When Han Cheng earned his engineering degree from Miami University two years ago, he wanted what every new graduate covets: a job. A native of China, Cheng, 23, always assumed he would be able to work in the United States for a few years before returning to his homeland to use the skills that he had learned here. What he didn't realize was how difficult it would be to obtain a temporary work visa.

When Han Cheng earned his engineering degree from Miami University two years ago, he wanted what every new graduate covets: a job.

A native of China, Cheng, 23, always assumed he would be able to work in the United States for a few years before returning to his homeland to use the skills that he had learned here.

What he didn�t realize was how difficult it would be to obtain a temporary work visa.

�When I was talking to recruiters back home about going to college in the United States, they all made it sound like it would be easy to get work because the degree would be so desirable,� Cheng said.

After graduation, he sent out more than 500 job inquiries but was unable to find a company willing to sponsor him for an H-1B visa, which allows employers to hire specialized foreign workers on a temporary basis.

The process is cumbersome and costly for many companies, he said. Companies with limited resources are less likely to hire foreign students, especially because there�s no guarantee they�ll get a visa, which could leave the employer with an unfilled position.

The visas are good for up to three years and can be extended for as long as six years. Those who want to remain in the U.S. longer then could apply for an employment-based green card. But green cards also involve waiting, often five years to even decades, depending on the applicant�s homeland and other factors.

According to data from the U.S. Citizenship and Immigration Services, more than 150,000 people with H-1B visas have filed for green cards since 2010.

Out of time to secure a position, Cheng returned to Shanghai last summer.

As the number of international students in the U.S. continues to grow, staying in the country after graduation only will get harder for students such as Cheng, immigration experts say.

Nearly 820,000 foreign students came to the U.S. to study last school year, mostly from China, India, South Korea, Canada and Saudi Arabia, according to a report by the Institute of International Education.

In Ohio, the number of international students increased 7.5 percent to 28,401 � making it eighth-highest in the country.

Every year at the beginning of April, employers race for the limited number of H-1B visas available � currently set at 85,000, which includes 20,000 reserved for foreign graduates with advanced degrees from American universities.

Competition is so fierce that last year�s cap was reached in only five days, and 39,000 requests by employers were denied, said Ken Robinson, a Columbus immigration lawyer.

�As more and more of these international students can�t get a job after graduation, it could have a chilling effect on the number of students who choose to come to the United State to study,� he said.

Many of the rejected applications had been filed by U.S. employers on behalf of foreign students who earned degrees in science, technology, engineering and mathematics, commonly called the STEM fields, said Michael Patrick, an immigration attorney in New York.

�We attract these great minds and dedicated people from all over the world, and it�s a shame to not give them a chance to help U.S. companies grow and hire more workers, including U.S. citizens,� he said.

The government needs to dramatically increase the visa numbers if it wants to help U.S. businesses satisfy their need for skilled workers, Patrick said. Employer requests have exceeded the number of visas issued every year except from 2001 to 2003, when the annual cap was raised temporarily to 195,000.

House and Senate attempts to overhaul the nation�s immigration system last year both included provisions to raise the H-1B cap. Those efforts stalled, but prospects are looking up with House Speaker John Boehner, a Republican from West Chester, indicating he might back limited reforms in individual bills this year.

In the meantime, international students shouldn�t give up hope, said Anant Gupta, who secured a job at Deloitte Digital in Chicago in November, six months after earning an M.B.A. from Ohio State University.

�You have to be confident and willing to fight it out,� said Gupta, 29, a native of India. �I used to work 18 hours a day applying for jobs and doing research and would get rejection letters every day.�

After finishing school, he was fortunate enough to get into a temporary training program that allows foreign students the opportunity to work in the U.S. for one year as long as their profession is related to their field of study. That bought him more time to find the job at Deloitte, where he had been rejected twice before.

Deloitte will file a visa application for Gupta this year, and Gupta has his fingers crossed that he will be one of the lucky ones.

�I�m hoping for the best, but I�m prepared for the worst,� he said. �If I don�t get a visa, I will have to go home, and there�s no crying about that. It is what it is.�

epyle@dispatch.com

@EncarnitaPyle