In subsaharan Africa, HIV prevention remains largely unsufficient

The prevention mainly depends on the relationship existing between man and woman within the couple In Africa, conjugal union can take multiple forms

We explore here two characteristics of the union : Communication about STD/HIV between HIV+ women and their partner, after HIV test, by the kind of union

  To have a co-wife or notTo live with the partner or not Which are related to : The communication on HIV within the couple HIV preventive practices used by the couple Managing the HIV/AIDS risks in subsaharan African couples. The roles of polygamy and co-residency. shares her partner with a co-wife the male domination is stronger there is competition between co-wives Dialogue with the partner is more difficult Women less keen to suggest HIV test or the use of condom to their partner  not in favour of the adoption of HIV preventive practices Hypothesis 2 Hyp 2 : Over the last decades new forms of polygamy have appeared in Africa. These are non official and caracterised by non co-residency of the partners. This can be related to a greater autonomy for women  in favour of the adoption of Social science part of a Prevention of the Mother-to-Child HIV transmission programme 322 HIV+ women and 353 HIV-women HIV tested during a pregnancy and followed 18 months after delivery Indicators of risk management : Indicators of communication about HIV within the couple Indicators of HIV preventive practices Variables :

  After HIV test, nearly all HIV-women communicate on HIV and/or STD with their partner After HIV test, 2/3 of HIV+ women communicate on HIV/STD with their partner Sometimes without disclosure of their serostatus : strategy of educated women Co-residency and monogamy are the sociodemographic characteristics strongest related to a complete communication with the partner about HIV % of systematic condom use at sexual resumption after delivery according to the level of communication on STD/HIV within the couple Managing the HIV/AIDS risks in subsaharan African couples. The roles of polygamy and co-residency. 12 Conclusions (1) Polygamy and non co-residency related to less communication on STD/HIV within the couple Use of HIV preventive practices depends on Partner notification of the wife's HIV test Communication on STD/HIV within the couple Instruction level of the partner on the risk of HIV infection But no direct link between polygamy and coresidency on HIV preventive practices. Managing the HIV/AIDS risks in subsaharan African couples. The roles of polygamy and co-residency. 13 Conclusions (2) It is necessary to take into account the specificity of the conjugal bond in order to improve HIV prevention within the couple  consider which indicators are to be collected so to catch this specificity, in addition to classical union indicators : Existence of a co-wife or an «official mistress » Partners co-residency Duration of the union Expectations of each partners regarding this union Etc.


Claudine Peyre

Ann Lingard

Pippa Goldschmidt

Rebecca Stott

Tracy Chevalier

Jennifer Cryer

Jennifer Rohn

Rebecca Nesbit

Peyre Claudine

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Dr Ann Lackie is a former lecturer and researcher in zoology. She taught at the university of Glasgow before switching to writing under the pen name Ann Lingard. She created SciTalk, a free resource site where scientists share their knowledge with writers. In her novel Seaside Pleasures (2003) science, history and geography are parts of the story framework.

When you write, to what extent do you think about the reader? Do you ever get the temptation to teach when you write fiction? (I'm referring to one of your interviews where you mentioned "Once a teacher, always a teacher"4 .) Did I say that? What a give-away! But rather than a question of teaching, it's more that I want to share / show what has captured my interest or puzzlement or excitement (or my curiosity -see your question below). It's probably only then that I think about the reader. When I'm immersed in what the characters are doing, how they are interacting with each other, then they and the story take over, and I'm certainly not thinking about or even be aware of a reader.

How do get your inspiration for your subjects? Is curiosity your main "fuel"?

Yes, curiosity, and interest in how people live their lives. Why would I want to write about a lame violinist, a woman living on an island, someone who is a mathematician, someone who is achondroplasic? Partly because I want to understand how they might live and conduct their lives, as individuals and as people who have to interact (or not) with other people, and their environment. That sounds cold and calculating: but I hope my fiction writing doesn't come across that way. In the real world, I have been very involved in the last few years talking to people -listening to people -and writing about them in terms of their work (eg in Solway Shore Stories) or their lives (in 'Lifetimes'see www.lbclifetimes.org -also available as an ebook). But, going back to 'inspiration'it also comes from all kinds of places, small incidents, something I have seen, or heard on the radio. Currently, I'm rather inspired by dogs...

How accurate do you try to be in the non-fictional parts of your novels?

Oh, that's very important. There's nothing worse than reading a good novel and finding a glaring error. But actually, the best part of writing a novel is, for me, doing the 'research' (in a writer's sense not a scientist's, obviously!). I love delving into new subjects, finding people who are 'experts', talking and writing to them to find out more, visiting libraries, galleries and so on. It's a form of 'work avoidance'the actual writing is the hard work, the research is exciting and fun.

What sort of process do you set up to make sure your books get finished? I don't. They will get finished.

Do you think that a writer has -to a certain extent -a pedagogic role?

The books that I most enjoy reading (other than quick-read holiday-time 'trash') are probably ones where I have learnt something new or had some new insights into ideas, or places, or a person. So I suppose that, yes, I admire writers who show (teach?) me something newand this is what I aspire to, as well. (I am very bored with self-referential novels about writers, or novels about the enclosed metropolitan world, where there is nothing new. Get out of the bubblefind out about something new, learn something new, and show it to your readers!)

Have you got a recipe to cross boundaries more easily in the academic world (apart from creating the SciTalk site!)? I've been out of academia for a long time now and the university system in the UK has changed dramatically. But these days scientists do seem to be very much better at talking about their subjects and enthusing audiences: I and my husband run our local 'Cafe Scientifique' and the speakers, especially the younger ones, are often extremely goodthey have to talk for 30 minutes without slides (they can bring a few photos or objects to pass round if that helps). This is challenging but it's an excellent way of crossing boundaries. There seem to be many small attempts to bring scientists and artists, musicians, etc. together, all over the place; but there's a lot of 're-inventing the wheel', and often it's not clear what use the outcome is. It's often transient, often baffling, often one-sided.

Pippa Goldschmidt

Pippa Goldschmidt has a PhD in astronomy and worked for at Imperial College for several years. She also graduated in creative writing. Both her fiction and non-fiction writings develop the subject of the links between science and literature. Her début novel The Falling Sky (2013) explores the fascinating world of astronomy through the experience of a post-doctoral researcher.

When you write, to what extent do you think about the reader?

I find that the process of writing fiction involves different types of thought-processes. Initially when I first have an idea, I'm not thinking about the reader at all. I'm solely intent on getting the story down, developing the characters in the way that I see them and finding interesting language (at least interesting to me) to tell the story in. In the later stages of editing and redrafting I think more about the hypothetical reader, and how they will understand the work in all its facets. When I have a decent draft of the work I will test it out on a reader (usually another writer!).

Do you think that a writer has -to a certain extent -a pedagogic role?

If they do, then this is incidental. I think that literature can teach a lot about how people think, and how the world works. But this is secondary to its function as art. Fiction goes wrong when it becomes primarily concerned with teachingfor example this can lead to propaganda. On the other hand, I have learnt a lot from fiction! One of my favourite books is 'Half of a Yellow Sun' by Chimamanda Ngozi Adichie which is about the Nigerian/Biafran war. I learnt a huge amount about Nigerian history from this book, but its main appeal was the artistic/literary qualities.

How do get your inspiration for your fiction subjects? Is curiosity your main "fuel"?

I get inspiration from other types of writing, such as newspapers, science magazines, non-fiction books, and online blogs. I also watch a lot of documentaries and go to art galleries. But it's difficult to say where an idea comes from. I have a lot of long-term preoccupations with aspects of science and also with Greek myths which inspire me. I'm intrigued by the way that science is presented and written about, and the pervasive metaphors that are used to communicate it. I'm also inspired by other fiction and also poetry -which helps me think not only about 'content' but also about 'form', how do other writers approach different subject matter? And yes, I think curiosity is a main driver. I often ask myself 'what if…' I think writing fiction is a bit like doing an experiment, because I write the story to find out what happened after thinking up an initial question or a scenario. Being an astronomer certainly helps in injecting scientific elements in the depths of a story, however, how accurate do you try to be in the non-fictional parts of your fiction? I tried to be as accurate as possible, by checking the facts and ensuring that the story was as realistic as possible. Unfortunately there are still a couple of errors in the novel which irritates me.

What sort of process did you set up to make sure your novel got finished?

Well, it took a long time (about 6 years) to write the novel and I wasn't aware of any sort of process at the beginning. I didn't know anything about writing, I just knew that I wanted to write a novel about real science. The first draft took a few years to write and didn't have any sort of plot, because I didn't know the plot at that point. It took two more drafts before it was recognisably the book that is now published. And during the writing process I did a Master's degree in creative writing, which helped me assess my own writing in a more rigorous and objective way. My second novel has much more of a recognisable 'process' but I don't think anything can guarantee that I will end up with a decent novel. So much of the initial stage is reliant on subconscious inspiration… Have you got a "recipe" to cross boundaries more easily in the academic world in order to fill the gap between the "two cultures"? I wish I did have a recipe, it would make my life easier! I know it is difficult to write good literature about science without becoming too didactic and losing sight of the essential artistic qualities of the writing. I have realised that it is easy to take for granted what you know and assume it is straightforward to understand, and that you really cannot include that much science in a work of fiction without losing your readers. I have a lot of bad fiction which makes the mistake of including too much science so that the characters simply become talking heads. In the academic world -I'm not sure what would help people fill the gap. I suppose more science outreach and encouraging a greater awareness by scientists of the value of interdisciplinary work would help. Also, the education system (particularly in England) encourages kids to specialise in humanities or sciences at a ridiculously early age. Most children don't study any science at all after the age of 16.

