Relationships among group delay, energy storage, and loss in dispersive dielectric mirrors

Abstract

We show that absorbed and stored electromagnetic energy are proportional to the reflection group delay in highly reflective dispersive dielectric mirrors over the high-reflectivity band. Our theoretical considerations are verified by numerical simulations performed on different dielectric mirror structures. The revealed proportionality between group delay and absorbed energy sets constraint on the application of ultrabroadband and/or dispersive dielectric mirrors in broadband or widely tunable, high-power laser systems.OCIS codes: 310. 6805, 140.3330, 260.2030. doi: 10.3788/COL201210.053101.In the last two decades, theoretical and experimental investigations on reflection delay time of optical pulses reflected by multilayer dielectric structures have been of scientific interest because frequency-dependent group delay (GD) of the dielectric mirrors can be well suited for intracavity or extracavity dispersion compensation of ultrashort pulse lasers [1] . Aperiodic dielectric mirror structures, which are often referred to as chirped mirrors, are advantageous, not only because they introduce a certain amount of negative dispersion, but also because they exhibit a considerably broader highreflectance band than standard, low-dispersion quarterwave (QW) mirror stacks. Aside from chirped mirrors, there is another group of dispersive mirrors referred to as: Gires-Tournois interferometer-type mirrors [2] . The fact that a relationship exists between the electromagnetic energy stored in the volume of a thin-film structure and its GD is known in the field of telecommunication technology [3] . This relationship is also a starting point in resolving the long-haul scientific problem of superluminal delay times of electromagnetic wave packets during transmission through highly reflective, lossless photonic bandgap structures [4] . In practical laser systems, however, one usually cannot neglect the absorption (or scattering) loss of dielectric multilayer mirrors because laser performance, such as intracavity loss, beam quality, maximum output power, laser damage threshold power, and others, strongly depends on these physical quantities. From this aspect, one can address the question of whether a general relationship exists between the reflection GD and the absorption loss of a dielectric multilayer mirror (throughout the letter, we mean one-photon or linear absorption when we use the word "absorption"). For QW-stack mirrors, GD and absorptance have been shown as proportional to each other at the central wavelength of the QW mirror when the loss is sufficiently low [5] . For a specific multistack multilayer mirror design, Ferencz et al. also found conspicuous, but unexplained, proportionality of these two physical quantities [6] . For a nonspecific, general, highly reflective dielectric mirror structure, however, neither the relationship between GD and the absorptance nor the relationship between GD and the stored energy in the presence of loss has been investigated systematically thus far.In this letter, we first theoretically d...

Stored Energy, Transmission Group Delay and Mode Field Distortion in Optical Fibers

“…Note that a similar discrepancy has been reported in Ref. [14] dealing with 1-D dispersive PBG structures.…”

“…where P i is the incident power to a dielectric surface, R and T are the reflection and transmission coefficients (R + T = 1), and τ r and τ t are group delays on reflection and transmission, respectively. Numerical simulations in 1-D PBG structures were carried out [14] indicating that the reflection group delay is proportional to the stored energy if the incident power is constant and the transmission of the mirror is negligible: τ r Ý U.…”