and are injected through rows of openings 302 and 302 39 defined in the nozzle plates 301 and 301 39 respectively to flow into a meeting chamber 319 since the openings 302 and 302 39 are arranged alternately these two molten polymers a and b injected through them form a layered structure as shown in fig3 a to flow as such into the meeting chamber 319 the channel defined between the nozzle plates 301 and 301 39 communicates to a funnel like portion 304 as shown in fig3 and the composite polymer fiber formed by passing the funnel like portion 304 and a final injection orifice 305 has a structure as shown in fig3 b in which thin films of polymers a and b are layered alternately accordingly the composite polymer fiber can exhibit excellent optical functions while the openings 302 to be defined in the nozzle plate 301 may have the same bore diameter and may be arranged at regular intervals openings 321 having a larger diameter may be defined at the central area or the intervals between the openings 302 may be reduced in such area so as to achieve smooth supply of the polymer a for forming the core s incidentally while the openings 302 and 321 are aligned in the example shown in fig3 they may be staggered as shown in fig4 b so as to facilitate machining and the like as described above if rows of openings 302 302 39 and 321 are defined in the nozzle plates 301 and 301 39.