What was the purpose in using different narrative voices in The Falling Sky?

There is only one voice (Jeanette's), but I used different registerssuch as the dominant realistic voice as well as the more dream-like one, for the short pieces in italics. I wanted to show that Jeanette's subconscious was also important and I also wanted to provide a bit of variety for the reader, a chance to read something a bit off-beat.

Rebecca Stott

Rebecca Stott is a novelist and non-fiction writer. She is also and professor of literature and creative writing. In her novel The Coral Thief (2009), she depicts the mysterious adventures of a promising young scientist. The novel weaves well-researched intellectual facts and scientific ideas of nineteenth century Paris.

When you write, to what extent do you think about the reader? Do you ever get the temptation to teach when you write fiction?

No -although I want to show my reader certain things and ideas that I find interesting I also know that as soon as I sound like I am teaching (what we call expository writing) I will lose my reader. So the aim is to work in ideas and information as naturally as possible so that people don't notice they are being 'shown' things: science, history, philosophy etc. This often means taking a lot of material out in the last stages of the book -or sinking it. What you don't want is any section that begins with a character saying 'Let me tell you about..'. In real life people don't tell each other about politics and things like that. They just talk about it. So the trick is finding a balance between what's natural and introducing historical ideas and information.

How do get your inspiration for your subjects? Is curiosity your main "fuel"?

Yes. I write about things about which I am curious. In The Coral Thief for instance I wanted to know what it was like to be a student at the Jardin just after Waterloo. I wanted to know what Paris was like and so I end up bringing the place alive for me as well as for my reader.

In one of your interviews about The Coral Thief, you mentioned the obsession of detail, so how accurate do you try to be in the non-fictional parts of your novels?

I try to be absolutely accurate as far as the historical records allow. This means reading guide books, finding pictures, working out distances between one place and another. The thing is that if you get these things wrong someone will write and tell you! So it is much better to over-research the little details and make sure that you get the street lights right for instance than to have to write and answer someone who is an expert on street lights in Paris in the nineteenth century who is upset to find you've got it wrong and writes to tell you.

CPeyre

What sort of process do you set up to make sure your books get finished?

It's a complicated process. I wrote Coral Thief in two years, thought I'd finished it and sent it to my agent. She sent it back and said she didn't think it was ready yet. There were problems with the plot with some characters etc. So I did another version. Eventually she said she thought it was ready. It went to the publishers. They bought it. They liked it. But they wanted changes too. My American publisher wanted changes. Then there were the Italians. All the time their suggestions are only suggestions and they don't always agree so the decision is always mine. But I generally find that publishers are really good at seeing things that can be altered or improved and I probably implement about half of them. Then there's copy editing and fact checking. Then there is the proofreading. A book has many many different stages to go through. The trick is to keep as fresh a pair of eyes as possible and to try to stay true to your original vision for the book. Do you think that a writer has -to a certain extent -a pedagogic role? Do you ever get the temptation to teach or to lecture when you write? Not really. I don't write to teach. I write to show or to resurrect. My job is to bring the streets and the characters and the time to life as much as I can with the information that is available in libraries and history books. That's the delight. My curiosity drives it: what 'was it like to walk down that street at 2am in the morning on the 27th of September, 1815 and you think you are being followed…?' etc. Then I have to find out how the street was lit, what the night sounds might have been etc.

Have you got a "recipe" to cross boundaries more easily in the academic world in order to fill the gap between the "two cultures"? Curiosity is the recipe. If you have really interesting questions like 'how did Cuvier's laboratory work?' or 'what did Cuvier like to read?' then the question dictates where you go and it makes you cross boundaries in trying to answer them. I have always been a roamer of libraries because I have always been following very interesting questions. 'Where and how was that piece of glass made? How did it travel from the glasshouse in Italy to the market in Cambridge in 1665?' Those last two questions (at the heart of my novel Ghostwalk) took me four months to work out. To answer them I had to read books on the history of glassmaking and the glass trade, trade monopolies in the British glass industry in the seventeenth century, the aftermath of the civil war, books about the history of the drainage of the Fens and books about recipes for glass. Fascinating. All interesting questions make us cross discipline boundaries I think. And they also yield fascinating new stories and complex connections.

Tracy Chevalier

After working as a reference book writer, she devoted herself to a master's degree in creative writing and began her career as a novelist in 1997 with the novel The Virgin Blue. In 1999 she wrote her second novel The Girl with a Pearl Earring, which was adapted from cinema in 2003. In 2016, her 8th novel, Remarkable Creatures was published, based on the life of Mary Anning, a nineteenth century fossil hunter.

When you write, to what extent do you think about the reader? And when you said "I feel comfortable looking into things I don't know much about. I want to learn.", don't you feel you somehow swap roles with the reader?

I think about the reader all the time. After all, I am writing for them. If an author doesn't think about the reader, they are writing a journal, for themselves. I'm not like that. It's not a swap since the reader doesn't become the writer, but I definitely become a reader as I'm writing. I'm always learning, and thinking about the story, questioning it, being entertained by itjust as a reader does.

You mentioned "All of my books start with a spark of an idea. I usually start by researching around that specific spark.". How do those sparks come to you? I never know when that spark is going to arrive. It can come when I'm lying in bed looking at a painting (Girl with a Pearl Earring), or going on a tour of a cemetery (Falling Angels), or going to a dinosaur museum and reading about an unusual person (Remarkable Creatures). Usually if I try to think up an idea, I fail. It has to jump on me when I'm not expecting it. Right away I know it's an idea for a novel. Rarely do I doubt it.

You also said "I start to write without having completed the research, because once you start writing, it opens up a lot of other questions that you need to do research on, and so I feel like my research process is never complete." How accurate do you try to be in the non-fictional parts of your novels? What sort of process do you set up to make sure your books get finished? I try to be as accurate as possible. Partly it's my training -I was a reference book editor before I started writing, and it's a point of pride to get things right. Also, I know that many people will read my novels about Mary Anning, or Highgate Cemetery, or Johannes Vermeer, and that is the only thing they will read about them, and will assume it's fact. Though it isn't all fact, I need to make what is factual as accurate as I can.

It can be hard to finish. I never feel I am 100 per cent on top of my subject. There are always things I don't quite understand, or I read about but not enough. I have lots of unfinished books that are research for my past novels. Or I read stuff for a book and then forget it immediately afterwards. I read a lot of Charles Lyell's Principles of Geology for Remarkable Creatures. Now? Can't remember a thing! I can't let research become a reason not to finish. In the end, it is the story that is most important, and I have to drive through to the end and then let it go.

Is curiosity your main fuel/inspiration?

Yes, I suppose it isthat and wanting to communicate my curiosity to other people. It's more complicated than that. First, I try not to have a specific agenda when writing. That can kill a book dead. Second, the majority of readers of novels are women, so I am never going to be targeting male readers. Finally, I was drawn to Mary Anning's story in part because she was a woman working in a man's world, but also because she was working class in a middle class world. It is really difficult to say which had the greater impact on Mary's life. She was just a surprise in every way. So the book is about both gender and class, and also about the unique qualities of genius. Mary has it; Elizabeth doesn't. Elizabeth is the reader, looking at this surprising genius. I am surprised your male colleague is surprised. Women made little impact on science for hundreds of years, and that is only now changing. Mary was treated by the scientists of the time as a servant rather than a colleaguea skilled servant, and there was respect for her talent, but they never would have seen her as equal to them.

When

Jennifer Cryer

Jennifer Cryer holds a PhD in biochemistry and one in creative writing. Her novel Breathing on Glass (2012) explores the strong relationships between two sisters in an exciting scientific background. The novel is set in the world of biotechnology, in particular the exploration of stem cell research.

When you write to what extent do you think about the reader?

I feel that the reader is an important "character" in a novel. If the story is not engaging to the reader it won't even be read so I think it is important to construct a novel in a way that is understandable and satisfying to the reader. In this context I found writing about science had particular difficulties, alongside all the usual ones of keeping the reader interested, of making the characters interesting if not appealing, and of presenting the information necessary to understand the plot in timely fashion. I felt constantly aware that many readers would not understand and perhaps be bored by the technicalities of the scientist's work although I was keen to include some as an illustration of their difficulties and to convey a sense of the way in which they approached their work problems influenced the way in which they negotiated their private lives.

Do you think that a writer hasto a certain extenta pedagogic role?

No. I think that a novelist's primary responsibility is to their narrative; to identify an appropriate story and to make it enthralling and meaningful. It's very tempting to inform the reader but unless it is done with consummate skill, I feel that tutoring detracts from the fiction, draws attention to the author and alienates the reader.

How did you get your inspiration for your fiction subject? Was curiosity your main fuel?

I think that my primary inspiration for a novel which mixed human relationships and science came from my own experience. When my children were young, I noticed that I "took off" my scientific persona along with my white coat when I returned home to care for them and I became interested in why I had unconsciously adopted this pattern and wanted to explore the rationale for it in a family situation.

