Fundamentals, Advances, and Artifacts in Circularly Polarized Luminescence (CPL) Spectroscopy

Objects are chiral when they cannot be superimposed with their mirror image. Materials can emit chiral light with an excess of right‐ or left‐handed circular polarization. This circularly polarized luminescence (CPL) is key to promising future applications, such as highly efficient displays, holography, sensing, enantiospecific discrimination, synthesis of drugs, quantum computing, and cryptography. Here, a practical guide to CPL spectroscopy is provided. First, the fundamentals of the technique are laid out and a detailed account of recent experimental advances to achieve highly sensitive and accurate measurements is given, including all corrections required to obtain reliable results. Then the most common artifacts and pitfalls are discussed, especially for the study of thin films, for example, based on molecules, polymers, or halide perovskites, as opposed to dilute solutions of emitters. To facilitate the adoption by others, custom operating software is made publicly available, equipping the reader with the tools needed for successful and accurate CPL determination.

Independent of the specific material class or envisioned device application, it is important that CPL is quantified accurately.Concerning the feasibility of a CPL measurement with a given spectroscopic setup, the magnitude of g lum is important but not the only decisive factor.The overall CPL efficiency B CPL also plays a key role, as bright CPL (high B CPL ) is easier to quantify than dim CPL (low B CPL ). [33]The spectroscopic method typically relies on the conversion of CPL to linearly polarized light which is subsequently filtered and detected. [28,64][84][85] In recent years, CPL spectrometers have also become commercially available from several manufacturers. [13,76,86,87]Approaches based on a PEM with either differential photon-counting or lock-in amplification were found to be reliable for the sensitive detection of dissymmetry factors as small as 10 −4 to 10 −5 for sufficiently bright samples. [6,73,74]Yet, each of these methods is susceptible to measurement artifacts that need to be carefully excluded.
We herein provide a detailed and easy-to-implement description of how to cost-effectively build a reliable CPL setup based on a PEM with a lock-in detection scheme and contrast it with the simpler quarter wave-plate approach, which we only recommend for broadband time-resolved measurements and large dissymmetry values.To lower the barrier for adoption, we also publish our custom Python code to control the setup components and explain important corrections that are required to obtain reliable results from raw data.Finally, we highlight key polarization artifacts for various material classes and sample types and propose best practices for CPL measurements in order to reliably identify and avoid these artifacts.

Setup Designs using a Quarter-Wave Plate
The most straightforward experiment to measure CPL is equipping an emission spectrometer with a quarter-wave plate set to ±45°relative to a linear polarizer (Figure 1a).A quarter-wave plate consists of a birefringent material that induces a 90°phaseretardance on the light passing through.It converts LCP and RCP to linearly polarized light with a plane of polarization at +45°and −45°relative to the fast axis of the optic, respectively.][67] By keeping the linear polarizer at a fixed angle, the detection of LCP and RCP can be switched by rotating the quarter-wave plate by 90°.Two emission spectra are recorded sequentially at the two orientations of the quarter-wave plate and the dissymmetry factor g lum is calculated using Equation (2).In principle, it is also possible to rotate the linear polarizer by 90°instead of the quarter-wave plate.However, as the performance of mirrors and gratings in the detection path is generally dependent on the polarization of incident light, this might introduce unwanted deviations between the two measurements. [68,72]Therefore, rotating the quarter-wave plate at a fixed detection polarization is preferable.
While this method is relatively simple to execute, there are several drawbacks that can limit its practicality.First, manual rotation of the quarter-wave plate introduces a source of error and variability, which is why high-precision and motorized rotational mounts with minimal backlash are recommended.More importantly, the time delay between the two measurements can lead to partial sample degradation or a drift in the excitation light intensity.Both effects change the luminescence intensity in the second spectrum, thus resulting in CPL artifacts, when the difference between the spectra is calculated. [28]In general, the quarter-wave plate setup is reliable for strong CPL signals (g lum ≥ 0.1), [6,13,14] but can prove difficult for small g lum values, which are more frequently observed. [27]An advantage of using superachromatic (broad-band) quarter-wave plates over using a PEM (see below) is their compatibility with broad-band CPL detection without having to scan the emission wavelength, which also enables time-resolved measurements in combination with fast array detectors like electronically time-gated charge-coupled device (CCD) cameras. [29,30]o avoid the aforementioned problems, both RCP and LCP can be detected at the same time using a 50/50 beam splitter after the quarter-wave plate with orthogonal linear polarizers and detectors on each beam path (Figure 1b). [30]This setup was shown to provide comparable results to one equipped with a PEM for the strong CPL of the prototype emitter Eu[(+)-facam] 3 ((+)-facam = 3-(trifluoromethylhydroxymethylene)-(+)-camphorate) with a high signal-to-noise ratio. [30]It should be noted, however, that in general, it is not advisable to place optics like a beam splitter between the sample and the polarization analyzers (in this ) of the sample.a) CPL is converted to linearly polarized light using a quarter-wave plate (/4), with LCP and RCP resulting in orthogonal polarizations, and then filtered with a linear polarizer (LP).To measure the opposite handedness of CPL, the case the quarter-wave plate) as these might lead to depolarization of the light. [73]In addition, small variations in the sensitivities of the two detectors or the detection pathways, the dependence of the gratings on the axis of linear polarization (see above), and imperfections in the quarter-wave plates may also result in artifacts that need to be corrected for upon data processing.For these reasons, typically only larger g lum (≥0.1) values are readily obtained, [30,68] like in the aforementioned experiment where a quarter-wave plate is rotated.
A more sensitive setup was recently reported by Baguenard et al. (Figure 1c) that expands on the beam splitter approach (Figure 1b) and is able to detect dim CPL with B CPL ≥ 10 −4 m −1 cm −1 . [68]The setup employs a polarizing beam splitter and instead of using separate detectors, the two linearly polarized components are directed onto the same CCD camera through fiber optics, yielding a top and bottom detection track ("spatial separation" of I L and I R ).After spectra are acquired with the quarter-wave plate at 45°, the wave plate is rotated to −45°.This switches the detection tracks for I L and I R , so both signals are imaged to the same spot on the camera in two consecutive scans ("temporal separation" of I L and I R ). [68] By combining the spectra obtained in both orientations of the quarter wave-plate, most CPL artifacts such as unequal transmission and wavelength mismatch of the two detection paths autocompensate.While an external calibration is not necessary, the cross-talk between the two detection tracks caused by stray light and beam splitter imperfections needs to be tackled by applying a spectral correction factor.Finally, CPL artifacts caused by linear polarization components in emission remain an issue. [68]

