Force-Detected Nanoscale Absorption Spectroscopy in Water at Room Temperatureusing an Optical Trap

Alexander Parobek,1 Jacob W. Black,1 Maria Kamenetska,2, 1 and Ziad Ganim1, ∗

1Department of Chemistry, Yale University, 350 Edwards St., New Haven, Connecticut 06520, United States2Boston University, Department of Chemistry, Department of Physics, Boston, MA 02215, United States

(Dated: February 23, 2018)

Measuring absorption spectra of single molecules presents a fundamental challenge for standardtransmission-based instruments because of the inherently low signal relative to the large backgroundof the excitation source. Here we demonstrate a new approach for performing absorption spec-troscopy in solution using a force measurement to read out optical excitation at the nanoscale. Thephotoinduced force between model chromophores and an optically trapped gold nanoshell has beenmeasured in water at room temperature. This photoinduced force is characterized as a function ofwavelength to yield the force spectrum, which is shown to be correlated to the absorption spectrumfor four model systems. The instrument constructed for these measurements combines an opticaltweezer with frequency domain absorption spectroscopy over the 400-800nm range. These mea-surements provide proof-of-principle experiments for force-detected nanoscale spectroscopies thatoperate under ambient chemical conditions.

INTRODUCTION

The ability to study a chemical reaction by simplywatching the change in the absorption spectrum of a sin-gle molecule may become possible with several recent ad-vances in single-molecule detection and spectroscopy[1–6]. Here, we report an instrument developed to measurephotoinduced forces between a surface-immobilized sam-ple and an optically trapped probe over the 400-800 nmrange. These force spectra are measured for CdSe/ZnSnanocrystals and organic dye model chromophores in wa-ter at room temperature (Figure 1A). The force spectraare comparable to linear absorption spectra obtained us-ing other methods. It is found that optically trapped goldnanoshells can serve as a near-field force probe, whichresponds to the photoexcited molecules by a mechanicaldisplacement that enables the readout of absorption. Themeasurement volume is estimated to contain ∼ 102 quan-tum dots. This proof-of-concept measurement sets upa new paradigm for performing absorption spectroscopyin solution and paves the way towards realizing singlemolecule absorption spectroscopy.

By which mechanism does a photoexcited moleculeexert a force on a gold nanoshell? Analogous force-encoded spectroscopies detected by atomic force mi-croscopy (AFM) have been explained using electro-static, dipole-induced dipole coupling or photother-mal expansion[7–9]. AFM-based infrared spectroscopy(AFM-IR) is a nanoscale spectroscopy that uses the AFMprobe to detect the thermal photoexpansion in a sam-ple resulting from infrared absorption.[3, 10–12] Photoin-duced force microscopy (PiFM) has demonstrated singlemolecule sensitivity in absorption, Raman, and pump-probe spectroscopies, and derives contrast not from mea-suring photoexpansion, but rather from the photoin-duced electromagnetic forces exerted onto the metal-coated cantilever.[5, 13, 14] Due to the radically different

thermal transport and electrostatic screening propertiesin solution, force-detected spectroscopies in solution mayderive contrast from other mechanisms.

Optical tweezers (OT) provide a compelling force-detection technique for force-detected absorption spec-troscopy in water at room temperature. The high Q fac-tor of AFM cantilevers in air is critical to the success ofAFM-IR,[3, 11, 12] PiFM,[5, 13, 14] and MRFM[15, 16]spectroscopies. As an order of magnitude estimate foran electrostatic dipole-induced dipole contrast mecha-nism, the force exerted between a dipole of µ = 1D andits image in a conductor separated by 1nm will be onthe order of ∼ µ2/4πε0r

4 = 0.1pN . In this regime,direct comparisons have found OT to be more sensi-tive than AFM[17, 18]. The sensitivity of AFM hasbeen estimated to be 200fN [9], whereas fN -scale forceshave been measured with OT to characterize the elec-trostatic potential between colloids[19, 20], the Casimirforce[21], and forces due to direct light scattering[22, 23].In our method, the exquisite force sensitivity of OT isexploited to measure molecular absorption spectra atthe nanoscale. The experiments presented here pro-vide proof of principle for a new method that adds to agrowing body of nanoscale non-fluorescence-based spec-troscopies, including surface-enhanced and tip-enhancedRaman[1, 4, 24], SEIRA[25], IR s-SNOM[26, 27], singleparticle spatial modulation spectroscopy[28], and pho-tothermal absorption spectroscopies[2, 6].

