Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition – I. Theoretical description

Weiguang Ma, Isak Silander, Thomas Hausmaninger, Ove Axner

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

Abstract

Doppler-broadened (Db) noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) is conventionally described by an expression (here referred to as the CONV expression) that is restricted to the case when the single-pass absorbance, α0L, is much smaller than the empty cavity losses, π/F [here termed the conventional cavity-limited weak absorption (CCLWA) condition]. This limits the applicability of the technique, primarily its dynamic range and calibration capability. To remedy this, this work derives extended descriptions of Db NICE-OHMS that are not restricted to the CCLWA condition. First, the general principles of Db NICE-OHMS are scrutinized in some detail. Based solely upon a set of general assumptions, predominantly that it is appropriate to linearize the Beer–Lambert law, that the light is modulated to a triplet, and that the Pound–Drever–Hall sidebands are fully reflected, a general description of Db NICE-OHMS that is not limited to any specific restriction on α0L vs. π/F, here referred to as the FULL description, is derived. However, this description constitutes a set of equations to which no closed form solution has been found. Hence, it needs to be solved numerically (by iterations), which is inconvenient. To circumvent this, for the cases when α0L<π/F but without the requirement that the stronger CCLWA condition needs to be fulfilled, a couple of simplified extended expressions that are expressible in closed analytical form, referred to as the extended locking and extended transmission description, ELET, and the extended locking and full transmission description, ELFT, have been derived. An analysis based on simulations validates the various descriptions and assesses to which extent they agree. It is shown that in the CCLWA limit, all extended descriptions revert to the CONV expression. The latter one deviates though from the extended ones for α0L around and above 0.1π/F. The two simplified extended descriptions agree with the FULL description for a larger range of than the CONV expression, viz. for the ELET description for α0L up to 0.3π/F and for ELFT for α0L up to 0.6 or 1.0 π/F (depending on the mode of detection). It is then demonstrated that the conventional view of Db NICE-OHMS, which states that the out-of-phase and the in-phase signals can be referred to as a pure absorption and dispersion signal, respectively, breaks down when the CCLWA condition does not hold. In this case, the out-of-phase signal is additionally affected by the phase shifts of the laser components (i.e. dispersion) while the in-phase signal is also influenced by their attenuation. Access to new descriptions broadens considerably the dynamic range of Db NICE-OHMS and facilitates calibration using standard references samples, and thereby its applicability.
Original languageEnglish
Pages (from-to)217-244
JournalJournal of Quantitative Spectroscopy and Radiative Transfer
Volume168
DOIs
Publication statusPublished - Jan 2016
MoE publication typeA1 Journal article-refereed

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Spectrometry
cavities
spectroscopy
Calibration
Phase shift
locking
dynamic range
Lasers
sidebands
iteration
constrictions
phase shift
breakdown
attenuation
requirements

Cite this

@article{7b7320b961a444ec85ff8656e566d356,
title = "Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition – I. Theoretical description",
abstract = "Doppler-broadened (Db) noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) is conventionally described by an expression (here referred to as the CONV expression) that is restricted to the case when the single-pass absorbance, α0L, is much smaller than the empty cavity losses, π/F [here termed the conventional cavity-limited weak absorption (CCLWA) condition]. This limits the applicability of the technique, primarily its dynamic range and calibration capability. To remedy this, this work derives extended descriptions of Db NICE-OHMS that are not restricted to the CCLWA condition. First, the general principles of Db NICE-OHMS are scrutinized in some detail. Based solely upon a set of general assumptions, predominantly that it is appropriate to linearize the Beer–Lambert law, that the light is modulated to a triplet, and that the Pound–Drever–Hall sidebands are fully reflected, a general description of Db NICE-OHMS that is not limited to any specific restriction on α0L vs. π/F, here referred to as the FULL description, is derived. However, this description constitutes a set of equations to which no closed form solution has been found. Hence, it needs to be solved numerically (by iterations), which is inconvenient. To circumvent this, for the cases when α0L<π/F but without the requirement that the stronger CCLWA condition needs to be fulfilled, a couple of simplified extended expressions that are expressible in closed analytical form, referred to as the extended locking and extended transmission description, ELET, and the extended locking and full transmission description, ELFT, have been derived. An analysis based on simulations validates the various descriptions and assesses to which extent they agree. It is shown that in the CCLWA limit, all extended descriptions revert to the CONV expression. The latter one deviates though from the extended ones for α0L around and above 0.1π/F. The two simplified extended descriptions agree with the FULL description for a larger range of than the CONV expression, viz. for the ELET description for α0L up to 0.3π/F and for ELFT for α0L up to 0.6 or 1.0 π/F (depending on the mode of detection). It is then demonstrated that the conventional view of Db NICE-OHMS, which states that the out-of-phase and the in-phase signals can be referred to as a pure absorption and dispersion signal, respectively, breaks down when the CCLWA condition does not hold. In this case, the out-of-phase signal is additionally affected by the phase shifts of the laser components (i.e. dispersion) while the in-phase signal is also influenced by their attenuation. Access to new descriptions broadens considerably the dynamic range of Db NICE-OHMS and facilitates calibration using standard references samples, and thereby its applicability.",
author = "Weiguang Ma and Isak Silander and Thomas Hausmaninger and Ove Axner",
year = "2016",
month = "1",
doi = "10.1016/j.jqsrt.2015.09.007",
language = "English",
volume = "168",
pages = "217--244",
journal = "Journal of Quantitative Spectroscopy and Radiative Transfer",
issn = "0022-4073",
publisher = "Elsevier",

}

Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition – I. Theoretical description. / Ma, Weiguang; Silander, Isak; Hausmaninger, Thomas; Axner, Ove.

