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The study of wavelength modulation off-axis integrated cavity output spectroscopy in the case of Lorentzian absorption profile
Optics Communications 284 (2011) 852–856
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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
The study of wavelength modulation off-axis integrated cavity output spectroscopy in the case of Lorentzian absorption profile Zhongqi Tan, Xingwu Long ⁎, Xianwang Feng, Zhimeng Wei Department of Optoelectronic Engineering, College of Optoelectronic Science & Engineering, National University of Defense Technology, Changsha 410073, China
a r t i c l e
i n f o
Article history: Received 12 May 2010 Received in revised form 24 August 2010 Accepted 28 September 2010 OCIS: 120.2230 120.6200 300.1030 300.6380
a b s t r a c t According to the property of optical cavity and the principle of signals and systems, the mathematical derivations for wavelength modulation off-axis integrated cavity output spectroscopy (WM-OA-ICOS) are presented. And based on the analytical method, the function expression of WM-OA-ICOS signal from Lorentzian absorption profile is obtained. To validate the analyses and deductions, some special cases in 2fharmonic detection of WM-OA-ICOS are studied and experimented with a built compact WM-OA-ICOS apparatus. It is found that the measured results can coincide with the deduced conclusions. The works can provide some references for the application of WM-OA-ICOS in the case of Lorentzian absorption profile. © 2010 Published by Elsevier B.V.
1. Introduction In the past decades, various high-sensitivity absorption spectroscopy techniques, which are mainly based upon the high-finesse optical cavity, have been developed and applied to detecting gas concentration or measuring absorption spectrum [1]. They include cavity ring down spectroscopy (CRDS) [2], phase-shift cavity ring down spectroscopy (PS-CRDS) [3], cavity enhanced absorption spectroscopy (CEAS) [4], integrated cavity output spectroscopy (ICOS) [5], and so on. In these techniques, when the continuouswave laser is used as the light source, the multiple-beam interference inside optical cavity is inevitable because the laser beam is often directed into optical cavity in an on-axis manner. In this case, the coincidence of the narrowband laser frequency with the cavity modes will bring the complexity of their apparatuses and increase their costs. In recent years, some new techniques have been proposed to avoid the interference effect in the high-fitness cavity, such as off-axis integrated cavity output spectroscopy (OA-ICOS) [6–8]. In this technique, the continuous-wave laser is coupled into the optical cavity with an off-axis configuration. And then the interference effect inside the optical cavity is eliminated systematically while preserving the absorption signal amplifying property of such low-loss cavity. In particular, when combining with the wavelength modulation absorption technique [9], the detectable sensitivity of OA-ICOS technique can be improved further. Nowadays, the so-called wavelength modulation off-axis integrated cavity output spectroscopy (WM-OA-ICOS) has
⁎ Corresponding author. E-mail address: [email protected] (X. Long). 0030-4018/$ – see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.optcom.2010.09.072
been applied in different fields successfully [10]. For example, 2fharmonic detection technique of WM-OA-ICOS has been used to measure the biogenic NO concentrations in human breath, and the detectable limit was achieved as 2.0 ppbv or better [11,12]. In the past research, the description of harmonic signal and the choice of optimum modulation index in WM-OA-ICOS were often in accordance with the theory of wavelength modulation direct laser absorption spectroscopy (WM-DLAS) [13]. However, in some cases, the traditional theory could not explain reasonably some special phenomena observed in the past experiments of WM-OA-ICOS. For instance, when the absorption loss of gaseous species in optical cavity was no longer smaller than the cavity mirror losses [14], we could find that the measured optimum modulation amplitude of laser wavelength for 2f-harmonic detection in WM-OA-ICOS was obviously bigger than its theoretical value. Beyond this current state, we deduce the universal basis for WM-OA-ICOS with another method in this paper. Furthermore, a set of compact WM-OA-ICOS system was built to verify our analyses and deductions. 2. Theory deduction The off-axis paths between two spherical mirrors of an optical cavity have been well understood and described [6,15], so we do not plan to repeat these contents. In this section, we emphasize the principle deduction of WM-OA-ICOS in the case of Lorentzian absorption profile. As we know, when the interference effect inside the optical cavity is ignored, the off-axis optical cavity can be abstracted into a linear time-invariant (LTI) system, because it is time invariant and satisfies the principle of superposition according to the principle of signals and
Z. Tan et al. / Optics Communications 284 (2011) 852–856
systems [16]. As shown in Fig. 1, the pulsed laser in this case can be regarded as an impulse, and the impulse response h(v, t) of this optical system can be then written as [17] 8 > < hðv; t Þ = k⋅ exp½−t = τ ðvÞ L : > : τ ðvÞ = c⋅½δ0 ðvÞ + α ðvÞ⋅L
ð1Þ