EXPERIMENTAL DESIGN

For force-detected spectroscopy, the signal arises fromdisplacement of a microscopic probe, which is here moni-tored using laser interferometry. Relative to low-light de-tection schemes, the optical dark noise and detector back-ground noise are negligible.[29] To optimize the sensitiv-

2

FIG. 1. A. Experiment schematic. An optically trapped gold nanoshell microsphere detects the wavelength-dependent pho-toinduced force change from chromophores adsorbed to a coverslip surface. B. Instrument schematic. L=lens, PBS=polarizingbeamsplitter cube, OC=output coupler, AOD=acousto-optic deflector, BB=beam block, G=grating, CHOP=chopper,BS=50/50 beamsplitter, DM=dichroic mirror, P=prism, Obj=objective, Cond=f=16mm NA=0.79, S=sample chamber,F=filter, QPD=quadrant photodiode

ity of a mechanical-oscillator probe to external forces,we will show that it is desirable to minimize the forceconstant or stiffness, κ. Photoexcitation of the sampleultimately exerts a force on the probe ∆F , which givesrise to an observable deflection, ∆x = ∆F/κ. Therefore,the signal increases as the stiffness is reduced; however,reduced stiffness also increases the noise. In solution,the noise is dominated by the thermal fluctuations of theparticle, which is described by the equipartition relation,12κ⟨x2⟩

= 12kBT. Therefore, the signal to noise ratio can

be estimated as:

S/N =∆x√〈x2〉

=∆Fκ√kBTκ

=∆F√kBTκ

. (1)

Equation 1 indicates that the signal to noise scales asκ−0.5, where κ = 5 − 10fN/nm in our work. To mea-sure the photoinduced force difference, the excitationlaser pulse train is modulated at frequency fmod and theforce difference between on and off periods is averagedto generate the force spectrum, ∆F (λ) =

⟨FOnY (t;λ)

⟩−⟨

FOffY (t)⟩

. To provide requisite contrast, fmod must be

slow enough to allow the probe to respond. The me-chanical relaxation time of the probe is characterized bythe corner frequency, fC , where the modulated laser ap-pears continuous for fC � fmod.[30] In our measure-ments, fC ≈ 100Hz and fmod = 3Hz, which allows theprobe to adequately sample an equilibrium distributionduring the laser-on and laser-off periods.

METHODS

The instrument for measuring optically induced forcesis shown in Figure 1B. A focused 1064 nm CW Yb fiberlaser (IPG Photonics) forms the optical trap. The free-space output passes through a λ/2 waveplate and po-larizing beamsplitter for intensity control followed by anacousto-optic deflector, which can be used to steer theoptical trap but was not utilized in these measurements.The beam is expanded by a telescope (L2:L1=6.7) tooverfill the back aperture of the objective before beingcoupled into the microscope body. The objective (Plan-APO 40x/1.4 Oil, Carl Zeiss) and sample holder (Nano-LP300 and MicroStage, Mad City Labs) are mounted ina modified stand (Axio Observer A1, Carl Zeiss). Thishigh NA objective has 65% transmission at 1064 nm andoutstanding apochromatic color correction from the UVto the IR. A condenser lens collects the transmitted and

scattered 1064 nm light for interferometric back-focal-plane detection[31, 32] on a quadrant photodiode (QPD,QP154-Q-HVSD, First Sensor). Data are acquired, low-pass filtered to 25 kHz, and saved to hard disk using afield-programmable gate array (National Instruments).

Brightfield Kohler illumination is provided by an 850nm LED, which is aligned to counter-propagate alongthe 1064 nm beam path by using a beamsplitter (DM2,ZT1064rdc-sp, Chroma Technology). This beamsplitteralso rejects visible excitation light from the QPD, whichis further suppressed by means of a notch filter (F1,FL1064-10, ThorLabs).