Being a scientist certainly helps in injecting scientific elements in the depths of a story, however, how accurate do you try to be in the non-fictional parts of your fiction?

I try, but perhaps don't always succeed, to be completely accurate. I enjoy reading stories that are very consistent within their frame of reference because they have a sense of coherence that makes a story feel possible and I feel that errors are glaring to the informed reader and make the story appear trivial.

What sort of process did you set up to ensure that your novel got finished?

I began the novel with a project plan that was an outline of the plot and characterization of the protagonists. As I wrote, I didn't follow the plan inflexibly but as the characters met new situations I let their personalities lead their responses to them. This created a "fuller" version of the initial story, and the minor characters but I did guide the plot back on course in order to retain control of the storyline and to ensure that the writing did get finished

Have you got a "recipe" to cross boundaries more easily in the academic world in order to fill the gap between the "two cultures"? Sadly, not. I have found that many people working in the humanities don't enjoy engaging with science, because they are self-conscious about their perceived lack of knowledge and that many people working in science don't want to engage too closely with the humanities because they feel that they lack the language to explore them. Education makes great demands on the specialist in any field and I think that people don't have the time to broaden their understanding.

In a 2013 article you said "Science is much too important, too influential in our lives, for society to leave it to the white coats"5 . Do you think it is important to bring science out of the labs?

I think that everyone can benefit from an understanding of the way that science works, in the same way that everyone can benefit from an understanding of the way that story-telling, or medicine, retail, money or any of the other facets of a complex society work. Our world is multi-dimensional and all these things influence the course of our lives. I don't think there is a great need for everyone to understand all of the technicalities of science but everyone should understand and contribute to the way in which science proceeds and how its benefits should be exploited.

Jennifer Rohn

Jennifer Rohn is a cell biologist at University College London and is the author of numerous science articles and blogs. On top of her career as a scientist she is also the author of novels that immerse the readers into the world of science. In Experimental Heart (2008) and The Honest Look ( 2010), the readers get immersed into the fascinating world of biotechnology. She is also the editor of the webzine Lablit.com I think about the reader constantly. Some literary authors think it is a sign of weakness to 'cater' to the readerthese writers believe that the point of writing is to create art that pleases themselves primarily (think, for example, of people who criticize certain Booker Prize winners for being too "popular"). I couldn't disagree more. I think that a successful novel is one that should engage the reader, that should tell a good story that inspires the reader to care about the characters and keep reading. Therefore a good storyteller will put themselves in the reader's shoes and ask, will this make sense, will it resonate? Will it keep the pages turning?

When putting complex ideas like science into a plot, one must pay particular attention to the level that one should be pitching. My readers will include non-scientists, so I feel very strongly that the science present in the novel must be correct but understandable. This requires a lot of thought about word choice and how to phrase the sentences. Dialogue is a particular problem, as you don't want scientist characters to speak to one another with language they wouldn't use in real life. After I write a science novel, I give it to a number of non-scientist readers to check that the science is understandable; when it isn't, I revisit the text and send it out again. I keep up this iterative process until I am satisfied that the science is at the right level.

I don't write fiction to 'teach' science. Instead, I write fiction to illuminate the complicated lives of scientists, to reveal their humanity. Readers may learn some scientific facts from reading my books, but that is not my object.

How do get your inspiration for your subjects? Is curiosity your main "fuel"?

My subjects are all based on the real life that I see around me in the scientific world. The books are not autobiographical by any means, but the ideas, situations and problems are adapted from my own experiences working in a lab for many decades, and the characters are a blend of real-life and fictional persona. For example, my idea for The Honest Look stemmed from the fact that I was, at the time, working in a biotech company based on a scientific premise that seemed too good to be true. As a novelist, I started to wonder what would happen if the premise indeed turned out to be wrong. Although in real life the premise was sound, The Honest Look became an in-depth exploration of that what-if situation: what happens when scientists invested in a particular theory are confronted with proof that the theory is wrong? Very interesting outcomes, it turns out…

In Experimental Heart, the narrator asks his friend: "… do you think we became scientists after being subconsciously influenced by [our family's] interest?" Do you have an answer to the general question of the background's influence on a potential "scientific calling"?

I have no ready answers. In my own case, my interest came out of nowhere: my parents were both artists and there were no scientists in our family or amongst my family's friends.[…] "For me, then, my interest in science was fostered as early as the toddler years, mostly by encouragement from parents who were inspired by the world around them."6

Being a scientist certainly helps in injecting scientific elements in the depths of a story, however, how accurate do you try to be in the non-fictional parts of your fiction?

It is very important that all the science described in my story is either perfectly true, or if not, at least follows the laws of science and nature that we know at the moment. So for example, in Experimental Heart, we hear about a gene called FRIP. FRIP does not exist in real life, but is reminiscent of a number of actual genes that do similar things in the cells of our body. It is no different to any novelist who will fictionalize various other aspects of real lifefor example, the hero taking a bus route through London that doesn't actually exist, but the bus "behaves" like a normal London bus.

What sort of process did you set up to make sure your books got finished?

I didn't really need a process: I was obsessed by the writing and wrote every day for as long as I could.

Both novels were finished in draft form in matter of months, and while the editing took much longer, it still happened every day. Unfortunately my life has grown more complicated since then, with a more demanding job and a small child, so I have not written regularly for some years. I have a third novel completed, but have not yet decided how to proceed with publication. I hope one day to return to the writing rhythms of my past life.

Do you think that a writer has -to a certain extent -a pedagogic role? Do you ever get the temptation to teach or to lecture when you write?

Not ever. I think readers are turned off by obvious preaching and I try to avoid it at all costs. The beauty of fiction is that it is a stealth media for introducing ideas and concepts, but you definitely don't want to lecture your reader or be obviously pedagogical.

Apart from your tremendous involvement in the webzine Lablit.com, have you got a "recipe" to cross boundaries more easily in the academic world in order to fill the gap between the "two cultures"?

I am not really convinced that the so-called 'two culture' divide really exists. There are many nonscientists interested in scienceyou encounter these people in various initiatives set up in London and other major cities. Non-scientists meet in pubs to hear scientists talk, attend events and cafes and even comedy nights devoted to science. Interest in science is seen as trendy and vital. Clearly, many scientists are also interested in music and the artsthis has always been the case. It is quite fashionable to suggest that there is a divide, but it feels artificial and untrue to me.

In Experimental Heart, the reader can feel a distortion between subjective time and objective time. Indeed, the rhythm slows down when the narration focuses on the personal development of the narrator's life and feelings and its pace gets back to "real" time when the narrator's work and science experiments are described. How intentional was this split or was it just … experimental?

I am going to need your help to answer this question…I am not sure what you mean!

Rebecca Nesbit

Rebecca Nesbit is a writer with a profound interest in ecological issues. Her background includes a PhD in butterfly migration. She writes fiction and non-fiction articles. Her début novel is A Column of Smoke (2010), a story about human relationships with a scientific background on the controversial issue of GMO.

When you write, to what extent do you think about the reader? Do you think that a writer has -to a certain extent -a pedagogic role?

I think about the reader quite a lot, and I'm often aware that my readers will have very different background knowledge so it will be hard to please everyone. I'm both thinking about whether I need to explain some science/scientific equipment/lab situation, and about how subtle I can be. If I want to show that a character feels a particular emotion or thinks about something in a particular way, how much do I need to spell it out?

One of my main motivations is to give people a glimpse into a different world. GM crops is a particularly interesting one as lots of images from NGOs are of evil scientists, so I wanted to show a very different reality. This does mean that I actually have to keep reminding myself this is a work of fiction, not science communication. I'm here to tell an enticing story, not to preach to people.

How do get your inspiration for your subjects in your novel and short stories? Is curiosity your main "fuel"?

I actually find it very easy to come up with ideas. If someone asks me for a short story it might only be a few hours before I have one planned out. I tend to think of a phrase or a situation which appeals to me and ask myself how I can make a story around it. Who would be in that situation? What could the character be wanting? Who else would be involved, and would they have conflicting interests? My ideas often start with real lifea conversation I heard on the train, or a difficult situation I found myself in. Sometimes I start with ethical issues I want to explore, hoping to help people empathise with an alternative point of view.

In What sort of process did you set up to make sure your book got finished?

Something that was really important for me was being part of a writing group. We met every month to share what we'd written which meant I always had a deadline to work to. It also gave me confidence -I think the voice in your head that says 'this is rubbish' is a real barrier for many people. Having positive, constructive feedback was really helpful and gave me the motivation to ignore that voice of self-doubt and decide to finish the book.

I have also done things such as set targets or rules for myselfwhen I was blogging regularly I said I would write a post every Tuesday night. If I was out on Tuesday I would do it on Wednesday, but I wouldn't just plan to 'write something soon'. I actually started the book in about 2006 and gave up. There were lots of reasons, including lack of support and the chaotic way I had approached it, writing whichever bit I fancied rather than writing it chapter by chapter. When I came back to it a few years later I didn't like any of what I'd written first time roundnot a single sentence made it into the final book even though the storyline barely changed. It was good practice though. I like to encourage anyone who's interested to give fiction a try. It's a

CPeyre great hobby even if you don't aspire to be published so 'I don't think I'd be any good' shouldn't be a barrier to having a go.

