Time was when, if anyone mentioned a female German politician with roots in the communist east and a doctorate in science, they were talking about Angela Merkel.

But these days there is a new woman on the block. Frauke Petry, the youthful leader of Germany’s main rightwing anti-immigrant party, Alternativ für Deutschland (AfD), is on a roll, profiting from the growing dissatisfaction with the chancellor’s refugee policy, which has led to more than 1.1 million refugees arriving in Germany in the last year.

Petry, 40, has hardly been out of the news since courting controversy last weekend for her insistence that Germany’s border police should be allowed to shoot at refugees trying to enter the country illegally. “People must stop migrants from crossing illegally from Austria [into Germany],” she said in an interview with a regional newspaper. “If necessary, [they] should use firearms. I don’t want this, but the use of armed force is there as a last resort.”

Her remarks, delivered immediately after an address to party faithful in Hanover, have prompted a storm of protest, not least because of their chilling echo of the cold war days, when people were shot for trying to escape the communist GDR, where Petry grew up.

Petry, who left Reading university with a degree in chemistry in 1998, has been the leader of AfD since last July, following the ousting of its academic founders who had established the party as an anti-euro group at the height of the Greek crisis in 2013. Since then she has been central in efforts to steer the party towards a populist, anti-immigrant stance, and is now viewed as one of the most vocal – and dangerous – critics of Merkel’s decision to put out the welcome mat for refugees last summer.

Merkel has stubbornly refused to concede to demands to close the borders or put a limit on the number of refugees who can come.

Opinion polls recently showed AfD to be on as much as 12%, making it potentially the third strongest political force in Germany. With elections due in three German states next month, it is now said to be on course to make considerable gains in the parliaments of Baden-Württemberg, Saxony Anhalt and Rhineland-Palatinate. It already has seats in five state parliaments and political observers say politicians from established parties can no longer continue to ignore it, as they largely have done until now.

Frauke Petry with her partner, AfD MEP Marcus Pretzell. Photograph: Clemens Bilan/Getty Images

Habitually dressed in sharp suits, Petry has become the youthful face of the AfD surge. On a TV political chat show debating whether Germany had shifted to the right, she dug the heel of her shoe into the carpet and insisted that it was wrong to label her party as populist and hard right. “It’s to do with politicians that either recognise that we need concepts that lead to solutions or not. Right and left are terms that haven’t fitted for a long time,” she said.

In the past AfD has tried to distance itself from the anti-immigrant, anti-Islamic campaign group Patriotic Europeans against the Islamisation of the Occident (Pegida) which, like Petry, originated in Dresden. But increasingly her party is being talked about as the political arm of Pegida. Petry has done little to persuade anyone otherwise.

Both deploy similar language, such as “liar press” as a blanket term for the media, or “traitor” to refer to Merkel and other supporters of her asylum policy, which they would like to see turned on its head, with controls along the entire length of Germany’s borders.

Just as at Pegida rallies, it has become common to see AfD placards calling for government figures to be lynched as punishment. Recently an AfD functionary called for the death penalty to be introduced so that the government could be “placed against a wall” and shot.

Jakob Augstein, a columnist with Der Spiegel, told Petry in the same chatshow: “You are the friendly smile on the face of the hordes that march through Dresden and beat people up … you are the democratic arm of those who bait foreigners and set fire to asylum-seekers’ homes.” Petry kept smiling as he continued: “I don’t underestimate you. I take you very, very seriously.”

Pretzell and Petry are like Bonnie and Clyde, pursuing a course of ambush through the German public Jakob Augstein, Der Spiegel

Not for a long time has so much been written and said about a single German politician (other than Merkel). Petry stands out from her largely grey-haired male supporters – recent statistics showed 71% of AfD voters are male – with her youthful looks and smiley demeanour.

A mother-of-four, she caused mild scandal last year when she announced she had left her husband, Sven Petry, a Lutheran pastor, for Marcus Pretzell, an AfD MEP. Her new partner has since swapped the AfD for Merkel’s Christian Democrats. Despite that move, there have been suggestions that Pretzell is responsible for Petry feeling increasingly comfortable about keeping the party on a rightwing populist course.

“Pretzell and Petry are the amour fou of the German right,” wrote Augstein in a recent column. “Like Bonnie and Clyde, they’re pursuing a course of ambush through the German public.”

If she weren’t in politics, Petry would be pursuing her scientific career, running the Leipzig company she set up in 2007 to manufacture environmentally-friendly polyurethanes, for which she holds a joint patent with her mother, a fellow chemist, and which earned her a medal of the Order of Merit in 2012. But she stepped back from the company at the end of last year, telling Die Welt in an interview that “combining politics on a national, state and local level with family and the company is simply not possible. I don’t want my children to accuse me later of never being there for them any more. I’m there too little as it is.”

Germans like their politicians to be serious and not overly preened, and the Petry smile has been viewed by many with suspicion. Calling her “Frau Dr Strangelove” – a reference to the ex-Nazi scientist adviser to the president in Stanley Kubrick’s 1964 film – Hans Hütt wrote in the leftwing newspaper Freitag: “Petry’s smile is a code. Every smile and grin gives the rank and file a signal: the others’ arguments are rubbish … [it] brings the terror back into German politics. It looks so nice, so outrageously nice.”

However, Manfred Güllner, the chief pollster of Forsa, believes it is unlikely that AfD will get much bigger, based on the number of non-voters in Germany and, at 85%, the high satisfaction rate Merkel still enjoys within her own party, despite the disgruntlement shown towards her.

But there is little doubt that Petry has inaugurated a new era for the AfD. Güllner said Petry’s comments about being able to shoot refugees on the border had had a twofold effect. “On the one hand there are the radical AfD voters, who feel endorsed. On the other hand, the gulf between the AfD and the majority of Germans will increase. If you like, Petry has made it clear precisely how the AfD ticks.”

RISE OF THE AfD

February 2013 Founded to protest against Germany’s handling of the eurozone crisis, in particular the decision to bail out Greece.

September 2013 Won 4.7% of the vote in the 2013 federal election, falling short of the 5% threshold needed to enter the Bundestag.

May 2013 Gained first representation in the state parliament of Hesse.

May 2014 Came fifth in Germany’s European elections, with 7.1% of the national vote and seven members of the EU parliament.

August 2014 Recorded 9.7% of the vote in the Saxony state election, winning 14 seats.

September 2014 Won 10.6% of the vote in the Thuringian state election and 12.2% in the Brandensburg state election, winning 11 seats in both state parliaments.

July 2015 Frauke Petry elected leader. Her appointment was seen as a shift to the right and prompted five MEPs to leave the party. The AfD’s founder, Bernd Lucke, announced he would form a new party, the Alliance for Progress and Renewal, citing a rise of xenophobic sentiment in the AfD.