Page 1 of 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Analytical Chemistry
Multi-Reflection Sum Frequency Generation Vibrational Spectroscopy Chi Zhang⊥†*, Joshua Jasensky§ and Zhan Chen⊥* Departments of ⊥Chemistry and §Biophysics, University of Michigan, 930 N. University Ave., Ann Arbor, MI, 48109, USA ABSTRACT: We developed a multi-reflection data collection method in order to improve the signal-to-noise ratio (SNR) and sensitivity of SFG spectroscopy, which we refer to multi-reflection SFG, or MRSFG for short. To achieve MRSFG, a collinear laser beam propagation geometry was adopted and trapezoidal Dove prisms were used as sample substrates. An in-depth discussion on the signal and SNR in MRSFG was performed. We showed experimentally, with “m” total-internal reflections in a Dove prism, MRSFG signal is ~m times that of conventional SFG; SNR of the SFG signal-to-background is improved by a factor of >m1/2 and 2500 cm-1, which is used when performing MRSFG in the C-H frequency range (2800-3100 cm-1). The double-side-polished silicon wafer has a transmission of ~50% for the mid-IR beam >1500 cm-1, which allows the collection of MRSFG signal in lower frequency range. In this work, SFG signals from the C=O vibration in poly(ethylene terephthalate) (PET) were collected using the double-side-polished silicon wafer. All other SFG data were obtained using the dichroic mirror. Pulse energy of the IR beam was measured to be ~100 µJ at 2800-3000 cm-1 and ~30 µJ at 1700-1800 cm-1. The visible beam was ~30 µJ in all experiments. Enhanced SFG signal is generated when the IR photon-energy matches the vibrational resonance of a particular mode. An SFG spectrum was produced by tuning the IR wavelength through a continuous range at 5 cm-1/step, and each data point was integrated ~2.5 s. The PMT for signal collection was gated and only opened when the signal pulse arrived. The gate for PMT signal acquisition was set to 100 ns. The system was operated under room light. Dove prisms made of CaF2 were customized and purchased from Chengdu Yasi Optoelectronics, China. The Dove prisms have a similar shape/geometry to the ATR crystals used in ATR-FTIR spectroscopy with a trapezoid cross-section as shown in Figure 1b. The base angle of the trapezoid is 45º. The prisms are ~18 mm long with various thicknesses (e.g., ~1.5 mm, ~2 mm, and ~3 mm), resulting in different numbers of reflections in the prisms. The Dove prisms were cleaned using ethanol (>99%) and detergent water solution (Contrex AP, Decon Laboratories), rinsed using deionized water, and further cleaned in an air plasma etching cleaner (PE-50, Plasma Etch Inc.) before use. A schematic of our MRSFG experimental geometry is shown in Figure 1a. In this system, the polarizations of the input and output beams can be controlled using half-wave plates and polarization beam splitters. SFG signal was collected in ssp (s-polarized signal beam, spolarized visible beam, p-polarized IR beam) or ppp polarization combinations. For comparison, a right angle CaF2 prism was used for a single-reflection geometry as in conventional SFG spectroscopy (Figure 1b).
Figure 1. (a) Schematic of MRSFG experimental setup. PBS: polarization beam splitter, HWP: half-wave plate, DC: dichroic mirror. The EKSPLA SFG laser system is not shown in the figure. (b) Examples of CaF2 prisms used in the experiment having 1, 5, or 9 reflections. Poly(methyl methacrylate) (PMMA) was purchased from Sigma Aldrich (Mw≈ 50 000), and was dissolved in toluene to form a 1.0 wt% solution for sample preparation. The PMMA solution was spin casted on the CaF2 prisms for SFG experi-
Page 2 of 8
ment. Poly(ethylene terephthalate) (PET) was purchased from Scientific Polymer Products Inc. (Mw≈ 30 000) and was dissolved in 2-chlorophenol to form a 1.0 wt% solution. Then the solution was spin coated on the CaF2 prisms. Ethanol (99.9 %, HPLC grade) was purchased from Sigma Aldrich. Ethanol was dropped on one side of the Dove prisms and dried using nitrogen gas. Then the Dove prisms were used for SFG study. Dipalmitoylphosphatidylcholine (DPPC) and deuterated (d-62) DPPC (DPPC-d) lipid samples were obtained from Avanti Polar Lipids. DPPC and DPPC-d were mixed at a 1:10 ratio and dissolved in chloroform at ~5.0 mg/mL for monolayer preparation. The lipid monolayers on prisms were constructed using Langmuir-Blodgett method.24,36 The monolayer on water was constructed using a commercial Langmuir trough (KSV2000 LB system, KSV NIMA) with a surface tension of ~34 mN/m and was transferred to the prisms. The procedures of lipid monolayer deposition are detailed in the Supporting Information I. Ultrapure water (18.2 MΩ·cm) was obtained from a Millipore Simplicity water purification system and was used for the lipid monolayer preparation. 3. Signal of MRSFG For the conventional single-reflection SFG, the signal intensity ISFG is proportional to the input laser intensities IIR, IVis, and the square of the second order nonlinear optical susceptibility χ eff( 2) of the material under study: 2
