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Method for artifact-free circular dichroism measurements
based on polarization grating
Clementina Provenzano,1Pasquale Pagliusi,1,2 Alfredo Mazzulla,2and Gabriella Cipparrone1,2,*
1Dipartimento di Fisica, Università della Calabria, I-87036, Rende, Italy
2Istituto per i Processi Chimico Fisici-Consiglio Nazionale delle Ricerche, Unità Organizzativa di Supporto, Cosenza, and Excellence
Centre Centro di Eccellenza Materiali Innovativi Funzionali.CAL, Ponte P. Bucci 33B, I-87036 Rende, Italy
*Corresponding author: gabriella.cipparrone@fis.unical.it
Received February 11, 2010; revised April 21, 2010; accepted April 23, 2010;
posted May 7, 2010 (Doc. ID 124075); published May 24, 2010
We propose a simple method to perform real-time measurements of circular dichroism (CD), which suppresses the
artifacts introduced by anisotropic samples and nonideal optical elements in conventional spectrometers. A single
polarization holographic grating is adopted, whose first orders of diffraction have amplitudes that are proportional
to the right and left circular polarization component of the input light. We demonstrate that, exploiting unpolarized
white light and the intrinsic spectral selectivity of the grating, the true CD spectrum is evaluated in parallel in the
spectral range of interest from the intensities of the two diffraction orders, Iþ1and I−1. © 2010 Optical Society of
America
OCIS codes: 300.0300, 090.2890, 260.2130, 230.5440, 120.6200.
Circular dichroism (CD) spectroscopy provides unique
information on chiral molecular structures [1,2] by mea-
suring their differential absorption with respect to the left
(LCP) and the right (RCP) circular polarization states of
light. Chirality is fundamental in biology, chemistry, and
material science, because it occurs in biomolecules (ami-
no acids, sugars, DNA, and RNA) but also in synthetic
chemicals and drugs [3,4].
Conventional CD spectrometers implement
polarization-modulation techniques. They require an in-
tense, broad-bandwidth light source and several optical
and electro-optical elements located before and after the
specimen to be investigated: dispersive elements (prism
or grating) narrow the light bandwidth and pick the
wavelength, polarizing elements (polarizer and photo-
elastic modulator) select, alternatively, the LCP and
the RCP of the light to be directed to the specimen, and
phase-sensitive detectors (lock-in amplifier) are tuned to
the frequency and phase of the modulator [1,2,5–9]. Be-
side its intrinsic limitation in real-time measurements, the
application of polarization-modulation CD spectroscopy
to all phases, including the solid state, is extremely com-
plex. Indeed, CD spectra are inevitably affected by para-
sitic artifacts that originate from the anisotropies of the
specimen, i.e., linear birefringence (LB) and dichroism
(LD), from imperfections of the optical and electronic
components (i.e., residual strain birefringence of the
photoelastic modulator, polarization-dependent detec-
tor’s response, etc.), or from data-processing methods
[6,10]. The resulting spurious CD signals are nearly
indistinguishable from the true CD ones and often give
rise to misinterpretations of the experimental results.
Several efforts have been made in the last few years
to understand the effect of the artifacts in polarization-
modulation spectroscopy and to deduce the true CD
spectrum by optimizing the quality and the alignment
of the components and developing new methods and in-
strumental designs [5,6,8–12]. The artifacts resulting
from the anisotropic specimen have been also consid-
ered in several works, where true CD spectra have been
obtained, exploiting the Mueller matrix method, from the
elaboration of the CD spectra recorded at different orien-
tations of the specimen [8,12]. Recently, a chiro-optical
spectrometer, capable of simultaneously measuring all
the macroscopic anisotropies, namely LB, LD, circular
birefringence (CB), and CD, has been proposed [9].
Nevertheless, the increased complexity of the optical
scheme and of the polarization-modulation detection
method intrinsically increases the sources of instrumen-
tal artifacts. In spite of the continuous efforts to improve
the reliability of the polarization-modulation techniques,
the development appears to be approaching its limit.
In this Letter we propose a method for real-time CD
measurements that reduces the instrumental and sample
artifacts suffered by the polarization-modulation tech-
niques. The method is based on a diffractive spectrograph
scheme, relying on a polarization grating (PG) [13,14]. The
presence of a single polarizing optical element (i.e., no
wave plates or polarizers; no moving or modulating ele-
ments, as photoelastic modulators; no lock-in amplifiers)
radically reduces the sources of instrumental artifacts.
