou | Integrating Superdirective Electrically Small Antenna Arrays in PCBs[END_REF]. Early works were mainly based on wire-type unit-elements [START_REF] Altshuler | A Monopole Superdirective Array[END_REF]- [START_REF] Yaghjian | Electrically Small Supergain End-Fire Arrays[END_REF]. Recently, multiple planar parasitic superdirective ESAs were presented [START_REF] Pigeon | Miniature and Superdirective Two Elements Endfire Antenna Array[END_REF]- [START_REF] Haskou | Design of Small Parasitic Loaded Superdirective End-Fire Antenna Arrays[END_REF]. In this paper, we present a parasitic superdirective three-element array. Then, we show the possibility to use this antenna as a unit-element to design a compact 3D array. 1The rest of the paper is organized as follows: The simulation results are given in section II. The 3D array inter-element distance effect is studied in section III. The experimental results are presented in section IV. Finally, conclusions are drawn in section V.

II. SIMULATIONS AND RESULTS

The initial unit-element used in this work is a miniaturized printed half-loop antenna [START_REF] Sentucq | Superdirective Compact Parasitic Array of Metamaterial-Inspired Electrically Small Antenna[END_REF]. It is printed on a 0.8mm-thick Rogers RO4003 substrate and its dimensions are 24×20mm 2 .

A. Superdirective Unit-Element

The method described in [START_REF] Haskou | Design of Small Parasitic Loaded Superdirective End-Fire Antenna Arrays[END_REF] is used to design a threeelement array for a 866M Hz with an inter-element distance of 0.1λ. The array is integrated in a Printed Circuit Board (PCB) via an analysis similar to the one presented in [START_REF] Haskou | Integrating Superdirective Electrically Small Antenna Arrays in PCBs[END_REF]. Fig. 1(a) shows the antenna geometry and dimensions in millimeters. The fully-driven array calculated excitation coefficients and the required optimal loads for transforming this array to a parasitic (loaded) one are given in Table I. The fully-driven array achieves a maximum simulated (ANSYS HFSS [9]) total directivity of 9.5dBi. However, as it can noticed, some negative resistances are required to transform this array to a parasitic one. Neglecting theses resistances, total directivities of 7.3dBi, 9.2dBi or 7.2dBi can be achieved in case of exciting the first-, second-or third-element. The highest directivity in the case of exciting the second element is due to two reasons. First, in this case, only one negative resistance is neglected. Second, the excitation coefficient of this element is the highest, and hence, the array directivity is more sensitive to the changes in this element's excitation. Fig. 1(b) shows the parasitic antenna (exciting the second element and loading the first and third one with 68Ω//4.5pF , 0.6pF ) simulated endfire directivity (D (θ=90 o ,ϕ=90 o ) ) and input reflection coefficient magnitude in dB. The figure shows that the end-fire directivity is maximum at the design frequency. The antenna has an impedance bandwidth (S 11 < -6db) of 2.8M Hz and a directivity bandwidth (D max -1dB) of 2.6M Hz. Fig. 1(c) shows the antenna 3D total directivity radiation pattern at the resonance frequency (866M Hz). The figure shows a directive pattern with a maximum directivity of 9.2dBi in the end-fire direction. This directivity is 2.44dBi greater than Harrington's normal directivity limit [START_REF] Harrington | On the Gain and Beamwidth of Directional Antennas[END_REF]. Fig. 3 shows the antenna 2D total directivity radiation patterns in horizontal (XoY) and vertical (YoZ) planes at the resonance frequency. The Half Power Beam-Width (HPBW) in horizontal and vertical planes are respectively 60 • and 72 • . The Front to Back Ratio (FBR) is about 16.9dB. Due to the mutual coupling, the antenna presents a relatively small radiation efficiency (11.2%). Finally, this antenna is significantly smaller than a Yagi-Uda antenna covering the same frequency band and with the same directivity which dimensions are about 500 × 152mm 2 [11]. However, the miniaturization comes with some decrement in the antenna efficiency.

B. Compact Array Design

Two elements of the planar array are stacked along Zaxis with an inter-element distance of 200mm(0.6λ) as shown in Fig. 2(a). The two driven-elements are excited with equal power. Fig. 2(b) shows the antenna input reflection coefficient magnitude and directivity. The figure shows that the antenna's total directivity is also maximal around the resonance frequency of 866M Hz. The antenna has an impedance bandwidth of 2.8M Hz and a directivity bandwidth of 3M Hz. Fig. 2(c) shows the antenna 3D total directivity radiation pattern. The figure shows a directive pattern with a maximum directivity of 11.6dBi in the direction (D (θ=90 o ,ϕ=90 o ) ). Fig. 3 shows the antenna 2D total directivity radiation patterns. The HPBW in horizontal and vertical planes are respectively 56 • and 42 • , the FBR is 17.2dB, and the Side Lobe Level (SLL) is -11.4dBi. Finally, the antenna presents a radiation efficiency of 9.7%. Comparing with the initial end-fire array, it can be noticed that the total directivity is increased by 2.4dB. The horizontal HPBW is almost the same, while the vertical one is divided by 1.7. As for antenna FBR and efficiency, they are approximately the same as the initial end-fire's ones. This antenna is significantly smaller than equivalent (presents the same directivity) commercial antennas which dimensions are about 698.5 × 215.9 × 88.9mm 3

III. DISTANCE EFFECT

To study the effect of the distance between the two parasitic arrays (d) (refer to Fig. 2(a)), we change this distance from 0.01λ to 1.4λ while monitoring the antenna reflection coefficient, total directivity and radiation efficiency. Fig. 4(a) shows the array simulated input reflection coefficient magnitude as a function of the distance. The figure shows that for d = 0.01λ the array does not have any resonances in the observed band. This is due to the high mutual coupling. As the distance increases the mutual coupling decreases and the array resonance frequency converges to the one of the unit-elements. Fig. 4(b) shows the array simulated maximum total directivity and radiation efficiency as a function of the distance. The figure shows that for very small distances, the antenna's efficiency is maximal and as the distance increases the efficiency decreases. This is mainly due to the the lost of superdirectivity for very small distances. Fig. 5 shows the array simulated 2D total directivity radiation patterns at the design frequency as a function of the distance. The figure shows that for very small distances, the array directive pattern is lost and the array has a quasi-omnidirectional radiation pattern. This is also due to the high coupling effect that makes the applied loads unsuitable for having directive unit-elements. As the distance increases, the achieved directivity also increases till 1.2λ when it starts decreasing again.

