In summary, we theoretically studied the optical properties of AGNRs/BN, employing TB calculations. We demonstrate that in AGNRs/BN only optical transitions from subbands with odd (even) indices to subbands with odd (even) indices are allowed. This transition rule is more restricted for AGNRs and completely different from that of ZGNRs. Our TB results are in agreement with first principle calculations which verifies the accuracy of our model. The applicability of AGNRs/BN as photodetectors is investigated. Our results indicate that due to more allowed transitions compared to conventional GNRs a larger photo current in AGNR/BN structures can be achieved. The results render AGNRs/BN as suitable candidates for infrared photodetectors and future optoelectronic applications.