Cecil Moore wrote:

Fields cannot
cancel unless those fields first exist.

Please clarify for us the distinction between canceled fields, and
fields which don't exist.

There is no energy traveling in the direction of fields that cancel;
E1xB1 and E2xB2 in this example.

Assume E1xB1
joules/sec associated with the first field and E2xB2
joules/sec associated with the second field. The fields
cancel. What happens to the E1xB1 joules/sec and the
E2xB2 joules/sec?

Since the fields cancel, and energy does not travel in the company of
nonexistent fields, there is no energy here with which to concern
ourselves.

Hint: Their energy components are
redistributed in a direction that allows constructive
interference. In a transmission line, there is only
one other direction available.

Producing a result which can only occur when there is no energy
traveling in the direction of E1xB1 and E2xB2.

73, Jim AC6XG