IV. EXPERIMENTAL RESULTS

A prototype of the planar array was fabricated and measured for results validation. Fig. 6(a) shows a photograph of the prototype. Fig. 6(b) shows the antenna measured input reflection coefficient magnitude in dB. The measured resonance is 903M Hz (4.7% shifted compared to the simulated one). This shift is mainly due to the coaxial cable effect and the dispersion of SMD components. Due to the antenna low efficiency, it is not easy to measure its far-field radiation pattern in the presence of a coaxial cable. Hence an optical probe from enprobe [13] was used and the measurements were performed in SATIMO stargate (SG 32) near-field measurement system. Fig. 6(c) shows the measured 3D total directivity radiation pattern at the resonance frequency (903M Hz). This pattern is in a good agreement with the simulated one. The measured directivity is 8.1dBi. Fig. 7 shows measured 2D total directivity radiation pattens in horizontal and vertical planes. The HPBW in horizontal and vertical planes are respectively 67.5 o and 73 o and the FBR is 8.5dB. The small difference may be attributed to the measuring system and environment as well as the dispersion of SMD components.

V. CONCLUSION

In this paper, a parasitic end-fire three-element superdirective antenna array for 866M Hz frequency band was proposed. The array dimensions were (0.32λ × 0.31λ) and it presented a total directivity of 9.2dBi and radiation efficiency of 11.2%. The proposed array was, in turn, integrated in 3D array of total dimensions of (0.58λ × 0.32λ × 0.31λ) achieving a total directivity of 11.6dBi and radiation efficiency of 9.7%. This array is significantly smaller than classical arrays achieving the same directivity.

Fig. 1 .

 1 Fig. 1. Superdirective unit-element geometry and simulated parameters. (a) Geometry and dimensions, (b) input reflection coefficient magnitude in dB and end-fire total directivity, and (c) 3D total directivity radiation pattern at the resonance frequency (866MHz).

  [12].

Fig. 2 .

 2 Fig. 2. Broadside array geometry and simulated parameters. (a) Geometry and dimensions, (b) input reflection coefficient magnitude in dB and end-fire total directivity, and (c) 3D total directivity radiation pattern at the resonance frequency (866MHz).

Fig. 3 .

 3 Fig. 3. Two arrays' simulated 2D total directivity radiation patterns at the resonance frequency (866MHz). (a) Horizontal plane and (b) vertical plane.

Fig. 4 .

 4 Fig. 4. Broadside array simulated parameters as a function of the distance (d). (a) Input reflection coefficient magnitude in dB, and (b) maximum total directivity and radiation efficiency.

Fig. 5 .

 5 Fig. 5. Broadside array simulated 2D total directivity radiation patterns at the resonance frequency (866MHz) as a function of the distance (d). (a) Horizontal plane and (b) vertical plane.

Fig. 6 .

 6 Fig. 6. Planar array experimental results. (a) Fabricated prototype, (b) input reflection coefficient magnitude in dB and (c) 3D total directivity radiation pattern at the resonance frequency (903MHz).

Fig. 7 .

 7 Fig. 7. Planar array measured 2D total directivity radiation patterns at the resonance frequency (903MHz). (a) Horizontal plane and (b) vertical plane.

TABLE I

 I

	.	FULLY-DRIVEN ARRAY CALCULATED CURRENT EXCITATION
	COEFFICIENTS AND REQUIRED LOADS FOR TRANSFORMING THE ARRAY TO
			A PARASITIC ONE
	Element no.	Magnitude [A]	Phase [degree]	Optimal Load [Ω]
	1		1	0	17.9-j30
	2		1.4	-146	-53-j45.3
	3		0.2	69	-3526.9-j3305.5

This work was done with the funding of the French National Research Agency as part of the project "SOCRATE" and the support of the "Images et Reseaux" cluster of Brittany region, France.


Abdullah Haskou
email: abdullah.haskou@univ-rennes1.fr

Ala Sharaiha
email: ala.sharaiha@univ-rennes1.fr

Sylvain Collardey
email: sylvain.collardey@univ-rennes1.fr

Compact Planar Arrays Based on Parasitic Superdirective Elements

Keywords: Superdirectivity, parasitic-element, directivity, radiation efficiency

This paper addresses the problem of designing compact antenna arrays for UHF band by using small superdirective unit-elements. A small parasitic two-element array is designed for 868M Hz European RFID band. This array with a size factor (ka = 1.1) has a total directivity of 7dBi and radiation efficiency of 43.4%. Then this array is integrated in a 2 × 2 planar array. A parametric analysis on the interelement distance is performed revealing the tradeoffs between the antenna-dimensions, -directivity and -efficiency. A small 2 × 2 antenna array with dimensions of 34 × 34cm 2 presenting a total directivity of 12.6dBi and radiation efficiency of 41% is designed.

I. INTRODUCTION

Reducing the size of antenna arrays is always of a great interest in the antenna engineering community. However, the conventional techniques for enhancing the directivity of arrays lead to a significant increase in their size. At the same time, there has been renewed interest in superdirective arrays and in particular electrically small superdirective arrays [START_REF] Altshuler | A Monopole Superdirective Array[END_REF]- [START_REF] Haskou | Design of Small Parasitic Loaded Superdirective End-Fire Antenna Arrays[END_REF].

In [START_REF] Haskou | Design of Small Parasitic Loaded Superdirective End-Fire Antenna Arrays[END_REF] we detailed the design procedure of small parasitic superdirective arrays. In this paper, we propose a new strategy for designing compact arrays by using small superdirective arrays as unit-elements. The constraints including the maximum directivity, the efficiency, the predefined number of elements and the distance between the elements are studied. Results are validated through the realization and measurement of a 2 × 2 array. 1

II. UNIT-ELEMENT DESCRIPTION

The initial antenna used in the designed array is a miniaturized half-loop antenna printed on a 0.8mm-thick Rogers RO4003 substrate [START_REF] Sentucq | Superdirective Compact Parasitic Array of Metamaterial-Inspired Electrically Small Antenna[END_REF] and integrated in a PCB of 8 × 8cm 2 as shown in Fig. 1(a). It has a simulated (ANSYS HFSS [12]) resonance around 864M Hz as shown in Fig. 1(c). Fig. 1(d) shows the antenna surface current distribution (the same color range will be used from now on). As it can be noticed, the current on the ground plane is mainly following Yo direction, hence, it acts as a monopole in the XoY plane and following the Y-axis. This explains the omnidirectional radiation in the XoZ direction and the null in the oY direction in the antenna far-field radiation pattern given in Fig. 1(e). The null is slightly rotated toward X-axis due to the edges radiation. The antenna has a directivity of 2.4dBi and radiation efficiency of 89.4%. A prototype of the antenna was fabricated and measured for results validation (Fig. 1(b)). Fig. 1(c) shows the measured input reflection coefficient magnitude in dB. The measured resonance is at 881M Hz (a shift of 2% compared to the simulation). The antenna far field radiation pattern was measured in SATIMO Stargate SG 32 near field measurement system. The measured 3D total directivity radiation pattern at the resonance is given in Fig. 1(e). The measured directivity is 3.1dBi. For more insight the antenna 2D total directivity radiation patterns in E (XoZ) and H (YoZ) planes are given in Fig. 2. The antenna radiation efficiency measured in a reverberation chamber [START_REF] Le Fur | Performances of UWB Wheeler Cap and Reverberation Chamber to Carry Out Efficiency Measurements of Narrowband Antennas[END_REF] is about 75%.