Using a Photoelastic Modulator with Lock-in Amplification
Due to the limitations of most quarter-wave plate-based methods outlined above, many modern setups rely on a PEM instead (Figure 1c).A PEM exploits the strain-induced birefringence of its optical window (in our case fused silica) and acts as a quarterwave plate whose fast axis orientation oscillates between 0°and 90°at a resonance frequency f (usually between 30 and 50 kHz).Hence, it alternatingly converts LCP and RCP at a specific wavelength to linearly polarized light at 45°which can then be filtered by a linear polarizer to be detected (Figure 1c).Unpolarized light quarter-wave plate needs to be rotated by 90°. [21,67]b) Instead of rotating the quarter-wave plate, LCP and RCP components are separated by using a 50/50 non-polarizing beam-splitter (BS) and two identical linear polarizers and detectors on orthogonal detection arms, detecting both handednesses of CPL simultaneously. [30]c) A polarizing beam splitter (PBS) spatially separates the two linear polarization components and fiber optics feed them onto a CCD camera with a monochromator as stacked detection tracks (as shown in the front view on the slit).Rotation of the quarter waveplate with a motorized mount switches the polarization of the two detection tracks, enabling the spatial and temporal separation of I L and I R . [68]) A photoelastic modulator (PEM) effectively acts as a quarter-wave plate that oscillates between +/4 and −/4 retardance (in our case at a modulation frequency of 42 kHz).When CPL is passed through the PEM and the linear polarizer, the intensity at the detector is modulated.The modulated CPL signal can be isolated from the unmodulated background by lock-in amplification using the square-wave signal of the PEM as a reference, [77] or alternatively using a differential photon counter (not shown).[64,73,74] 4)-( 6)).Modulation frequency f = 42 kHz.
is not modulated by the PEM.For luminescence with a given excess in circular polarization, this results in a modulated signal at the detector (Figure 2c), thus allowing for the separation of very small CPL from a large unpolarized background, that is the precise measurement of g lum values down to ≈10 −5 . [73]As the PEM always operates at only one specific tunable wavelength at a time, a wavelength-scan is necessary in order to record an emission spectrum, rendering a PEM incompatible with broad-band detection.
There are two ways to extract the CPL from the detector signal: Differential photon counting and lock-in amplification.[72][73][74] These counts can then be used to calculate the dissymmetry factor g lum using Equation (2), the standard deviation of which can be calculated from the total photon count N as √ 2∕N. [27]For an in-depth discussion of the technique the reader is referred to excellent resources on the topic. [70,71,73,74]erein, we want to focus on the lock-in amplification scheme (Figure 2d) that was first reported by Steinberg and Gafni [80] in 1972 and that we implemented in our setup (see SI for details).Early lock-in amplification setups suffered from electronic problems such as ground-loop noise, [70,88] but nowadays lockin amplification with modern hardware and differential photon counting are equally reliable approaches. [6]In general, a dualchannel lock-in amplifier outputs the unmodulated average luminescence intensity (the "DC component", Equation ( 4)) and the CPL as the intensity component modulated at the frequency f (the "AC component", Equation ( 5)).
Specifically, the lock-in amplifier uses the PEM's reference signal, which communicates its modulation frequency f (in our case 42 kHz, Figure 2a), to isolate the amplitude R AC and the phase  AC of the modulated CPL signal from the noisy detector signal (which consists of the typically larger unpolarized luminescence component, the typically much smaller CPL component, and any background signal from light pollution or electronic noise) (Figure 2d; Figure S2, Supporting Information).This so-called demodulation process works by mixing the detector signal with a reference sine wave and applying a low-pass frequency filter (see ref. [88] for more details).It is worth noting that the low-pass filter introduces a rise-time to the signal during which the signal approaches its true value. [88]sually, the detector signal is split to detect the AC component via lock-in amplification on one end and the constant DC component using, for example, a voltmeter on the other. [49,64,78,89]owever, it is beneficial to use a second channel of the lock-in amplifier with demodulation at 0 Hz for the detection of the DC component instead.This approach guarantees that both components can be detected synchronously because the same low-pass filters with the same rise times apply to both signals.The result is a smaller spread in individual g lum values recorded at a specific wavelength, as all intensity fluctuations will affect AC and DC signals at the same time and in the same way.Moreover, by using the same device for both AC and DC measurements systematic errors may be avoided and calibration of the setup would, in principle, become superfluous.To summarize briefly, in this PEM-based experimental technique, the lock-in amplifier records the amplitudes R and phases  of the AC and the DC channel at different wavelengths.
Unfortunately, in the literature, one can find various different, sometimes even contradictory equations on how to calculate the figure of merit g lum from raw data within the framework of the lock-in amplification approach. [77,78]To make the powerful PEMbased CPL technique more accessible we present here a consistent set of equations (Equations ( 4)-( 6)) for a CPL spectrometer using a dual-channel lock-in amplifier and correct phase offset calibration (see Section 3.2): In Equations ( 4) and ( 5), J 1 (x) is the first-order Bessel function of the first kind and sgn(x) is the signum function.In the following, we discuss the rationale behind the individual parts of these equations, as well as common pitfalls and artifacts in CPL measurements.