The excitation light is generated by a supercontinuumsource (WhiteLase SC400-4, Fianium) operating at 40MHz. The output passes through a home-made grat-ing monochromator producing ∼1mW across the 400-800 nm region (excitation spectra are shown in Fig.4).This approach was found to be superior to the use of ahigh-speed acousto-optic tunable filter for wavelength se-lection, and maintained the high mode quality from thefiber output[33]. The 40 MHz excitation pulse train ischopped mechanically to allow differential force detec-tion. The excitation light underfills the back aperture ofthe objective and is overlapped spatially with the opticaltrap, but focused to 10µm diameter to minimize genera-tion of additional optical gradient forces. The excitationlaser is linearly polarized ( ~E ∝ y, as defined in Fig. 1A).

The optical excitation is combined with the 1064 nmtrapping laser using a dichroic mirror (DM1, ZT1064rdc-sp, Chroma Technology) housed in the filter-cube assem-bly of the microscope stand. Epifluorescence, backscat-tered excitation light, and the brightfield illuminationare split off from the excitation path using a broadband50/50 beamsplitter (BS) and imaged onto a CMOS cam-era. Removable filters allow for visualization of the scat-tered 1064nm trapping laser, scattered visible excitation,fluorescence, or the brightfield image (F2, NF1064-44,Thorlabs; and/or ET570lp, T565lpxr, Chroma Technol-ogy). A description of the sample chamber constructionand functionalization with semiconductor nanocrystalsor organic dye appears in the supplementary text of theEPAPS.

3

FIG. 2. A. Calibration showing that the stiffness in the y-direction, κ, as a function of power is linear in the regimeof interest. B. Plot showing the power spectra that were fitto extract the stiffness and sensitivity. The latter graph isannotated with the excitation modulation frequency, fmod,which is chosen to be much lower than the corner frequency,fC . The spike at 25 Hz arises from the oscillatory drivingforce necessary for calibration.

RESULTS

Calibration

Figure 2 shows the results of calibrations performed toconvert the QPD outputs into physical displacements ofthe probe and the attendant forces. Following the proce-dure outlined by Tolic-Nørrelykke et al.[34], a nanoshellbead was trapped d = 5µm away from the coverslip sur-face, with the nanostage being driven by a sine wave(amplitude=180 nm and fdrive=25 Hz). The QPD out-puts, designated as S1, S2, S3, and S4, were acquired at25 kHz and digitized in the following combinations:

SX = [(S1 + S2)− (S3 + S4)] /S0 (2)

SY = [(S1 + S3)− (S2 + S4)] /S0 (3)

S0 = S1 + S2 + S3 + S4 (4)

These hybrid signals were Fourier transformed to obtaincorresponding power spectral densities, as exemplifiedby:

PSY (f) =2

T

⟨∣∣∣∣∫ ∞−∞

dtei2πftSY (t)

∣∣∣∣2⟩T

, (5)

where T is the measurement time.[34] Typically tencalibrations that were acquired over 10s durations wereaveraged. The power spectral densities were fit to aLorentzian spectrum to obtain the trap stiffness (κ infN/nm) and the response at the driving frequency wasfit to obtain the sensitivity (β in nm/V ). Figure 2Ashows the power dependence of the trap stiffness. Lin-earity over this power regime demonstrates that opticallytrapping the gold nanoshells does not cause significantheating.[35] We choose a relatively weak trap that main-tains stable optical trapping to maximize the signal tonoise (Eq. 1). Figure 2B shows selected PSY (f) profilesat specific incident powers to demonstrate how the cornerfrequency scales with laser intensity. These calibrationswere used for all trapping distances, without correctionfor the altered diffusion near the coverslip surface, andresult in a (15% error) in the reported forces.

FIG. 3. A. Time-resolved displacement of the probe during ameasurement at the peak in a force spectrum. The raw data,SY , is shown converted to displacement and force (left andright axes, respectively) using the trap stiffness, κ in fN/nm,and sensitivity, β in nm/V . The chopper signal is overlaidin red. No clear variation is visible during on/off periods.Panel B presents a histogram of SY during excitation on/offperiods, which reveals a slight shift in the probe position dueto excitation of the sample on resonance.

Light-Induced Forces

A gold nanoshell bead is translated into the opticaltrap by moving the microstage, after which it is broughtinto contact with the bottom coverslip surface coatedwith sample, the excitation light is turned on, and thesignal is collected for 30 seconds per wavelength. Thedisplacement of the probe from the center of the trap,y(t), is obtained from the QPD output using the sensi-tivity, β, y(t;λ) = βSY (t;λ). The force on the probe isobtained from the displacement using the trap stiffness,κ, FY (t;λ) = κy(t;λ) = βκSY (t;λ).

