How laser beam comes to laser rod, if first mirror is HR?
Or it is only HR for generated wavelength?
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The coating on the rod is only HR for red. It is also HT for blue. Blue light can get into the rod at this end, but very little red light can get out.
The laser resonator extends from the HR coating to the output coupler OC, which also has a HR coating. The sketch is misleading : only a very small amount (less than 1%) of the light energy in the resonator can be allowed to escape through OC, otherwise it is not able to build up into a strong coherent beam by making many round trips through the rod, in which it gains energy from the blue beam, which is called the pump beam.