Unit Conversion of AC and DC Values
Lock-in amplifiers provide the amplitude of the AC component R AC in voltage units of V rms (rms = root-mean-square). [88]Hence, a factor of √ 2 is used in Equation ( 4) to convert V rms to V pk (pk = peak).The amplitude of the DC component R DC , on the other hand, needs to be scaled by a factor of 1∕ √ 2 that arises from the lock-in amplification scheme (Equation ( 5), see Equations S1-S5, Supporting Information for details).

How to Infer the Correct Sign of the Amplitude R from the Phase 𝜽
The amplitudes R will always appear as positive values, so their sign must be inferred from the phase , which can range from −180°to +180°.In general, the phase of negative CPL is shifted by 180°with respect to positive CPL.In an idealized PEM, the reference signal and the modulation of the luminescence intensity are perfectly in sync (Figure 2b, dotted line).However, in reality, there is a temperature-dependent phase offset between the two, caused by the electronics and the physical resonance of the PEM (Figure 2b, solid trace).This phase offset needs to be calibrated for in the lock-in amplifier using a source of strong CPL-like emission of the aforementioned Eu[(+)-facam] 3 in dry dimethyl sulfoxide (DMSO) at 595 (neg.CPL) and 613 nm (pos.CPL) upon photoexcitation with UV light, before attempting to measure reliable results.
The phase offset determines which phases  AC+ and  AC− will be detected on average for positive and negative CPL, respectively.The distribution of phases around these average values is narrow for strong CPL and broad for weak CPL.In theory, the phase offset could be chosen arbitrarily and the specific values of  AC+ and  AC− should not impact the results.However, we found that in our setup, the choice of  AC+ and  AC− affects the g lum baseline obtained from achiral samples.The unpolarized emission of achiral molecular samples in solution did not produce entirely random phases  AC as expected but showed a slight bias for phases with small magnitudes | AC | instead.This bias might stem from phase instability that is caused for small signals by the arctan2 function in the calculation of  AC (see Equation S8, Supporting Information).When the phase offset is chosen in a way to give  AC+ = ±180°and  AC− = 0°(so | AC | > 90°corresponds to a positive and | AC | ≤ 90°to a negative sign of R AC , see Figure 3a and Figure S2c (Supporting Information), Setting I), the bias for small phases yields a g lum baseline below 0, on the order of −5 × 10 −4 (see Figure S3, Supporting Information).Hence, we recommend setting the phase offset in a way that yields  AC+ = +90°and  AC− = −90°on average (Setting II in Figure 3b; Figure S2d, Supporting Information).
In this case, a zero-baseline is obtained for achiral samples after a recent phase offset calibration, and the sign of the amplitude R AC can simply be determined by the sign of the phase  AC (sgn( AC ) term in Equation ( 5)).When the phase offset is not calibrated correctly (so  AC+ and  AC− are not exactly at ±90°on average), the quality of the baseline is not affected (Figure 3b; Figure S4, Supporting Information).However, an additional error source is introduced for weak CPL (g lum < 10 −3 ), as the phase distributions for positive and negative CPL tail into the regions of the opposite sign (Figure 3c).We found that for a relatively strong CPL signal, as found for Eu[(+)-facam] 3 ≈680-700 nm with a g lum of ≈0.02, the effect of extreme miscalibrations of the phase offset (up to ±20°relative to the correct value) on the extracted g lum value was small (Figure S5, Supporting Information).An alternative way to determine the amplitude and sign using the X and Y components provided by the lock-in amplifier (Figure S2, Supporting Information) instead of R and  that also avoids the phase instability mentioned above is described in the SI.
In contrast to CPL, the average luminescence intensity (i.e., the DC component) can only be positive.However, as our photomultiplier outputs a slightly negative DC value of −20 μV in the dark, a sign term is included in Equation (4) as well.Here, a phase offset of 0°is set for the demodulator so that the sign of R DC equals the sign of  DC , yielding positive and negative DC values at exactly +90°and −90°, respectively.For the DC channel, there is no modulation, so no additional calibration is necessary.
To summarize, the phases  AC and  DC serve to determine the signs of the respective amplitudes R AC and R DC .With regards to  AC , two aspects are particularly important: the phase offset between the reference and the actual modulation of the PEM i) should be set in a way that phases of ±90°are obtained for positive and negative CPL and ii) should be calibrated correctly on a regular basis.