Apart from your regular involvement in the webzine Lablit.com, have you got a "recipe" to cross boundaries more easily in the academic world in order to fill the gap between the "two cultures"? I'd like to see us move away from a 'two cultures' vision, and also to move away from the view which is often perpetuated at school -you're either an arts person or a science person. I don't like discussions of 'scientists and the public' being framed in a very 'them and us' way. We are all people, all members of the public, and we share interests and motivations.

I think there are some great outreach programmes run by universities, whether this is school visits, science fairs, online videos or interactions with the media. The more that academics give insights into their world the better.

In A Column of Smoke, Sally, feels torn between the pursuit of her career and moral questions. Do you think that the question of ethical issues should be part of education in science?

Definitely, and I'm glad to hear that it increasingly is. There are lots of ethical issues surrounding science. For a start, pretty much all research is 'dual-use'it can be used for good or bad. Explosives are an obvious, simple example. There are also some ethical issues in the process of doing science, such as the use of animals or human subjects in medical research. Many new discoveries or technologies come with both benefits and risks, which need to be considered, and these are often unequally distributed within society. AI is an obvious example of something which has both huge potential and huge risks. Perhaps what's most fascinating for me is who gets to choose. If scientists say GM is safe yet many members of the wider public disagree, should EU countries still opt out and say they won't grow them? How much does someone have to know for their opinion to be valuable on a scientific topic? Should scientists be trying to influence the opinion of the wider public, or simply to present their research and information about how they do it?

  you said "I don't want to be a teacher, I want to be a storyteller", don't you think that any writer has -to a certain extent -a pedagogic role? What's the point of writing otherwise? Sure, of course. But I don't want the pedagogic part of the book to swamp the simple pleasure of reading a story and wanting to know what happens. That is my primary task. If someone reads Remarkable Creatures to find out what happens to Mary Anning and Elizabeth Philpot, that's great. If they learn a bit about fossils and deep time and the role of women in the 19th century, even better.One of my colleagues, a professor of geology, read Remarkable Creatures (French version) and was amazed to see the lack of recognition from the scientific community towards Mary Anning at the time. Did you write this novel with the purpose of developing gender awareness from the part of the (masculine) readers?

  When you write, to what extent do you think about the reader? Do you ever get the temptation to teach when you write fiction?

A Column of Smoke, Sally the narrator can trace back her love of science from a specific school event when she was around 12 years old. Do you have an answer to the general question of the background's influence on a potential "scientific calling"?

  My family point to different stories of my origins of being a scientisttracking snails in the garden, seeing the insects in my grandparents' water trough... I think for me it was a cumulation of lots of such events and influences, and it's probably the same for most people. Like many people, my interest in science started out as an interest in nature. This is something I deal with in my day job too. I am part of the Nobel Prize Inspiration Initiative, taking Nobel Laureates to meet students at universities around the world. Some of them share their stories of early inspiration, e.g.: https://www.youtube.com/playlist?list=PLc8JX9rbkV0ulrck0cEyQzsJHa0AYz7UN It's interesting that there are multiple examples of Nobel Laureates who also had Laureate fathers. Yet that are others who explicitly went against their parents' wishes to become scientists. Randy Schekman for example has a great story about buying his first microscope: http://www.nobelprize.org/nobel_prizes/medicine/laureates/2013/schekman-bio.html

Being a scientist certainly helps in injecting scientific elements in the depths of a story, however, how accurate do you try to be in the non-fictional parts of your fiction?

  I think it very much shows that I'm a scientist -I try to be very accurate in the portrayal of science and scientific life, yet am happy to use artistic license when dealing with, for example, legal issues. This has changed a bit in the current novel I am writing, which goes further beyond what I am familiar with so has required far more research.

It's good to SciTalk -Ann Lackie on her life, her novels and a new organization that brings writers and scientists together, 8 November 2005, lablit.com

Jennifer Cryer, www.walesonline.co.uk/lifestyle/science-passion-collide-book-breathing-5379796 (Aug 3d 2013)

Jenny Rohn's view on her the appeal of science on women. http://www.theguardian.com/science/occamscorner/2015/dec/10/boys-toys-hair-dryers-gender-parity-lab

The reference novels used for the interviews are the following: Ann Lingard, Seaside Pleasures, Littoralis Press (2003) Pippa Goldschmidt, The Falling Sky, Freight Books (2013) Rebecca Stott, The Coral Thief, Orion Books Ltd (2009) Tracy Chevalier, Remarkable Creatures, HarperCollins (2009) Jennifer Cryer, Breathing on Glass, Abacus (2012) Jennifer L. Rohn, Experimental Heart, Cold Spring Harbor Laboratory Press (2008) Jennifer L. Rohn,The Honest Look, Cold Spring Harbor Laboratory Press (2010) Rebecca Nesbit, A Column of Smoke, Brambleby Books (2014)


Théo Delage

Olivier Pascal

Jérôme Sokoloff

Valentin Mazieres

Experimental demonstration of virtual critical coupling to a single-mode microwave cavity

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

Experimental Demonstration of Virtual Critical Coupling to a Single-Mode Microwave Cavity

Théo Delage, [START_REF] Raizer | Gas Discharge Physics[END_REF] Olivier Pascal, [START_REF] Raizer | Gas Discharge Physics[END_REF] Jérôme Sokoloff, 1 and Valentin Mazières 2 1) LAPLACE, Université Fédérale de Toulouse, 31062 Toulouse Cedex 9, France 2) ISAE-SUPAERO, Université Fédérale de Toulouse, 31055 Toulouse, France (*theo.delage@laplace.univ-tlse.fr) (Dated: 24 March 2023) We present an experimental realisation of the virtual critical coupling in microwave, i.e. the virtual perfect absorption of an incident wave by a resonant cavity, through the transient time modulation of its amplitude. The design of a waveform matched to the ignition process of a plasma, characterised in a simplified way by two operating modes over time (plasma off/plasma on) motivates this first step in the practical realisation of virtual critical coupling in microwaves. We propose a time domain method for extracting the necessary parameters for the realisation of the virtual critical coupling, especially the complex frequency called zero of the S-matrix. To this end, we start from the experimental characterisation of a single-mode and single-access microwave cavity including metal protrusions for future plasma ignition. Then, the method relies on the analysis of the harmonic response of the overcoupled cavity during three time periods: the transient under excitation, the steady state under excitation, and the transient after the excitation cut-off. Finally, an experimental demonstration of the virtual critical coupling is performed.

I. INTRODUCTION

Plasma source motivation and context: Plasma, frequently defined as the fourth state of matter, is an ionised and macroscopically electrically neutral gas [START_REF] Raizer | Gas Discharge Physics[END_REF] . The ignition of a plasma can be achieved by using electromagnetic energy. This energy is brought in different ways through devices called plasma sources [START_REF] Conrads | Plasma generation and plasma sources[END_REF] . The particularity of such plasma sources is their operation, i.e. the supply of energy, in two configurations over time: plasma off (transient before ignition) and plasma on (steady-state after ignition). Generally, the ignition of the plasma can strongly modify the properties of the plasma source [START_REF] Lacoste | Experimental study of energy coupling and plasma breakdown in a pulsed high frequency resonant cavity[END_REF] . In the context of RF or microwave plasma sources, for instance the ignition of plasma into a microwave cavity, it can lead to a mismatch between the cavity and the energy generator, and in the worst case, to the extinction of the plasma. This mismatch affects the efficiency of the energy transfer between the generator and the cavity. As the powers involved can be significant, the reflection caused by the mismatch can be a problem for the components placed before the cavity receiving the plasma. Strategies to overcome the reflection problem are then to absorb and dissipate this reflection by adding isolators or circulators. More sophisticated matching techniques are based on careful dimensioning or geometrical adjustment of the structure, or the use of impedance matching systems [START_REF] Silva | Microwave engineering of plasma-assisted CVD reactors for diamond deposition[END_REF] . All these techniques rely on adjusting the system, but not the excitation.

Recently, a new type of plasma source was developed. Inspired by works about time reversal of electromagnetic waves [START_REF] Lerosey | Time reversal of electromagnetic waves[END_REF] , it is based on the spatio-temporal control of microwaves by the shaping of the temporal waveform transmitted to a cavity. It allows the space-time steering of microwave plasmas [START_REF] Mazières | Plasma generation using time reversal of microwaves[END_REF][START_REF] Mazières | Space-time plasma-steering source: Control of microwave plasmas in overmoded cavities[END_REF] . However, the design of this method mainly considers the plasma-off configuration and does not lead to a matched cavity in the two operating modes. On the other hand, the idea of playing on the shape of the excitation of the plasma source could be extended to match the generator sig-nal during the ignition process, considering the cavity's properties would evolve in time [START_REF] Kalluri | Electromagnetics of Time Varying Complex Media: Frequency and Polarization Transformer[END_REF] . Moreover, the ignition phase is transitory, which leads us to consider transient shapes of excitations.