III. PARASITIC SUPERDIRECTIVE UNIT-ELEMENT DESIGN

Two elements of the above-mentioned antenna are stacked along Z-axis with an inter-element distance d 1 is varying from 0.69cm to 6cm. Fig. 3(a) shows the effect of the inter-element distance on the resonance frequency. We note that for very small distances, the resonance is shifted to 910M Hz and as the distance increases this resonance converges to the one of the unit-element. Fig. 3(b) shows the array directivity as a function of the distance. As it can be noticed, the driven array directivity is maximal for small distances and as the distance increases this directivity decreases. The parasitic (loaded) array directivity is close to the fully-driven one till 3.5cm where a negative resistance is required and neglecting this resistance significantly decreases the array directivity. As for the array efficiency, it increases as the distance increases (Fig. 3(c)). This is due to the decrement in the mutual coupling and the disturbance in the superdirectivity phenomena. Based on this study and as compromise between the antenna-directivity and efficiency, we optimized a two-element array for 868M Hz European RFID frequency band with an inter-element distance of 2.5cm(0.07λ) as shown in Fig. 4(a). In this array, the first element is excited while the second is loaded by 3.3pF . Fig. 4(c) shows the antenna simulated input reflection coefficient magnitude in dB. As it can be noticed, the antenna has a resonance at 868M Hz. Fig. 4(d) shows the antenna surface current distribution. The figure shows that the current on the two elements is out of phase which is the condition for having superdirectivity for very small inter-element distance. Fig. 4(e) shows the antenna 3D total directivity radiation pattern. The figure demonstrates a directive pattern with a directivity of 7dBi toward z-axis. This directivity is 1.9dB greater than Harrington's normal directivity limit [14] for an antenna with the same size factor (ka = 1.1). The HPBW in E (XoZ) and H (YoZ) planes are respectively 100 o and 86 o and FBR is 8.2dB. Due to the current opposition, the antenna presents a radiation efficiency of 43.4%.

A prototype of the antenna was fabricated and measured (Fig.

4(b)

). Fig. 4(c) shows the antenna measured input reflection coefficient magnitude in dB. The measured resonance is at 880M Hz (a shift of 1.4% compared to the simulation). The antenna measured 3D total directivity radiation pattern at the resonance is given in Fig. 4(e). The measured directivity is 6.5dBi. The HPBW in E and H planes are respectively 95.6 o and 84 o and FBR is 6.7dB (Fig. 5). The antenna radiation efficiency measured in a reverberation chamber is about 40%.

IV. PLANAR ARRAY DESIGN

Four elements of the precedent parasitic array are integrated in 2 × 2 planar array as shown in Fig. 6(a). The spacing between the elements d (calculated between the excitation ports) is changed from 12cm to 30cm. Fig. 6(c) shows the mutual coupling as a function of the distance. As expected, the figure shows a higher coupling for small separations and as the distance increases the coupling decreases. Fig. 6(e) shows the antenna maximum directivity as a function of the distance. As the distance increases the coupling effect decreases and the achieved directivity increases till it reaches its maximum value around 0.8λ where it starts decreasing again. As for the antenna efficiency, as the distance increases it decrease (Fig. 6(f)). This is mainly due to the lost of the superdirectivity for small distances (superdirectivity is achieved by a current opposition on the two unit-elements (Fig. 4(d)) which cancels the antenna radiation in some directions and hence reduces its efficiency). Finally, Fig. 7 shows the 3D total directivity radiation pattern for a distance of 26cm ≈ 0.75λ. The achieved directivity is 12.6dBi, and the radiation efficiency is 41%. The HPBW in E (XoZ) and H (YoZ) planes are respectively 37 o and 35 o and FBR is 8.9dB and the Side Lobe Level (SLL) is 3.2dB. A prototype of the antenna was fabricated and measured (Fig. 6(b)). A power divider from Mini-Circuits [15] and UFL cables are used for the feeding system. Fig. 6(d) shows the antenna with the feeding system measured input reflection coefficient magnitude in dB. As it can be noticed, the resonance frequency is always at 879M Hz. It can also be noticed that the feeding system introduces a loss of about 1.5dB. This loss is due to the UFL cable, the power divider and the coaxial connections. The antenna directivity given in Fig. 6(e) shows the same trend as in the simulation. The antenna measured 3D total directivity for a distance of 26cm is in a good agreement with the simulated one (Fig. 7). The measured directivity is 12.1dBi. The HPBW in E and H planes are respectively 39.4 o and 33.8 o and FBR is 18.8dB (Fig. 8). The antenna reveals a measured radiation efficiency (also in a reverberation chamber) of about 39.8% after compensating the losses in the feeding system.

In all cases, the small difference between the simulated and measured results is due to the measurement environment (the connector, the excitation cable, ..), the measurement incertitude and the tolerance on the reference antennas' parameters namely directivity for radiation pattern measurement and radiation efficiency in the efficiency measurement.

V. CONCLUSION

In this paper, a two-element parasitic superdirective antenna array was designed. These array was later integrated in 2 × 2 planar antenna array. A parametric analysis on the interelement distance revealed the tradeoffs between the antenna dimensions, directivity and efficiency. For an inter-element distance of 26cm and for total dimensions of 34×34cm 2 a total directivity of 12.6dBi and radiation efficiency of 41% were achieved. This antenna is significantly smaller than classic arrays with the same directivity.

Fig. 1 .Fig. 2 .

 12 Fig. 1. The unit-element simulated and measured parameters. (a) Geometry and dimensions, (b) fabricated prototype, (c) input reflection coefficient magnitude in dB, (d) surface current distribution and (e) 3D total directivity radiation pattern.

Fig. 3 .

 3 Fig. 3. Parasitic two-element array parameters as a function of the interelement distance. (a) simulated input reflection coefficient magnitude in dB, (c) total directivity, and (c) radiation efficiency.

Fig. 4 .

 4 Fig. 4. Two-element array with 2.5cm spacing simulated and measured parameters. (a) Geometry and dimensions, (b) fabricated prototype, (c) input reflection coefficient magnitude in dB, (d) surface current distribution and (e) 3D total directivity radiation pattern.

