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Dynamic response of the optical resonant cavity to light-wave

Jinjun Feng, Chi Ruan, Yuntao Wang

Published Aug 1, 2015• 0 citations
OpenAlex

Abstract

The dynamic response of optical resonant cavity has been theoretically studied, by taking resonant cavity as a linear and time invariant system and through the approach of Signal Processing. The mathematical description obtained could fit any form of light waves. From the perspective of Signal Processing, the traditional pulse and continues wave cavity ring-down spectroscopy could be considered as observation of impulse response and step response respectively. Furthermore, the cavity response to the light-wave linearly frequency chirped has been studied, in the condition of slow chirp. The Fourier analysis of light power passed through cavity has been made and an analytic description has been given, which reveals the fact that the signal spectrum of light power is related to the absorption spectrum of material inside cavity. Based on this theoretic analysis, a new approach of cavity enhanced absorption spectroscopy has been put forward, called Frequency Domain Cavity Ring-Down Spectroscopy. The result would facilitates the research of cavity enhanced spectroscopy techniques, as well others using resonant cavity, such as P-D-H laser frequency stabilization. ©, 2015, Chinese Optical Society. All right reserved.

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The dynamic response of optical resonant cavity has been theoretically studied, by taking resonant cavity as a linear and time invariant system and through the approach of Signal Processing. The mathematical description obtained could fit any form of light waves. From the perspective of Signal Processing, the traditional pulse and continues wave cavity ring-down spectroscopy could be considered as observation of impulse response and step response respectively. Furthermore, the cavity response to the light-wave linearly frequency chirped has been studied, in the condition of slow chirp. The Fourier analysis of light power passed through cavity has been made and an analytic description has been given, which reveals the fact that the signal spectrum of light power is related to the absorption spectrum of material inside cavity. Based on this theoretic analysis, a new approach of cavity enhanced absorption spectroscopy has been put forward, called Frequency Domain Cavity Ring-Down Spectroscopy. The result would facilitates the research of cavity enhanced spectroscopy techniques, as well others using resonant cavity, such as P-D-H laser frequency stabilization. ©, 2015, Chinese Optical Society. All right reserved.
The dynamic response of optical resonant cavity has been theoretically studied,by taking resonant cavity as a linear and time invariant system and through the approach of Signal Processing.The mathematical description obtained could fit any form of light waves.From the perspective of Signal Processing,the traditional pulse and continues wave cavity ring-down spectroscopy could be considered as observation of impulse response and step response respectively.Furthermore,the cavity response to the light-wave linearly frequency chirped has been studied,in the condition of slow chirp.The Fourier analysis of light power passed through cavity has been made and an analytic description has been given,which reveals the fact that the signal spectrum of light power is related to the absorption spectrum of material inside cavity.Based on this theoretic analysis,a new approach of cavity enhanced absorption spectroscopy has been put forward,called Frequency Domain Cavity Ring-Down Spectroscopy.The result would facilitates the research of cavity enhanced spectroscopy techniques,as well others using resonant cavity,such as P-D-H laser frequency stabilization.
Cavity ring-down is becoming a widely used technique in gas phase spectroscopy. It holds promise for further important extensions, which will lead to even more frequent use. However, we have found widespread confusion in the literature about the nature of coherence effects, especially when the optical cavity constituting the ring-down cell is excited with a short coherence length laser source. In this paper we use the superposition principle of optics to present a general and natural framework for describing the excitation of a ring-down cavity regardless of the relative values of the cavity ring-down time, the input pulse coherence time, or the dephasing time of absorption species inside the cavity. This analysis demonstrates that even in the impulsive limit the radiation inside a high finesse cavity can have frequency components only at the natural resonance frequencies of the cavity modes. As an immediate consequence, a sample absorption line can be detected only if it overlaps at least one of the cavity resonances. Since this point is of particular importance for high resolution applications of the technique, we have derived the same conclusion also in the time domain representation. Finally, we have predicted that it is possible to use this effect to do spectroscopy with a resolution much higher than that of the bandwidth of the excitation laser. In order to aid in the design of such experiments, expressions are derived for the temporal and spatial overlap of a Fourier transform limited input Gaussian beam with the TEMmn modes of the cavity. The expressions we derive for the spatial mode overlap coefficients are of general interest in applications where accurate mode matching to an optical cavity is required.
Optical cavities serve as powerful tools for sensing experiments, often relying on narrow-linewidth laser sources to minimize the impact of optical coherence on measurements. However, demands for affordable integrated and miniaturized sensing platforms in point-of-care diagnostics, environmental monitoring, and similar applications motivate switching to sources with broader linewidths suitable for both monolithic and heterogeneous integrations. Time-domain measurement techniques such as cavity ring-down spectroscopy (CRDS) are widely used in conjunction with optical cavities, but to date there has been no universal model that quantifies the impact of partial coherence on the cavity temporal transfer function. We apply a linear systems theory approach to develop a closed-form analytic model for cavity-based sensing that quantifies the influence of source bandwidth (i.e., temporal coherence) on spectroscopic measurements in the time domain. This approach can be applied to a variety of cavity-based spectroscopies. In this study, cavity-enhanced absorption spectroscopy (CEAS) and CRDS paradigms have been examined using standing- and traveling-wave resonator examples. Results show that although increased cavity loss is the primary factor reducing output power and photon lifetime in both CEAS and CRDS, broader source linewidths can also influence cavity buildup and transmission and must be accounted for when modeling the system response. The model is consistent with known results in the literature and provides a framework for evaluating source detuning and coherence effects on cavity dynamics.
It is experimentally demonstrated that a narrow band continuous wave (cw) light source can be used in combination with a high-finesse optically stable cavity to perform sensitive, high-resolution direct absorption and optical rotation spectroscopy in an amazingly simple experimental setup, using ideas from the field of cavity ring down spectroscopy. Light from a scanning narrow band cw laser is coupled into the cavity via accidental coincidences of the laser frequency with the frequency of one of the multitude of modes of the cavity. The absorption and polarization rotation information is extracted from a measurement of the time-integrated light intensity leaking out of the cavity as a function of laser wavelength.
We introduce optical feedback frequency stabilized cavity ring-down spectroscopy (OFFS-CRDS), a near-shot-noise-limited technique that combines kilohertz resolution with an absorption detection sensitivity of 5×10(-13) cm(-1) Hz(-1/2). Its distributed feedback laser source is stabilized to a highly stable V-shaped reference cavity by optical feedback and fine-tuned by means of single-sideband modulation. The stability of this narrow laser is transferred to a ring-down (RD) cavity using a new fibered Pound-Drever-Hall (PDH) locking scheme without a dedicated electro-optic phase modulator, yielding several hundred RD events per second. We demonstrate continuous coverage of more than 7 nm with a baseline noise of 5×10(-12) cm(-1) and a dynamic range spanning six decades. With its resonant intracavity light intensity on the order of 1 kW/cm2, the spectrometer was used for observing a Lamb dip in a transition of carbon dioxide involving four vibrational quanta. Saturating such a weak transition at 160 μW input power, OFFS-CRDS paves the way to Doppler-free molecular overtone spectroscopy for precision measurements of hyperfine structures and pressure shifts.