Béatrice Cointe

| Hélène Guillemot

Hélène Guillemot
email: helene.guillemot@cnrs.fr

Domain Matthias Heymann

A history of the 1.5 C target

Keywords:

The 1.5 C target is now widely considered as the maximum acceptable limit for global warming. However, it is at once recent and, as it appears increasingly unreachable, already almost obsolete. Adopted as an aspirational target in the Paris Agreement in 2015, the 1.5 C objective originated with a political impetus within UNFCCC negotiations. The Intergovernmental Panel on Climate Change (IPCC) endorsed this policy-driven target when it produced the Special Report on 1.5 C. This article highlights the continuity of the history of the 1.5 C target with that of the 2 C target, but also the differences between the two. Because the 1.5 C target considerably raises the bar on mitigation efforts, it exacerbates political tensions and ambiguities that were already latent in the 2 C target. This article retraces the emergence of the 1.5 C in diplomatic negotiations, the preparation of the IPCC Special report on 1.5 C, and the new kinds of debates they provoked among climate scientists and experts. To explain how an unreachable target became the reference for climate action, we analyze the "political calibration" of climate science and politics, which can also be described as a codependency between climate science and politics.

forward by the COP26 Presidency (UK Government, 2021, cited in Schenuit, 2022), have been growing louder. How did an almost impossible target become the point of reference for climate action? How does it maintain its legitimacy despite the incompatibility between ambitions and actions that it makes evident?

This article retraces the short but eventful history of the 1.5 C target. It is a direct extension of the literature on the 2 C target [START_REF] Aykut | La gouvernance du changement climatique: Anatomie d'un schisme de réalité[END_REF][START_REF] Cointe | 2 C: History of a science-policy nexus[END_REF][START_REF] Morseletto | Governing by targets: Reductio ad unum and evolution of the two-degree climate target[END_REF][START_REF] Randalls | History of the 2 C climate target[END_REF], because the emergence and establishment of the 1.5 C target is itself an extension of the history of the 2 C target. This history also invites us to question the relations between climate science and politics in the light of the contradictions and ambiguities behind the 1.5 C target. Previous analyses have emphasized the co-production of climate science and policy [START_REF] Miller | Climate science and the making of a global political order[END_REF] and, more recently, described the effect of mitigation pathways as performative [START_REF] Beck | The IPCC and the new map of science and politics[END_REF]. We argue that the history of the 1.5 C target is better described in terms of a codependency of science and policy. On the one hand, science-especially as mediated by IPCC reports, but also by Structured Expert Dialogues under the UNFCCCinforms and shapes climate negotiations, giving legitimacy to targets and/or highlighting their inconsistencies with current policies. On the other hand, the quest for policy relevance influences scientific research agendas to some extent. This generates tensions and difficulties on both sides of the science-policy interface. These are further exacerbated in the case of the disciplines featured in Working Group III (WGIII) of the IPCC, which grapple directly with the societal, political and economic logic of emissions reductions objectives.

Our history of the 1.5 C target is based on our previous work on climate negotiations, climate scenarios, the IPCC, and integrated assessment models (IAMs). It builds on a diversity of empirical material collected in several projects between 2015 and 2021: a set of interviews with integrated assessment modelers, an ethnographic study of COP21, and a master's thesis. 2 We complemented this material with a review of the literature on post-Copenhagen climate negotiations, as well as on the evolution of climate science-policy interactions.

Histories of the 2 C target highlight its co-production by science and politics over several decades. By contrast, the 1.5 C target originated in climate negotiations, and scientists only really started to consider it (somewhat reluctantly) once it was politically approved. The target remains a source of discomfort among scientists, as shown in November 2022 by the call from Scientist Rebellion to admit that "there is no plausible pathway to 1.5 C". 3 We thus begin by retracing the emergence of the 1.5 C target in UNFCCC negotiations ahead of COP21. We then analyze the preparation of the IPCC Special Report on 1.5 C (SR1.5), and the debates and criticisms that the target provoked among climate experts. To put this history in perspective, we continue with a flashback to the time of the production of the first 2 C mitigation scenarios, which allows us to discuss the "political calibration" of climate targets [START_REF] Van Beek | Navigating the political: An analysis of political calibration of integrated assessment modelling in light of the 1.5 C goal[END_REF] and to account for some of its contradictions.

| THE IRRUPTION OF THE 1.5 C TARGET AT THE NEGOTIATING TABLE

While the 2 C target has a relatively long, intricate and entwined political-scientific history, the 1.5 C target emerged relatively rapidly, and its origins are clearly on the diplomatic side. The 2 C long-term temperature target was constructed in long and complex exchanges between climate science and policy [START_REF] Cointe | 2 C: History of a science-policy nexus[END_REF][START_REF] Randalls | History of the 2 C climate target[END_REF]. After the adoption of the UNFCCC in 1992, the literature focused on what was to be stabilized: greenhouse gas emissions, atmospheric concentrations or global temperature. In 1996, Germany adopted the 2 C temperature target, associated with a target for greenhouse gas concentrations, soon followed by the European Union. However, at the international level the IPCC focused on emissions and concentrations, and negotiations were concerned with short-term emissions reduction objectives, which were the focus of the Kyoto Protocol. This changed in 2007, when the Bali Action Plan referred to a long-term global goal. Over this period, the success of the "burning embers" diagram, first published in 2001 in the IPCC Third Assessment Report, established the increase in global temperatures as a measure of climate risks [START_REF] Mahony | The colour of risk: An exploration of the IPCC's "burning embers" diagram[END_REF]. 4 As a result, during the 2000s the 2 C temperature threshold became increasingly prominent in the scientific literature and in global politics.

The 1.5 C target has a shorter and more overtly political history. It first appeared in the lead-up to the 2009 COP15 in Copenhagen, as part of discussions on the long-term global goal that were converging toward a 2 C limit [START_REF] Cointe | 2 C: History of a science-policy nexus[END_REF][START_REF] Guillemot | The necessary and inaccessible 1.5 C objective: A turning point in the relations between science and politics[END_REF][START_REF] Livingston | Taking science by surprise: The knowledge politics of the IPCC special report on 1.5 degrees[END_REF]. 5 The Alliance of Small Island States (AOSIS) considered 2 C an unacceptable level of warming and an existential threat (Livingston & Rummukainen, 2020, p. 11;Tschakert, 2015). In 2009, they engaged in diplomatic work to advocate for 1.5 C instead, building an alliance with the Least Developed Countries (LDC) group and rallying the support of heads of states and ministers in the Climate Vulnerable Forum (ICCCAD, 2016). They viewed the 2 C target as the objective of the rich countries, and 1.5 C as the only safe limit for poor and vulnerable countries. The Copenhagen Accord set 2 C as the limit to the increase in global temperature, while concluding on an invitation to consider "strengthening the long-term goal… including in relation to temperature rises of 1.5 degrees Celsius" (UNFCCC, 2009, para. 12). 6 One year later in Cancun, the COP adopted the objective of "hold[ing] the increase in global average temperature below 2 C above pre-industrial levels" and decided on a periodic review of the adequacy of this goal, confirming the possibility of strengthening it to 1.5 C (UNFCCC, 2010, paras. 4 and 138).

The first review took place from 2013 to 2015 and included a Structured Expert Dialogue (SED) between parties to the UNFCCC and over 70 scientific experts (UNFCCC, 2015a). The implications of limiting global warming to 1.5 C versus 2 C were a central topic in all four sessions of the SED (Tschakert, 2015;UNFCCC, 2015a). One of the 10 messages put forward in the SED report was that "while science on the 1.5 C warming limit is less robust, efforts should be made to push the defence line as low as possible" (UNFCCC, 2015a, p. 33). This temperature was in fact outside the range considered in the IPCC's AR5, the most recent assessment of the literature available at the time. Only a handful of emissions scenarios among the 1200 in the AR5 WGIII scenarios database had explored the likelihood of staying below 1.5 C of warming (UNFCCC, 2015a, p. 92 para. 132). Regarding impacts, experts in the SED repeatedly noted that the literature was too scarce to robustly assess the difference between 1.5 C and 2 C (UNFCCC, 2015a, p. 67 para. 27, p. 73 para. 53). All the same, as Tschakert (2015, p. 8) noted about the fourth session of the SED, the "consensus… was that a 2 C danger level seemed utterly inadequate."

The output of the SED helped AOSIS make the case for 1.5 C. Indeed, the SED itself was part of their negotiating strategy and among their achievements. As noted by Benjamin and Thomas (2016, pp. 2-3) and [START_REF] Ourbak | The Paris agreement and climate change negotiations: Small Islands, big players[END_REF]Magnan (2017, p. 2203), it was AOSIS that pushed the initiative to hold a Structured Expert Dialogue that would consider strengthening the long-term global goal and conclude before the Paris negotiations, and that later advocated for the SED's report to be put before the COP. In parallel, they garnered support for the 1.5 C target from NGOs and from other countries, especially within the so-called High Ambition Coalition [START_REF] Fry | The Paris Agreement: An insider's perspective. The role of Small Island developing states[END_REF][START_REF] Ourbak | The Paris agreement and climate change negotiations: Small Islands, big players[END_REF]. The eventual adoption of 1.5 C as an aspirational goal in the Paris Agreement (UNFCCC, 2015a, 2015b, art. 2) was nonetheless the result of intense and difficult negotiations [START_REF] Benjamin | 1.5 C to stay alive? AOSIS and the long term temperature goal in the Paris Agreement[END_REF][START_REF] Brun | Conference diplomacy: The making of the Paris Agreement[END_REF][START_REF] Ourbak | The Paris agreement and climate change negotiations: Small Islands, big players[END_REF].