Figure 3A shows the QPD output, calibrated to indi-cate the displacement, y(t;λ), and the force, FY (t;λ), forfive seconds of data acquisition overlaid with the chop-per output signal. No displacement of the probe is vis-ible by simple inspection of the excitation on/off peri-ods, but a histogram analysis reveals a 13 nm shift inthe average position of the probe particle (Figure 3B).The wavelength is stepped in 5 nm or 10 nm incre-ments from 400-700 nm with 30s of data acquisitionper point to acquire a set of FY (t;λ) profiles. Theforce trajectories are converted to force spectra, ∆F (λ),by averaging the difference between on and off periods,

∆F (λ) =⟨FOnY (t;λ)

⟩−⟨FOffY (t)

⟩.

Spectroscopy

To assemble a force spectrum, the analysis presentedin the previous section is repeated for each wavelength.The data shown in Fig. 3 corresponds to the 510 nm datapoint of Qdot525 (c.f., gray dashed circle in Fig. 4A).Figure 4A-E shows how the force spectra change for dif-ferent samples and as the probe is moved away fromthe surface. Three sizes of semiconductor nanocrystalswere chosen to study the correlation between the absorp-tion spectrum and the force spectrum; an organic dye,Alexa555, was studied to test if the signal arises froma nanocrystal-specific effect. Distance-dependent spec-tra are acquired by translating the cover slip towardsthe optically trapped probe in ∆d = 50nm or 100nmincrements with d = 0 defined as the point of surface-to-surface contact. At the current level of data anal-ysis, finer spatial resolution is not justified; while the

4

FIG. 4. Force spectra acquired at different distances between the probe and the coverslip surface for (A) Qdot525, (B) Qdot565,(C) Qdot585, (D) Alexa555, and (E) a blank slide. The scaled sample absorption and the excitation spectrum are shown forcomparison. No features are observed in the absence of a sample or when the probe is retracted by 50 nm. (F) A diagramdrawn to scale indicates the probability distribution for where the surface of the probe particle may be as it undergoes restricteddiffusion within the optical trap. The solid black circle shows the bead surface when it is centered in the trap. The dashedlines indicate the surface of the probe particle according to the probability distribution shown in Figure 3B, and are drawn in1σ increments (σx = σy ≈ 85nm, σz ≈ 150nm).

center of the optical trap can be controlled accurately,the probe particle undergoes restricted diffusion withinthe optical trapping potential. This causes the probeto sample a distribution of positions with respect to thesurface (illustrated in Figure 4F) and the spectra shownin Figure 4A-E represent an averaged force exerted onthe particle when the trap is at the distance specified.Finer spatial resolution may be extracted at the expenseof signal to noise by further analysis of data such as thatshown in Figure 3A in post-processing.

The force spectra in Figure 4A-D appear to probe thesame energy levels observed in the conventional absorp-tion spectra. For each sample, a peak is seen only at theclosest approach (gray arrows) and moving the centerof the trap 50nm away from the surface greatly dimin-ishes the signal. No signal is seen in the control exper-iment with an uncoated glass slide (Fig. 4E). This con-trol demonstrates that direct scattering of the excitationlight off the probe particle and heating of the probe par-ticle may contribute to noise but do not yield peaks inthe force spectra. Despite the fact that all of the modelsystems are bright fluorophores, the observed peaks cor-relate with the bulk absorption spectrum rather than theStokes-shifted fluorescence. However, it is evident thatthe bulk absorption spectra are not faithfully reproducedin the nanoscale force spectra. The major differences inthe nanoscale force spectra are that the bands appearnarrower and some transitions are absent relative to thebulk absorption. While the signal to noise precludes line-shape analysis, narrowed bands have been observed inhole-burning[36] and single particle photon-correlationspectroscopies[37] of CdSe clusters, and ascribed to in-complete ensemble averaging. For the nanocrystal sam-ples, transitions that are higher in energy than the lowestexciton (1S ← 2S1/2) are absent. This may arise if theforce spectra are sensitive to the lifetime of the popu-lated state; it has been observed that electronic relax-ation into the lowest energy exciton occurs on a rapid,30 fs timescale.[38] The presence of signal for Alexa555demonstrates that the signal does not arise from a featurespecific to the nanocrystals, such as static charging.