Fig. 5 .

 5 Fig. 5. Two-element array with 2.5cm spacing simulated and measured 2D total directivity radiation pattern. (a) E plane and (b) H plane.

Fig. 6 .

 6 Fig. 6. Planar array simulated and measured parameters as a function of the separation. (a) Geometry, (b) fabricated prototype, (c) mutual coupling, (d) input reflection coefficient magnitude in dB, (e) total directivity and (f) radiation efficiency.

Fig. 7 .

 7 Fig. 7. Planar array 3D total directivity radiation pattern for d=26cm. (a) Simulated and (b) measured.

Fig. 8 .

 8 Fig. 8. Planar array 2D total directivity radiation pattern for d=26cm. (a) E plane and (b) H plane.

This work was done with the funding of the French National Research Agency as part of the project "SOCRATE" and the support of the "Images et Reseaux" cluster of Brittany region, France.

ACKNOWLEDGMENT

The authors would like to thank Mr. Jérôme Sol from IETR UMR CNRS 6164-INSA de Rennes for all the time he dedicated to the measurements presented in this manuscript.


Abdullah Haskou
email: abdullah.haskou@univ-rennes1.fr

Dominique Lemur
email: dominique.lemur@univ-rennes1.fr

Sylvain Collardey
email: sylvain.collardey@univ-rennes1.fr

Ala Sharaiha
email: ala.sharaiha@univ-rennes1.fr

Miniature and Wide-Band ILA Antenna with Non-Foster Matching

Keywords: Electrically small antenna, miniaturization, non-Foster

In this paper, we present a miniature, wide-band, Inverted L Antenna (ILA) with non-Foster matching. The antenna size is 9.5 × 19.5 mm 2 and it is integrated on a Printed Circuit Board (PCB) of 100 × 60 mm 2 . The antenna covers the whole frequency band of (0.76 -2.17) GHz and the circuit is stable throughout this band.

I. INTRODUCTION

Antenna miniaturization is the key for a compact wireless technology. The main drawbacks of Electrically Small Antennas (ESAs) are their low efficiencies and narrow bandwidths even when a passive matching circuit is used. The maximum achievable bandwidth with passive matching is limited by the theoretical limits of Bode-Fano [START_REF] Fano | Theoretical Limitations on the Broadband Matching of Arbitrary Impedances[END_REF] and Chu-Harrington [START_REF] Chu | Physical Limitations of OmniDirectional Antennas[END_REF], [START_REF] Harrington | On the Gain and Beamwidth of Directional Antennas[END_REF]. A possible solution is the use of non-Foster matching that surpass these limits [START_REF] Hirvonen | Bandwidth Limitations of Dipoles Matched with Non-Foster Impedances[END_REF] and enhance miniature antenna performance in reception [START_REF] Aberle | Two-Port Representation of an Antenna with Application to Non-Foster Matching Networks[END_REF]. A.J. Bahr showed that using an active coupling network with a receiving antenna (a short monopole) can significantly improve its Noise Figure (NF) [START_REF] Bahr | On The Use of Active Coupling Networks with Electrically Small Receiving Antennas[END_REF]. Sussman-Fort experimentally showed that using a negative capacitor for matching a 152.4-mm monopole for (20 -110) M Hz frequency band presents a significant improvement in the Signal to Noise Ratio (SNR) compared to the same antenna without matching [START_REF] Sussman-Fort | Matching Network Design Using NonFoster Impedances[END_REF]. Koulouridis and Volakis demonstrated that using a non-Foster circuit to match a 152.4-mm loop can highly increase its bandwidth and decrease its resonance frequency [START_REF] Koulouridis | Non-Foster Circuits for Small Broadband Antennas[END_REF]. G. Mishra et al presented a Bowtie antenna covering (0.6 -1.1) GHz frequency band using a non-Foster circuit [START_REF] Mishra | Non-Foster Matching of Eclectically Small Bowtie Antenna Covering 600MHz to 1100MHz[END_REF]. The design of non-Foster circuits becomes more challenging when targeting at higher frequencies (due to the active components non-Linearity) and when targeting high impedance values (due to the parasitic elements). In this paper, we present a broadband miniature Inverted L Antenna (ILA) with a non-Foster matching. In particular, we focus our attention on exploiting the parasitic capacitance of the transistors in order to match this antenna requiring a high reactance value. By using the proposed non-Foster circuit, we demonstrate three times improvement in the antenna -10 dB bandwidth compared to the passive antenna. The realistic implementation and stability issues are discussed throughout the paper.

II. ANTENNA STRUCTURE AND NON-FOSTER CIRCUIT

The proposed antenna is an ILA of 9.5 × 19.5 mm 2 integrated on a Printed Circuit Board (PCB) 100 × 60 mm 2 as shown in Fig. 1(a). This antenna, printed on a 0.8mmthick Rogers Duroid 5880 substrate, has a measured resonance frequency of 2.39 GHz (1(b)). To eliminate the reactance of the antenna at 910 M Hz, a negative capacitor of 0.7 pF is required. We optimized a Linvill floating type [START_REF] Linvill | Transistor Negative-Impedance Converters[END_REF] Negative Impedance Convertor (NIC) circuit to realize this capacitance as shown in Fig. 2. The active components in the circuit are BFR93A transistors [11]. The circuit is supplied by 4 V DC , it consumes a current of 24mA or equivalently a DC power of 96mW . The measured reactance of this circuit is shown in Fig. 3(a). As it can be noticed, the circuit reactance decreases with frequency which means that the circuit has a non-Foster behavior (negative capacitance). The value of the equivalent capacitance is given in Fig. 3(b).

III. ACTIVE ANTENNA PERFORMANCE

A prototype of the antenna with the non-Foster circuit was realized and measured. Fig. 4 shows a photograph of the active antenna with the NIC circuit on the bottom side. Fig. 5 shows the antenna measured input reflection coefficient magnitude in dB. It can be noticed that antenna has an impedance bandwidth of 100 % (matched throughout (0.76 -2.17) GHz frequency band). The antenna was also tested for transistors non-linearity effect by increasing the input power level from -35 dB to 10 dBm. The measurement results given in Fig. 6 shows that the antenna is well suited for RF power levels less than 5 dBm. Finally, the antenna stability has been underlined using a spectrum analyzer (RIGOL DSA1030 [12]) with a Power Spectral Density (PSD) of -134 dBm/Hz. Fig. 7 shows the noise floor of the spectrum analyzer. It can be noticed that no visible additive noise affect the bandwidth of interest. To investigate the added noise by the non-Foster circuit, we compare the output of the spectrum analyzer when connected to the non-Foster antenna and when connected to a 50Ω load. The measurement conditions are the same as before, however, the results are averaged on 10 cycles for fair comparison. The obtained results given in Fig. 8 shows that the added noise by the non-Foster circuit is negligible.