Scientists and politicians are not alone in the game. Other groups of actors-think tanks, NGOs, philanthropic foundations, etc.-interact with researchers and political negotiators through networking, coordination, capacity building, lobbying and financing. These other actors played a central role in the inclusion of the 1.5 C objective in the negotiations and in the Paris Agreement, as shown by [START_REF] Morena | Follow the money: Climate philanthropy from Kyoto to Paris[END_REF]. From 2010, several foundations involved in climate discussions sought to change their strategy after what they saw as the failure of the Copenhagen COP. At the instigation of the European Climate Foundation (ECF), international groups, NGOs and think-tanks (Climate Analytics, Ecofys, PIK, CAN, and WRI, to name a few) came together in the International Policies and Politics Initiative (IPPI) to pool resources and strategies to build positive "momentum" around COP 21 in Paris [START_REF] Morena | Follow the money: Climate philanthropy from Kyoto to Paris[END_REF]. Think tanks and foundations from developed countries thus provided support to negotiators from AOSIS and LDCs to promote the 1.5 C target.

In the immediate aftermath of COP21, the adoption of the 1.5 C target was met with surprise and skepticism [START_REF] Livingston | Taking science by surprise: The knowledge politics of the IPCC special report on 1.5 degrees[END_REF][START_REF] Guillemot | The necessary and inaccessible 1.5 C objective: A turning point in the relations between science and politics[END_REF]Hulme, 2016). Many climate scientists considered it unrealistic, especially since it came without proportionate commitments to reduce global greenhouse gas emissions. Despite this reluctance from scientists to support a politically driven target, the key role of the SED shows that science was instrumental in the process, identifying pockets of consensus and large areas of insufficient research. 7

| THE SPECIAL REPORT ON 1.5 C: FROM SKEPTICISM TO OWNERSHIP

In December 2015, alongside the Paris Agreement, the COP requested that the IPCC provide a Special Report on global warming of 1.5 C, to be delivered in 2018 to inform the political negotiations toward the first revision of the NDCs. In its April 2016 plenary, the IPCC decided to prepare three special reports: one on land, one on oceans and the cryosphere, and one on the 1.5 C target, described (and ultimately titled) in full as "a Special Report on the impacts of global warming of 1.5 C above pre-industrial levels and related global greenhouse gas emission pathways… in the context of strengthening the global response to the threat of climate change, sustainable development, and efforts to eradicate poverty." This broadened the scope of the Special Report to encompass sustainable development and poverty eradication, which was necessary to get all countries on board (interview with Masson-Delmotte, 2018). In this section we will see that SR1.5, initially met with reluctance by scientists, has been an unprecedented success, with scientific, methodological and conceptual innovations and record media coverage.

Responding to government requests is part of the IPCC's mandate. Nevertheless, the request for a report on the 1.5 C target was first met with concern or discontent among most scientists. As this report was obviously responding to a political demand, many saw it as a political instrumentalization of the IPCC, "a form of hypocrisy, raising false hopes for the public and the most vulnerable countries" [START_REF] Boucher | In the wake of Paris Agreement, scientists must embrace new directions for climate change research[END_REF]. Many, for whom the 1.5 C target was a "lost battle," saw this research as a waste of time and resources. Moreover, producing the report in such a short timeframe, when very little work existed on impacts or trajectories corresponding to 1.5 C, was a real challenge. The WGI co-chair in charge of SR1.5 therefore had reasons to fear that few researchers would want to get involved (interview with Masson-Delmotte, 2018).

However, the opposite happened: 560 researchers applied to be authors and 42,000 comments were sent in during the review phases-a record for IPCC reports (although some scientists refused to participate). Just as with the mention of the 1.5 C target in the Paris Agreement, scientists' position on the SR1.5 report evolved very quickly, from outrage to acceptance and ownership. 8 The 1.5 C target's official status changed the situation, giving it an authority that legitimized research. Many researchers wanted to participate in the political process, and to avoid cutting themselves off from the developing countries [START_REF] Renaudin | Les relations entre sciences et politique dans le régime climatique. Le cas du rapport spécial 1.5 C du GIEC[END_REF]. Finally, just as European Union funding encouraged IAM modelers to produce pathways limiting warming to 2 C [START_REF] Cointe | Organising policy-relevant knowledge for climate action: Integrated assessment modelling, the IPCC, and the emergence of a collective expertise on socioeconomic emission scenarios[END_REF][START_REF] Lövbrand | Co-producing European climate science and policy: A cautionary note on the making of useful knowledge[END_REF], funders have begun to support research on the 1.5 C objective. 9 In August 2016, a scoping meeting was organized by the co-chairs of the IPCC's three working groups to produce a first outline. The new IPCC Bureau, appointed just before COP21, intended to take advantage of this request in order to establish the target as a topic for scientific inquiry, and to correct some of the shortcomings pointed out in previous reports, such as the importance of carbon dioxide removal (CDR) (see below). The innovations generated by SR1.5 illustrate scientists' ability to reformulate questions to make them scientifically interesting and show that, as is often the case, their ability to align to political expectations opens up new scientific perspectives [START_REF] Lövbrand | Co-producing European climate science and policy: A cautionary note on the making of useful knowledge[END_REF] and provides an "innovation boost" [START_REF] Cointe | Organising policy-relevant knowledge for climate action: Integrated assessment modelling, the IPCC, and the emergence of a collective expertise on socioeconomic emission scenarios[END_REF]. One of the main novelties of the report lies in the organization of the work behind its production. While in previous IPCC reports the three working groups worked separately, scientists from all three WGs participated in the preparation of the five chapters of SR1.5, which were conceived as complementing and responding to each other [START_REF] Renaudin | Les relations entre sciences et politique dans le régime climatique. Le cas du rapport spécial 1.5 C du GIEC[END_REF]. The social sciences, in particular, played a more important role than before. One of the authors' ambitions was to better link climate change with other environmental and social issues such as poverty, health and inequality.

The request in the Paris Agreement for a special report inspired calls for papers and dedicated research programs that rapidly increased the amount of work on the impacts and implications of 1.5 C of warming [START_REF] Livingston | Taking science by surprise: The knowledge politics of the IPCC special report on 1.5 degrees[END_REF]. The first task of the report was to document the difference between the impacts of 1.5 C and 2 C of warming. A large body of new work showed very significant differences in a variety of areas, particularly for ecosystems. The second message of SR1.5 concerned the pathways to reach this objective: not exceeding 1.5 C of warming before the end of the century implies reaching CO 2 neutrality by 2050. The 1.5 C objective is thus associated with the "net zero emissions" objective: CO 2 neutrality is physically necessary in order to stabilize global temperatures, and the deadline for achieving it gets closer as the temperature target gets more ambitious. Another outcome of SR1.5 is the establishment of a close connection between the target and the short term: "1.5 C compatible" trajectories require CO 2 emissions to be halved by 2030.

To what extent should the pathways provided by integrated assessment models be allowed to rely on CDR to achieve such drastic decarbonization? This question was hard-fought in the SR1.5 writing process [START_REF] Van Beek | Navigating the political: An analysis of political calibration of integrated assessment modelling in light of the 1.5 C goal[END_REF]. In AR5, all scenarios that achieved warming below 2 C by 2100 relied on a temporary overshoot of atmospheric CO 2 concentrations, followed by the removal of CO 2 from the atmosphere in the second half of the 21st century through CDR (also referred to as negative emission technologies, or NETs)-the form most used in the models being bioenergy with carbon capture and storage (BECCS). This large-scale use of BECCS, a type of technologies that do not exist on the required scale and that may have negative side effects, provoked heated debate and criticism [START_REF] Anderson | The trouble with negative emissions[END_REF]. In the months and years following the release of AR5, many articles and reports have been published on CDRs, analyzing their potential, limitations and risks [START_REF] Fuss | Negative emissions part 2-Costs, potentials and side effects[END_REF]. One issue with BECCS was the huge areas of arable lands it requires for bioenergy production, at the expense of food production and biodiversity. With its inclusion of questions of ecology, development and poverty, SR1.5 provided a more critical perspective on BECCS. It introduced different categories of CDR, highlighting "nature-based solutions" (e.g., afforestation or soil carbon sequestration). However, the issue of finding "an acceptable level of overshoot" gave rise to intense science-policy negotiations (van Beek et al., 2022, p. 197). A few "no overshoot" scenarios reaching 1.5 C without CDR (10 out of 578) were published just before the SR1.5 deadline. These scenarios, responding to the criticism from experts and civil society that most scenarios favored technological solutions without questioning the dominant economic growth paradigm, made very strong assumptions of global decrease in energy consumption and demand, along with large-scale afforestation.

The report could not avoid the delicate question of whether it is in fact feasible to limit warming to 1.5 C at all. Several IPCC meetings were organized to address this issue. Asked to answer what was "not a scientific question" (interview, SR1.5 author, 2019), the SR1.5 authors responded by dividing feasibility into six dimensions (geophysical, environmental, technological, economic, sociocultural, and institutional) that "interact in complex and place-specific ways" (IPCC, 2018, pp. 71-72). Dealing with feasibility in several chapters as well as in a dedicated box, SR1.5 claims that limiting global warming to 1.5 C is "geophysically feasible" (since past emissions do not yet exceed the limit) and specifies the associated feasibility conditions. Through this new example of boundary work, the report confirms the geophysical feasibility of the goal while drawing a boundary between this and more political forms of feasibility. This "geophysical feasibility" allowed SR1.5 to maintain policy neutrality while conveying the message that it was not too late to stay below the 1.5 C threshold-depending on technological, economic, social and political choices that do not lie within the "policy neutral" remit of the IPCC.

SR1.5 received remarkably extensive, high-profile and long-lasting media coverage, far beyond previous IPCC reports [START_REF] Boykoff | Now or never: How media coverage on the IPCC special report of 1.5C shaped climate-action deadlines[END_REF]. Several factors probably contributed to this success. The IPCC Bureau devoted a great deal of effort to communication (careful illustrations, media training for the authors, etc.), and wanted the report to reach a wide audience beyond policymakers (interview with Masson-Delmotte, 2018). NGOs and foundations were deeply involved in promoting the report and its conclusions [START_REF] Morena | Follow the money: Climate philanthropy from Kyoto to Paris[END_REF]. Its publication coincided with the rise to fame of Greta Thunberg and the proliferation of school strikes and climate movements in 2018, contributing to its success. However, headlines and slogans were often limited to very simple watchwords-essentially "only 12 years left to save the climate." This claim has been criticized as not reflective of the substance of the report [START_REF] Asayama | Why setting a climate deadline is dangerous[END_REF], and the scientists involved preferred to emphasize the message that "every tenth of a degree counts." By contrast, some of the report's messages, particularly the considerable changes needed to limit warming to 1.5 C-including carbon removal-were scarcely discussed. NGOs refer to the report to claim that the target is still achievable and that "the blockage is not technical, but political," 10 without mentioning that almost all pathways to limiting global warming to 1.5 C require large amounts of CDR [START_REF] Renaudin | Les relations entre sciences et politique dans le régime climatique. Le cas du rapport spécial 1.5 C du GIEC[END_REF].

| THE IMPOSSIBLE 1.5 C TARGET: HYPOCRISY OR PUSH TO ACTION?