Moreover, we demonstrate that when unpolarized white
light is directed to the specimen, the contribution of the
LB, LD, and CB in the CD spectrum is strongly suppressed.
The working principle of the proposed diffrac-
tive method for CD measurement is illustrated by the
simplified scheme reported in Fig. 1. The unpolarized
Fig. 1. (Color online) Working scheme of the CD spectro-
graph: WL, white unpolarized light impinging on the specimen;
PC, computer-controlled acquisition card.
1822 OPTICS LETTERS / Vol. 35, No. 11 / June 1, 2010
0146-9592/10/111822-03$15.00/0 © 2010 Optical Society of America
white-light beam impinges on the investigated specimen,
without further bandwidth or polarization manipulation,
and the transmitted component is directed to the PG. The
latter diffracts the light into the zero-order (0) and the
two first-order (1) beams [15–17]. The broad-bandwidth
light transmitted through the specimen is spectrally dis-
persed by the PG into the 1orders of diffraction, whose
intensities are detected by two linear detector arrays
(LDAs) to evaluate the CD spectrum of the specimen.
The central optical element of the proposed CD spectro-
graph is the PG, i.e., a diffraction grating recorded by
polarization holography in a photosensitive material. The
PG considered here is produced by the interference of
two planar waves with opposite circular polarization
(i.e., LCP and RCP). In the interference region, where
the intensity is almost uniform, the light is linearly polar-
ized and the polarization direction periodically rotates
along the grating wave vector [15–17].
Stokes–Mueller formalism is adopted here to explain
the new method [10,18], with ordering of the Stokes para-
meters defined by Eq. (4) in [10]. The unpolarized light,
propagating along Zand impinging on the sample, is
described by the Stokes vector S0:
S0¼ð1;0;0;0Þt;ð1Þ
where the superscript tindicates the transpose. Accord-
ing to the scheme in Fig. 1, the Stokes vectors of the 1
orders at each wavelength are given by
Sþ1¼Tþ1CS0;S
−1¼T−1CS0;ð2Þ
where Cis the 4×4Mueller matrix of the sample, i.e., a
general anisotropic medium (GAM) having simulta-
neously LD, LB, CD, and CB [10], and T1represent the
Mueller matrices associated to the 1orders of the PG.
The Mueller matrix Chas been adapted from [10]
C¼expð−HÞ;
H¼
0
B
B
B
B
B
@
AeLDsin2χ−CD LDcos2χ
LDsin2χAeLB cos 2θCB
−CD −LBcos2θAeLBsin 2θ
LDcos2χ−CB −LBsin 2θAe
1
C
C
C
C
C
A
;ð3Þ
where Aeis the mean absorbance, LD and LB are referred
to their respective axes, χand θare the angles of the LD
and LB axes, respectively, in a fixed coordinate system in
space (see Table II and Eq. (13) in [10]). The exponential
Mueller matrix Cin [3] can be expanded in a power
series:
C¼e−H¼e−AeI−Fþ1
2F2−
1
3!F3þ……;
F¼H−AeI; ð4Þ
where Iis the 4×4identity matrix. It is worth noting that
referring the sample’s LD and LB axes to the polarization
direction is not necessary here, because of the use of un-
polarized light, consequently; only the relative angle
(χ−θ) is relevant for the present method.
The Mueller matrices T1of the PG can be evaluated
starting from the PG’s Jones matrix [10]. For polarization-
sensitive materials with linear photoinduced anisotropy
(i.e., LD or LB), the Jones matrix of the PG is [15,16]
G¼aþbðeiδþe−iδÞibðe−iδ−eiδÞ
ibðe−iδ−eiδÞa−bðeiδþe−iδÞ;ð5Þ
where δ¼ð2π=ΛÞxis the phase difference between the
LCP and the RCP writing waves versus xand Λis the
spatial periodicity of the PG. In the case of amplitude
PG (photoinduced LD), ais the average transmission
of the PG, a¼Ta¼ðTpar þTperÞ=2, and b¼iΔT=2,
where ΔT¼ðTpar −TperÞ=2. In the case of phase PG
(photoinduced linear birefringence) a¼cosðΔϕÞand
b¼isinðΔϕÞ=2, where Δϕ ¼πdΔn=λ,dis the film thick-
ness, Δnis the photoinduced birefringence, and λis the
wavelength of the writing waves. In a simplified proce-
dure that enables us to obtain the light out of the PG
in the far field, the Jones matrix Gin Eq. (5) can be se-
parated in three matrices, related to the zero-order and
the two first-order beams, respectively,
G¼G0þGþ1þG−1¼a10
01
þbeiδ1−i
−i−1
þbe−iδ1i
i−1:ð6Þ
The Mueller matrices T1related to the 1orders can
be calculated from the corresponding G1Jones ma-
trices, following the procedure reported in Table I of [10]:
Tþ1¼2jbj20
B
B
B
@
1010
0000
−10−10
0000
1
C
C
C
A
;
T−1¼2jbj20
B
B
B
@
10−10
00 0 0
10−10
00 0 0
1
C
C
C
A
:
ð7Þ
The results in Eq. (7) are validated by a more rigorous
approach, where the spatial-angular Mueller matrices of
the diffraction orders of a PG have been calculated
adopting the Wigner formalism [19].