IV. CONCLUSION

In this paper, we presented a miniature broadband ILA. The passive antenna resonant at 2.39 GHz was matched in the (0.76 -2.17) GHz band using a Linvill floating-type non-Foster circuit. The measurement results show that the antenna is stable and demonstrates a good behavior across the band of interest.

Fig. 1 .

 1 Fig. 1. Passive ILA. (a) The realized prototype, (b) measured input reflection coefficient magnitude in dB.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Proposed NIC circuit. (a) General schematic of Linvill floating circuit and (b) photograph of the prototype.

Fig. 4 .Fig. 5 .

 45 Fig. 4. A photograph of the fabricated active antenna. (a) Top view and (b) bottom view.

Fig. 6 .

 6 Fig.6. The measured input reflection coefficient magnitude in dB of the active antenna for different input power levels.

Fig. 7 .Fig. 8 .

 78 Fig. 7. The noise floor level of the spectrum analyzer terminated at the input with the non-Foster matched antenna. (a) On (0.01-3) GHz frequency band and (b) on (0.81 -1.01) GHz frequency band.

ACKNOWLEDGMENT

This work was done with the funding of the French National Research Agency as part of the project "SENSAS".


Florent Guichard
email: florent.guichard@institutoptique.fr

Yoann Zaouter

Marc Hanna

Khanh-Linh Mai

Franck Morin

Clemens Hönninger

Eric Mottay

Patrick Georges

High-energy chirped-and divided-pulse Sagnac femtosecond fiber amplifier

Keywords: Ultrafast lasers, (140.3510) Lasers, fiber, (060.2420) Fibers, polarization-maintaining

We report on the generation of 1.1-mJ, 300-fs pulses at 50 kHz by implementing an amplifier architecture whereby four stretched pulse replicas are created in the temporal and spatial domains, allowing pulse energy scaling by the same factor. The whole spatiotemporal coherent combining geometry is passive, avoiding the need for active electronic stabilization loop systems. The combining efficiency remains above 90% at all power levels.

High-power femtosecond fiber lasers are now wellestablished as compact and reliable sources of ultrafast pulses. The guiding properties of the amplifying medium guarantees excellent optical-to-optical efficiency and beam quality, but limits the achievable pulse energy because the mode area cannot be scaled arbitrarily. Despite this limitation, femtosecond pulses carrying energy of several microjoules have been generated from such systems [1]. This has been made possible by using very large mode area rod-type fibers and the chirped pulse amplification (CPA) architecture with significant stretching ratios of several nanoseconds. The pulse energy is thereby spread in time and space, limiting the peak intensity that causes detrimental optical nonlinear effects. However, these large stretching ratios are obtained by using very large and expensive diffraction gratings that cannot be reasonably further scaled.

To reach higher energies or reduce the footprint of high energy ultrafast fiber sources, recent experimental efforts have focused on coherent combining of several independently amplified pulses, either in the space or time domains, to further decrease the peak intensity in the amplifying medium. Active coherent beam combining [2], passive coherent beam combining [3], and divided pulse amplification (DPA) [4,5] have all been recently demonstrated to allow energy scaling. Active parallel beam combination can in principle be scaled arbitrarily, and record performances have been recently obtained using four rod-type fiber amplifiers [6].

In contrast, it is more difficult to scale the number of pulses that can be coherently combined passively, i.e., without the need for active feedback on the optical phase of the pulses. High-energy passive DPA systems [7] are limited by the onset of gain saturation that breaks the symmetry between successive pulse replicas in the amplifiers. This effect limits the number of replicas that can be combined efficiently at high energy to only two [8]. The same is true for passive coherent beam combining [9], because the Sagnac interferometer (SI) only produces two counter-propagating beams. Multiple beams same-path interferometers can in principle be devised, but these architectures are not well suited to high-gain fiber amplifiers due to parasitic laser effect. Scaling the performances of passive coherent combining systems therefore requires the use of spatial and temporal strategies simultaneously. In particular, DPA can be used in conjunction with CPA [8], or with passive coherent combining [9], to allow even further increase of performances.

In this report, we use simultaneously four strategies in the space and time domains to decrease the peak intensity inside Yb-doped amplifying fibers: very large mode area rod-type fibers, CPA, DPA, and passive coherent beam combining embodied in an SI. The full use of passive combining techniques allows the generation of high temporal quality 300-fs pulses with 1.1-mJ energy at a repetition rate of 50 kHz, corresponding to an average power of 55 W. This is achieved by an optical setup with a limited footprint of 120 cm × 60 cm.

The experimental setup is shown in Fig. 1. The front end is composed of a passively mode-locked ultrafast oscillator, a pulse picker, a stretcher, and a low-power fiber preamplifier. The oscillator generates pulses at the central wavelength of 1030 nm and pulse duration of 200 fs. The incident pulses are stretched to 500 ps, and stretching parameters are designed to introduce a dispersion mismatch between the stretcher and the compressor units in order to partially compensate for the residual phase accumulated in the moderately nonlinear main amplifier [10]. The repetition rate of the oscillator is reduced by an acousto-optic modulator pulse picker to obtain a train of pulses at 50 kHz. This train of pulses is sent through an isolator that is also used to extract the final amplified and recombined beam. A freespace unbalanced interferometer with polarizers used as splitting and recombining components creates two linearly and orthogonally polarized replicas in the time domain. Depending on the orientation of the input linear polarization, the power fraction sent in each replica can be adjusted. The path length difference of this Mach-Zehnder interferometer corresponds to a delay of 1.2 ns. The divided-pulse beam then propagates through a combination of Faraday rotator and quarter wave plate prior to the SI to ensure proper spatiotemporal recombination on the way back through the system as detailed in [9].

Each time-domain replica is split in two spatially separated beams in the SI. This loop interferometer includes two state-of-the-art ytterbium-doped double-clad rodtype fiber amplifiers. The mode field diameter of each rod is 60 μm, and their length 80 cm. Furthermore, they are arranged in a completely symmetric geometry to ensure that the spatial properties of the counter-propagating beams to be combined are as identical as possible in order to yield high combining efficiency. Each fiber amplifiers is pumped from the SI splitter/recombiner side with a 180-W diode lasers emitting system at 976 nm and coupled into 200-μm multimode fibers. No additional optical elements were added to prevent reinjection of a pump diode into the other, since the pump light is almost completely absorbed in 1.6 m of rod-type fibers. Seed coupling from one fiber amplifier to the other is done through relay imaging. The SI also includes two quarterwave plates between the splitter and both fiber inputs to operate the amplifiers in circular polarization, thereby decreasing accumulated optical nonlinearities. After propagating through the SI, the polarization state of each beam is flipped by 90°and is routed back through the DPA Mach-Zehnder. The overall optical arrangement and polarization evolution results in an identical optical path for all four spatiotemporal replicas, and the pulses coherently combine without the need for active stabilization devices. By design, this architecture is immune to phase noise at frequencies lower than the inverse propagation time in the system, around 10 MHz. After extraction by the input polarizer associated to the isolator, the amplified pulses are finally sent to an 85% efficiency gratings-based compressor.