In terms of the failure to focus clearly on its concrete implications, the 1.5 C target fared no better than the 2 C target, which has been analyzed as a "disembedded object" [START_REF] Morseletto | Governing by targets: Reductio ad unum and evolution of the two-degree climate target[END_REF] or as part of a "schism of reality" [START_REF] Aykut | Taking a wider view on climate governance: Moving beyond the 'iceberg', the 'elephant' and the 'forest[END_REF][START_REF] Aykut | La gouvernance du changement climatique: Anatomie d'un schisme de réalité[END_REF]. Ahead of COP21, the discrepancy between ambition and action was the main cause of criticism of the 2 C target and, a fortiori, of skepticism about raising the ambition to 1.5 C. SR1.5 reaffirmed the need for rapid and radical action and the inadequacy of existing policies, but at the same time it gave scientific legitimacy to the 1.5 C target. It also clarified some debates, especially on CDR and feasibility (see above). Despite the overall shift in climate scientists' attitudes toward the 1.5 C target, some criticisms persisted, especially with regard to the ambiguous character of such an aspirational target. These debates were initially largely confined to academic publications, but made their way into the media during COP27 in 2022. 11 Climate scientist Kevin Anderson has denounced the "duality" and hypocrisy of keeping targets that currently cannot be achieved without massive amounts of negative emissions while not recognizing the revolutionary nature of the transformations that this implies [START_REF] Anderson | Duality in climate science[END_REF]. This line of criticism reflects the still-controversial status of CDR and negative emissions, which are sometimes denounced as a way of delaying action and preserving the status quo [START_REF] Carton | Carbon unicorns and fossil futures. Whose emission reduction pathways is the IPCC performing[END_REF]. The IAMs that produce mitigation pathways with high negative emissions have been subjected to lively academic debate [START_REF] Anderson | Debating the bedrock of climate-change mitigation scenarios[END_REF], although their reliance on NETs was somewhat moderated following SR1.5.

Questioning the political usefulness of the target, climate policy expert Oliver Geden has argued that, given that models always seem able to produce emissions pathways that are compatible with increasingly ambitious targets using devices such as NETs or overshoot, the "doomsday clock" is stuck at "five minutes to midnight" (Geden, 2016a). In other words, the urgency remains but it is never too late, so ambitions can be preserved while action is postponed. This recalls what [START_REF] Aykut | Incantatory' governance: Global climate politics' performative turn and its wider significance for global politics[END_REF] call "incantatory governance": the ambition of climate mitigation targets acts not as a binding limit, but as a signal that is supposed to set relevant actors in motion in the right direction. It is thus imperative that the target appears urgent, but within reach. In a less confrontational fashion, there have also been calls to not let the long-term global target obscure discussions on short-term, local or national transformations-including the production of expertise and scenarios relevant to short-term, local-scale action [START_REF] Boucher | In the wake of Paris Agreement, scientists must embrace new directions for climate change research[END_REF]. 12 These criticisms coexist with another position on the role of the 1.5 C target, which recognizes the "incantatory" character of the target but considers that character as its raison d'être. In this view, whether the target is reached or overshot is secondary; the purpose of the 1.5 C target is to meet the demand of poor and vulnerable countries, to give them diplomatic weapons (Tschakert, 2015) and to raise global ambition. As a SR1.5 author who worked on the box on feasibility puts it: "In fact [1.5 C] is a way of reinforcing the climate objective more than a climate objective as such."

Finally, the tensions and contradictions of the 1.5 C target have drawn attention to potential changes in the relations between climate science and politics, and in particular to the role of the IPCC. Some scholars have suggested that these tensions challenge the IPCC's "policy neutrality" [START_REF] Lahn | Boundary objects[END_REF] and called for reflection on the future role of the IPCC [START_REF] Beck | The IPCC and the new map of science and politics[END_REF]. All the same, following SR1.5, the IPCC's framing of the boundary between policy relevance and policy prescription was reaffirmed: "We have delivered the message to governments, we have provided them with the evidence, and it is up to them to decide on the final feasibility step," the co-chair of WGIII, Jim Skea, said at a press conference on the report.

| THE "POLITICAL CALIBRATION" OF IAMs TO PRODUCE LOW-CARBON PATHWAYS

To understand the 1.5 C target and the science-politics interactions that hold it together, it is useful to look back to the 2 C target. Many of the ambiguities and contradictions of the 1.5 C objective were already present with the 2 C target, only not as glaringly so. These ambiguities and contradictions were made manifest in the development of low emissions pathways that are compatible with increasingly ambitious temperature limits. These pathways are a keystone of IPCC reports, and are also used to assess mitigation options. They are instrumental in bringing climate policy targets into existence and maintaining them over time. Since the mid-2000s, a small but growing research community has emerged to develop the integrated assessment models that are used to explore long-term mitigation options [START_REF] Cointe | Organising policy-relevant knowledge for climate action: Integrated assessment modelling, the IPCC, and the emergence of a collective expertise on socioeconomic emission scenarios[END_REF][START_REF] Van Beek | Anticipating futures through models: The rise of integrated assessment modelling in the climate science-policy interface since 1970[END_REF]. 13 van Beek et al. (2022, p. 198) proposed the concept of "political calibration" to analyze the interplay between IAM research and climate policymaking. They define it as "a process of iterative adjustment between modelers and policymakers, in which the fit and focus of the model analysis and the requirements of the policy community are negotiated." It was through this process of political calibration, they show, that the 1.5 C target made its way into the range of explored futures.

Before the Paris Agreement, the 1.5 C limit was outside the range of explored pathways. It was deemed unrealistic, and thus irrelevant [START_REF] Livingston | Taking science by surprise: The knowledge politics of the IPCC special report on 1.5 degrees[END_REF][START_REF] Van Beek | Navigating the political: An analysis of political calibration of integrated assessment modelling in light of the 1.5 C goal[END_REF]. After the Paris Agreement, pathways compatible with 1.5 C became widespread in the literature. A similar process had occurred for the 2 C target a decade earlier. Prior to 2007, there were hardly any scenarios compatible with a 2 C target. Among 177 stabilization scenarios assessed in IPCC AR4, only six fell in the range of 2.0-2.4 C warming, and none below 2 C (IPCC, 2007, p. 20). IAM researchers really started to explore pathways likely to limit global warming to 2 C after the IPCC Expert Meeting on New Scenarios held in Noordwijkerhout in 2007 [START_REF] Moss | Towards new scenarios for analysis of emissions, climate change, impacts, and response strategies[END_REF]. At this meeting, a new suite of reference emissions scenarios was selected from the available literature to replace the scenarios defined in the Special Report on Emissions Scenarios (or SRES): the "Representative Concentration Pathways" (RCPs). Among the contenders was RCP2.6, a recent scenario published by [START_REF] Van Vuuren | Stabilizing greenhouse gas concentrations at low levels: An assessment of reduction strategies and costs[END_REF] where GHG concentrations peak and decline before stabilizing at 400 ppm CO 2 equivalent, and which was considered compatible with a "below 2 C" goal.

At the time, this was the lowest stabilization scenario in the literature. As one IAM modeler explained us in an interview, this scenario was developed precisely to remedy the lack of modeling studies on the conditions needed to meet the 2 C target advocated by the EU, following a discussion between this modeler and Bert Metz, then the head of IPCC Working Group III. Studies considering response strategies had until then focused on stabilization at 550 ppm, which was increasingly seen as insufficient to meet a 2 C target (interview, Modeler 2, 2015). The scenario required drastic and rapid emissions reductions in all sectors, as well as BECCS to enable so-called "negative emissions" later in the century. Despite the exploratory character of this scenario, participants in the Noordwijkerhout meeting, including researchers, government officials, international organizations and NGOs, favored it as the low-end option. Ahead of the meeting, a position paper prepared by Malte Meinshausen and Bill Hare made the case for the RCP2.6 scenario based on two main arguments: its consistency with the long-term objectives considered in political discussions, and the scientific interest of using its "peak-and-decline" shape to study the climatic response to declining greenhouse gas concentrations (Moss et al., 2008, Appendix 4). 14 The meeting's final report reflects this position and uses the same arguments (Moss et al., 2008, p. xix). 15 To confirm the selection of this scenario, other IAM teams were asked to try and reproduce it with other models [START_REF] Weyant | Report of 2.6 versus 2.9 Watts/m 2 RCP evaluation panel[END_REF]. Gradually, 2 C-compatible scenarios became common in the literature, even though they could be extremely challenging to model (Guivarch & Hallegatte, 2013, p. 188). Despite their optimistic assumptions and drastic emissions reductions requirements, they contributed to ascertaining the feasibility in principle of the 2 C target [START_REF] Lövbrand | Co-producing European climate science and policy: A cautionary note on the making of useful knowledge[END_REF][START_REF] Van Beek | Navigating the political: An analysis of political calibration of integrated assessment modelling in light of the 1.5 C goal[END_REF]. 16 This established negative emissions as an all but indispensable element in the portfolio of climate action (Beck & Mahony, 2018a). In a way, BECCS and NETs expanded the so-called "possibility space."