Towards a matched transient excitation: In this way, also considering resonant systems such as cavities, the unusual phenomena of wave scattering, characterised by spectral singularities, have received significant attention in recent years [START_REF] Krasnok | Anomalies in light scattering[END_REF] . We can for example mention the theory of reflectionless scattering modes, a general theory for impedance matching of waves in complex scattering structures and geometries (multichannel, overlapping modes, etc) [START_REF] Sweeney | Theory of reflectionless scattering modes[END_REF] . Coherent perfect absorption can then be seen as a special case of this theory, for which impedance matching is possible by adding dissipative losses to the scattering system, leading to purely irreversible loss mechanisms [START_REF] Chong | Coherent perfect absorbers: Time-reversed lasers[END_REF] . However, these concepts refer to stationary phenomena, and some of them, such as coherent perfect absorption for which energy is dissipated, do not lead to a significant electromagnetic energy rise of the resonator (that is useful in order to ignite a plasma).

Lately, the idea of virtual absorption [START_REF] Baranov | Coherent virtual absorption based on complex zero excitation for ideal light capturing[END_REF] has provided a new perspective on the transfer of energy from a generator to a resonant structure. This concept highlights transient phenomena during the coupling of energy to the cavity. It allows to observe the excitation of a resonator without reflection or transmission, with most of the incident energy stored inside for the limited time of the excitation. It is based on the temporal modulation of the resonant structure itself [START_REF] Mirmoosa | Time-varying reactive elements for extreme accumulation of electromagnetic energy[END_REF][START_REF] Sounas | Virtual perfect absorption through modulation of the radiative decay rate[END_REF] , or on the temporal modulation of the generator [START_REF] Baranov | Coherent virtual absorption based on complex zero excitation for ideal light capturing[END_REF][START_REF] Longhi | Coherent virtual absorption for discretized light[END_REF][START_REF] Zhong | Coherent virtual absorption of light in microring resonators[END_REF][START_REF] Marini | Metasurface-bounded open cavities supporting virtual absorption: free-space energy accumulation in lossless systems[END_REF][START_REF] Farhi | Excitation of absorbing exceptional points in the time domain[END_REF] . The latter option has been studied experimentally for elastodynamic waves [START_REF] Trainiti | Coherent virtual absorption of elastodynamic waves[END_REF] and water waves [START_REF] Euve | Transient total absoprtion for water waves : a two port setup[END_REF] . It has also been theoretically and numerically applied to the excitation signal of a single-mode cavity coupled to a single access. Referring to the well-known critical coupling [START_REF] Cai | Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system[END_REF] , this led to the formulation of the concept of virtual critical coupling [START_REF] Ra'di | Virtual critical coupling[END_REF] (note that a generalization to multiaccess resonator is possible). In this case, the modulation of the oscillating incident signal consists in shaping an exponential growth of its amplitude, characterised by a precise com-plex frequency. These conditions make it possible to balance the exponential growth of the signal amplitude that leaks from the cavity during excitation by destructive interference. This leads to the transient excitation of the resonant structure without scattering. This compensation is achievable for a discrete number of complex frequencies, called zeros of the S-matrix. They are more generally part of what are called singularities of the S-matrix [START_REF] Krasnok | Anomalies in light scattering[END_REF][START_REF] Grigoriev | Optimization of resonant effects in nanostructures via weierstrass factorization[END_REF] . Note that we will use the term real frequency to refer to the usual frequency. This real frequency is actually the real part of the complex frequency. Its imaginary part reflects an exponential modulation of the signal amplitude.

On extracting S-matrix zeros for experiment: Although the singularities of the S-matrix have been described theoretically [START_REF] Krasnok | Anomalies in light scattering[END_REF][START_REF] Grigoriev | Optimization of resonant effects in nanostructures via weierstrass factorization[END_REF] , many works are interested in how to extract them for practical scattering systems. The Harmonic Inversion technique [START_REF] Wall | Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short-time segment of a signal. i. theory and application to a quantum-dynamics model[END_REF][START_REF] Mandelshtam | Harmonic inversion of time signals and its applications[END_REF] is widely documented and used in order to identify the resonances, i.e. the poles of the S-matrix, of a scattering system which may be multi-channel and multimodal with overlapping [START_REF] Wiersig | Fractal weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering[END_REF][START_REF] Kuhl | Resonance widths in open microwave cavities studied by harmonic inversion[END_REF] . However, the search for the zeros of the S-matrix via this method is little mentioned [START_REF] Osman | Chaotic scattering with localized losses: s-matrix zeros and reflection time difference for systems with broken timereversal invariance[END_REF] , or even rejected because it seems less direct [START_REF] Chen | Use of transmission and reflection complex time delays to reveal scattering matrix poles and zeros: Example of the ring graph[END_REF] . For the extraction of the S-matrix zeros, in the article about coherent virtual absorption of elastodynamic waves [START_REF] Trainiti | Coherent virtual absorption of elastodynamic waves[END_REF] , the S-matrix of the experimental device has been formulated analytically as a function of frequency. However, the S-matrix of most scattering systems cannot be easily specified in this way. Recently, many efforts have been made to encounter the zeros of the S-matrix from experimental data. Most of them are in fact based on parametric analysis and optimisation of the absence of scattered waves for real frequencies, i.e. zeros placed on the real axis. The parametrisation can be done by frequency and attenuation sweeps, leading to the extraction of zeros at arbitrary real frequencies [START_REF] Pichler | Random anti-lasing through coherent perfect absorption in a disordered medium[END_REF][START_REF] Chen | Perfect absorption in complex scattering systems with or without hidden symmetries[END_REF] . Other efforts have been made to fix the real frequency of the zero, via the use of metasurfaces [START_REF] Imani | Perfect absorption in a disordered medium with programmable meta-atom inclusions[END_REF][START_REF] Frazier | Wavefront shaping with a tunable metasurface: Creating cold spots and coherent perfect absorption at arbitrary frequencies[END_REF][START_REF] Del Hougne | On-demand coherent perfect absorption in complex scattering systems: Time delay divergence and enhanced sensitivity to perturbations[END_REF][START_REF] Del Hougne | Coherent wave control in complex media with arbitrary wavefronts[END_REF][START_REF] Sol | Meta-programmable analog differentiator[END_REF] . However, these solutions imply modifying the resonator properties at each parametric variation (attenuation with localised loss modulation or configuration change of the metasurface). The generalization of these methods is difficult to consider in order to find complex zeros of a given resonator, which are sought to achieve virtual absorption. Moreover, the optimisation time might be problematic for the purpose of adapting the cavity (and not the generator signal) between plasma off and plasma on configurations. Optimisation and analytical description are also used to try to identify and observe the coalescence of several real zeros [START_REF] Wang | Coherent perfect absorption at an exceptional point[END_REF][START_REF] Suwunnarat | Non-linear coherent perfect absorption in the proximity of exceptional points[END_REF] . Finally, we must mention the very recent work that seems to offer a way to extract the zeros of the S-matrix from the experimental measurement of the latter [START_REF] Chen | Use of transmission and reflection complex time delays to reveal scattering matrix poles and zeros: Example of the ring graph[END_REF][START_REF] Chen | Generalization of wigner time delay to subunitary scattering systems[END_REF] . So far, this frequency method works for multichannel resonators and isolated resonances. These different works show the complexity of the extraction of singularities of the S-matrix from real practical scattering systems and experimental measurements. Yet, the realisation of virtual critical coupling for a given cavity relies on the knowledge of the zeros of the S-matrix.

Organisation of the paper: The objective of the work presented in this paper is the experimental demonstration of virtual critical coupling for a microwave resonant cavity. In Sec. II, we present the single-mode and single-access cavity including metal protrusions on which our experimental demonstration is based. Sec. III recalls the theoretical bases associated with the excitation of the S-matrix zero of our cavity. To achieve our main objective, we propose in Sec. IV an alternative time domain method to extract the complex frequency associated with this zero. This time domain method is based on the measurement of the resonator S-matrix and, on the analysis of the harmonic response of the cavity, in line with the study of virtual critical coupling in the article mentioned above [START_REF] Ra'di | Virtual critical coupling[END_REF] . Finally, we show in Sec. V, the practical realisation of the excitation of a S-matrix zero of our cavity, in other words, to the authors' knowledge, a first experimental realisation of virtual critical coupling in the microwave domain.

II. PRESENTATION OF THE CAVITY

To study virtual critical coupling in practice, we choose a single-access, single-mode cavity that works in a frequency band suitable for the instrumentation available to us (see Sec. V). Recently in our laboratory, B. Fragge et al. were interested in the design of a plasma source at atmospheric pressure in a microwave cavity for the ignition of liquid fuels [START_REF] Fragge | A versatile set-up to study plasma/microwave sources for liquid fuel ignition[END_REF] . The microwave cavity for the realisation of a virtual critical coupling excitation is the one designed and characterised in the cited article. This versatile aluminium cavity (AU4G 2017A), forms a rectangular parallelepiped, and is coupled to a microwave generator through a copper coaxial probe partly surrounded by PTFE. One of the original features of this cavity is the possibility to place concentrators, i.e. metal rods facing each other, forming a gap in which the electric field is concentrated, which favours the ignition of plasma (see Fig. 1b). For the excitation of the T E 012 resonant mode, these are located on a maximum electric field. This electric field is even more concentrated in the gap. This has allowed the ignition of non-equilibrium plasmas, in air and at atmospheric pressure, for an incident power of 200 W [START_REF] Fragge | A versatile set-up to study plasma/microwave sources for liquid fuel ignition[END_REF] .