Possible phase mismatch in space and time between replicas can alter the coherent combining process. This corresponds to a fraction of power being directed toward the uncombined output of Fig. 1. In time, parasitic replicas can appear at delay values corresponding to the DPA Mach-Zehnder path length difference. Experimentally, the combining efficiency is defined as follow: η P combined P combined P uncombined ;

where P combined and P uncombined , respectively, correspond to the average power measured along the combined and uncombined output. Moreover in our setup, the SI arrangement leads us to define another residual average power output, denoted as the unpolarized output in Fig. 1. This power fraction is related to polarization evolution effects that occur during propagation in the SI and is not taken into account in the coherent combining efficiency since it is independent on the relative phase mismatch between counter-propagating beams. In particular, residual birefringence in the fiber amplifier leads to cross-phase modulation, imparting a time-dependent polarization state that causes this unpolarized output power to reach 1 W at the highest pump power. The combined, uncombined, and compressed powers are plotted as a function of the total pump power in Fig. 2, along with the combining efficiency. The laser is operated at 50 kHz and the output average power linearly increases, with a slope efficiency of 44%, to finally reach a maximum value of 64 W before compression, corresponding to an energy of 1.27 mJ. This slope efficiency is calculated with respect to the combined average output power, which constitutes the useful power fraction. Finally, the 85% efficiency compressor unit leads to the generation of ultrashort pulses with 1.1 mJ and 55 W of average power. Without any coherent combining strategy, and using the same stretching ratio and fiber amplifier, the achievable output compressed pulse energy is 350 μJ, limited by optical damage. This illustrates the benefit of passive coherent combining that provides a performance scaling factor in energy very close to the number of replicas.

The maximum combining efficiency of ∼94% is obtained for a combined and compressed average power of 10 W, corresponding to a low accumulated B-integral per replica of only 2.4 rad. The efficiency then slightly decreases to 90.5% when the output energy is increased. To maintain the highest possible combining efficiency, a careful adjustment of the half-waveplates that controls the amount of energy sent into each time-domain replica is necessary. This optimization requirement can be understood as follows: as the amplified energy increases, saturation of the gain occurs, leading to temporally decreasing gain value. This decreasing energy distribution among pulse replicas in the time domain can in turn be translated into a differential phase by two mechanisms: self-phase modulation and Kramers-Krönig coupling between gain and refractive index along the fiber. This differential phase then hinders proper coherent combining. By adjusting the waveplate, the differential phase can be controlled and leads to optimal DPA combining via the minimization of phase difference between the different temporal replicas to be recombined. It is to be noted that this phase mismatch optimization does not lead to pulse replicas with equal intensities. This effect increases with saturation-dependent differential phase, which explains the drop of combining efficiency at high energies.

In our setup, a phase mismatch between counterpropagating beams can also is translated into a nonrectilinear output polarization state. This can lead to parasitic temporal replicas after propagation in the Mach-Zehnder interferometer, adding a temporal contribution to the combining efficiency. This contribution is defined by the amplitude ratio between the main pulse and the sum of all temporal contributions. The temporal efficiency is measured by sending a portion of the compressed output beam into a fast photodiode and oscilloscope, with an overall bandwidth of 4 GHz. Results are shown in Fig. 3 where parasitic replicas are hardly found around the main pulse (see orange curve) with an estimated contribution of less than 1% at all energy levels when the amplifier is properly optimized. In order to emphasize the temporal position of these replicas, we have unbalanced the SI on purpose, thus generating an important phase mismatch between both beams finally leading to the appearance of clear replicas (blue curve) at 1.2 ns around the main pulse. Note that this misalignment would be equivalent to a combining efficiency of less than 60%

Temporal characterizations of the output pulse at maximum energy are carried out with a secondharmonic-generation frequency-resolved optical gating (SHG-FROG) device together with independent spectrum and autocorrelation measurements. This data set is plotted in Fig. 4. Electric field reconstruction is carried out on a 512 × 512 grid [see Fig. 4(a)] and quickly converges to a very low FROG error of 22 × 10 -4 . Independent temporal and spectral measurements are in full agreement with the retrieved data and are plotted in Figs. 4(b) and 4(c). The full width at half-maximum (FWHM) of the spectrum is 7.3 nm. The spectral phase is also plotted in Fig. 4(b) (green curve) and shows a residual structure, mainly dominated by a cubic term characteristic of the nonlinear phase compensation induced by the dispersion mismatch between the stretcher and the compressor. In the time domain, the measured and retrieved autocorrelations FWHM are 420 fs [see Fig. 4(c)] corresponding to a retrieved temporal pulse profile FWHM of 300 fs. The high-quality retrieved temporal profile is shown in Fig. 3(d) and has a FWHM timebandwidth product of 0.63. It also exhibits a low-pedestal due to the partial compensation of the nonlinear phase accumulated during amplification. With combined and compressed pulse energy of 1.1 mJ, the retrieved pulse profile has a peak power of 3.1 GW.

Finally, we systematically analyze the beam quality at the output of the compressor. High beam quality is expected from the rod-type fibers and the SI as the spatial coherent combining process also acts as a spatial filter for the coherently combined output. The far-field beam profile has a nearly Gaussian shape (see Fig. 5), and M 2 measurements reveal near diffraction limited values of, respectively, M 2

x 1.24 and M 2 x 1.25 at all energy levels. These values are similar to what is obtained using the same fiber in a standard CPA amplifier.

In summary, we demonstrate that the integration of several passive coherent combining schemes can lead to the generation of ultrashort multi-GW peak-power pulses from very large mode area rod-type fibers in very compact setups. By implementing the DPA principle before an SI, we generate up to four stretched spatiotemporal replicas of the incoming pulses and scale the output energy by the same factor to generate 300-fs, 1.1-mJ pulses. This is achieved in a moderately nonlinear CPA architecture with stretched pulse durations of only ∼0.5 ns. Therefore, peak power scaling toward >10 GW can be envisioned by applying multi-ns stretching ratio as in recently published work [1,11]. Our fully passive system compares favorably to the active DPA setup that also implements four replicas reported in [12], with similar compressed pulse energy and a higher average power and combining efficiency, although the stretching ratio is 4 times lower in our setup. This illustrates the robustness of the passive combining approach. However, the active approach provides potential scalability in terms of number of replicas that can be used. The average power is currently limited by thermally induced beam pointing drifts that prevent proper combination of the output beams over an extended period of time. This is a technical issue that can be solved with careful thermomechanical design of the optical mounts. Average power scaling is therefore possible because of the separate fiber outputs, enabling power levels beyond the modal instability threshold of a single amplifier.