according to the pulsed laser cavity ring down technique. Where k is the coupling coefficient between input light power and the inner power of cavity (traveling in each direction) [6,8], τ(v) is the decay time of light in optical cavity at the laser frequency v, δ0(v) is the total loss of cavity mirror (transmittance plus scattering and absorption), α(v) is the absorption coefficient of gaseous species closed in cavity, and L is the cavity length. Based upon this equation, the output signals of optical cavity excited by different input light signals can be obtained readily via the convolution operation between the input signal and the impulse response function. It is known, when the laser wavelength is modulated in a small spectral region by current tuning the laser diode, the optical system serves as the WM-OA-ICOS scheme. To deduce the basis for WM-OA-ICOS, we suppose the intensity Iin(t) and wavelength v of incident laser are expressed as
Iin ðt Þ = I0 + ΔI⋅ cosð 2π ft Þ ; v = v1 +Δv⋅ cosð 2π ft Þ
ð2Þ
respectively, when the nonlinear character of laser diode is ignored. Thereinto, f is the modulation frequency of laser current, I0 and v1 are the central values of light intensity and wavelength, ΔI and Δv are their modulation amplitudes caused by the current modulation of DFB laser diode, respectively. In the case of no absorption species closed in the cavity, cavity loss is insensitive to the scanning of laser wavelength because the loss spectrum of mirror is almost a smooth curve in a small spectral region. Then the system is still a linear system, and the cavity output signal can be inferred and analyzed with Eqs. (1) and (2). On the contrary, if some absorption species are closed in the cavity, the cavity ring down time (corresponding to the cavity loss) will change obviously with the laser wavelength scanning, and then yield the lineshape of absorption spectrum. As we know, the system in this case is no longer a linear system. To calculate the cavity output signal under this condition, we can divide the input laser at the time of t into a series of pulsed lasers. Their intensity and wavelength are shown as Eq. (2), and their time interval is expressed as Δt = 2L / c. The cavity output signal at the time t can be then written as the total response of these pulsed lasers, as following: 8 1 +∞ n⋅Δt > > > < I ðt Þ = 2τ ⋅ ∑ fI0 +ΔI⋅ cos½2π f d ðt−n⋅Δt Þg⋅k⋅ exp − τ ðt−n ΔtÞ dΔt ⋅ 1 n=0 > 1 ∞ −x > > :≈ ∫ fI + ΔId cos½2π f ⋅ðt−xÞg⋅k⋅ exp dx 2τ 1 ⋅ 0 0 τ ðt−xÞ
ð3Þ
853
where n is an integer, and τ1 is the ring down time related with the transmittance loss δ1 of mirrors. Here, the cavity output is calculated by dividing τ1 from the inner power of cavity according to the property of optical cavity, and the factor 2 accounts for the fact that the light leaves through both mirrors. To simplify Eq. (3), a hypothesis of f · τ b b 1 is introduced. Since the intensity and wavelength of laser can be regarded as an invariant approximately during the effective integrated time, Eq. (3) is then written as: Iðt Þ = ½I0 + ΔI⋅ cosð 2π ft Þ⋅k⋅τ ðt Þ = 2τ 1 Taking the Lorentzian absorption profile into account [18], and then the output signal of the optical cavity, which is excited by an incident laser modulated as Eq. (2), can be given as: 8 > > > < α ðvÞ⋅L =
S N⋅L π⋅γ ⋅ ½ðv1 −v0 Þ=γ + Δv⋅ cosð 2π ft Þ=γ 2 + 1
> > > : I ðt Þ = ½I0 + ΔI⋅ cosð 2π ft Þ⋅
k⋅δ1 ðvÞ 2⋅½δ0 ðvÞ + α ðvÞ⋅L
ð4Þ
where S is the absorption intensity of gaseous species, N is the absorption molecule density, and γ is the half-width at half-maximum (HWHM) of Lorentzian lineshape. In a special case, a non-modulated laser is used to exit the optical cavity, namely, Δv = ΔI = 0, the cavity integrated output signal can be then obtained to determine the inner absorption of optical cavity, and this is the basis of OA-ICOS. In WM-DLAS, it is known that the light signal can be expressed as h
L
i
I ðt Þ= ½I0 +ΔI⋅ cosð 2πft Þ⋅ exp −∫ α ðvÞ⋅dl ≈½I0 +ΔI ⋅ cosð 2πft Þ⋅½1−α ðvÞ⋅L 0
ð5Þ when α(v) ⋅ L b b 1. Comparing Eqs. (4) with (5), we can find, despite both the WM-OA-ICOS and WM-DLAS are all based on the wavelength modulation technique, their signals have different function expressions. It is known that the modulation amplitude of laser wavelength is a very important parameter for harmonic detection in WM-DLAS, and its optimization value has ever been studied in the past years. In the case of Lorentzian lineshape absorption, the theoretical optimization value for even-harmonic detection, which can maximize the even-order Fourier coefficient of a wavelength-modulated Lorentzian lineshape on resonance, has been deduced as Eq. (6) [19] if not considering the residual amplitude modulation (RAM) effect. ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2ffi Δvnopt n u 2 t η= = pffiffiffi 1 + 1 + n γ 2
ð6Þ
where η and Δvnopt are the optimum factor and optimum amplitude of laser wavelength modulation, respectively. According to this equation, we obtain the maximal 2f-harmonic intensity from the detected signal of WM-DLAS when the condition of Δv ≈ 2.2γ is satisfied. To obtain the optimization modulation value of laser wavelength in WM-OA-ICOS, Eq. (4) is transformed into the same function form as Eq. (5). And it is shown as Eq. (7) 8 i 0 ½I +ΔI ⋅ cosð 2π ftÞ⋅k⋅δ1 ðvÞ ½I0 +ΔI⋅ cosð 2π ftÞ⋅k⋅δ1 ðv0 Þ h > > Iðt Þ= 0 ≈ > ⋅ 1−x > > 2⋅½δ0 ðvÞ + α ðvÞ⋅L 2⋅δ0 ðv0 Þ > > > > < α ðv0 Þ⋅L
0 α ðv Þ⋅L + δ0 ðv0 Þ > > x =" sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > #2 > > > ð Þ ð Þ v −v δ v Δv δ0 ðv0 Þ > 1 0 0 0 > + cosð 2π ftÞ +1 > ⋅ ⋅ ⋅ : γ γ δ0 ðv0 Þ + α ðv0 Þ⋅L δ0 ðv0 Þ +α ðv0 Þ⋅L
ð7Þ
Fig. 1. Schematic diagram of WM-OA-ICOS.