The Non-Sinusoidal PEM Modulation Must be Corrected For
When working with a PEM, it is important to consider that the intensity modulation is not sinusoidal.Instead, the PEM modulates the luminescence intensity I(t) according to Equation (7), with the unpolarized component I 0 , the CPL intensity I CPL , the amplitude of modulation A (note that A = /2 for quarter-wave retardance), time t, modulation frequency f, and phase .To find out how this non-sinusoidal modulation affects the lock-in amplification, we can deconvolute Equation (7) to a sum of sine waves using the Jacobi-Anger expansion (Equation ( 8)), where J n (x) is the nth order Bessel function of the first kind. [90]The first two terms of the expansion (Equation ( 9)) are generally sufficient to approximate Equation (7).
Figure 3.The phase offset affects the g lum baseline obtained with achiral samples and the accuracy of g lum for weak CPL emitters.The plots show the schematic distributions of counts N with certain phase values  AC for non-CPL emitters with a bias for small absolute phase values (gray) and weak CPL emitters (blue = negative, red = positive).a) Setting I: The phase offset is chosen such that positive and negative CPL yield phases of ±180°and 0°, respectively (Figure S2c, Supporting Information).Since small absolute phases are more prevalent, this yields a negative CPL artifact for non-CPL active emitters.b) Setting II: The phase offset is chosen such that positive and negative CPL yield phases of +90°and −90°, respectively (Figure S2d, Supporting Information).Since positive and negative phases are equally prevalent, a non-CPL-active sample yields the expected g lum value of 0. This is true even when the phase offset calibration is suboptimal (dotted line).c) Setting II: However, at a significant miscalibration of the phase offset, the dissymmetry factor of weakly CPL-emissive samples is not determined correctly because a part of the phases belonging to the negative CPL appears in the positive sign region and vice versa.d) Setting II: With the correct phase offset calibration, weak CPL is quantified correctly.
Two observations can be made from Equation ( 9): i) for CPL the PEM yields oscillating components at its modulation frequency f (the AC signal) and the third harmonic (3f); and ii) the amplitude of the 1f signal, R AC , which the lock-in amplifier detects, is higher than the actual intensity modulation amplitude of the PEM, I CPL because the 1f and 3f components partially cancel each other out (Figure 4).This needs to be corrected for (Equations ( 10) and ( 5)), as otherwise dissymmetry factors would be overestimated by ≈13%.
Unfortunately, this correction factor is seldom accounted for in the existing literature.
Next, we discuss more broadly encountered artifacts in CPL measurements.Normalized CPL intensity as modulated by a PEM (black solid trace, using Equation (7) with A = /2, and f = 42 kHz).The 1f (red dashed trace) and 3f components (blue dotted trace) of the Jacobi-Anger expansion (Equation ( 9)) of the PEM modulation are shown.The amplitude of the 1f sine wave, R AC , is ≈13% higher than that of the original modulation, which needs to be corrected to accurately determine CPL magnitude and g lum .

Calibration, Validation, and Processing of g lum Data
Two enantiomers of the same molecule should show mirrorimaged CPL signals crossing at 0 (the same is true for their CD signals).Furthermore, a valid CPL spectrometer gives a dissymmetry factor g lum of 0 for unpolarized luminescence.As CPL artifacts can be highly sample-specific (varying with phase, thickness, morphology, solvent, lab environment, etc.) as well as wavelength-and intensity-dependent, one must not apply a factor of correction to g lum values directly (e.g., via a g lum baseline correction).Instead, the origin of the deviation in the hardware must be identified and resolved. [89]hile some CPL spectrometers require calibration of the g lum values (e.g., because AC and DC values are recorded by different devices), all setups should be validated using a chiral and an achiral standard on a regular basis.Different approaches have been used over the years.The most common chiral standard is certainly the nuclear magnetic resonance shifting agent Eu[(+)facam] 3 in DMSO which shows a strong CPL response in the red spectral region.While the reported values show a certain variance (−0.76 to −0.92 at 595 nm), [29,74,[91][92][93] which may be due to the water sensitivity of the chiroptical response of the complex, [73,94] most commonly g lum values of −0.78 at 595 nm and +0.072 at 613 nm are cited as the correct values. [74,89]We were able to reproduce these values within error (see Figure S6, Supporting Information) with our CPL setup with the dual-channel lockin amplifier approach described above without the need to calibrate using known g lum values.A downside of Eu[(+)-facam] 3 is that only one enantiomer is commercially available.An alternative europium-based standard with good stability and accessibility of both enantiomers was recently developed but is not yet commercially available. [95]Other studies report using camphor quinone [78] or passing light through a solution with known CD. [6,64,78] These methods can be used to validate a CPL setup in the blue-to-green spectral region, which is especially useful if the desired signals lie in this area.Alternatively, specific degrees of circularly polarized light can be generated with a light source equipped with a linear polarizer and a quarter-wave plate. [80]In our experiments, the latter approach resulted in significant residual linear polarization in the emission (see Figure S7, Supporting Information), likely due to incomplete conversion of linear to circular polarization by the quarter-wave plate which could affect the determined g lum values as described below (Section 5.1).This error may become significant when CPL with small g lum values is generated using this method.While the deviation is likely small for very strong CPL (g lum ≈ 1.5-1.8), [77]we discourage the use of artificial CPL for validation or calibration purposes.
The spectra of the luminescence dissymmetry can be very noisy because g lum is usually small when there is CPL, and undefined when the luminescence intensity is zero (Equation ( 2)).Since smoothing of the data risks concealing small sharp bands (especially for lanthanide complexes), Zinna and DiBari proposed to use a small correcting constant  to calculate a smoothed glum instead (Equation ( 11)). [27]um = ΔI I 0 +  (11)   The baseline in CPL spectra in the literature was often found to strongly deviate from 0, if shown at all, shedding doubt on the stated g lum values.To better judge the validity of reported CPL spectra we propose that reports on new CPL-active materials should always include total emission spectra (I 0 vs ), CPL spectra (ΔI vs ), and dissymmetry factors (g lum vs ), for both enantiomers and the racemate.If the racemate is not available, it is important to include a broader spectral range than only the one covering the band of interest, to help the reader estimate the value for the baseline.