In analogy to [13], where the CD of an isotropic speci-
men (LD ¼LB ¼0) has been evaluated, we are inter-
ested in the logarithm of the ratio of the first-order
intensities Iþ1and I−1. Exploiting Eqs. (1), (2), (4),
and (7), we calculate the first-order series expansion
of the logðIþ1=I−1Þwith respect to LD, LB, CD, and CB:
1
2logIþ1
I−1≅CD þLD LB CB
6cos 2ðχ−θÞ
−LD LB
2sin 2ðχ−θÞ;ð8Þ
June 1, 2010 / Vol. 35, No. 11 / OPTICS LETTERS 1823
which, assuming χ¼θ, reduces to
1
2logIþ1
I−1≅CD þLD LB CB
6:ð9Þ
According to Eq. (9), the CD of a GAM could be evalu-
ated from the half-logarithm of the first-order intensities
ratio, the correction term being LD · LB · CB=6. If CD,
CB, LD, and LB are all nonzero, the relative discrepancy
between the true CD and its calculated value log
ðIþ1=I−1Þ=2is usually very small (i.e., less than 10%), even
considering thar LB and LD are much larger than CB and
CD. Typical relative discrepancy on the true CD is about
1%, following the numerical evaluation of the log
ðIþ1=I−1Þ=2from Eqs. (1), (2), (4), and (7) for realistic va-
lues of LB ¼LD ¼10−1and CB ¼CD ¼10−5. Moreover,
the numerically evaluated value of the logðIþ1=I−1Þ=2
matches almost perfectly (within 1%) the approximate
series expansion of Eq. (9), validating the truncation of
the series to the first order. Apparent CD signals may only
occur when CD is identical to zero or it much smaller
than CB (i.e., CD ≤LD · LB · CB ∼10−2CB). Nevertheless,
these scenarios apply to a small number of practical cases,
as, for example, a cholesteric liquid crystal in which achir-
al dye molecules are dissolved [8]. The above conclusions
hold true even in the general case χ≠θ, provided that the
half-sum of two experimental spectra logðIþ1=I−1Þ=2, ac-
quired by rotating the sample by 180° around any axis in
the xy plane, is considered. Indeed, (χ−θ) changes sign as
a result of the sample rotation; consequently, the term LD ·
LB · sin 2ðχ−θÞin Eq. (8) vanishes in the half-sum
½logðIþ1=I−1Þ0°þlogðIþ1=I −1Þ180°=4
≅CD þðLD · LB · CB=6Þcos 2ðχ−θÞ:ð10Þ
In conclusion, we report a method for artifact-free
measurements of CD, which suppresses both the effects
of the linear anisotropies of the specimen and the arti-
facts arising from the imperfect optical elements. The
proposed method relies on the use of unpolarized white
light and a PG. Adopting the Stokes–Mueller formalism,
we have demonstrated that the true CD of any anisotro-
pic specimen could be achieved from the half-logarithm
of the ratio of the first-order intensities Iþ1and I−1, limit-
ing the incidence of artifacts to the sole case when
CD ≤LD · LB · CB. The proposed method could be imple-
mented in a very simple CD diffractive spectrograph
based on a single-polarization holographic grating that
strongly reduces the instrumental artifacts of the conven-
tional CD spectrometers while also enabling real-time
measurements. Indeed, the entire CD spectrum can be
achieved using two linear array detectors for parallel ac-
quisition of the spectrally dispersed diffracted beams.
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1824 OPTICS LETTERS / Vol. 35, No. 11 / June 1, 2010
