You may remember in this connection Tennyson's phrase "the bearded barley" in the "Lady of Shalott," and Longfellow's term "bearded grain" in his famous poem about the Reaper Death.

When a person's beard is very thick, we say in England to-day "a full beard," but in the time of Shakespeare they used to say "a well filled beard"-- hence the phrase in the second line of the first stanza.
In the third line the term "delicious tear" means dew,--which the Greeks called the tears of the night, and sometimes the tears of the dawn; and the phrase "drunk with dew" is quite Greek--so we may suspect that the author of this poem had been reading the Greek Anthology.

In the third line of the second stanza the word "poppy" is used for sleep--a very common simile in Elizabethan times, because from the poppy flower was extracted the opiate which enables sick persons to sleep.

The Greek authors spoke of poppy sleep.

"And when thy poppy works," means, when the essence of sleep begins to operate upon you, or more simply, when you sleep.