Artifacts Due to Linear Polarization Components of the Emission
When measuring CPL in a setup equipped with a PEM it is extremely important to be aware of any partial linear polarization of the detected light, as this will introduce artifacts and lead to wrong g lum values. [64,73,96]Sources of linear polarization can be reflections or scatter of polarized excitation light, emission from anisotropic samples, photoselection (see Section 5.3), or backreflections from certain linear polarizers (see Section 5.2).
A linearly polarized component in emission I lin (t) is modulated by the PEM according to Equation ( 12) with I lin,0 being the intensity of the linearly polarized light. [90]Again, we can use a Jacobi-Anger expansion (Equation ( 13)) to deconvolute the cos(sin(x)) to a series of sine functions and see that linearly polarized light is transformed into even harmonics of f by the PEM (0f = DC, 2f, 4f, …). [90]Thus, a linear polarization component of whatever origin affects R DC (Equation ( 14)) and hence g lum .
= I lin,0 Additionally, the small, yet significant static birefringence of the PEM itself can convert the linearly polarized light into CPL artifacts. [89,90]In summary, a linear component in emission affects g lum via both the AC and the DC values.Importantly, the sign and magnitude of these artifacts are very sensitive to small realignments of the sample or the setup. [64]Hence, a baseline correction is not suited to resolve this problem.In general, it is possible to derive analytical expressions for the effects of linear polarization artifacts on the CPL signal.However, this approach requires knowledge about the polarization responses of all the optics used and a thorough Stokes-Müller matrix analysis of the setup. [76]Measuring CPL spectra at different degrees of rotation of the sample around the excitation light propagation axis can give an estimate of the magnitude of the artifacts. [92]Also, a (quantitative) mirror-image relationship between CPL spectra of enantiomeric materials may indicate that the influence of artifacts is small. [92,97]But generally, without elaborate corrections, [76] CPL signals that arise while there is a linearly polarized (2f) component should not be trusted.
In our setup, we can record DC, AC, and the 2f signal at the same time and as such check for partial or residual linear polarization in emission for each measurement.This in situ check for linear polarization artifacts is another strong, rarely-stated benefit of using a PEM-based CPL detection, as opposed to that based on a quarter-wave plate introduced earlier (even when high g lum values are expected).

Artifacts due to Back-Reflections when using Wire-Grid Polarizers
The linear polarizer in the detection path is an important component in every CPL spectrometer as it eventually enables the discrimination of LCP and RCP.Different types of linear polarizers produce different beam paths and have their own advantages and drawbacks.For example, a Glan-Thompson polarizing prism deflects the ordinary beam at an angle to a beam trap and only transmits the extraordinary beam with a certain linear polarization. [98]It shows excellent extinction ratios (>10 −8 achievable), but typically has a small aperture due to manufacturing complexity and is disadvantageous for use in ultrafast timeresolved measurements with polarization control due to its thickness, inducing significant chirp.In contrast, a wire-grid polarizer mostly works by reflecting light with a certain linear polarization.It is thin, which makes it more desirable for use in ultrafast measurements but has a worse extinction ratio (>10 −5 ) and a smaller damage threshold than the Glan-Thompson polarizer.The wire-grid polarizer offers, however, typically a large aperture. [98]s the wire-grid polarizer reflects linearly polarized light, linear polarization artifacts can occur because of back-reflections from other components of the setup.In our experiments, we observed the most prominent back-reflections from a 1 cm path-length square cuvette in an orthogonal excitation geometry (Figure 5a).After passing through the PEM, the luminescence of the sample is partially reflected by the wire-grid polarizer, which introduces linear polarization.The reflected beam passes through the PEM on its way back and is reflected again by the sample towards the detector.In our tests, this back-reflection resulted in a significant 2f component which was proportional to the emission intensity of the sample.Back-reflections also occurred to a lesser extent at other components of the setup (like the PEM).They can be avoided effectively by slightly tilting the wire grid polarizer.
Alternatively, a Glan-Thompson polarizing prism can be used to suppress polarized back-reflections as it redirects the unwanted linear polarization downward to a beam trap instead of reflecting it back (Figure 5b).As the smaller aperture of the prism is limiting light throughput in our setup and thus leads to a weaker This linearly polarized back-reflected beam (dashed lines) can be reflected by the sample to the detector leading to linearly polarized components in emission that can distort the results.b) A Glan-Thompson polarizing prism does not cause linearly polarized back-reflections because the ordinary beam is deflected to a beam dump.
signal intensity at the detector, we typically use a wire-grid polarizer.In case linear polarization components are detected, we use a Glan-Thompson prism to exclude linear artifacts that occur via back-reflections.