In: Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 168, 01.2016, p. 217-244.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Doppler-broadened NICE-OHMS beyond the cavity-limited weak absorption condition – I. Theoretical description

AU - Ma, Weiguang

AU - Silander, Isak

AU - Hausmaninger, Thomas

AU - Axner, Ove

PY - 2016/1

Y1 - 2016/1

N2 - Doppler-broadened (Db) noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) is conventionally described by an expression (here referred to as the CONV expression) that is restricted to the case when the single-pass absorbance, α0L, is much smaller than the empty cavity losses, π/F [here termed the conventional cavity-limited weak absorption (CCLWA) condition]. This limits the applicability of the technique, primarily its dynamic range and calibration capability. To remedy this, this work derives extended descriptions of Db NICE-OHMS that are not restricted to the CCLWA condition. First, the general principles of Db NICE-OHMS are scrutinized in some detail. Based solely upon a set of general assumptions, predominantly that it is appropriate to linearize the Beer–Lambert law, that the light is modulated to a triplet, and that the Pound–Drever–Hall sidebands are fully reflected, a general description of Db NICE-OHMS that is not limited to any specific restriction on α0L vs. π/F, here referred to as the FULL description, is derived. However, this description constitutes a set of equations to which no closed form solution has been found. Hence, it needs to be solved numerically (by iterations), which is inconvenient. To circumvent this, for the cases when α0L<π/F but without the requirement that the stronger CCLWA condition needs to be fulfilled, a couple of simplified extended expressions that are expressible in closed analytical form, referred to as the extended locking and extended transmission description, ELET, and the extended locking and full transmission description, ELFT, have been derived. An analysis based on simulations validates the various descriptions and assesses to which extent they agree. It is shown that in the CCLWA limit, all extended descriptions revert to the CONV expression. The latter one deviates though from the extended ones for α0L around and above 0.1π/F. The two simplified extended descriptions agree with the FULL description for a larger range of than the CONV expression, viz. for the ELET description for α0L up to 0.3π/F and for ELFT for α0L up to 0.6 or 1.0 π/F (depending on the mode of detection). It is then demonstrated that the conventional view of Db NICE-OHMS, which states that the out-of-phase and the in-phase signals can be referred to as a pure absorption and dispersion signal, respectively, breaks down when the CCLWA condition does not hold. In this case, the out-of-phase signal is additionally affected by the phase shifts of the laser components (i.e. dispersion) while the in-phase signal is also influenced by their attenuation. Access to new descriptions broadens considerably the dynamic range of Db NICE-OHMS and facilitates calibration using standard references samples, and thereby its applicability.

AB - Doppler-broadened (Db) noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) is conventionally described by an expression (here referred to as the CONV expression) that is restricted to the case when the single-pass absorbance, α0L, is much smaller than the empty cavity losses, π/F [here termed the conventional cavity-limited weak absorption (CCLWA) condition]. This limits the applicability of the technique, primarily its dynamic range and calibration capability. To remedy this, this work derives extended descriptions of Db NICE-OHMS that are not restricted to the CCLWA condition. First, the general principles of Db NICE-OHMS are scrutinized in some detail. Based solely upon a set of general assumptions, predominantly that it is appropriate to linearize the Beer–Lambert law, that the light is modulated to a triplet, and that the Pound–Drever–Hall sidebands are fully reflected, a general description of Db NICE-OHMS that is not limited to any specific restriction on α0L vs. π/F, here referred to as the FULL description, is derived. However, this description constitutes a set of equations to which no closed form solution has been found. Hence, it needs to be solved numerically (by iterations), which is inconvenient. To circumvent this, for the cases when α0L<π/F but without the requirement that the stronger CCLWA condition needs to be fulfilled, a couple of simplified extended expressions that are expressible in closed analytical form, referred to as the extended locking and extended transmission description, ELET, and the extended locking and full transmission description, ELFT, have been derived. An analysis based on simulations validates the various descriptions and assesses to which extent they agree. It is shown that in the CCLWA limit, all extended descriptions revert to the CONV expression. The latter one deviates though from the extended ones for α0L around and above 0.1π/F. The two simplified extended descriptions agree with the FULL description for a larger range of than the CONV expression, viz. for the ELET description for α0L up to 0.3π/F and for ELFT for α0L up to 0.6 or 1.0 π/F (depending on the mode of detection). It is then demonstrated that the conventional view of Db NICE-OHMS, which states that the out-of-phase and the in-phase signals can be referred to as a pure absorption and dispersion signal, respectively, breaks down when the CCLWA condition does not hold. In this case, the out-of-phase signal is additionally affected by the phase shifts of the laser components (i.e. dispersion) while the in-phase signal is also influenced by their attenuation. Access to new descriptions broadens considerably the dynamic range of Db NICE-OHMS and facilitates calibration using standard references samples, and thereby its applicability.

U2 - 10.1016/j.jqsrt.2015.09.007

DO - 10.1016/j.jqsrt.2015.09.007

M3 - Article

VL - 168

SP - 217

EP - 244

JO - Journal of Quantitative Spectroscopy and Radiative Transfer

JF - Journal of Quantitative Spectroscopy and Radiative Transfer

SN - 0022-4073

ER -