I SFG ∝ χ eff(2) I IR IVis
(1)
( 2 ) can be experimentally measured and fit using a where χ eff sum of Lorentzian functions:3
2 ( 2) ( 2) χ eff( 2 ) = χ NR + χ R( ) = χ NR +∑ q
Aq
(2)
ω − ω q + iΓ q
( 2) is a term given to the nonresonant contributions from χ NR the material. For a vibrational transition q, Aq is the amplitude of the SFG resonant term, ωq is the center frequency of the SFG vibrational transition, Γq is the damping factor of the transition, ω is the output signal frequency. In MRSFG, signals from multiple reflection spots are generated in series. Here we first assume that the number density of the molecules giving the SFG signal is the same throughout all the reflection spots, and there are totally “m” reflection spots contributing SFG signal. We also assume that the sizes of beam spots are the same for all reflections, and ignore such factors as laser beam dispersion caused by the substrate, phase shifts caused by TIR and dispersion, laser beam attenuation by the sample, and the spatial and temporal “walk-off” of the laser beams. In this ideal condition, the overall MRSFG signal intensity is enhanced by the constructive interference from multiple reflection spots and gives:37
I SFG , m = m 2 I SFG
(3)
Eq 3 indicates that in a theoretically ideal condition, the SFG signal should be quadratically dependent on the number of reflection spots. To test this theoretical equation, we collected SFG spectra from the following surfaces: (1) ethanol molecules adsorbed on a CaF2 right angle prism and Dove prisms; (2) PMMA thin films spin coated on a right angle CaF2 prism and Dove prisms; (3) lipid monolayers with mixed DPPC and DPPC-d (1:10) lipids deposited on a CaF2 right angle prism and Dove prisms; (4) PET thin films spin coated
2 ACS Paragon Plus Environment
Page 3 of 8
on a CaF2 right angle prism and Dove prisms. SFG spectra of PET were collected at ~1725 cm-1 using a silicon wafer for spatial overlapping of the two beams. SFG spectra in all other cases were collected in the C-H region using a dichroic mirror for spatial overlapping. The detailed spectra are shown in Figure S1. Figure 2 summarizes the dependence of SFG signal intensities of selected peaks versus the number of reflection spots m. Different from that predicted by eq 3, our results indicate a near-linear dependence of SFG signal intensity versus m. This reduced signal enhancement may be caused by several reasons in combination: (1) For conventional SFG, laser beam focusing is optimized to a single focal spot. However, for MRSFG, this optimized focus is impossible to achieve for all the reflection spots, but only for one spot. This might reduce the signal generated from the remaining m-1 reflection spots. (2) The laser beam might be slightly attenuated by the sample. (3) The spatial collinear overlap of the two input beams might not be perfect in our experimental condition, resulting in spatial walk-off of the beams. (4) Chromatic dispersion of the laser beams can reduce the temporal overlap of the input laser beams, and their overlap with the SFG signal. Such dispersion in CaF2 substrate would affect the MRSFG signal enhancement. In picosecond-SFG systems, such dispersion tends to have less effect compared to that in the femtosecond broadband SFG systems. (5) Caused by the dispersion and the TIR of laser beams, the dephasing of SFG signals from different spots reduces the constructive interference of the SFG signals. The issues mentioned above in combination could reduce the MRSFG signal enhancement in ideal condition and eventually gives a non-quadratic but near-linear correlation (4) I SFG , m ≈ mI SFG
4. Signal-to-Noise Ratio of MRSFG We next evaluate the SNR improvement using MRSFG. The general definition of SNR for a single frequency can be expressed as:38 (5) µ is SNR = = 2 σ ∑σ i
as shown in our experimental results in Figure 2 and Figure S1. Eq 4 is empirical and is used for the following SNR analysis.
Here kB is the Boltzmann constant, T is the temperature in Kelvin, and R is the effective resistance. ∆f is the detector bandwidth, which can be correlated to signal integration time constant t through ∆f = 1 / 2t . Thermal noise is independent of
a
120
Intensity (a.u.)