Influence of Sample Anisotropy, Excitation Geometry, and Excitation Polarization
To avoid polarization artifacts, it is important to first consider the potential anisotropy of the sample and then choose the excitation scheme (i.e., the angle between excitation and detection beam paths, and the excitation polarization) accordingly, as different combinations of sample, geometry, and polarization vary in their susceptibility to causing artifacts. [64]In this section, we will discuss the most common excitation geometries (90°, 180°), excitation polarizations (unpolarized, linear, circular), and three types of samples: Type 1: Isotropic emitters, such as solutions of spherical emitters, Type 2: Samples with random distributions of molecules but restricted molecular rotation, for example, non-spherical emitters in viscous solutions, frozen solutions, amorphous films, emitters in KBr pellets, Type 3: Highly oriented samples, such as single crystals, liquid crystals, and crystalline films.
The most important concept for the discussion of sample types 1 and 2 is that of photoselection, that is, the preferential excitation of a subset of electronic dipoles (molecules) whose orientation matches the excitation polarization, which can give rise to linear polarization artifacts (fluorescence anisotropy). [64]This photoselection effect can occur for samples of type 2 where the reorientation of the excited molecules is slow compared to the luminescence lifetime (e.g., fluorescein in water) or completely restricted (as in frozen solutions). [64,99]Isotropically emitting samples (type 1), for example, spherical lanthanide complexes in solution, are typically not prone to photoselection. [27,64]n the literature, three excitation geometries are commonly discussed to reduce the effects of photoselection in CPL measurements for samples of type 2: [64,92,100] 1. 180°with unpolarized excitation, 2. 90°with linearly polarized excitation oriented parallel to the emission path, 3. 180°with circularly polarized excitation.
Unpolarized light-emitting diodes (LEDs) in a 180°geometry are safe choices to exclude photoselection artifacts but may introduce additional stray light signals from the excitation source for samples with small Stokes-shift (see Section 5.4). [70,101]Generally, one should still carefully check for a fraction of linear polarization from LED chips, which are typically not fully isotropic emission sources, using our above-stated approach.
While unpolarized excitation in a 90°geometry is useful when investigating isotropically emitting samples (type 1), this excitation scheme can cause photoselection artifacts for samples with anisotropic emission (type 2). [78]To measure these samples in the 90°geometry, linearly polarized excitation, for example, from a laser is recommended to exclude artifacts arising from emission anisotropy. [92]Specifically, the axis of linear polarization must be aligned parallel to the emission direction to ensure that the excited subpopulation of emitters is isotropic in the plane perpendicular to the emission direction. [6,77,89,102,103]However, care must be taken to avoid leakage of the linearly polarized laser light into the detection path via reflections or scatter, as discussed above.Another approach is the use of magic-angle settings for rigid systems, that is, a 54.75°excitation geometry with a linear polarizer for the excitation light at 35.25°. [104]However, as this excitation scheme is hardly used in literature, we cannot comment on its performance in suppressing linear polarization artifacts.
While rather rare in literature, in some experiments it might be useful to excite the sample with circularly polarized light.For circularly polarized excitation, again a 180°geometry is advisable to avoid photoselection in samples of type 2. [64] However, in this case, it is important to consider that excitation of racemic mixtures with circularly polarized light can yield CPL due to the differential absorption of the two enantiomers. [64]Moreover, for certain materials like halide perovskite semiconductors, strong spin-orbit coupling leads to optical selection rules conserving the total angular momentum, meaning that circularly polarized light of a certain handedness leads to the excitation of a specific total angular momentum state.This can result in CPL activity as a consequence of the excitation condition, even from nominally achiral materials. [105]cquiring reliable CPL spectra of highly oriented samples with large optical anisotropy (type 3) is very challenging, as these commonly give rise to strong linear polarization artifacts. [76]In contrast to samples of type 2, these artifacts can usually not be avoided by simply using a certain excitation scheme.One exception is single crystals, where optical anisotropy should vanish when their unique optical axis is aligned precisely along the emission direction. [106]For cases where this is not possible, the safest way of determining the "true" CPL of strongly anisotropic sam-ples is a rigorous Stokes-Müller matrix approach that takes the polarization response of all optics into account.Harada et al. reported such a spectrometer design that uses a 180°geometry with unpolarized or linearly polarized excitation light and excludes linear polarization artifacts from anisotropic samples via a Stokes-Müller matrix approach.Additionally, this setup allows for the measurement of CD spectra without rearrangements. [76]t may also be possible to avoid the effect of linear polarization artifacts by rotation of the PEM, orienting its birefringent axis parallel to the plane of linear polarization of the emission.As a side note, the polarization axis of the linear polarizer needs to be readjusted to 45°relative to the PEM.In our opinion, one should be cautious when applying this strategy, as we expect the linear polarization component (2f) at the detector to vanish in two cases: 1) When the birefringent axis of the PEM is properly aligned to the linear polarization axis, as described above, and 2) when the linear polarization component is filtered by the linear polarizer in the setup.We suspect that the CPL artifact arising from the static birefringence of the PEM persists in case 2. Additionally, birefringence in other parts of the setup can hamper this approach as described in the literature. [89,90]n summary, when dealing with isotropic samples such as solutions we recommend using an unpolarized excitation source in a 90°geometry for the accurate determination of g lum values in the first instance.Still, it is mandatory to check for photoselection that manifests itself as linear polarization artifacts.For these samples with anisotropic emission (type 2), a laser in a 90°excitation geometry with its polarization axis carefully oriented parallel to the emission direction is a feasible alternative.Reliable CPL spectra of samples with strong anisotropy such as single crystals, liquid crystals, or crystalline films (type 3) are notoriously difficult to obtain and usually require dedicated setups in combination with a thorough polarization analysis.