What happened following the adoption of the 1.5 C target was similar. IAM teams developed pathways compatible with 1.5 C to meet the demand, relying on temporary overshoot and negative emissions, but also expanding the range of mitigation options they considered (van Beek et al., 2022, p. 198). Back in 2017, one modeler explained that when he started, for him "2 C was impossible, but as I kept seeing it, it has become something very common. The same thing is happening with 1.5 C even if there are many arguments against it" (interview, Modeler 3, 2017). All the same, it is no secret that these scenarios are very challenging to produce: they stretch models to their limits. The same modeler explained: "For us, 1.5 C is very difficult, very costly. When we model, we open up a spectrum of possibilities, and this one we had not anticipated at all. We are working at the limits of the model, of the equations, of the production functions, with substitution effects that drive us to extreme cases, and we have asked ourselves whether our model is really credible for this kind of scenarios" (interview, Modeler 3, 2017). In other words, in order to achieve 1.5 C pathways, modelers have needed to use such strong assumptions that it put to the test their ability to control or trust their models. This was already the case for 2 C pathways: for instance, Guivarch and Hallegatte (2013, p. 188) note that " van Vuuren et al. (2010a, b) indicate that the low stabilization levels compatible with the 2 C target are close to the maximum achievable emissions reduction potential in their model." A similar caveat is expressed in Annex III to the WGIII contribution to IPCC AR6, which remarks that "overshoot was particularly allowed for low concentration and temperature targets as many models could not find a solution otherwise" (IPCC, 2022, p. II-55).

Modelers' persistence in "working at the limits" in order to model pathways to 1.5 C may appear paradoxical, but it can be explained by the fact that policy relevance is a constitutive dimension of IAM research [START_REF] Cointe | Organising policy-relevant knowledge for climate action: Integrated assessment modelling, the IPCC, and the emergence of a collective expertise on socioeconomic emission scenarios[END_REF][START_REF] Lövbrand | Co-producing European climate science and policy: A cautionary note on the making of useful knowledge[END_REF][START_REF] Van Beek | Anticipating futures through models: The rise of integrated assessment modelling in the climate science-policy interface since 1970[END_REF][START_REF] Van Beek | Navigating the political: An analysis of political calibration of integrated assessment modelling in light of the 1.5 C goal[END_REF], and indeed of "WGIII science" more broadly. In fact, the multiplication of 1.5 C scenarios spurred by SR1.5 has made it possible to correct some of their initial excesses, particularly on CDR; and the debates around NETs and IAMs have opened up new directions of research, for instance on feasibility, no-overshoot scenarios and, more recently, post-growth scenarios.

| CONCLUSION

The 1.5 C objective for climate policy action is a continuation of the 2 C objective and is subject to the same ambiguities, especially regarding the use of negative emissions. With its origins in a political impetus provided by a broad coalition of vulnerable states, NGOs and philanthropic foundations in UNFCCC negotiations, this objective is even more unattainable than 2 C. And because it is considerably more demanding, it intensifies and brings to the fore political tensions and inconsistencies that were already present.

Faced with these contradictions, scientists initially reacted with surprise, concern or skepticism when the target was adopted in 2015. This changed with the preparation and publication of IPCC SR1.5: by producing this report, the IPCC endorsed this policy-driven target. The report increased knowledge and clarified some debates, but it could not resolve the inconsistency between the long-term global goal and actual mitigation commitments. This gave rise to two coexisting positions among scientists and experts: some take the target literally and denounce its hypocrisy, while others see it as an aspirational target meant to raise ambition. The political realism of the latter position assumes an "inherent inconsistency" between discourse, decisions and action [START_REF] Geden | The Paris Agreement and the inherent inconsistency of climate decision making[END_REF].

The process that has allowed the 1.5 C target to exist and be sustained has been analyzed as "political calibration" [START_REF] Van Beek | Navigating the political: An analysis of political calibration of integrated assessment modelling in light of the 1.5 C goal[END_REF]. Like that of many concepts developed to understand and address climate change, the history of the 1.5 C target has been marked by the continuous mutual adjustments of "scientific knowledge, policy goals and expectations about policy relevance" that Lahn (2022, p. 6) emphasized in the history of the carbon budget. But these adjustments do not always follow the same pattern. While the 2 C target is usually analyzed as the result of the coproduction of science and politics, the history of 1.5 C is rather one of codependency: political objectives require scientific backing to be legitimate, and research needs to attune to political discussions if it is to remain policy-relevant. The question remains whether the exacerbation of contradictions brought by the 1.5 C objective serves the fight against climate change, and whether it is tenable. scientists are unaware of the fact that a 1.5 C warming is being discussed by policymakers" (UNFCCC, 2015a, p. 73 para. 53). 8 As expressed, for instance, by an author of SR1.5 in an interview in 2019: "Honestly, as a scientist, I thought it was a bad idea to produce a report on 1.5 C, but in fact, after having done so, I think it was a good idea. So, even though it was very much driven by political motivation, I think that there was still an intuition behind it that was quite powerful." 9 The vast majority of research projects on pathways to 1. 12 This is reflected in the IPCC AR6 WGIII report, which includes both a chapter on long-term transformation pathways and a chapter on short-term and national pathways. 13 The field is dominated by a dozen models and research groups, the majority of which are now based in Europe. Currently, the three biggest IAM teams are at IIASA in Austria, PIK in Germany and PBL-RIVM in the Netherlands. 14 Bill Hare is a climate scientist, but also the founder and CEO of the NGO Climate Analytics. He has advised small island states and Least Developed Countries in climate negotiations, especially during the negotiations toward the Paris Agreement. The position paper was supported by 26 climate scientists and experts. 15 The position paper makes the case for the policy relevance of RCP2.6 in somewhat stronger terms than the report: excluding the lowest mitigation pathways from the scientific debate would be policy-prescriptive, because scientists would then be making "decisions about what are feasible mitigation pathways and what aren't" (Moss et al., 2008: 105). 16 Guivarch and Hallegatte (2013, p. 188) further note that "failed experiments tend not to be published," so that infeasible pathways do not appear in the literature, which tends to reinforce the apparent feasibility of stringent targets: for each possible 2 C or 1.5 C pathway that was identified and published, we do not know how many modeling attempts failed.

FURTHER READING

  5 C are Horizon 2020 projects funded by The European Commission. Other funders of research projects involving IAMs include JPI Climate, DG CLIMA, and the German and UK governments, as well as foundations such as ECF, Ikea, Hewlett and the Children's Investment Fund. See the website of the Integrated Assessment Modeling Consortium: https://www.iamconsortium.org/resources/projects/ (accessed on August 25, 2022) 10 See the press release about SR1.5 from French NGOs (including Greenpeace, WWP, Oxfam, etc.) posted on the Climate Action Network website (in French): http://reseauactionclimat.org/wp-content/uploads/2018/10/dossier-giec-15.pdf 11 For example: "Say Goodbye to 1.5 C", The Economist, November 5, 2022; Chelsea Harvey, "The World Will Likely Miss 1.5 Degrees C -Why Isn't Anyone Saying So?", Scientific American, 11/11/2022; Bill McGuire, "The 1.5 C target is deadto prevent total failure, GOP27 must admit it", The Guardian, November 12, 2022; Audrey Garric, "Faut-il déclarer qu'il n'est plus possible de limiter le réchauffement climatique à 1,5 C?", Le Monde, November 15, 2022.

  Cointe, B. (2022). Scenarios. In K. De Pryck & M. Hulme (Eds.), A critical assessment of the Intergovernmental Panel on Climate Change (pp. 137-147). Cambridge University Press. Lahn, B. (2020). A history of the global carbon budget. WIREs Climate Change, 11(3), e636. https://doi.org/10.1002/wcc.636

The first version of this article was written in the spring and summer of

2022, and it was revised during COP27 in November 2022. We have attempted to take into account the latest developments, while acknowledging that the climate debate is in a state of flux. 2 This article is based on fieldwork and interviews conducted during several projects in which the authors participated.As part of the collaborative research project ClimaCOP on COP 21, Hélène Guillemot conducted eight interviews with scientists at and around the Paris COP in 2015 and 2016[START_REF] Guillemot | The necessary and inaccessible 1.5 C objective: A turning point in the relations between science and politics[END_REF]. As part of a collaboration with Christophe Cassen, Béatrice Cointe conducted 15 interviews with integrated assessment modelers in 2015-2016, as well as observation in meetings of the Integrated Assessment Modeling Consortium (IAMC) (2015, 2021)[START_REF] Cointe | Organising policy-relevant knowledge for climate action: Integrated assessment modelling, the IPCC, and the emergence of a collective expertise on socioeconomic emission scenarios[END_REF]. The materials used to prepare this article also include 10 interviews conducted in 2019 by Audrey Renaudin for her master's thesis on SR15[START_REF] Renaudin | Les relations entre sciences et politique dans le régime climatique. Le cas du rapport spécial 1.5 C du GIEC[END_REF]). 3 Scientist Rebellion, "A united academia can fight climate failure," https://signon.scientistrebellion.com/ [accessed on November 23, 2022] 4 The phrase 'burning embers' refers to a figure entitled "reasons for concern," which was first published in IPCC TAR(IPCC, 2001, p. 5, Figure SPM-2), and was updated in subsequent IPCC reports. It uses a color scale from yellow to purple to indicate levels of threat on different dimensions, according to increases in global temperatures.[START_REF] Reisinger | An IPCC special report on the impacts of global warming of 1.5 C above preindustrial levels and related global greenhouse gas emission pathways[END_REF] As one anonymous reviewer pointed out, in a 1993 paper William Nordhaus referred to a policy proposal to "stabili[ze] climate so that the change in global average temperature is limited to no more than 0.2 degrees C per decade with an ultimate limitation of 1.5 degrees C"(Nordhaus, 1993, p. 21), suggesting that the 1.5 C limit was already on the table, if only briefly, in the 1990s. However, Nordhaus does not source this proposal, and we have not been able to retrace it to its origin(s).6 The Copenhagen Accord was not formally adopted by the COP, but only "take[n] note of."7 As an example of the process of joint agenda setting for climate research and negotiations, during the SED an expert suggested that the scarcity of research on the impacts of 1.5 C of warming "may also be due to the fact many

Funding information Grant/Award Number: ANR-21-CE03-0011-01 (PROCLIMEX

AUTHOR CONTRIBUTIONS Béatrice Cointe: Conceptualization (equal); investigation (equal); writingoriginal draft (equal). Hélène Guillemot: Conceptualization (equal); investigation (equal); writingoriginal draft (equal).