We propose to consider the cavity in the presence of cylindrical concentrators for this study, which sets the resonance of the desired mode around 2.41 GHz. Moreover, this configuration makes it difficult to express its S-parameters analytically. This makes us consider an alternative method for the extraction of S-matrix singularities of this cavity necessary for the realisation of virtual critical coupling (see Sec. IV). Fig. 1a illustrates the cavity through the 3D electromagnetic simulation software HFSS. It gives the reader an idea of the architecture of the structure and the electric field distribution for the T E 012 resonant mode.

III. THEORETICAL BACKGROUND

The main objective of this paper is to excite the desired resonant mode of the cavity described in the previous section with transient suppression of reflection of the incident signal. The careful design of the excitation should thus lead to the full transfer of the incident energy to our cavity. This cavity FIG. 1: (a) Electric field calculated by the HFSS solver for resonant cavity excitation around 2.41 GHz. This versatile cavity for plasma ignition at atmospheric pressure, widely described in [START_REF] Fragge | A versatile set-up to study plasma/microwave sources for liquid fuel ignition[END_REF] , measures 136 × 86 × 43 mm 3 here, and is excited through a 14 mm long coaxial feeding to allow overcoupling. Two 20 mm long cylindrical concentrators are positioned 30 mm from the right wall, at the location of an electric field peak. The physical parameters to be considered for the analytical study of the temporal dynamics are also illustrated. (b) Photograph of the cavity considered in this paper, with a side face removed. We can identify the concentrators, also called "initiators" in the article already mentioned [START_REF] Fragge | A versatile set-up to study plasma/microwave sources for liquid fuel ignition[END_REF] .

is coupled to a single access, is single-mode in the real frequency band of interest (presence of a single resonance), and has intrinsic losses. The temporal coupled mode theory (TCMT) [START_REF] Haus | Waves and fields in optoelectronics[END_REF][START_REF] Suh | Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities[END_REF] synthesises, through two equations, the energy exchanges between the scattering system's eigenmodes and the coupling of these modes to one or more incident signals. As detailed in the literature [START_REF] Krasnok | Anomalies in light scattering[END_REF][START_REF] Sounas | Virtual perfect absorption through modulation of the radiative decay rate[END_REF][START_REF] Ra'di | Virtual critical coupling[END_REF] , it can be used to describe the scattering properties of our cavity over time. Thus, applied to our singlemode and single-access cavity, we write the dynamic equation of the resonance amplitude of the mode :

da(t) dt = ( jω 0 -γ int -γ ext ) a(t) + κs inc (t) (1)
and the equation for the global reflected signal :

s re f (t) = -s inc (t) + κa(t) (2)
Fig. 1a illustrates the intrinsic characteristics of the cavity and those related to the coupling of a signal through its unique access. The cavity is characterised by a resonant normal mode at the angular real frequency ω 0 and a decay rate γ. The latter specifies the way in which the energy stored in the cavity is lost. A distinction is made between intrinsic losses by dissipation at the walls (γ int ) and external losses by the leakage of energy from the resonator to the coaxial feed (γ ext ). Each decay rate is associated with a quality factor according to the expression Q = ω 0 /2γ. We write a(t) the resonance amplitude [START_REF] Haus | Waves and fields in optoelectronics[END_REF] of the mode, and |a(t)| 2 defines the energy stored over time. Finally, we provide energy via the incident signal s inc (t), and characterise the coupling of this signal to the cavity by the κ coefficient. The latter is directly related to the external decay rate by [START_REF] Suh | Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities[END_REF] κ = √ 2γ ext . The reflected signal that may result from this coupling is denoted s re f (t). The squared modulus of these signals describes the incident and reflected powers respectively. With these details, we see that Eq. ( 2) describes the reflected signal as the superposition of two contributions. The first is linked to the direct reflection of the incident signal at the cavity access. The second is related to the energy leakage from the cavity to the coaxial cable.

From these two equations, we can establish the conditions for cancellation of the reflected signal in time. For a time convention in e jωt (s inc (t) ∼ e jωt ), and assuming the complex angular frequency plane with ω = ω ′ + jω ′′ , we adopt from the literature the expression of the reflection coefficient r = s re f /s inc as a function of the excitation complex angular frequency [START_REF] Ra'di | Virtual critical coupling[END_REF] :

r ω ′ , ω ′′ = (γ ext -γ int + ω ′′ ) -j (ω ′ -ω 0 ) (γ ext + γ int -ω ′′ ) + j (ω ′ -ω 0 ) (3)
We then see the existence of the singular complex angular frequency ω = ω 0 + j (γ intγ ext ) which allows the cancellation of the numerator of Eq. ( 3). It thus gives a condition on the incident signal to achieve cancellation of the reflected signal during the excitation. This complex angular frequency is one of the singularities of the reflection coefficient. Since our cavity has only one access, studying this reflection coefficient is in fact the same as being interested in the S-matrix of the resonator. This complex angular frequency is then generalizable as a singularity of the S-matrix, and is called zero of the S-matrix [START_REF] Krasnok | Anomalies in light scattering[END_REF] . We can write it ω zero . It satisfies the ingoing boundary condition [START_REF] Krasnok | Anomalies in light scattering[END_REF][START_REF] Grigoriev | Optimization of resonant effects in nanostructures via weierstrass factorization[END_REF] . Thus, an excitation signal of the form s inc (t) ∼ e jω 0 t e (γ ext -γ int )t , should theoretically allow us to transfer energy to the cavity without reflection, and more generally without back-scattering, for the time of the excitation.

For γ int = γ ext , this complex angular frequency becomes pure real and we find the so-called critical coupling condition. In this case, a sinusoidal excitation (CW) fulfils the ingoing boundary condition. In order to obtain this equality, it is necessary, for example, to modify the length of the coaxial feed in the cavity (modification of γ ext ), or to add absorbers in the cavity (modification of γ int ). However, it has been shown that this excitation is not necessarily the most efficient in terms of energy stored in the resonant system compared to the amount of incident energy (excitation efficiency [START_REF] Ra'di | Virtual critical coupling[END_REF] ). In fact, a large part of the latter is directly dissipated [START_REF] Ra'di | Virtual critical coupling[END_REF] . Also, during the transient phase of the excitation, i.e. a thousand periods of the incident signal (about 450 ns) for our cavity with the adjusted size of the monopole, this coupling presents an important part of reflected energy. Nevertheless, this strategy is usually sought and implemented when one wishes to transfer energy to a resonant device [START_REF] Pozar | Microwave Engineering[END_REF] .

The originality recently highlighted consists in understanding that even if the cavity is not matched in the classical sense of the term, i.e. with different intrinsic and external quality factors, it is possible via the temporal modulation of the excitation, to force the transient absorption of the excitation signal by the cavity [START_REF] Ra'di | Virtual critical coupling[END_REF] . Specifically, in the case where γ int < γ ext , for which the cavity is said to be overcoupled, the time modulation consists of generating an incident signal with an exponentially increasing amplitude over time. We then speak of virtual absorption [START_REF] Baranov | Coherent virtual absorption based on complex zero excitation for ideal light capturing[END_REF][START_REF] Longhi | Coherent virtual absorption for discretized light[END_REF][START_REF] Zhong | Coherent virtual absorption of light in microring resonators[END_REF][START_REF] Marini | Metasurface-bounded open cavities supporting virtual absorption: free-space energy accumulation in lossless systems[END_REF][START_REF] Trainiti | Coherent virtual absorption of elastodynamic waves[END_REF] , or in reference to the usual case mentioned above, of virtual critical coupling [START_REF] Ra'di | Virtual critical coupling[END_REF] . An excitation whose amplitude increases exponentially does not seem to be sustainable over long periods of time. However, it presents the advantage of not necessarily having to seek to modify the resonant system to limit the reflection. Also, virtual critical coupling seems to pave the way to the matching of the excitation signal to a cavity whose properties would evolve in time, for example during the ignition of a plasma [START_REF] Kalluri | Electromagnetics of Time Varying Complex Media: Frequency and Polarization Transformer[END_REF] . Unlike the classical critical coupling, it allows an excitation efficiency close to unity [START_REF] Ra'di | Virtual critical coupling[END_REF] .

Moreover, let us note that the complex angular frequency ω = ω 0 + j (γ int + γ ext ) makes it possible to cancel the denominator of Eq. ( 3). We have here a new singularity of the Smatrix, called the pole, and satisfying the outgoing boundary condition [START_REF] Krasnok | Anomalies in light scattering[END_REF][START_REF] Grigoriev | Optimization of resonant effects in nanostructures via weierstrass factorization[END_REF] . In other words, the cut-off of the excitation, thus the absence of incident wave on our cavity, will lead to the release of the energy stored in the cavity during the excitation period. This takes place according to an exponential decay at this complex angular frequency.

Finally, in the case of a cavity with no intrinsic losses (γ int = 0), time-reversal symmetry imposes that the poles and zeros of the S-matrix are conjugate. When the cavity has intrinsic losses, as in the case of our cavity, this symmetry is broken and the poles and zeros are no longer conjugate [START_REF] Krasnok | Anomalies in light scattering[END_REF] .