Artifacts in the DC Channel Affect g lum of CPL-Active Samples
To accurately determine g lum values, care must be taken to exclude any contamination of the measured average luminescence intensity (DC signal) by other sources of light or emission. [27]Examples include but are not limited to stray ambient light, emissive impurities in the sample, solvent Raman bands, the scattered and reflected excitation light, and its second (or higher-) order diffraction. [89]Ambient light can be excluded by shielding the beam paths/the full spectrometer setup or by using a chopper. [103]Excitation light reflections and scatter become especially problematic for thin cuvettes or films (desirable for ultrafast measurements) which typically need to be mounted at an angle to be employed in geometry with orthogonal excitation and emission beam paths.A suitable long-pass filter placed in front of the monochromator may help to alleviate the effect but may not fully suppress directly reflected excitation light.The reflection of excitation light can also introduce a dependence of the measured g lum on the slit width of the emission monochromator, as such a reflection may not be imaged homogenously on the slits (Figure 6).Recording the g lum value measured for different slit widths is a useful way to exclude this artifact.In general, wide slits lead to an artificial broadening of the recorded (CPL) emission bands.In materials with sharp emission bands or bisignate CPL response, such as lanthanides, this can lead to a loss of resolution and slit-dependent g lum values. [93]nother way to correct for reflections or scatter is the subtraction of a DC baseline spectrum using a solvent cuvette.However, this requires the sample and blank cuvette to be mounted in exactly the same position as well as have the same scattering properties, and drift in excitation intensity over time to be negligible, neither of which are realistic scenarios.Hence, we recommend avoiding mounting samples at an angle, if possible.If necessary, unwanted reflections of excitation light should be minimized with irises, or by deviating from a sample mounting angle of 45°, such that the specular reflection of the excitation beam does not enter the detection path.
Importantly, a wrong DC value only affects the luminescence dissymmetry of CPL-active samples.Samples that do not show CPL will still produce a flat g lum baseline.While optimizing a CPL spectrometer setup to yield a baseline for unpolarized sample emission is required to obtain reliable results (see Section 4), it is thus not sufficient for demonstrating the overall validity of a setup.

Artifacts due to Circular Dichroism of the Sample
Many CPL emitters reported in the literature are small chiral organic molecules that typically show a small Stokes shift between absorption and emission (Figure 7a). [35]Usually, these molecules also feature a strong CD (Equation ( 15)).In these cases, the detected CPL might be affected by a combination of reabsorption and CD, that is, differential reabsorption of the sample.The artifact CPL that arises from reabsorption has the opposite sign of the CD band causing it. [6,35]In small organic molecules, the dissymmetries in absorption and emission (g abs and g lum ) are positively correlated. [35]Hence, reabsorption might erroneously lead to attenuated CPL intensity or even bisignate CPL (Figure 7b).In samples that are not CPL-active, differential reabsorption can also give rise to CPL artifacts, that is, apparent CPL (Figure 7c).
In previous works, Equations ( 16) and ( 17) were derived to correct for CD reabsorption of CPL. [6,101]In these equations, DC corr and AC corr are the corrected DC and AC values, respectively, T is the transmission of the sample as obtained from absorption spectroscopy, ΔA is the CD (Equation ( 15)) and  is a geometrical factor that depends on the different optical path lengths in the CD and CPL experiment (the original study used  = 2.5). [6,101](17)   To rule out this artifact, we recommend measuring g lum for a concentration series of samples in solution or to change the focal point of the excitation in the cuvette to increase or decrease the path length that the emitted light has to travel through it, thus varying the degree of potential reabsorption.For solid-state samples, such as thin films or single crystals, ideally, a thickness series should be measured to rule out artificial CPL originating from CD and reabsorption.Moreover, recording g lum values as a function of the rotation of the sample or crystal (at least by performing a second measurement where the sample is rotated by 90°, Figure S8, Supporting Information) is recommended to check for linear dichroism artifacts due to sample anisotropy.For a more in-depth discussion on linear dichroism and linear birefringence, the reader is referred to ref. [4].In general, opposite signs of the lowest energy CD and the highest energy CPL warrants further checks. [6,35]he CD effect of a sample can also introduce CPL artifacts via photoexcitation.Linearly polarized and unpolarized light can be described as coherent and incoherent superpositions of RCP and LCP with equal magnitudes, respectively. [100]Hence, the preferential absorption of one-handedness of circularly polarized light by a sample with significant CD results in partially circularly (elliptically) polarized excitation at the beam focus (Figure 7d).In halide perovskites and other semiconductors, circularly polarized excitation can lead to CPL (see Section 5.3). [105]The field of halide perovskites is moving particularly fast and high dissymmetries of chiral perovskite materials reported recently. [57]Since these materials are also prone to causing CPL artifacts via linearly polarized emission, extra care must be taken with CPL spectroscopy, for example, by using unpolarized excitation and testing for CD reabsorption as described above.