FUNDING INFORMATION

The authors are employed by the Centre national de la recherche scientifique (CNRS). This paper benefitted from funding by the French Agence nationale de la recherche (ANR) under grant ANR-21-CE03-0011-01 (PROCLIMEX).

CONFLICT OF INTEREST

No conflict of interest.

DATA AVAILABILITY STATEMENT

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

ORCID


Diego Bermúdez-Martín
email: diego.bermudez-martin@insa-rennes.fr

Raphaël Gillard

Carlos Molero

Hervé Legay

María García-Vigueras

Methodology for Improving Scanning Performance Loading an Array Element with a 3D All-Metal WAIM

Keywords: equivalent circuit, improving scanning, TEM waveguide unit-cell, 3D all-metal

All-metal 3D printing technologies are allowing the conception of new structures for different applications. This publication explores the potential of employing for the first time an all-metal 3D unit-cell topology to perform wide-angle impedance matching layers. A new equivalent circuit is derived for the oblique incidence, providing a good estimation of the cell response for the scanning range (θ = [0 • , 55 • ]) in the main scanning planes for a linearly polarized radiated field. This analytical model is later used to develop a wide-angle impedance matching design methodology for a generic antenna. This methodology is tested in practice to match a phased array made of metallic horns at 18 GHz. An improvement of 5 dB is obtained in the simulations for angles θ > 35 • for the H-plane.

Introduction

Wide scanning capabilities are usually required when using radar systems, modern communication systems, such as in 5G applications [START_REF] Tekkouk | Continuous beam steering antenna with large 2D coverage for 5G applications[END_REF], or communications with low earth orbit (LEO) satellites [START_REF] Faridani | A Compact Beam-Steerable Integrated Reflectarray Antenna for LEO Applications[END_REF]. As it is well known, while steering the beam, the coupling between the elements in the array may deteriorate the antenna active matching, possibly resulting in scan blindness [START_REF] Pozar | Scan blindness in infinite phased arrays of printed dipoles[END_REF]. It is particularly difficult to conceive an element for a phased array that scans at a wide angle, because its periodicity has to be smaller than 0.5λ to avoid grating lobes. Some methods have been developed to avoid these problems, such as the use of mechanical steering [START_REF] Densmore | A satellite-tracking K-and K/sub a/-band mobile vehicle antenna system[END_REF]. Other methods try to alleviate the problem while allowing for electrical scanning, which consist of the use of matching networks in the antenna elements [START_REF] Doane | Wide Scanning Tightly Coupled Dipole Array With Integrated Balun (TCDA-IB)[END_REF], reconfigurable active structures [START_REF] Alibakhshikenari | Improved adaptive impedance matching for RF front-end systems of wireless transceivers[END_REF][START_REF] Valagiannopoulos | PT-symmetric planar devices for field transformation and imaging[END_REF] or matching layers placed above the antenna. Such layers are commonly known as wide-angle impedance matching (WAIM) surfaces. This article proposes an innovative topology and the associated design methodology for a WAIM that can be built employing only metal. Indeed, 3D additive manufacturing methods allow to build a full structure in just one metallic piece, avoiding the use of connections or welds that could cause problems or deformations in the final response, as well as increasing the fabrication process speed. In addition, it avoids the use of dielectric materials in the structure, preventing problems such as intrinsic losses in these materials and the outgassing phenomenon [START_REF] Gollor | HV design of vacuum-insulated power supplies for space applications[END_REF] that dielectrics may suffer when they are used in space.

The use of these innovative manufacturing technologies results in a large number of 3D all-metal structures that are used in a wide range of applications. It can be found in frequency selective surfaces (FSS) acting as spatial filters [START_REF] Sanz-Izquierdo | Frequency selective surfaces formed by partially metalising 3D printed shapes[END_REF][START_REF] Liang | Subwavelength three-dimensional frequency selective surface based on surface wave tunneling[END_REF][START_REF] Tang | Waveguide 3-D FSSs by 3-D printing technique[END_REF], or as polarizers [START_REF] Molero | Circuit Modeling of 3-D Cells to Design Versatile Full-Metal Polarizers[END_REF][START_REF] Jimenez | All-Metal 3-D Frequency-Selective Surface with Versatile Dual-Band Polarization Conversion[END_REF][START_REF] Molero | Broadband 3D-Printed Polarizer based on Metallic Transverse Electro-Magnetic Unit-Cells[END_REF], metallic antennas [START_REF] Rojas-Nastrucci | Ka-Band Characterization of Binder Jetting for 3-D Printing of Metallic Rectangular Waveguide Circuits and Antennas[END_REF][START_REF] Huang | Application of 3-D metal printing to microwave components and antennas[END_REF][START_REF] Xiong | A Metallic 3D Printed Miniaturized Quasi Log Periodic Koch-Dipole Antenna Using T-Shaped Top Loading[END_REF] as well as metallic arrays [START_REF] Zhang | A Highly Integrated 3-D Printed Metallic K-Band Passive Front End as the Unit Cell in a Large Array for Satellite Communication[END_REF][START_REF] Foged | Investigation of Additive Manufacturing for Broadband Choked Horns at X/Ku Band[END_REF][START_REF] Pfeiffer | 3-D Printed Metallic Dual-Polarized Vivaldi Arrays on Square and Triangular Lattices[END_REF]. Lenses are also being made as 3D metallic structures [START_REF] Yamamoto | Measurements of a 3-D negative refractive index slab lens composed of periodic wired metallic spheres[END_REF][START_REF] Diallo | All-metal Ku-band Luneburg lens antenna based on variable parallel plate spacing Fakir bed of nails[END_REF][START_REF] Liao | Compact Multibeam Fully Metallic Geodesic Luneburg Lens Antenna Based on Non-Euclidean Transformation Optics[END_REF] and microwave filters as well [START_REF] Rojas-Nastrucci | Ka-Band Characterization of Binder Jetting for 3-D Printing of Metallic Rectangular Waveguide Circuits and Antennas[END_REF][START_REF] Vallecchi | 3-D Printed Bandpass Filters With Coupled Vertically Extruded Split Ring Resonators[END_REF]. To the best knowledge of these authors, there is no proposal for a metallic WAIM in the literature yet.

Classical WAIM solutions can be classified according to their topology, such as single dielectric layers [START_REF] Magill | Wide-angle impedance matching of a planar array antenna by a dielectric sheet[END_REF][START_REF] Lee | Radiation from dielectric-loaded arrays of parallel-plate waveguides[END_REF][START_REF] Yun | Design of an Active Beam-Steering Array With a Perforated Wide-Angle Impedance Matching Layer[END_REF][START_REF] Zhou | Planar Ultra-Wideband Wide-Angle Scanning Array Antenna with Improved WAIM Layer[END_REF], single layer metamaterials [START_REF] Cameron | Analysis and Characterization of a Wide-Angle Impedance Matching Metasurface for Dipole Phased Arrays[END_REF][START_REF] Oliveri | Multiscale System-by-Design Synthesis of Printed WAIMs for Waveguide Array Enhancement[END_REF][START_REF] Oliveri | Metamaterial-by-Design-A Paradigm for the Industrial Synthesis of EM Manipulation Devices[END_REF][START_REF] Oliveri | SbD-Based Synthesis of Low-Profile WAIM Superstrates for Printed Patch Arrays[END_REF][START_REF] Sajuyigbe | Wide angle impedance matching metamaterials for waveguide-fed phased-array antennas[END_REF], multilayer metamaterials [START_REF] Oliveri | Synthesis of Multilayer WAIM Coatings for Planar-Phased Arrays Within the System-by-Design Framework[END_REF][START_REF] Syed | Wide-Scan Planar Array of Connected Slots Loaded With Artificial Dielectric Superstrates[END_REF][START_REF] Mehdipour | Broadband WAIM Metasurface Structure for Electronically Beam Scanning Holographic Antenna for Ku-Band Satellite Communications[END_REF] and 3D WAIMs [START_REF] Sun | 3D Wide-Angle Impedance Matching for X-Band Phased Array[END_REF]. Their design methodologies can also be classified into those that make use of optimization algorithms during all of the design process [START_REF] Oliveri | Multiscale System-by-Design Synthesis of Printed WAIMs for Waveguide Array Enhancement[END_REF][START_REF] Oliveri | Synthesis of Multilayer WAIM Coatings for Planar-Phased Arrays Within the System-by-Design Framework[END_REF][START_REF] Manica | Wideband multilayer WAIM design and optimization[END_REF], or others that use an equivalent circuit (EC) [START_REF] Cameron | Analysis and Characterization of a Wide-Angle Impedance Matching Metasurface for Dipole Phased Arrays[END_REF][START_REF] Mehdipour | Broadband WAIM Metasurface Structure for Electronically Beam Scanning Holographic Antenna for Ku-Band Satellite Communications[END_REF][START_REF] Sun | 3D Wide-Angle Impedance Matching for X-Band Phased Array[END_REF] with which the cell is modeled. The optimization algorithms take into account all the degrees of freedom from a unit-cell and adjust them until obtaining the desired response. On the other hand, the ECs change the geometrical parameters of the unit-cell according to the EC elements required (an optimization process is also present but at the end of the design). This strategy is very useful to know the response of the global structure (antenna plus WAIM) without the need for a full-wave simulation, which highly reduces the computing time and the needed resources.

It should be noted that other alternative techniques (analytical and quasi-analytical) have been proposed in the literature to model the discontinuities in waveguides or open structures [START_REF] Valagiannopoulos | High Selectivity and Controllability of a Parallel-Plate Component with a Filled Rectangular Ridge[END_REF][START_REF] Li | Waveguide Simualtion Using Mode Matching Method[END_REF]; however, they have not been considered here for the sake of simplicity.

