The diversity of workload requirements and increasing hardware heterogeneity in emerging high performance computing (HPC) systems motivate resource disaggregation. Resource disaggregation allows compute and memory resources to be allocated individually as required to each workload. However, it is unclear how to efficiently realize this capability and cost-effectively meet the stringent bandwidth and latency requirements of HPC applications. To that end, we describe how modern photonics can be co-designed with modern HPC racks to implement flexible intra-rack resource disaggregation and fully meet the bit error rate (BER) and high escape bandwidth of all chip types in modern HPC racks. Our photonic-based disaggregated rack provides an average application speedup of 11% (46% maximum) for 25 CPU and 61% for 24 GPU benchmarks compared to a similar system that instead uses modern electronic switches for disaggregation. Using observed resource usage from a production system, we estimate that an iso-performance intra-rack disaggregated HPC system using photonics would require 4x fewer memory modules and 2x fewer NICs than a non-disaggregated baseline.