Poetry can be describe as "beautiful language" - painting a picture with words. Usually well structure and with purpose or "on purpose". Zen poetry is in the 'moment'. Much peotry has structure. Zen poetry has no structure.
November in Warsaw
by Zen Master Seung Sahn
November in Warsaw
Fifty people together in one room.
Sitting Zen for three days.
Try mind. Bread
And potatoes and onions.
Fifty people eating together.
Get energy. Find the true way.
What is the true way?
Don't know? Primary point?
Before thinking?
Someone appears. Hits the floor.
WHACK!
But is that the true way?
November in Warsaw.
The sky is dark.
Fifty faces are shining.
A long time ago in Japan, there was a well-known region called Matsushima. Matsushima is a place by the ocean, with mountains, rivers, trees, and flowers. Matsushima inspired many beautiful poems. At one time the famous Zen Master and poet named Basho decided to visit. When Basho saw the beauty of this place he wrote this poem:
Matsushima --
ah, Matsushima!
Matsushima!
Three clear lines! This is a very famous poem. Only Matsushima is Matsushima -- it is very simple. That is the most important point. This is great Zen poetry.
In Zen one is taught there is only the moment. No right or wrong. No good or evil. Just this monent. Zen mind, poetry mind, writing mind, practicing mind, all are not different. - see clearly, hear clearly, smell clearly, and think clearly. My thinking is clear, not checking anything. just think clearly, then make your poem.
This form of writing reminds me of a book called "The Artist Way" by Julia Cameron. A workshop book to help expand ones creative (and to break writer's block). One of your daily practice was to, immediately upon awaking, write what was call "the morning pages". Each morning, in silence, (coffee and cigarettes acceptable) you would write all thoughts  that raced through your mind. It did not matter if any of it made sense or if one thought was related to the next thought. (by the way this techique is very effected)
You didnt think about your thoughts you just wrote them down. The same with Zen poetry, one does not think or make a poem, one just does in the monent. Like the Cameron's Morning Pages, Zen poetry can be very effective with your creative process.
Zen poetry, morning pages
lost mind. beginners mind;
sip coffee; sexual depuration.
look at time, sigh -
morning breeze, a red cardinal flys by
write Zen, clear mind - explain.
look at computer, sip coffee;
breath deep; stretch.
Zen mind, beginners mind.
Try this yourself, take a deep breathe, clear your mind, without thinking then just write what ever thoughts flow through your inner vision. Dont try, just do. Give it a whirl - Its fun!