The WAIM proposed in this article is based on a 3D structure that has been proposed by some of the authors [START_REF] Molero | Broadband 3D-Printed Polarizer based on Metallic Transverse Electro-Magnetic Unit-Cells[END_REF]. It works as a simple waveguide that allows the excitation of low dispersive transverse-electromagnetic (TEM) modes. Thus far, the structure has been employed as a polarizing radome, and it was modeled by an EC that was only valid for normal incidence. In order to synthesize the WAIM, this paper proposes an improved EC that also accounts for the incident angle. This extension is a great contribution because characterizing the structure for oblique incidence is necessary for WAIM applications. For the methodology presented in this publication, a specific radiating element has been used, but the methodology is valid for any other element. This paper is organized as follows. Section 2 describes the topology that is used for the WAIM application and its characterization in an EC conceived to work with oblique incidence. Section 3 explains the methodology developed to design a WAIM layer. Finally, Section 4 shows the general conclusions of this contribution and the possible next steps.

Proposed Unit-Cell and Equivalent Circuit

Description of the Structure

The basic unit-cell considered in this manuscript is based on the structure proposed by some of the authors in [START_REF] Molero | Broadband 3D-Printed Polarizer based on Metallic Transverse Electro-Magnetic Unit-Cells[END_REF], consisting of an innovative periodic cell that supports TEM modes when illuminated by an impinging wave under normal incidence. It is formed by four metallic corners, as it is sketched in Figure 1a. Such a structure was employed in [START_REF] Molero | Circuit Modeling of 3-D Cells to Design Versatile Full-Metal Polarizers[END_REF] to design a polarizing screen. For the purpose of designing a WAIM, the unit-cell can be loaded by a shunt impedance placed at the loading plane (as it was also performed in [START_REF] Molero | Broadband 3D-Printed Polarizer based on Metallic Transverse Electro-Magnetic Unit-Cells[END_REF] in order to synthesize the polarization conversion and to provide physical support to the four metallic corners, because they are floating). The interest in using this kind of 3D unit-cell is to benefit from its multiple degrees of freedom, broad operation bandwidth and avoidance of dielectric materials. The possibility to interact independently with the fields impinging in the two main scanning planes (H-and E-planes, taking as reference the Y polarization like in Figure 1b) is particularly appealing for the WAIM application. The interest in using this kind of 3D unit-cell is to benefit from its multiple degrees of freedom, broad operation bandwidth and avoidance of dielectric materials. The possibility to interact independently with the fields impinging in the two main scanning planes (H-and E-planes, taking as reference the Y polarization like in Figure 1b) is particularly appealing for the WAIM application. The interest in using this kind of 3D unit-cell is to benefit from its mu of freedom, broad operation bandwidth and avoidance of dielectric materi bility to interact independently with the fields impinging in the two main sc (H-and E-planes, taking as reference the Y polarization like in Figure 1b) appealing for the WAIM application.

Description of the EC

Description of the EC

Figure 2 depicts the proposed EC for the generic cell in Figure 1a. Th an infinite periodic array excited by a plane wave under oblique incidence ( 𝜃 angle, in one of the principal planes). This field is vertically polarized (elec ponent parallel to y axis). The EC mainly consists of two transmissions line of length 𝑙 + 𝑙 , propagation of a TEM vertical mode in the quasi-parallel-plate waveguide by the opposite pairs of metal corners on top and bottom (separated by the of width 𝑤 ). 𝑍 𝜃 and 𝛽 𝜃 are, respectively, the characteristic impeda constant of this line. Shunt impedances 𝑍 𝜃 are used to mimic the dis the input and output, whilst 𝑍 𝜃 stands for the possible shunt load plac ing plane along the cell length. The propagation constant inside the cell related to the fundamental m ferent expression depending on the incident plane. It can be approximate assuming the cell behaves as an infinite PPW. In the H-plane (𝜙 = 0), the w side the unit-cell remains the same as the incident wave vector in free spac Thus, it divides into two components, 𝑘 and 𝑘 . The propagation constan ing to 𝑘 , can be expressed as in Equation (1), being 𝑓 the working frequ and 𝑐 the speed of light.

𝛽

= 𝑘cos 𝜃 where 𝑘 = However, in the E-plane (𝜙 = 𝜋/2), the wave vector inside the cell doe 𝑘 component (as enforced by the incident wave vector in free space). Then tion constant is the unique 𝑘 component, whose value is shown in Equat The EC mainly consists of two transmissions line of length l 1 + l 2 , describing the propagation of a TEM vertical mode in the quasi-parallel-plate waveguide (PPW) formed by the opposite pairs of metal corners on top and bottom (separated by the horizontal slits of width w y ). Z 1 (θ) and β(θ) are, respectively, the characteristic impedance and phase constant of this line. Shunt impedances Z cap (θ) are used to mimic the discontinuities at the input and output, whilst Z x (θ) stands for the possible shunt load placed in the loading plane along the cell length.

The propagation constant inside the cell related to the fundamental mode has a different expression depending on the incident plane. It can be approximated analytically assuming the cell behaves as an infinite PPW. In the H-plane (φ = 0), the wave vector inside the unit-cell remains the same as the incident wave vector in free space, whatever θ. Thus, it divides into two components, k x and k z . The propagation constant, corresponding to k z , can be expressed as in Equation ( 1), being f 0 the working frequency (18 GHz) and c the speed of light.

β H-plane = k cos(θ) where k = 2π f 0 c (1)
However, in the E-plane (φ = π/2), the wave vector inside the cell does not have any k x component (as enforced by the incident wave vector in free space). Then, the propagation constant is the unique k z component, whose value is shown in Equation [START_REF] Faridani | A Compact Beam-Steerable Integrated Reflectarray Antenna for LEO Applications[END_REF].

β E-plane = k (2)
This important difference also suggests that the mismatching at the entrance of the cell is stronger for the E-plane, especially when θ increases. Indeed, in this case, the k y component of the incident wave vector is not compatible with the propagation within the PPW, which may lead to increased reflection.

This EC can be seen as an extension of the one shown in [START_REF] Molero | Broadband 3D-Printed Polarizer based on Metallic Transverse Electro-Magnetic Unit-Cells[END_REF], that was limited to normal incidence. By taking into account the dependency on θ for most of the EC elements, this upgraded EC is now suitable to WAIM applications where oblique incidence gets compulsory for scanning.

Derivation of Circuit Elements

The numerical evaluation of the circuit elements is performed in two steps. First, the EC of the unit-cell without the central load Z x (θ) is analyzed to extract the characteris-tic impedance of the transmission line Z 1 (θ) and the input/output discontinuity shunt impedances Z cap (θ). In a second step, the load is added to the unit-cell and the shunt impedance Z x (θ), produced by this load, is extracted. All the circuit elements are extracted for each θ and incident plane.

For the unloaded case, the S-Parameters of the cell for each incident plane and θ angle are first computed with full-wave simulations under infinite periodic conditions. A circuit simulator (Keysight ADS) is then used to fit the circuit elements, so they best match the full-wave S-Parameters.

Once the circuit elements have been obtained for the unloaded case, the same process is followed with the loaded case to obtain the value of Z x (θ).

EC Validation

As a validation example, a unit-cell is designed at f 0 = 18 GHz. It has the following geometrical parameters: p = 4.5 mm, t = 0.42 mm (metal thickness) w y = 0.15p and l = 0.352λ 0 where λ 0 is c/ f 0 . The validation of the EC is performed comparing the unit-cell full-wave S-Parameters with the EC S-Parameters. The considered frequency band is [START_REF] Jimenez | All-Metal 3-D Frequency-Selective Surface with Versatile Dual-Band Polarization Conversion[END_REF][START_REF] Molero | Broadband 3D-Printed Polarizer based on Metallic Transverse Electro-Magnetic Unit-Cells[END_REF][START_REF] Rojas-Nastrucci | Ka-Band Characterization of Binder Jetting for 3-D Printing of Metallic Rectangular Waveguide Circuits and Antennas[END_REF][START_REF] Huang | Application of 3-D metal printing to microwave components and antennas[END_REF][START_REF] Xiong | A Metallic 3D Printed Miniaturized Quasi Log Periodic Koch-Dipole Antenna Using T-Shaped Top Loading[END_REF][START_REF] Zhang | A Highly Integrated 3-D Printed Metallic K-Band Passive Front End as the Unit Cell in a Large Array for Satellite Communication[END_REF][START_REF] Foged | Investigation of Additive Manufacturing for Broadband Choked Horns at X/Ku Band[END_REF] GHz. This validation is realized for five θ angles and both Eand H-planes.

Firstly, the validation of the EC for the unit-cell without any load is shown in Figure 3. These results show a very good agreement for all θ values and for both scanning planes.

pedances 𝑍

𝜃 . In a second step, the load is added to the unit-cell an ance 𝑍 𝜃 , produced by this load, is extracted. All the circuit elemen each 𝜃 and incident plane.

For the unloaded case, the S-Parameters of the cell for each incide gle are first computed with full-wave simulations under infinite per circuit simulator (Keysight ADS) is then used to fit the circuit elements the full-wave S-Parameters.

Once the circuit elements have been obtained for the unloaded cas is followed with the loaded case to obtain the value of 𝑍 𝜃 . The second example is the cell loaded by two vertical columns in the loading plane of the cell as in Figure 4, with the geometrical parameters: A x = 0.775 mm, R = 0.32 mm and l 1 = l 2 = l 2 . The results are shown in Figure 5. These results also show a quite good agreement for the five θ cases and for both incident planes, although the discrepancy with the full-wave simulations is a bit larger. The mutual coupling between the load and the input/output discontinuities may affect the accuracy of the EC, especially because the cell length is quite small. Moreover, the modeling does not account for the real dimensions of the columns (especially their radius R), as it assumes the loading is concentrated in a single vertical plane along the cell.

EC Validation

onics 2022, 11, x FOR PEER REVIEW

The second example is the cell loaded by two vertical colum of the cell as in Figure 4, with the geometrical paramet 0.32 mm and 𝑙 = 𝑙 = . The results are shown in Figure 5. These results also show for the five 𝜃 cases and for both incident planes, although the d wave simulations is a bit larger. The mutual coupling between th put discontinuities may affect the accuracy of the EC, especially quite small. Moreover, the modeling does not account for the re umns (especially their radius R), as it assumes the loading is con tical plane along the cell. The results are shown in Figure 5. These results also show a qu for the five 𝜃 cases and for both incident planes, although the discrep wave simulations is a bit larger. The mutual coupling between the load put discontinuities may affect the accuracy of the EC, especially becau quite small. Moreover, the modeling does not account for the real dim umns (especially their radius R), as it assumes the loading is concentr tical plane along the cell. The load used in this example mostly produces an inductive effec 0° to 55°, the extracted 𝑍 𝜃 changes from 60j to 54j in the H-plane, w it does not depend on the angle. Therefore, for the sake of simplicity, it is considered that 𝑍 does not depend on 𝜃.

