Nature - USA (2020-01-02)

Nature | Vol 577 | 2 January 2020 | 55

In FRS, temporal isolation of (wave-cycle-scale) fractions of the GMF

renders the weakest detectable molecular response largely immune

against the noise of excitation intensity, as is apparent from the cyan line

in Fig. 1c. This is indicated by the expression for the MDA obtained by time-

domain modelling of the molecular system with an isolated Lorentzian

oscillator of dephasing time TL (Supplementary Information section II):













t

T

MDA=^2

DR

exp(2)

E

FRS

B

L

Here, the dynamic range DRE is defined as the ratio of the spectral ampli-

tude of the electric field of the overall signal reaching the detector at

the centre frequency of the Lorentzian oscillator to that of the weakest

signal detectable after passage through a temporal filter opening at tB.

The parameter tB is defined as the instant when the temporal window

for an infrared-background-free measurement begins.

This is the case when the numerical difference between two subse-

quent measurements (in this case, of liquid water) reaches the detec-

tion noise floor (Fig. 2a). In our proof-of-principle measurement with

the quantum-efficiency-maximized FRS setting, this occurs at about

tB = 1,500 fs, yielding a value of DRE in excess of 10^6 for absorptions

with centre frequencies between 1,080 cm−1 and 1,190 cm−1 (for a 7-ps

time window and 37-s effective measurement time, see right panel of

Fig. 2b). For a dephasing time of the order of a picosecond, typical for

an aqueous environment^9 , equation ( 2 ) predicts a minimum detectable

absorbance of the order of 10−6.

–0.5 0.0 0.5 1.0 1.5 2.0 2.5 3. 03 .5 4. 04 .5 5. 05 .5 6. 06 .5

100

101

102

103

104

105

106

107

2.00 2.25 2.50

–1 × 103

0

× 103

5.50 5.75 6.00

–10

0

10

–0.5 0.0 0.5 1.0 1.5 2.0 2.5 3. 03 .5 4. 04 .5 5. 05 .5 6. 06 .5

0.1

1

10

–0.5 0.0 0.5 1.0 1.5 2.0 2.5 3. 03 .5 4. 04 .5 5. 05 .5 6. 06 .5

10

100

Time (ps)

Time (ps)

Magnitude of normalized signals

Time (ps)

Serum

Water reference

Difference of serum and water measurements

Difference of two serum measurements,

including sample exchange

Detection noise floor

Normalized signals

Relative RMS of

amplitude fluctuations (%)

Result of statistical evaluation

Trend

b

c

RMS of field

zero crossings (as)

Resultofstatisticalevaluation

Trend

a

Time (ps)

Time (ps)

Fig. 4 | GMFs of human blood serum and their reproducibility. a, Magnitude of the EOS signals, recorded with quantum-efficiency-optimized FRS (see key). The
insets show linear-scale representations of the signals depicted in the main panel in two different time windows. b, c, Relative (b) and absolute (c) r o o t-m e a n -
square (RMS) of oscillation amplitude and zero crossings of five hundred measurements of the GMF of a serum sample (without sample exchange) (see
Supplementary Information section V).