In times of the Roman Empire, the Parthians blocked the ancient Romans from advancing too far East, fiercely defending their trade secrets and territory from invaders. Most likely, the Roman army never progressed further east than the western provinces of China.
While the Roman knowledge of Asia was fairly limited, they didn’t know about Japan.
Although Japan was known to neighboring countries early in its history, it wasn’t until the 16th century that Europe discovered it, and the Roman Empire fell around 400 AD, almost a thousand years prior.
So, how much did the Roman world know about the Western world and the East?
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Discovery of Roman Artefacts in Japan
During the controlled excavations of the Katsuren Castle in Uruma, Okinawa in Japan, Roman coins of the 3rd and 4th centuries AD were discovered. Some Ottoman coins from the 1600s were also found. 
Some Roman coins had the bust of the Roman emperor Constantine the Great, popular for his military campaigns and acceptance of Christianity. This implies that these coins from Constantinople were brought to the Ryukyu islands, 8,000 kilometers away.
The castle was built about a thousand years after the 4th century and was occupied between the 12th – 15th centuries. By 1700, the castle was abandoned. So, the question of how those coins got there arises.
Had Roman traders, soldiers, or travelers actually traveled to Japan?
There are no records in history stating the Romans went to Japan. The chances of these coins belonging to someone’s collection or coming to the castle through Japan’s trade links with China or other Asian countries seem more likely.
Links With Asia
The Romans were involved in direct trade with the Chinese, Middle Easterners, and Indians. The Roman Empire consisted of a territory called ‘Asia,’ now the southern part of Turkey.
Roman trade included exchanging gold, silver, and wool for luxury goods like textiles and spices.
There are plenty of Roman coins in Southern India and Sri Lanka, indicating trade with the Roman world. It’s quite possible that Roman traders could’ve been present in Southeast Asia from about the 2nd century AD.
However, since places in Far East Asia didn’t directly trade with Rome, Roman coins had no value. Roman glass beads have also been discovered in Japan, within a 5th-century AD burial mound near Kyoto.
The Sino-Roman relations had indirect trade of goods, information, and occasional travelers between Han China and the Roman Empire. It continued with the Eastern Roman Empire and various Chinese dynasties. 
Roman knowledge of Chinese was fairly limited to knowing they produced silk and were on the far side of Asia. The Silk Road, a famous trade route between Ancient Rome and China, had high volumes of silk exported along it.
The ends of this great trade network were occupied by the Han Dynasty and Romans, respectively, with the Bactrian Empire and Persian Parthian Empire occupying the middle. These two empires protected the trade routes and didn’t permit the Han Chinese political envoys and Romans to reach each other.
Trade with the Middle East was along the Incense Route, named for the large amounts of myrrh and frankincense imported to Rome along it. It also included spices, precious stones, and textiles. 
The Extent of Roman Exploration in the Far East
While the Romans might not have explored as far as Japan, their trade routes led to the Middle East, India, China, and other regions of West Asia.
Many countries (or at least areas of them) in West Asia and the Middle East were part of the Roman Empire. Israel, Syria, Iran, and Armenia, among other countries, were included in the Roman Empire, as were parts of modern-day Turkey.
The Roman trade routes traversed much of continental Asia. Sea routes brought trade from the Middle East, including the city of Petra in Jordan.
It’s possible that some Greek or Roman merchants visited China. The Chinese account of a Roman diplomatic mission most likely referred to some Roman merchants from India since the gifts these Romans presented were local to India or the Far East.
The earliest Chinese records show Rome and China’s first official contact was in 166 AD, when a Roman envoy, probably sent by Roman Emperor Antoninus Pius or Marcus Aurelius, arrived in Luoyang, the Chinese capital.
The Indian Ocean trade network was only one of the vast short and medium-distance trade routes involving multiple regions, exchanging culture and goods. 
When Did Japan Become Popular?
Through Marco Polo, the Mediterranean world and the rest of Western Europe learned about Japan’s existence around the 14th century. Until then, only a few Europeans had traveled to Japan.
Between the 17th and the mid-19th centuries, Japan had a long period of isolationism. It was isolated for much of world history, mainly because of being an island.
Marco Polo traveled to several places, like Afghanistan, Iran, India, China, and many oceanic countries in South East Asia. Through his book about his travels titled II Milione, or The Travels of Marco Polo, people became familiar with many Asian countries, including Japan. 
In 1543, a Chinese ship with Portuguese travelers drifted ashore on a small island near Kyushu. This marked the first visit to Japan by Europeans, followed by several Portuguese traders. Next came Jesuit missionaries during the 16th century to spread Christianity. 
Until 1859, the Chinese and Dutch had exclusive trading rights with Japan, following which the Netherlands, Russia, France, England, and the United States began commercial relations.
While the Romans knew about several other Asian countries, they didn’t know about Japan. Only around the 14th century did Europe learn about Japan through Marco Polo’s journeys.