WAIM Design Methodology

This section makes use of the previous EC for designing a WA generic antenna to be matched. The load used in this example mostly produces an inductive effect. As θ varies from 0 • to 55 • , the extracted Z x (θ) changes from 60j to 54j in the H-plane, while in the E-plane, it does not depend on the angle. Therefore, for the sake of simplicity, in the next section, it is considered that Z x does not depend on θ.

WAIM Design Methodology

This section makes use of the previous EC for designing a WAIM placed above a generic antenna to be matched.

General Design Methodology

Figure 6 depicts the global EC of one array element extracted from an infinite periodic phased array together with its associated WAIM, as represented in Figure 7b. Note that the phased array scans the radiating beam, producing the oblique incidence on the WAIM. Henceforth, the corresponding incident direction is named the scanning direction. It is defined by θ and φ, where φ is either equal to 0 (H-plane in previous section) or π/2, (E-plane). Here, the periodicity of the WAIM unit-cell is the half of an individual array element, which means each array element is covered by four WAIM unit-cells (Figure 7a). The array element is represented by a 2-port network expressing the power exchanges between its feeding port and the fundamental radiated Floquet mode. It is assumed that all higher-order modes are evanescent at the frequency of design (array periodicity is less than 0.5λ 0 , being λ 0 the free-space wavelength at 18 GHz) and they do not contribute to the interactions with the WAIM structure.

Electronics 2022, 11, x FOR PEER REVIEW 6 of 11

General Design Methodology

Figure 6 depicts the global EC of one array element extracted from an infinite periodic phased array together with its associated WAIM, as represented in Figure 7b. Note that the phased array scans the radiating beam, producing the oblique incidence on the WAIM. Henceforth, the corresponding incident direction is named the scanning direction. It is defined by 𝜃 and 𝜙, where 𝜙 is either equal to 0 (H-plane in previous section) or 𝜋/2, (Eplane). Here, the periodicity of the WAIM unit-cell is the half of an individual array element, which means each array element is covered by four WAIM unit-cells (Figure 7a). The array element is represented by a 2-port network expressing the power exchanges between its feeding port and the fundamental radiated Floquet mode. It is assumed that all higher-order modes are evanescent at the frequency of design (array periodicity is less than 0.5𝜆 , being 𝜆 the free-space wavelength at 18 GHz) and they do not contribute to the interactions with the WAIM structure. This 2-port network is followed by a transmission line that represents the separation distance between the array and the WAIM (𝑑 ). As will be shown later, this distance is a possible degree of freedom in the design process. The other characteristics of the line, 𝑍 and 𝛽 , are defined by the scanning direction and can be derived analytically. The WAIM with its EC, as defined in Section 2.2, is connected with the 2-port network through this transmission line.

The design methodology can be divided into four main steps. As a preliminary step, a data-base is computed to obtain the circuit elements of the unloaded WAIM unit-cell, using full-wave simulations. It consists of deriving 𝑍 𝜃 and 𝑍 𝜃 for a discretized set of geometries (only varying 𝑤 ) and for a discretized set of scanning directions. A fullwave simulation is needed for each geometry and each direction, but these simulations are relatively quick. In the second step, the S-matrix of the array element is also computed Electronics 2022, 11, x FOR PEER REVIEW 6 of 11

General Design Methodology

Figure 6 depicts the global EC of one array element extracted from an infinite periodic phased array together with its associated WAIM, as represented in Figure 7b. Note that the phased array scans the radiating beam, producing the oblique incidence on the WAIM. Henceforth, the corresponding incident direction is named the scanning direction. It is defined by 𝜃 and 𝜙, where 𝜙 is either equal to 0 (H-plane in previous section) or 𝜋/2, (Eplane). Here, the periodicity of the WAIM unit-cell is the half of an individual array element, which means each array element is covered by four WAIM unit-cells (Figure 7a). The array element is represented by a 2-port network expressing the power exchanges between its feeding port and the fundamental radiated Floquet mode. It is assumed that all higher-order modes are evanescent at the frequency of design (array periodicity is less than 0.5𝜆 , being 𝜆 the free-space wavelength at 18 GHz) and they do not contribute to the interactions with the WAIM structure. This 2-port network is followed by a transmission line that represents the separation distance between the array and the WAIM (𝑑 ). As will be shown later, this distance is a possible degree of freedom in the design process. The other characteristics of the line, 𝑍 and 𝛽 , are defined by the scanning direction and can be derived analytically. The WAIM with its EC, as defined in Section 2.2, is connected with the 2-port network through this transmission line.

The design methodology can be divided into four main steps. As a preliminary step, a data-base is computed to obtain the circuit elements of the unloaded WAIM unit-cell, using full-wave simulations. It consists of deriving 𝑍 𝜃 and 𝑍 𝜃 for a discretized set of geometries (only varying 𝑤 ) and for a discretized set of scanning directions. A fullwave simulation is needed for each geometry and each direction, but these simulations are relatively quick. In the second step, the S-matrix of the array element is also computed This 2-port network is followed by a transmission line that represents the separation distance between the array and the WAIM (d WAI M ). As will be shown later, this distance is a possible degree of freedom in the design process. The other characteristics of the line, Z 0 and β 0 , are defined by the scanning direction and can be derived analytically. The WAIM with its EC, as defined in Section 2.2, is connected with the 2-port network through this transmission line.

The design methodology can be divided into four main steps. As a preliminary step, a data-base is computed to obtain the circuit elements of the unloaded WAIM unit-cell, using full-wave simulations. It consists of deriving Z 1 (θ) and Z cap (θ) for a discretized set of geometries (only varying w y ) and for a discretized set of scanning directions. A full-wave simulation is needed for each geometry and each direction, but these simulations are relatively quick. In the second step, the S-matrix of the array element is also computed using full-wave simulations for the same set of directions. Once again, a new full-wave simulation is needed for each direction.

In the third step, the optimization of the WAIM EC is carried out. To do so, the global EC in Figure 6 is analyzed using a circuit simulator (Keysight ADS) and the possible degrees of freedom (l 1 , l 2 , d WAI M , Z x and Z 1 ) are optimized in order to minimize the input active reflection coefficient.

To be noted, the optimization is run for all scanning directions simultaneously, so that, a unique WAIM design is obtained in the end. Moreover, for the sake of simplicity, we assume Z x does not depend on θ as explained before. Finally, it is important to point out that the choice of Z 1 enforces the cross-section geometry of the cell. As a consequence, Z cap and β must be defined correspondently. This is of course automatically managed through the WAIM data-base that opportunely links all interdependent parameters in the EC. On the contrary, l 1 , l 2 and d WAI M are completely independent degrees of freedom which can be optimized quite freely. It should be emphasized that this optimization step does not require any supplementary full-wave simulation because it is performed with the EC only. This is a definitive advantage of this methodology regarding the huge number of WAIM configurations that may be involved along the successive iterations of the process.

The fourth and last step is a post-processing for Z x . Indeed, the optimization process just provides a theoretical value for the optimal load to be used, together with the crosssection of the cell (defined by Z 1 as we already have seen). Then, this last step consists of selecting the appropriate load geometry that complies with these outputs. This step relies on the use of a pre-computed data-base, obtained with full-wave simulations as well, that gathers possible candidate loads.

Application of the Methodology

The methodology is applied for a case where the array element is a metallic horn partially filled in with dielectric (Figure 7a). Thanks to this dielectric, the horn has a periodicity smaller than 0.5λ 0 at the design frequency, avoiding triggering of grating lobes at maximum angle of scanning.

The active reflection coefficient of the array without the WAIM is shown in Figure 8 in black, and efforts are focused on matching the H-plane, as the matching becomes worse earlier in this scanning direction. The matching of the array is worse than -10 dB for steering angles higher than θ = 45 • and θ = 55 • in the Hand E-plane, respectively. Following the aforementioned design steps, the optimizable circuit elements for a slit w y = 0.15p are: d WAI M = 0.004λ 0 , l 1 = l 2 = 0.176λ 0 and Z x = 37j Ω. Figure 8 (red curve) shows the matching in H-plane at θ = 55 • is improved by more than 10 dB. Note that the matching in E-plane has been slightly degraded, but it was not considered in the optimization. Next, the load impedance has been synthetized using vertical columns with R = 0.483 mm and A x = 0.633 mm, and a full-wave simulation is performed, placing the WAIM as shown in Figure 7b, and yielding green curve in Figure 8. Unfortunately, the performance is not as good as expected, especially in the higher θ angles. The main reason for the disagreement is the close proximity between the antenna and the WAIM (d WAI M = 0.004λ 0 ). This placement of the WAIM in the direct vicinity of the antenna results from the brute optimization process and further investigations demonstrated it was effectively the best solution. However, for such a reduced spacing, the EC is not so accurate due to tight coupling effects. Then, in order to overcome this limitation, a post-processing is applied. Indeed, starting from the EC result, a simple refinement in the radius of the columns is sufficient to improve the final response. By decreasing R = 0.483 mm to R optim = 0.465 mm, new full-wave results are obtained (blue curve in Figure 8a). These results show significant improvements in the H-plane matching all θ angles. Furthermore, there is an improvement of more than 5 dB, compared with the initial matching (black curve), in θ = 45 • , 50 • and 55 • . Such an improvement is not reached in the E-plane.

Additional Validation

An additional validation is presented to demonstrate that the agreement between full-wave and EC is satisfactory in the case where 𝑑 is not as small as in the previous case. To do so, a re-optimization is conducted where the minimal value of 𝑑 is limited to 0.1𝜆 .