At this point, it is not clear what is the most rele-vant bulk measurement for comparison. The data shownin Figure 4 do not allow for the photoinduced forces tobe decomposed into contributions from electostatic, pho-tothermal, and plasmonic contributions. We have cho-sen to present minimally processed data, ∆F (λ), rather

than normalizing for the excitation source, ∆F (λ)I(λ) . There-

fore, the bulk comparisons shown in Figure 4A-D arethe molar absorptivity scaled by the excitation spectrum,I (λ) ε (λ). Further understanding of the underlying sig-nal generation mechanism will allow for a better choiceof a bulk comparison, as well as suppressing sources ofnoise and background. The baseline in the force spectramay be influenced by mechanical vibrations of the sam-ple chamber relative to the position of the optical trap,which peak when the probe is in contact with the sam-ple chamber at d = 0nm. Currently, it is believed thatthe non-uniformity of the gold coating on the nanoshellparticles is a major contributor to the noise (see Supple-mentary Figures in EPAPS).

DISCUSSION AND CONCLUSIONS

In this work, we have presented the first evidence thatoptically trapped gold nanoshells may be used to measurea fN -scale photoinduced force that reports on the ab-sorption spectrum of chromophores located in the near-field of the probe in water at room temperature. How-ever, the experiments herein raise many questions aboutthe underlying physical mechanism. The photoinducedforces characterized by PiFM are on the 10pN scale,[8]which is two orders of magnitude larger than the effectobserved here. Thermal and electrostatic contributionshave been considered as contrast mechanisms for AFMphotoinduced microscopies,[9, 13] and the same controlsmay be used to study the mechanism of optical tweezersforce-detected spectroscopy. Electrostatic contributionshave been shown to result in dispersive line shapes sen-sitive to the real component of the first-order responseand to show a steep, d−4 distance dependence.[5, 8, 13]By varying the thermal conductivity and heat capac-ities of the solvent, one may quantify the magnitudeof a photothermal contrast.[39] Solvent-dependent forcespectra may be measured using the recently developedtechnology to stably trap core/shell microspheres in or-ganic solvents.[40] A study on the effects of metal-coatingthickness will reveal the importance of electrostatic con-tributions to force-detected spectra and the possible roleof a plasmon enhancement to the excitation.

The mechanistic studies listed above will also be crit-ical to understanding the information content of forcespectra for its application to molecular spectroscopy. The

5

finite excitation bandwidth and potentially the spectrumof the nanoshell plasmon resonance must be factored outin order to observe intrinsic molecular properties. Forthe gold nanoshell beads used here, the model of Averittet al. predicts that the plasmon resonance peaks near4500nm[41], and, thus, is not expected to play a signifi-cant role. However, TEM images of the nanoshell parti-cles demonstrate that the gold coating is neither uniformnor contiguous, and thus the plasmon resonance mayvary on a particle-to-particle basis (see EPAPS, FigureS5-S6). Additional signal weighting may be caused by thelifetime of the electronic state populated, as suggested bythe absence of spectral features from higher-energy exci-tons in the quantum dots. Expanding the samples mea-sured to include excited states of different symmetries,extinction coefficients, fluorescence quantum yields, andrelaxation times will allow for a better understanding ofhow force spectra encode molar absorptivity.

The signal to noise ratio of the data presented heremay be improved by utilizing advances in optical trap-ping technology. Optical sources of noise may includelocalized heating of the gold nanoshell beads induced bythe excitation and scattering. The latter is a trivial pho-toinduced force signal caused by direct scattering of theexcitation off the probe always accompanies the excita-tion and is oriented in the +z direction. As the forcespectrum is detected in an orthogonal direction (y), thisbackground may couple if the optical trapping laser andexcitation laser are not perfectly collinear and parallel tothe surface normal vector. The Mie scattering that de-scribes optical scattering and gradient forces is known tohave a complicated wavelength dependence.[42]

As the ultimate goal of signal to noise improvements isto reach single molecule sensitivity, it is worth estimat-ing the number of molecules in the observation volume.As a conservative estimate, if the microscope coverslipwas covered in a monolayer of nanocrystals (15nm di-ameter/particle after passivation and coating.[43]) andthe probe particle is in contact with the surface, then 40qdots will be within 3 nm of the probe particle. For alonger range force, (i.e., 10 nm range), then 140 qdotswill be within proximity of the probe particle. The dis-tance dependence of the force responsible for generatingcontrast is a key parameter in determining the currentsensitivity and how much of an improvement is necessaryto reach the single molecule limit. While the particle dis-placements measured here are on the order of 10 nm, dis-placements as small as 0.1nm may be measured with dif-ferential back-focal-plane detection[44] while maintainingstability over the course of hours[45]. The advantages ofthis sensitive detection technology, coupled with its ap-plicability to measure nanoscale force spectra in water atroom temperature, make it a compelling path forwardtowards broadly applicable single molecule absorptionspectroscopy.

