Sterilize a scalpel in rubbing alcohol. Cut the end off the stem where it broke, using the sterilized scalpel. Make the cut 1 inch before and 1 inch after a growth node. Make several stem cuttings to increase your chances of success. Fill a sterilized glass with a 10 percent bleach and water solution. Soak the stems for 15 minutes, agitating the solution occasionally.
Put the flasked media into a pressure cooker filled with enough distilled water to cover the flasks. Let it cook for 20 minutes and then remove from heat and allow to cool naturally. These are the containers with the prepared food into which you will plant the stem pieces.
Use tweezers to pull off the skinlike covering over the growth nodes. Cut 1/8 inch more off each end of the stem pieces. Put 1 level teaspoon of agar per flask into a pan. Add just enough water to thin it and cook on low to medium-low heat, stirring constantly until the agar is completely dissolved.
Cool the agar slightly, then pour it into the containers to a depth of 1/2 inch per flask. Use the tweezers to immerse the ends of the stem pieces in the flasks. The agar gel will hold them upright. Put the lids on the flasks again. You should see swelling at the base in a week or two.
Cut the plant off with a sterile scalpel when it reaches 1/4 inch high. Repeat the process of sterilizing flasks and make fresh agar. Replant the new plants so they can grow roots. Keep the plantlets moist and in low light. Once there are signs of roots, gradually introduce the plants to light. The new orchids will be ready for the green house in 6 to 12 months. Your single stem has now produced numerous plants that are exact clones of the stem.