The recalculated circuit elements for the same slit size ( 𝑤 = 0.15𝑝 are now: 𝑑 = 0.1𝜆 , 𝑙 = 𝑙 = 0.1𝜆 and 𝑍 = 51𝑗 Ω. The corresponding results are shown in Figure 9 (red curve). As suggested before, the matching improvement in the H-plane is not as good as in Figure 8 because 𝑑 is now limited. However, what is important is that the agreement with full-wave simulation (green curve) is now much better. This suggests the extremely low value of 𝑑 in the previous example was the main reason for a loss of accuracy in the EC prediction. Note that the agreement is quite sensitive to the used value of 𝑍 and, consequently, it might be improved by accounting for its variations with θ. This design can be compared with the literature in Table 1.

Additional Validation

An additional validation is presented to demonstrate that the agreement between full-wave and EC is satisfactory in the case where d WAI M is not as small as in the previous case. To do so, a re-optimization is conducted where the minimal value of d WAI M is limited to 0.1λ 0 .

The recalculated circuit elements for the same slit size (w y = 0.15p) are now: d WAI M = 0.1λ 0 , l 1 = l 2 = 0.1λ 0 and Z x = 51j Ω. The corresponding results are shown in Figure 9 (red curve). As suggested before, the matching improvement in the H-plane is not as good as in Figure 8 because d WAI M is now limited. However, what is important is that the agreement with full-wave simulation (green curve) is now much better. This suggests the extremely low value of d WAI M in the previous example was the main reason for a loss of accuracy in the EC prediction. Note that the agreement is quite sensitive to the used value of Z x and, consequently, it might be improved by accounting for its variations with θ.

Additional Validation

An additional validation is presented to demonstrate that the agreement between full-wave and EC is satisfactory in the case where 𝑑 is not as small as in the previous case. To do so, a re-optimization is conducted where the minimal value of 𝑑 is limited to 0.1𝜆 .

The recalculated circuit elements for the same slit size ( 𝑤 = 0.15𝑝 are now: 𝑑 = 0.1𝜆 , 𝑙 = 𝑙 = 0.1𝜆 and 𝑍 = 51𝑗 Ω. The corresponding results are shown in Figure 9 (red curve). As suggested before, the matching improvement in the H-plane is not as good as in Figure 8 because 𝑑 is now limited. However, what is important is that the agreement with full-wave simulation (green curve) is now much better. This suggests the extremely low value of 𝑑 in the previous example was the main reason for a loss of accuracy in the EC prediction. Note that the agreement is quite sensitive to the used value of 𝑍 and, consequently, it might be improved by accounting for its variations with θ. This design can be compared with the literature in Table 1. This design can be compared with the literature in Table 1. Affects mostly the H-plane.

Single dielectric layer. No information.

[33]

-H-plane is matched up to θ = 55 • .

-E-plane is not shown. E-plane is not shown.

Single-layer metamaterial.

[29]

-H-plane improved from θ = 52 • to θ = 65 • .

-D-plane improved from θ = 62 • to θ = 81 • .

-E-plane does not vary.

Affects mostly the Hand D-plane.

[30]

-φ = 0 • → θ = 80 • . -φ = 45 • → θ = 75 • . -φ = 90 • → θ = 77 • .
Without WAIM the antenna is unmatched.

Affects the 3 scanning planes.

[35]

Compensates mismatching produced by back reflector.

-H-plane up to θ = 50 • .

-E-plane up to θ = 50 • .

Affects the 2 scanning planes. Multilayer metamaterial.

[36]

-Scanning up to θ = 60 • (not specifying the scanning plane).

-Improving the gain of the antenna between 3 to 5 dB.

No information.

[37]

-H-plane improved up to θ = 81 • .

-E-plane improved up to θ = 67 • . Affects 2 planes for 1 polarization. 3D WAIM (dielectric + metal).

Loaded TEM unit-cell (this work)

-H-plane improved up to θ = 55 • .

-E-plane degraded. Affects 2 planes for 1 polarization. 3D WAIM (all-metal).

Conclusions

In this contribution, a 3D all-metal unit-cell has been characterized for oblique incidence and in the two main scanning planes. Its successful characterization allows its use in applications requiring a wide scanning angle, such as the WAIM application.

Additionally, a new methodology based on the use of an EC has been described, which drastically reduces the total number of needed full-wave simulations. It has been tested with a phased array made of metallic horns, showing a more than 5 dB improvement in the H-plane, for θ angles larger than 35 • . This optimal result was obtained for an extremely small spacing between the WAIM and the antenna, which suggests there could be some interest in integrating the 3D matching structure with the antenna. It was also demonstrated that the agreement provided by the EC gets better when the spacing is increased, due to the used assumptions in the modeling. The methodology may be further improved by following other approaches, such as the mode-matching technique at the cost of increased complexity. Future works will focus on the simultaneous matching of Eand H-planes as well as dual-polarization performance.

Figure 1 .

 1 Figure 1. TEM unit-cell: (a) general structure, (b) incidence planes considering Y polarization.

Figure 1 .

 1 Figure 1. TEM unit-cell: (a) general structure, (b) incidence planes considering Y polarization.

Figure 2

 2 Figure2depicts the proposed EC for the generic cell in Figure1a. The cell is part of an infinite periodic array excited by a plane wave under oblique incidence (defined by the θ angle, in one of the principal planes). This field is vertically polarized (electric-field component parallel to y axis).

Figure 1 .

 1 Figure 1. TEM unit-cell: (a) general structure, (b) incidence planes considering Y po

Figure 2 .

 2 Figure 2. EC of a generic loaded unit-cell with θ dependence.

Figure 2 .

 2 Figure 2. EC of a generic loaded unit-cell with θ dependence.

  As a validation example, a unit-cell is designed at 𝑓 = 18 GHz. I geometrical parameters: 𝑝 = 4.5 mm, 𝑡 = 0.42 mm (metal thickness) 0.352𝜆 where 𝜆 𝑖𝑠 𝑐/𝑓 . The validation of the EC is performed com full-wave S-Parameters with the EC S-Parameters. The considered freq 19] GHz. This validation is realized for five 𝜃 angles and both E-and Firstly, the validation of the EC for the unit-cell without any load is These results show a very good agreement for all 𝜃 values and for bo

Figure 3 .

 3 Figure 3. Reflection coefficient validation unloaded unit-cell: (a,b) H-plane and tude and phase, respectively.

Figure 3 .

 3 Figure 3. Reflection coefficient validation unloaded unit-cell: (a,b) H-plane and (c,d) E-plane, magnitude and phase, respectively.

Figure 4 .

 4 Figure 4. TEM unit-cell with loads.

Figure 5 .

 5 Figure 5. Reflection coefficient validation loaded unit-cell: (a,b) H-plane a

Figure 4 .

 4 Figure 4. TEM unit-cell with loads.

Figure 4 .

 4 Figure 4. TEM unit-cell with loads.

Figure 5 .

 5 Figure 5. Reflection coefficient validation loaded unit-cell: (a,b) H-plane and (c, and phase, respectively.

Figure 5 .

 5 Figure 5. Reflection coefficient validation loaded unit-cell: (a,b) H-plane and (c,d) E-plane, magnitude and phase, respectively.

Figure 6 .

 6 Figure 6. Global EC: antenna S-Parameters plus space between antenna and WAIM plus WAIM EC.

Figure 7 .

 7 Figure 7. (a) Phased array of stepped horns with four unit-cells with half-periodicity (one unit-cell represented in red) per one array element (represented in green) (illustrative) and (b) global structure: phased array plus WAIM structure with infinite periodic conditions.

Figure 6 .

 6 Figure 6. Global EC: antenna S-Parameters plus space between antenna and WAIM plus WAIM EC.

Figure 6 .

 6 Figure 6. Global EC: antenna S-Parameters plus space between antenna and WAIM plus WAIM EC.

Figure 7 .

 7 Figure 7. (a) Phased array of stepped horns with four unit-cells with half-periodicity (one unit-cell represented in red) per one array element (represented in green) (illustrative) and (b) global structure: phased array plus WAIM structure with infinite periodic conditions.

Figure 7 .

 7 Figure 7. (a) Phased array of stepped horns with four unit-cells with half-periodicity (one unit-cell represented in red) per one array element (represented in green) (illustrative) and (b) global structure: phased array plus WAIM structure with infinite periodic conditions.

Figure 8 .

 8 Figure 8. Active reflection coefficient at f = 18 GHz without limiting 𝑑 : (a) H-plane and (b) Eplane; phased array (PA), full-wave (FW).

Figure 9 .

 9 Figure 9. Active reflection coefficient at 𝑓 = 18 GHz limiting 𝑑 : (a) H-plane and (b) E-plane; phased array (PA) and full-wave (FW).

Figure 8 .

 8 Figure 8. Active reflection coefficient at f = 18 GHz without limiting d WAI M : (a) H-plane and (b) E-plane; phased array (PA), full-wave (FW).

Electronics 2022 , 11 Figure 8 .

 2022118 Figure 8. Active reflection coefficient at f = 18 GHz without limiting 𝑑 : (a) H-plane and (b) Eplane; phased array (PA), full-wave (FW).

Figure 9 .

 9 Figure 9. Active reflection coefficient at 𝑓 = 18 GHz limiting 𝑑 : (a) H-plane and (b) E-plane; phased array (PA) and full-wave (FW).

Figure 9 .

 9 Figure 9. Active reflection coefficient at f = 18 GHz limiting d WAI M : (a) H-plane and (b) E-plane; phased array (PA) and full-wave (FW).

[ 27 ]

 27 -H-plane improved at θ = 70 • from Γ in = -7 dB to Γ in = -12 dB. -E-plane already matched at θ = 70 • . Affects mostly the H-plane. [28] -H-plane scans up to θ = 50 • . -E-plane scans up to θ = 60 • . No results shown without WAIM.

Table 1 .

 1 Comparison of the proposed design with the literature. -H-plane improved up to θ = 56 • . -E-plane already matched at θ = 56 • (almost unmodified).

	Matching Range Improvement	Dual Scanning Plane Performance	WAIM Type
	[25]

Conflicts of Interest:

The authors declare no conflict of interest.