This can be done with a recursive CTE. You can find many examples on the internet.

It should be something like this:

WITH RCTE AS(

select T1.a1, T1.a2, T1.a3,

T2.b1, T2.b2, T2.b3, T2.b4

from T1

JOIN T2 ON T1.a2=T2.a2

WHERE T1.a1 IS NULL

UNION ALL

select T1.a1, T1.a2, T1.a3,

T2.b1, T2.b2, T2.b3, T2.b4

from T1

JOIN T2 ON T1.a2=T2.a2

JOIN RCTE ON T1.a1 = RCTE.a2

)

SELECT *

FROM RCTE;