I haven't and I'd love to! On by bucket list.
Note - they are a far cry from "non-population growth." They're shrinking at an alarming rate.
Why is it "alarming?" Japan is the 10th largest country in the world with 126 million.
Japan's fertility rate is 1.41 compared to Germany's 1.45 and China's 1.60. All are below the replacement rate of 2.1. South Korea is even lower with 1.26 and Taiwan with 1.13 and Singapore with .83. The US has a 1.87 rate.
The nine highest fertility rates are countries in Africa with Niger having the highest with 6.49.
Here are Japan population numbers—
1976 = 114 million
1989 = 124 million
2002 = 128 million
2015 = 127 million
As I understand Japanese immigration laws, people from densely populated Asian countries are allowed to come to Japan to work, but they are not allowed to stay forever.
The laws are probably more complicated than that, but the essence of their immigration policy is to maintain a Japanese culture.
I personally find Japan as near the top of all countries to visit. You may want to move it higher on your bucket list.