The authors believe that this laser source is for example an ideal pump source for high repetition rate white-light seeded OPA/NOPA working from UV to mid-IR [13] that are of considerable interest for ultrafast science communities.

Fig. 1 .

 1 Fig. 1. Experimental setup of the passively combined DCPA Sagnac amplifier. FR, Faraday rotator; HWP, half-waveplate; QWP, quarter waveplate.

Fig. 2 .

 2 Fig. 2. Combining efficiency measured at 50 kHz. Uncombined (blue), combined (red), and compressed (green) average power of DCPA-Sagnac amplifier.

Fig. 3 .

 3 Fig. 3. Combined and compressed temporal traces recorded with a 4-GHz oscilloscope. Blue trace corresponds to an unbalanced SI configuration in order to emphasize the temporal position of parasitic replicas.

Fig. 4 .

 4 Fig. 4. (a) Measured (top) and retrieved (bottom) FROG trace at 1.1 mJ. (b) Independently measured and retrieved spectrum, green curve corresponds to the retrieved spectral phase. (c) Independently measured and retrieved autocorrelation profiles. (d) Temporal profile and peak intensity of the retrieved pulse.


Aymeric Van De Walle
email: aymeric.van-de-walle@institutoptique.fr

Marc Hanna

Florent Guichard

Yoann Zaouter

Alexandre Thai

Nicolas Forget

Patrick Georges

Spectral and spatial full-bandwidth correlation analysis of bulk-generated supercontinuum in the mid-infrared

Keywords: Supercontinuum generation, (320.7090) Ultrafast lasers, (320.7110) Ultrafast nonlinear optics

Supercontinuum (SC) generation is an extremely nonlinear phenomenon used to generate optical spectra that can extend over several octaves. First reported in bulk media in 1970 [1], it was later observed and studied in optical fibers, where the required power level is much lower. This has enabled SC generation in all temporal regimes, from CW to femtosecond, and triggered numerous applications [2]. The very rich physics of SC generation has been a widely studied subject, both in bulk media [3] and in fibers [2], including recent studies on single-shot characterization [4] and shot-to-shot correlation properties of SC [5][6][7]. These studies have mostly focused on fiber-generated SCs, since it has been shown that coherence can be quickly lost in this case.

On the other hand, there is an increasing interest for bulk-generated SC to be used as a seed for broadband optical parametric amplification (OPA) systems [8]. In particular, robust high-power ytterbium-based amplified femtosecond laser systems delivering pulses with a duration in a range of 300 fs-1 ps can be used both as a pump source for the OPA system and for the SC generation [9], thereby providing optical synchronization between signal and pump. This is increasingly important in systems where the stretched pulse duration is in the range of 300 fs-10 ps, which are more sensitive to relative timing fluctuations. Bulk SC-seeded OPAs at 800 nm have been extensively studied [10], but are less common in the midinfrared, despite a large interest in this wavelength range for molecular multidimensional spectroscopy and attophysics applications [11,12]. Although it is known that by operating in the single filament regime, a stable SC beam can be generated in bulk media, there are few reported studies of bulk SC spectral fluctuations and correlations to the best of our knowledge [13,14]. These works focus on the visible part of the SC generated by a Ti:Sa laser in bulk CaF 2 or YAG at low repetition rate. However, the spatial correlation properties have not been investigated yet, a legitimate concern for bulk SCs. Since they are being considered for use as a seed for large OPA-based laser facilities, the question of their spectral and spatial fluctuation dynamics is particularly important.

In this Letter, we report on the full bandwidth spectral and spatial correlation analysis of a mid-infrared SC generated by focusing microjoule femtosecond pulses from a high-energy ytterbium-doped fiber amplifier in bulk YAG. Shot-to-shot measurements at a repetition rate of 1 MHz are obtained by implementing the time-stretch dispersive Fourier transform in an optical fiber to map the spectral domain to the time domain, a technique used in the context of fiber SCs [5][6][7]. A fast real-time oscilloscope is used to retrieve the temporal data for each shot. Spatial correlations are measured by sampling two copies of the beam at different locations. The results show the overall stability of single-filament bulk SCs, and a correlated noise behavior in the 1.4-1.7 μm wavelength range. The spatial fluctuations are also correlated, and a good spectral homogeneity is observed. Finally, a long-term multi-shot spectral measurement reveals excellent stability over hours. These results support the strong interest of Yb laser-pumped SC-seeded OPA systems in the mid-infrared.

The experimental setup is described in Fig. 1. A halfwave plate and a polarizer are used to sample a pulse energy of 1.8 μJ from an ytterbium-doped rod-type fiber amplifier (Tangerine, Amplitude Systemes). This laser system delivers 400 fs pulses at 1030 nm, with an optical bandwidth of 6 nm at a repetition rate of 1 MHz. The 1.5 mm diameter beam (FWHM) is focused in a 10 mm long YAG crystal with a 125 mm focal length lens to generate the single filament SC. Loose focusing is known to increase the spectral content in the near-infrared [15]. The SC is collimated by another 125 mm lens, filtered to remove the 1 μm pump and isolate the bandwidth of interest, and split into two beams using a broadband beamsplitter. Each beam is focused down to a diameter of 150 μm (FWHM), where standard SMF28 fibers are located. The difference between the diameter of the focused beam and the 9 μm diameter of the fiber allows spatially selective coupling in the fibers, and scanning the fiber position gives access to spectral measurements that are spatially resolved in the near field. For spatial correlation measurements, both fibers are then coupled to a single fiber using a standard broadband fiber coupler, with a relative delay of 25 ns corresponding to a 5 m fiber additional path length difference. This signal is sent to 260 m of dispersion compensating fiber that introduces a large amount of dispersion to perform the time stretch Fourier transform. A fast InGaAs photodetector and oscilloscope, with overall bandwidth of 8 GHz, allow detection of the stretched pulses. The RMS value of the detection noise is evaluated to be 0.4% of the full detected scale. A single detection fiber is used to measure the spectral correlation properties, and to measure the spectral homogeneity of the beam by scanning the fiber. Both detection fibers are used to compute spatial correlations, since they allow observation of the same train of pulses at two different locations in the beam. Finally, the 1 μm pump is detected independently to measure energy fluctuations of the SC excitation, with a typical value of 1% RMS.