This material is based upon work supported by the Na-

tional Science Foundation Graduate Research Fellowshipunder Grant No. DGE1122492 to J.W.B. A.P. acknowl-edges support from an NIH Biophysical Training Grant#T32GM008283. We would also like to acknowledge theanonymous reviewer who suggested the Alexa555 exper-iments.

∗ To whom correspondence should be addressed:ziad.ganim@yale.edu

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Steering Optical Trap Microscope

Fluorescence/

Brightfield

Imaging

Ultraviolet/Visible

Excitation

Optical Trap

DetectionBrightfield

Illumination

CMOS

Obj

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QPD

PBS

AOD

λ/2 DM2

BS

Cond

LEDDM1

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L1 L2

L8

L9

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L10L5

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L3

BB

OC

F1

F2

Yb Laser

1064nm, 5W CW

Supercontinuum Laser

400-2400nm

0.1-40 MHz, 4W

400-800 nm1064 nm

Fluorescence850 nm

1064nm,

15 mW CW

400-800 nm,

~1 mW,

15 nm FWHM,

40 MHz + 3 Hz

modulation

OCG

L6

L7CHOP

OpticalTrap

SiO2@Au

tunableexcitation

Surface-boundChromophores

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Beam Paths

0 20 40 60 80 100

Power (mW)

0

20

40

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en

sity (

nm

2/H

z)

Frequency (Hz)

A

B fmod fC

0

-600

-400

-200

200

400

600

Dis

pla

ce

me

nt

(nm

)

0

4

3

2

1

-1

-2

-3

-4

Fo

rce

(pN

)

0 1 2 3 4 5

Time (s)

ChopperSY(t; λ=510nm)

SY (On)

SY (Off)

ΔSY

x3

600-600 0

Displacement (nm)

Force (pN)420-2-4

Re

lati

ve

Fre

qu

en

cy

0

1

0.5

A B

400 450 500 550 600 650 700

Excitation Wavelength (nm)

0

100

200

300

400

d = 0 nm

50 nm

100 nm

150 nm

Excitation I(λ)Qdot525 I(λ)∗ε(λ)

Fo

rce

(fN

)

Po

we

r (mW

)0

1

2

Sc

ale

d

Ab

so

rpti

on

(A

U)

0

1

A

400 450 500 550 600 650 700

Excitation Wavelength (nm)

0

100

200

300

400

500

d = 0 nm

50 nm

100 nm

150 nm

200 nm

Excitation I(λ)Qdot565 I(λ)∗ε(λ)

Fo

rce

(fN

)

Po

we

r (mW

)0

1

2

Sc

ale

d

Ab

so

rpti

on

(A

U)

0

1

B

400 450 500 550 600 650 700

Excitation Wavelength (nm)

0

100

200

300

400

500

d = 0 nm

50 nm

100 nm

150 nm

200 nm

Excitation I(λ)

Fo

rce

(fN

)

Po

we

r (mW

)0

1

2

C

Sc

ale

d

Ab

so

rpti

on

(A

U)

Qdot585 I(λ)∗ε(λ)

400 450 500 550 600 650 700

Excitation Wavelength (nm)

0

100

200

300

400

500

d = 0 nm

50 nm

100 nm

150 nm

200 nm

Excitation I(λ)(No Sample Control)

X

Fo

rce

(fN

)

Po

we

r (mW

)0

1

2

E F

400 450 500 550 600 650 700

Excitation Wavelength (nm)

0

150

300

450

d = 0 nm

100 nm

200 nm

300 nm

Excitation I(λ)Alexa555 I(λ)∗ε(λ)

Fo

rce

(fN

)

Po

we

r (mW

)0

1

2

Sc

ale

d

Ab

so

rpti

on

(A

U)

0

1

D

d