"I've talked about this with some physics colleagues and they are worried because they value international exchange and discussion," Chang said.

In the fields most in demand among US employers, such as computer science and engineering, international students represent a majority of such graduate programs at US universities, according to the foundation's report, Science and Engineering Indicators 2018.

From 1995 to 2015, US universities awarded nearly 221,000 science and engineering doctorates to temporary visa holders. Among them, about 64,000 were from China, which accounted for more than 25 percent of international recipients, the report said.

Angel Cabrera, president of George Mason University in Virginia, wrote in an article for The Washington Post in November, "While other countries work hard to attract international students, we are managing to send a message that talented foreigners are not welcome here, just when we most need them.

"Some of the most successful startup companies in the United States had at least one immigrant founder, including Uber and SpaceX," he said.

Rahul Choudaha, executive vice-president at StudyPortals, a US company that recruits international students online, said graduate students come to the US with higher expectations of career outcomes and, as a result, are more sensitive to changes in job opportunities and immigration policies.

His view is echoed by Chu, who has several postdoctorate students from China.

"Virtually all the Chinese postdocs and graduate students I deal with, if they had an opportunity to work in the United States, would want to stay here," Chu said.

"The policies are being complicated by the federal government," he said. "The restrictions will ultimately drastically lower the number of students in post-doctorate and STEM (science, technology, engineering and mathematics)."