For lumped-element electro-optic modulators, the sensitivity (partial deriv
ative phi/partial derivativeV) of the phase, phi, in response to an applied
voltage V is related to the optical group delay, T-g, and the bandwidth, D
elta omega. This relationship imposes a fundamental trade-off between the s
ensitivity and the bandwidth of electro-optic modulators: (partial derivati
ve phi/partial derivativeV)Delta omega) = (dn/dV)(omega /n), where n is the
optical index. A similar relationship for traveling-wave modulators sets a
n upper limit on (partial derivative phi/partial derivativeV) that is propo
rtional to T-g. (C) 2001 Optical Society of America.