IV. TIME DOMAIN METHOD TO EXTRACT S-MATRIX SINGULARITIES OF THIS CAVITY FROM THE EXPERIMENTALLY MEASURED S-MATRIX

Now that we have recalled some theoretical bases, we wish to determine the pole and the zero of the S-matrix for the T E 012 resonant mode of our cavity. The final objective is to excite the zero and realise virtual critical coupling. It requires the extraction of the intrinsic and external decay rates associated with our scattering system, consisting of the cavity and its coaxial feed, and for the resonant mode considered. In this section, we propose a time domain method for extracting these complex angular frequencies from the S-matrix of the cavity. This approach is based on several steps summarised in Table I which we will detail through the direct application to the cavity described previously.

ω zero = ω 0 + j (γ int -γ ext ) ω pole = ω 0 + j (γ int + γ ext ) → Plot of s re f (t) = exp( jω zero t) * s 11 (t)
A. Identification of pole and zero real part ω 0 As seen in Table I, the identification of ω 0 is done through different operations. Recall that the theory expresses ω 0 as the real part of the pole and zero of the single-mode cavity. The first step consists in acquiring the spectrum of the S-matrix. Here, it involves measuring the modulus and phase of S 11 (ω) in the frequency band of interest. Fig. 2 illustrates the spectrum of S 11 that we measured with the Keysight E5071C Vector Network Analyser (VNA) over the 2.2 to 2.6 GHz band. The modulus indicates a cavity resonant mode around 2.41 GHz, with a minimum at -1.2 dB. This means a significant steady-state reflection level for CW excitation. We are clearly not in the presence of a critically coupled cavity, for which this modulus of the reflection coefficient would be much lower. The phase must then be observed to understand that we are in the presence of an overcoupling of the cavity. Indeed, for an undercoupling regime, it is the contribution of the direct reflection at the access that dominates. This contribution and the incident signal are 180 • out of phase. Thus, the phase of S 11 at resonance on the spectrum remains at ±π. In contrast, for a case of overcoupling such as this one, it is the contribution of the leakage from the cavity to the coaxial cable that constitutes the major part of the global reflected signal. Then we see around the resonance a continuous evolution of the phase between +π and -π. It is particularly the phase transition through 0 that is of interest for the excitation of the zero of the S-matrix.

Two intermediate steps are necessary to obtain the real part of the pole and the zero. We know that the pole associated with the excited mode corresponds to the complex angular frequency of the release signal observed in the absence of an incident wave (outgoing boundary condition [START_REF] Grigoriev | Optimization of resonant effects in nanostructures via weierstrass factorization[END_REF] ). This complex angular frequency is unique whatever the real or complex angular frequency of the initial mode excitation signal, considering a single-mode resonator (see supplementary materials, sec. I). To obtain the release signal associated with the mode, the first of these steps is to fill the cavity. For example, we choose a harmonic excitation s inc (t) = e j2π f 1 t at the real frequency f 1 = 2.4085 GHz corresponding to the zero phase FIG. 2

F s re f num (t) = F [s inc (t)] • S 11 ( f ) (4)
We numerically construct this signal in the time domain by inverse discrete Fourier transform. We obtain a response similar to the one plotted on Fig. 3 (not for f 1 in this figure, see supplementary materials sec. I for the one corresponding to the f 1 excitation). Note that for all such chronogram in the article, the yellow part corresponds to the reflected signal before excitation cut-off, i.e. the time interval during which the incident signal in blue is different from zero. The red one corresponds to the reflected signal after excitation cut-off (the incident signal is zero). For each of the figures, the reflected signal is calculated or measured at once, the colour differentiation (yellow and red) being only a visual distinction. Moreover, the chosen time interval does not allow the oscillations of the signals (with a period of about 0.4 ns) to be visually distinguished. Then, to identify the real part of the pole, we carry out a spectral study of the signal scattered by the cavity after excitation cut-off (in red). The observed exponential decay, characterised by a time constant of 15.59 ns, is displayed in Fig. 4 as a Lorentzian in the frequency domain. This is centred on a real frequency, invariant to the way the cavity mode was excited (real or complex angular frequency -see supplementary materials sec. I). It is the real part of the pole of the S-matrix, and by identification thanks to the theory for our case, that of the zero. We note it ω 0 = 2π f 0 , with in our case f 0 = 2.41135 GHz. Let us add that the linewidth ∆ω = 2π∆ f of the Lorentzian is proportional to the imaginary part of the pole (∆ω = 2Im[ω pole ]), and inversely proportional to the time constant of the decay (τ = 1/Im[ω pole ]).

FIG. 3: Numerical construction of the temporal response of

the cavity from a CW excitation at the real part of the frequency of the singularities at the studied resonance. In the legends, ω exci = 2π f exci refers to the frequency of the incident excitation signal.

FIG. 4: Frequency spectrum of the scattered signal after the CW excitation cut-off (in red on Fig. 3). The centre frequency of the Lorentzian corresponds to the real part of the pole (and consequently the zero), ω 0 = 2π.Re[ f pole ] = 2π f 0 . The imaginary part of the pole is estimated here from the Lorentzian linewidth ∆ f .

B. Identification of the decay rates γ int and γ ext

Now, let us consider the peculiar case of the harmonic excitation of the cavity at the real part of the pole and the zero, s inc (t) ∼ e jω 0 t , without stored energy at t = 0. Eqs. ( 1) and ( 2) of the TCMT applied to our cavity allow us to formulate the temporal evolution of the reflection coefficient r(t) = s re f (t)/s inc (t) as a function of the decay rates:

r(t) = 2γ ext γ ext + γ int 1 -e -(γ ext +γ int )t -1 (5)
We can also build up the reflected signal during excitation associated with this special case, using the numerical method described earlier. Fig. 3 shows the result of this construction. The signals are normalised by the maximum amplitude of the incident signal. The envelope of the normalised reflected signal (in yellow) then represents the time evolution of the reflection coefficient. This evolution is expressed analytically by Eq. ( 5). We can observe a transient period characteristic of overcoupling [START_REF] Ra'di | Virtual critical coupling[END_REF] . Indeed, the reflection decreases until an instant of zero reflection, before increasing to reach the steady state. At the cut-off of the excitation, we find the exponentially decaying amplitude signal associated with the pole of this cavity resonance (in red). Note that this type of response to CW excitation, including during the transient phase, could be observed through the experimental set-up described in the next section, and can be used directly to fit the theory at the cost of more noise and uncertainty (see supplementary materials sec. II). Then, from Eq. ( 5), we derive a system of two equations with two unknowns to calculate γ int and γ ext . A first equation comes from the knowledge of the instant t r=0 for which the reflection coefficient cancels during the transient phase, r(t) = 0. The second equation is found by considering the reflection coefficient in the steady state, i.e. the measurement of r ∞ for t → ∞ during the excitation. From these equations, we identify the intrinsic decay rate:

γ int = 1 -r ∞ 2t r=0 ln 1 + r ∞ r ∞ (6)
and the external decay rate :

γ ext = 1 + r ∞ 2t r=0 ln 1 + r ∞ r ∞ (7)
Finally, the knowledge of these decay rates leads us to find the imaginary part of the pole (which could already be calculated using the spectral analysis of the exponential decay of the cavity leakage signal at the excitation cut-off) ω ′′ pole = γ ext + γ int , and to calculate the imaginary part of the zero ω ′′ zero = γ intγ ext , which we are mainly interested in. Table II summarises the quantities calculated through our extraction time domain method.

C. Verification of zero reflection with a plot

The last step is to verify the validity of the identified zero by a new numerical construction. As before, we calculate from the spectrum of S 11 measured with the VNA, the signal reflected over time by the cavity for the ideal excitation of the zero of the S-matrix. This ideal incident signal, constructed numerically, is of the form s inc (t) = s 0 e j(γ ext -γ int )t e jω 0 t , with s 0 the amplitude of the incident signal at t = 0. The result is TABLE II: Characteristics of the cavity found by our extraction time domain method. Here, the sign of the imaginary parts of the pole and the zero is imposed by our convention in e jωt . Injected into this, we find an exponentially decaying amplitude for the pole, growing for the zero [START_REF] Grigoriev | Optimization of resonant effects in nanostructures via weierstrass factorization[END_REF] .

ω 0 2π•(2.41135 GHz) t r=0
11.86 ns r ∞ 0.8773 Here, the initial peak amplitude of the incident signal is set to 0.5 mV, and the duration of the excitation is set for a final peak amplitude of 0.3 V. plotted in Fig. 5. We observe the absence of reflected signal during the excitation period (in yellow), confirming the possibility of exciting a zero of the S-matrix of our cavity. Finally, at the cut-off of the excitation, we observe, as in the case of the CW excitation, the decaying signal that leaks out of the cavity through the pole associated with the resonance under study. The observed exponential decay has the same time constant as in Fig. 3, also calculated in Table II.