100
100 80
40
40
-1
2940 cm
20 0
20
c
1
2
3
2955 cm
20 0 5 0 800
4
m
d
2
4
6
600
8
m
5
2945 cm 0
2
4
6
m
8
-1
300
C=O peak -1 1725 cm
200 100 10
0
0
1
2
3
4
5
σJ =
4kBT ∆f 2kBT = R Rt
(6)
e ( ip + iD )
(7)
t
Here e is the elementary charge. ip and iD represent, respectively, the photocurrent and the detector dark current, and usually iD«ip. Therefore, shot noise of the MRSFG signal (including resonance signal and nonresonant background) σshot,s,m and the conventional SFG signal σshot,s satisfies σ shot , s , m = mσ shot , s .
400
C-H3 peak
signal. In experimental measurements, signal can be measured from the photocurrent generated by the detector, as represented by is in eq 5. The noise fluctuation in photocurrent is denoted as σi, where i represents different sources of noise. In an SFG spectrum, we define two types of SNR: (1) SNR at a single frequency when vibrational SFG signal is generated (SNRs-s), and (2) SNR of the SFG signal with respect to the background where no vibrational SFG signal is generated (SNRs-b). SNRs-s is the capability of resolving a signal from noise. SNRs-b represents the spectral profile quality when the peak can be resolved. Three major noise terms usually affect SNR in laser spectroscopy: Johnson-Nyquist noise, shot noise, and 1/f noise attributed to laser intensity. These noises may cause random photocurrent fluctuations on both the signal and background. Johnson-Nyquist noise is also called thermal noise, arising from the thermal agitation of electrons in resistors in the detector. It can be expressed as:39
σ shot = 2e ( ip + iD ) ∆f =
10
PET 2 r =0.994
500
10
Here, µ is the mean value of the targeted SFG signal. Noise σ is the standard deviation of all unwanted fluctuations on the
-1
700
DPPC 2 r =0.980
15
C-H3 peak
60
C-H3 peak
i
the laser signal. Therefore the thermal noise of MRSFG σJ,m and conventional SFG σJ is the same: σJ,m=σJ. Shot noise originates from the random fluctuation of photons and electrons and can be expressed as:40
PMMA 2 r =0.999
120
60
0
b
140
Ethanol 2 r =0.988
80
0
Intensity (a.u.)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Analytical Chemistry
6
m
Figure 2, SFG signal intensity versus the number of reflection spots m for (a) the peak at 2940 cm-1 of ethanol molecules adsorbed on the CaF2 prisms; (b) the peak at 2955 cm-1 of PMMA thin films spin coated on the CaF2 prisms; (c) the peak at 2945 cm-1 of DPPC molecule from DPPC:DPPC-d (1:10) lipid monolayers deposited on the CaF2 prisms; (d) The peak at 1725 cm-1 from PET thin films deposited on the CaF2 prisms. The spectra were all collected using ssp polarization. Dots are experimental data, lines are linear fitting results, r2 is the coefficient of determination.
Since the gate time for PMT signal collection is ~100 ns, which is much longer than the signal pulse width (~20 ps), ambient light leaking might also contribute to shot noise. Additionally, if the visible laser beam is not completely blocked by the filters before the detector, it would also contribute to the overall shot noise. These noise terms can be combined to be light leaking shot noise σshot,l,m. However, such shot noise is not dependent on m: σ shot ,l ,m = σ shot ,l . Laser intensity 1/f noise causes fluctuation on the detector output photocurrent and can be expressed as:
3 ACS Paragon Plus Environment
Analytical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
σ1/ f = α ⋅∆f ⋅ PG =
α 2t
SNRSFG , avg ( m )
(8)
PG
=
Here α is the proportional factor of noise with respect to signal. P is the average laser power detected by the photodetector, G is the responsivity (unit: Ampere/Watt) of the detector. The laser 1/f noise on MRSFG signal (including resonance signal and nonresonant background) σ1/f,s,m and conventional SFG signal σ1/f,s satisfies: σ 1/ f , s , m = mσ 1/ f , s . For the possible visible laser beam leakage (as mentioned previously) in both cases, σ 1/ f ,l , m = σ 1/ f ,l . Additionally, for SNRs-b, energy variation of the IR laser beam at different frequencies might affect the background and can be considered as another noise term σIR. Theoretically, if the spectral background has no contribution from nonresonant signal, σIR should vanish. In experimental conditions, a portion of the SFG spectral background might arise from the nonresonant contribution from the sample and the substrate, denoted as σIR,spl and σIR,sub, respectively. For the sample contribution, we have σv,spl, m=mσv,spl. However, for the substrate contribution, we can obtain from geometry that σIR,sub,m=aσIR,sub, where 1.5
