On Fresnel Re;ection and
Evanescent Gain
OPN recently published an article by
A.E. Siegman, titled “Fresnel Reflection,
Lenserf Reflection and Evanescent Gain”
(January 2010). We argue that many of
the claims in the article are incorrect.
For example, the article states that:
“Satisfying the boundary conditions
for the E and H fields at the interface
provides a recipe for finding k2 as a
function of the incident k1.” Actually,
k2 as a function of the incident k1 does
not depend on the boundary conditions
for the fields. ;e article goes on to state
that the, “imaginary part corresponds
to absorption loss if n2i is negative, and
to gain if n2i is positive.” In fact, the correct signs are opposite.
Siegman also states, “…k2x taking on
the same positive sign for equal values
of either loss or gain.” We argue that
signs of k2x are opposite in lossy and
gainy cases. In addition, according to
0.270 –0.274 –0.546 –0.818 – 1.09–1 –0.66–0.33 0
Gainy
Lossless
Lossy
0.33 0.66 1.0 1. 34
the article, “g2x takes on positive and
negative signs for the gainy and lossy
cases, respectively.” However, in the TIR
regime, g2x has the same negative sign
for both the gainy and lossy cases.
We also take issue with the follow-
ing point: “;e contours for the lossy
and gainy amplitudes … progress in
opposite directions around the unit
circle.” No, actually, they progress in the
same clockwise direction. In addition,
Siegman states: “;e magnitude of the
reflection coe;cient always remains less
than unity for any angle of incidence
and for any value of loss or gain.” But
in fact the TIR reflection coe;cient for
the gainy case is larger than unity. We
propose that our figure, included here,
reflects the correct situation.
THE AUTHOR RESPONDS: I appreciate
this response from F.V. and V.K. Igna-tovich. However, I continue to believe
that my description of Fresnel reflection,
and especially of total internal reflection
from a lower-index but gainy medium, is
the physically correct one. Some of their
responses seem to me to reflect simply
di;erences in sign conventions; others
Our thumb is on the pulse
of INFRARED OPTICS.
IN-STOCK & AVAILABLE!
6 | OPN Optics & Photonics News
www.osa-opn.org