Q int = ω 0 /(2γ int ) 1926 Q ext = ω 0 /(2γ ext ) 126 ω ′′
In this section, we have shown a time domain method for extracting the pole and the zero of a single-channel, overcoupled, single-mode cavity over a fairly wide frequency band. This extraction has been carried out from the S-matrix via its spectral measurement with a VNA. This time domain method enables to verify that proper design of the incident signal should allow the virtual critical coupling to be achieved, even in the presence of intrinsic losses. It relies on the analysis of the temporal waveform of the reflected signal in order to extract S-matrix singularities, with the theory hypothesis that the pole and zero real parts are similar (see Eq. ( 3)). Hence, it seems of particular interest for analysing time-varying cavities, such as cavities used for plasma ignition [START_REF] Lacoste | Experimental study of energy coupling and plasma breakdown in a pulsed high frequency resonant cavity[END_REF][START_REF] Kalluri | Electromagnetics of Time Varying Complex Media: Frequency and Polarization Transformer[END_REF] . It is the practical way of shaping the incident signal that will interest us in the following part in order to really excite this zero.

V. EXPERIMENTAL GENERATION OF THE CAVITY S-MATRIX ZERO

A. Experimental set-up Fig. 6 shows a schematic and a picture of the experimental set-up for the purpose of performing and characterising the zero excitation for mode T E 012 of the cavity presented in the plasma context, around 2.41 GHz. For this purpose, our experimental work relies on Keysight's 33600A Arbitrary Waveform Generator (AWG), offering a bandwidth of 120 MHz. This generator is used to design the envelope of the incident signal. This envelope can be found in green in Fig. 7. A Tektronix TSG4104A RF signal generator is used to generate the carrier of the incident signal. With a resolution of 1 µHz in the 950 kHz -4 GHz band, it will be able to generate the harmonic signal at the real part of the zero with the required accuracy. The final construction of the incident signal goes through a Polyphase QM2040A modulator, operating between 2 and 4 GHz. It receives the AWG envelope on the I channel, with the Q channel shorted, and performs the carrier modulation.

To characterise the validity of the zero excitation, we wish to measure the signals incident on and reflected by the cavity. We have therefore chosen to create two measurement channels, incident and reflected, by the presence of a power splitter, operating between 2 and 4.2 GHz. The information carried by the signal at the output of the modulator is therefore found on both channels, but attenuated by about 3 dB. The output of the power splitter to the incident channel is fed directly to the oscilloscope through coaxial cables. The signal output on the other channel of the power splitter should be directed to the cavity. A circulator operating between 2.4 and 2.6 GHz is placed just before the cavity to direct the reflected signal to the oscilloscope. It also isolates this measurement from a contribution from the incident signal. An isolator is placed between the power splitter and the circulator to isolate the incident channel from a possible return of the reflected signal from the cavity. This isolation is 32 dB at 2.41 GHz. Therefore, this experimental set-up allows us to measure incident and reflected signals that are not affected by external contributions. Finally, the Keysight MSO9254A oscilloscope with a bandwidth of 4 GHz and a sampling frequency of 20 GSa/s makes it possible to measure our signals with a vertical resolution of 1 mV and a horizontal resolution of 1 ps.

The modulator accepts on its channel I a signal with a maximum peak amplitude of 0.32 V. It constrains the exponential growth of the incident signal amplitude (characterised by the envelope generated by the AWG) to stop once this value is reached. In addition with the oscilloscope resolution that constrains the initial amplitude of the incident signal, this also limits the duration of the excitation, which is about a hundred nanoseconds according to the numerically constructed signal, seen Fig. 5. Characterisation of the different elements of the microwave circuit (consisting, as shown in Fig. 6, of an isolator, a circulator, coaxial cables, ...) has been conducted, in term of losses and time delay. Therefore, we recover the amplitudes of the incident and reflected signals at the coaxial connector of the cavity access. Temporal synchronisation was achieved by generating a CW signal at the real part of the zero over 400 ns, and for the cavity replaced by a short circuit. The signal measured on the reflected channel is then the 180 • out of phase image of the signal measured on the incident channel, and delayed by 2.4 ns, more or less two periods (±0.83 ns). Taking into account these effects, the incident and reflected signals at the cavity access can be plotted and compared in term of amplitude and time delay. Thanks to the temporal resolution of the oscilloscope, we can also verify the phase correspondence of the signals.

B. Practical results

Fig. 7 illustrates the result of our measurements with the experimental set-up, for the excitation of a zero of the S-matrix of our cavity. In a similar way to the figure constructed numerically earlier, we observe a reflected signal that is almost zero during the excitation, whereas the incident signal sees its amplitude increasing over time. It therefore brings more and more energy to the cavity. We show here the feasibility of the excitation of a zero of the S-matrix for a microwave device and then the realisation of virtual critical coupling.

The incident signal used for this experimental demonstration has a complex frequency f exci = 2.4090 -j0.0090 GHz. Recall that for our e jωt convention, this complex frequency with negative imaginary part corresponds to an exponentially growing amplitude. The real part has been slightly tuned to clearly identify the time t r=0 for an harmonic excitation. For real frequencies different from even 1 MHz, the reflection was no longer exactly zero at this time (see supplementary materials sec. III). However, we found an imaginary part of the complex excitation frequency similar to the one previously extracted, thus validating our extraction time domain method.

We show the envelope generated by the AWG, duplicated for negative amplitudes in Fig. 7. The amplitude of this envelope takes into account the correction related to the attenuations undergone if it propagated to the cavity access. The cut-off of the excitation is represented by the vertical dotted line. It serves as a reference for identifying the signal reflected during the excitation (in yellow) and the one measured once the excitation is cut off (in red). Thus, we can see that for the time during which the incident signal can be shaped according to the zero, the measured reflected signal has an amplitude in the measurement noise. This can be viewed as the absence of scattering sought by the virtual critical coupling. As soon as the incident signal returns to zero, the energy stored in the cavity is released. The associated signal measured on the oscilloscope follows an exponentially decaying amplitude. It is characterised by a time constant identical to that calculated by the numerical reconstruction. The decay therefore seems to take place for the pole associated with this resonance mode.

VI. CONCLUSION

The experimental implementation of virtual critical coupling to a microwave resonant cavity has been demonstrated. To achieve this, we proposed a time domain method for extracting the scattering system parameters. This relies on the S-matrix measurement and the analysis of the cavity harmonic response over time. It allows the calculation of the singular complex angular frequencies that are the poles and zeros of the S-matrix, taking into account the effect related to the losses in the cavity. The cavity used was not specifically designed for the needs of this experiment. It is therefore possible to replicate our approach for other types of single-access overcoupled cavities of arbitrary shape, in a frequency band in which the FIG. 7: Observation of a zero of the S-matrix of our cavity through our practical set-up.

resonance modes are isolated. Moreover, the experimental demonstration of the excitation of an overcoupled cavity without reflection can lead us to consider the principle of a new efficient strategy of plasma ignition in cavity and maybe to a transient time control of the cavity behaviour during plasma ignition process. This strategy would no longer be based on a modification of the system [START_REF] Conrads | Plasma generation and plasma sources[END_REF][START_REF] Silva | Microwave engineering of plasma-assisted CVD reactors for diamond deposition[END_REF] , but rather on a temporal modulation of the energy generator. This principle reinforces the need to overcome the lossless hypothesis for the realisation of virtual absorption. The cavity will indeed see its load changing during the ignition process, and through it, the intrinsic losses of the cavity and the coupling regime. In addition to the implementation of this matching strategy, the temporality of the excitation and the power level to be reached for the plasma breakdown seem to be major additional challenges to be met, notably from a hardware point of view. A detailed and comparative energy analysis of the different coupling options (critical coupling, virtual critical coupling), among others in the presence of intrinsic losses, may help to better define the limits. This study for the ignition of plasmas in resonant cavities should be the object of our future work.

SUPPLEMENTARY MATERIALS

See (supplementary materials link) for a detailed study of the scattered signal at the excitation cut-off. We also show the measurements made for CW excitation using our experimental set-up. We complete our experimental results on the zero excitation by a comparison with excitations at complex frequencies close to the zero.

FIG. 5 :

 5 FIG. 5: Numerical construction of the temporal response ofthe cavity from the zero excitation. Here, the initial peak amplitude of the incident signal is set to 0.5 mV, and the duration of the excitation is set for a final peak amplitude of 0.3 V.

FIG. 6 :

 6 FIG. 6: (a) Scheme and (b) photograph of the experimental set-up.

TABLE I :

 I Proposed time domain method for the extraction of the S-matrix singularities of our cavity for the purpose of exciting a S-matrix zero. F refers to Fourier transform.

	Step	Description
		S 11 overcoupled
	A. Identification of ω 0	→ Choice of ω 1 → s re f (t) = exp( jω 1 t) * s 11 (t) → F s re f cut-o f f (t)
		→ ω 0
	B. Identification of γ int and γ ext	r(t) = s re f (t)/ exp( jω 0 t) → t r=0 and r ∞ → γ int and γ ext
	C. Verification of
	zero reflection

  : Measured reflection coefficient S 11 spectrum of the electromagnetic cavity. of the measured S 11 . The response s re f num (t) of the cavity to this excitation, using the measured S 11 as a transfer function, can be written s re f

num (t) = s inc (t) * s 11 (t) in the time domain, which gives in the frequency domain by application of the Fourier transform F :

ACKNOWLEDGMENTS

The authors would like to thank Béatrice Fragge for her contribution concerning the cavity used in this paper.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

AUTHORS DECLARATIONS

The authors have no conflicts to disclose.