The use of the time-stretch dispersive Fourier transform requires a calibration to map the measured time trace to the spectrum. This is achieved by identifying distinct spectral features and comparing the time signal with an independently measured spectrum from an optical spectrum analyzer. The group-delay introduced by the fiber as a function of wavelength is shown in Fig. 2, with calibration points and a polynomial fit. The oscilloscoperetrieved spectrum using this calibration is shown against an independently measured optical spectrum in the inset. The 1.4-1.7 μm wavelength range is mapped to a 4 ns time window. Taking into account the bandwidth of the detection system, this corresponds to a spectral resolution of 10 nm in this range.

We first examine spectral correlations of the SC by positioning one fiber at the center of the beam, while the other fiber is not used. A data set of 500 successive pulses is acquired and processed. The spectral correlation between two wavelengths, λ 1 and λ 2 , in the SC is defined as in Ref. [5], equivalent to the Pearson correlation in Ref. [13]:

ρλ 1 ; λ 2 hIλ 1 • Iλ 2 i -hIλ 1 i • hIλ 2 i hI 2 λ 1 i -hIλ 1 i 2 • hI 2 λ 2 i -hIλ 2 i 2 p : (1)
For comparison purpose, the YAG crystal and filter can be removed to generate a fiber SC in the first few meters of SMF28 fiber. The resulting correlation map, along with the accumulated spectra, is shown in Fig. 3. As in previous works on fiber SCs, large spectral instabilities are observed (13.8% RMS near the generation wavelength) with correlation maps similar to previous observations [7]. The correlation is low in the mid infrared, and a feature distinctive of wavelength jitter is observed around the pump wavelength.

In contrast, bulk SC data obtained when a dichroic mirror is used to attenuate the 1 μm pump is shown in Fig. 4. Pump filtering ensures that the highly dispersive fiber does not induce significant nonlinear effects after bulk SC generation. The transmission of the dichroic mirror is not flat over the investigated wavelength range, but this does not affect the statistical properties of the SC. The most obvious difference with the fiber case is the high stability of spectral features. Although the magnitude of the correlation is always high, illustrating the coherence of the bulk SC process, two spectral ranges exhibiting different qualitative features are observed: (1) rapid alternate correlation and anti-correlation areas for low wavelengths closer to the pump, and (2) a large area where the correlation is large and positive at wavelengths above 1.4 μm. A similar behavior has been observed in the visible range of an SC generated from a Ti:Sa laser at 800 nm [13].

By replacing the dichroic mirror with a long-pass filter at 1.4 μm, we observe specifically the large correlated wavelength band in the near infrared with a better signal-to-noise ratio and wavelength fidelity as shown in Fig. 5. This band is of particular interest for ytterbium systems-pumped mid-IR OPA systems, since it allows the generation of an amplified signal around 1.55 μm, corresponding to a carrier-phase envelope stable idler at 3 μm. The smooth generated spectrum is fully correlated, indicating that the spectrum shape does not fluctuate. The decrease of the correlation value beyond 1500 nm is most probably because of the fact that uncorrelated detection noise becomes nonnegligible compared to the signal. To quantify the stability of this signal, the RMS shot-to-shot relative intensity noise of the spectral component at 1550 nm over 500 pulses is 3.4%, compared to 1.2% for the pump intensity noise. This value is particularly important for seeding applications since it impacts the final laser stability.

Long term stability is also a major concern in OPCPA systems. In particular, since SC is generated at intensity levels close to crystal breakdown, slow alteration of the crystalline matrix can occur. The spectrum of the SC is recorded for 40 h to monitor possible spectral drifts, along with the average power of the pump laser. As shown in Fig. 6, the SC spectrum is very stable, except for a slight broadening because of the slow increase of pump power.

We now investigate spatial properties of the SC in the 1.4-1.7 μm range. Since complex spatiotemporal dynamics is involved in bulk SC generation, including filamentation, the question of spectrospatial couplings in the SC beam is natural. Color rings can be routinely observed in such beams [3], indicating large spatial inhomogeneities in the visible region. By translating the collecting fiber in the SC beam (shown in the inset of Fig. 1 as recorded using an InGaAs camera), the mid-infrared spectrum is retrieved as a function of radial coordinate using a standard spectrum analyzer. The power in each retrieved spectrum is normalized to remove the decrease in intensity because of lateral displacement, and this data is plotted in Fig. 7. The spectral homogeneity in this band is remarkably good, with only a slightly larger extension toward the long wavelength side for the outer part of the beam.

By using both collecting fibers, we can measure spatial correlations in the beam to track potential fluctuations of the beam shape at the shot-to-shot level. The spatial correlation between two positions, x 1 and x 2 , at a given wavelength λ is given by

1 ; x 2 ; λ hIx 1 ; λ • Ix 2 ; λi -hIx 1 ; λi • hIx 2 ; λi hI 2 x 1 ; λi -hIx 1 ; λi 2 • hI 2 x 2 ; λi -hIx 2 ; λi 2 p : (2)
The correlation map between the center of the beam (x 1 0) and the beam sampled at a given radial coordinate as a function of wavelength is plotted in Fig. 8. The wavelength correlation map shows a fully correlated behavior of the mid infrared beam. The decrease of the correlation coefficient at long wavelengths is because of the limited signal to noise ratio: uncorrelated detection noise is not negligible in this case and decreases the correlation coefficient.

In conclusion, we have studied spectral and spatial statistical properties of bulk SC generated by focusing 1.8 μJ 400 fs pulses at the wavelength of 1030 nm in bulk YAG. The stability and correlation properties of this radiation in the near infrared wavelengths between 1.4 and 1.7 μm are remarkably good, with only a minor degradation of RMS relative noise intensity compared to the pump. The spatial homogeneity and correlations are also well behaved, advocating the use of these SCs as seed beams for near-infrared ultrafast OPAs. This work was supported by the FUI project STAR and LABEX PALM project MIROPCPA.

Fig. 1 . 1 Fig. 2 .Fig. 3 .

 1123 Fig. 1. Experimental setup and spatial profile of the SC mid-IR part. HWP, half-wave plate; P, polarizer; DCF, dispersion compensating fiber; PD, photodetector. Inset: spatial profile of the SC recorded with an InGaAs camera after a 1400 nm longpass filter.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Results for bulk SC generation. Top: accumulated retrieved spectra. Bottom: spectral correlation map according to Eq. (1).

Fig. 6 .

 6 Fig. 6. Top: average pump power as a function of time. Bottom: SC spectrum recorded with an optical spectrum analyzer (log scale) as a function of time over 40 h.

  ρx

Fig. 7 .Fig. 8 .

 78 Fig. 7. Normalized SC spectrum as a function of radial coordinate across the beam.