A new family of two-dimensional (2-D) wavelength-hopping time-spreading codes, which employs wavelength hopping algebraically under prime-sequence permutations on top of time-spreading optical orthogonal codes, is studied and analyzed. Different from other 2-D codes, our new codes allow the number of wavelengths and code length to be chosen independently and, at the same time, the code cardinality is a quadratic function of the number of wavelengths without sacrificing the maximum cross-correlation value (i.e., still at most one). They are particularly suitable for high bit-rate optical code-division multiple-access systems with broadband mode-locked lasers, in which the number of time slots is very limited, and system capacity can only be grown by increasing the number of wavelengths, rather than code length. Finally, a novel wavelength-aware detector for wavelength-hopping time-spreading codes is discussed and shown to provide improved code performance.