Conclusion
Circularly polarized luminescence has long since left the niche of method development and fundamental photophysics.Today, this phenomenon is the basis of promising spin-optoelectronic applications, ranging from energy-efficient displays to drug discrimination and quantum information technologies.Consequently, an increasing number of groups are entering the field, many of which are assembling their own spectroscopic setups or using commercial ones.In this work, we outlined the working principles of several CPL detection designs and discussed their respective advantages and disadvantages, providing a complete picture with a theoretical background and data We also provided the source code for our custom software enabling the reader to build and run a highly sensitive PEM-based CPL setup.Finally, we highlighted potential pitfalls to avoid, and best practices to consider for the accurate measurement and reporting of CPL, especially with respect to increasingly relevant thin film technologies, like those based on chiral molecules, polymers, or halide perovskites.With highly efficient CPL emitters on the rise, we hope that this work will support the reader and consequently some exciting future developments in this field.

Figure 1 .
Figure 1.Overview of different experimental setups for CPL detection.The conversion of LCP (blue curly arrow) and RCP (red curly arrow) emission into linear polarization (straight arrows) is shown schematically for the respective beam paths upon photoexcitation (Exc.) of the sample.a) CPL is converted to linearly polarized light using a quarter-wave plate (/4), with LCP and RCP resulting in orthogonal polarizations, and then filtered with a linear polarizer (LP).To measure the opposite handedness of CPL, the

Figure 2 .
Figure 2. Modulation of the detector signal by a PEM in different detection schemes.a) Square-wave reference signal of the PEM.b) Ideal modulation (dotted line) and actual, phase-shifted modulation (solid line) of the wave retardance caused by the PEM on the light passing through.c,d) Modulated intensity signal of CPL at the detector with important quantities for differential photon counting (c) and for a lock-in detection scheme (d) (see Equations (4)-(6)).Modulation frequency f = 42 kHz.

Figure 4 .
Figure 4.The non-sinusoidal modulation by the PEM results in an overestimation of CPL if left uncorrected.Normalized CPL intensity as modulated by a PEM (black solid trace, using Equation(7) with A = /2, and f = 42 kHz).The 1f (red dashed trace) and 3f components (blue dotted trace) of the Jacobi-Anger expansion (Equation (9)) of the PEM modulation are shown.The amplitude of the 1f sine wave, R AC , is ≈13% higher than that of the original modulation, which needs to be corrected to accurately determine CPL magnitude and g lum .

Figure 5 .
Figure 5. Paths of beams reflected by different polarizers in a CPL setup.a) A wire grid polarizer reflects light that matches its polarization axis.This linearly polarized back-reflected beam (dashed lines) can be reflected by the sample to the detector leading to linearly polarized components in emission that can distort the results.b) A Glan-Thompson polarizing prism does not cause linearly polarized back-reflections because the ordinary beam is deflected to a beam dump.

Figure 6 .
Figure 6.Reflection of excitation light can induce slit-dependent artifacts.Samples that are mounted at an angle can lead to the reflection of excitation light into the detector.This can lead to artifacts in the average luminescence intensity (DC signal) that affect the g lum values of CPL-active samples.The emitted light (red) and the reflected excitation light (blue) are not necessarily focused on the same spot at the slit of the detector (inset).In this case, the slit width can change the relative intensity of luminescence and artifacts, and therefore the impact of the artifacts on g lum .

Figure 7 .
Figure 7. CPL artifacts introduced by strong CD for samples with small Stokes shifts.a) Schematic spectra of absorbance A and emission intensity I of a sample with a small Stokes shift.b) Schematic CD (blue), apparent CPL (red), and real CPL spectra (dotted line), where CD and CPL bands overlap.The CPL intensity appears attenuated, or its sign can be reversed by differential reabsorption due to the sample's CD.In the strongest case, this results in artificial bisignate CPL.c) Preferential reabsorption of circularly polarized light with a certain handedness can also introduce CPL artifacts in non-CPL active samples that should otherwise give a CPL baseline at 0 (dotted line).d) Top-view on a sample cuvette (orange) with positive CD and CPL which is excited with linearly polarized or unpolarized light (blue cone).The arrows show the circular polarization components of the light at different positions to visualize the effect of preferential absorption of a certain handedness of circularly polarized light in excitation and emission.
ΔA = A L − A R (