where α(v0) is the peak absorption coefficient. Because the mirror loss in a small spectral range was known as a constant, δ0(v), δ1(v) in Eq. (7) has been replaced by δ0(v0), δ1(v0), respectively. Comparing Eq. (7)
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with Eq. (5), we can find the numerator of modulated signal function is multiplied by a large coefficient 1/ [α(v0) ⋅ L + δ0(v0)] for α(v0) ⋅ L + δ0 (v0) b b 1. This is why WM-OA-ICOS can reach a higher sensitivity than the traditional WM-DLAS in a short cavity. Finally, the optimization value η in WM-OA-ICOS can be determined as ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n u 2 δ ðv Þ + α ðv0 Þ⋅L t η = pffiffiffi 1 + 1 + ⋅ 0 0 n δ0 ðv0 Þ 2
ð8Þ
by referring to Eq. (6). Same as the other methods [13], it is found that the optimization values η of different methods are all the same when δ0 (v0) = 1 − R N N α(v0) ⋅ L (R is the reflectivity of mirrors).
measured as ~0.05% at 6592 cm− 1 (Lambda950, Perkin-Elmer). The light transmitted from the cavity was focused into a detector (PDA10CS, Thorlabs) with a 6.3 cm-diameter lens (focal length 6.3 cm), the detected signal was then sent to a special integral circuit for OA-ICOS measurement or to the DSP lock-in amplifiers SR830 for harmonic detection. To record the stable 2f-harmonic spectrum, the integrator was used again to integrate and digitize the output harmonic signal from the lock-in amplifier SR830, and the laser wavenumber was scanned by current tuning of DFB laser. Once the harmonic intensities of transmitted light signals at different laser wavelengths were recorded, they were sent to the computer via the UART for saving and analyzing. Need to add, to remove the interference effect and improve the stability of cavity output signal further, a micro-pump was mounted on the bellow to dither the cavity length randomly.
3. Experimental apparatus 4. Experimental results and analyses As depicted in Fig. 2, an experimental apparatus is built to verify our deductions and analyses, and it is mainly composed of seven parts, including light source, collimator, low-loss optical cavity, detector, lock-in amplifier, and so on. In our apparatus, a DFB laser (NLK1556STG, NEL) was used as the light source, and it has been integrated with a thermal electric coolers (TEC) and a thermistor sensors. The DFB laser was placed on a butterfly laser diode mounter (LM14S2, Thorlabs), and its temperature and current were controlled by a temperature controller (WTC3243, Wavelength Electronics) and a laser diode driver (LDD200-1P, Wavelength Electronics), respectively. As is known, the central wavelength of laser diode can be tuned in a small spectral range via adjusting its operating temperature or injection current. Accordingly, when the temperature and current of DFB laser were changed in 15–31 °C and 20–80 mA, respectively, it was found that the wavelength of DFB laser could be tuned in the spectral range of 6587–6595.5 cm−1. Furthermore, with the help of a high-precision wavemeter (WA-1500-NIR, EXFO Burleigh) and a spectrum analyzer (WA-650, EXFO Burleigh), the temperaturewavenumber and current-wavenumber coefficients of our DFB laser could be determined accurately. In Fig. 2, to modulate the laser wavelength for WM-OA-ICOS measurement, a sine signal, which came from the reference output of a DSP lock-in amplifier (SR830, Stanford Research Systems), was used as the input signal of LDD200-1P to modulate the injection current of laser diode. Then the modulated narrow-band laser (linewidth ~ 2 MHz) was then passed through a fiber collimator (F240APC1550, Thorlabs), and transformed into a ~1.5 mm-diameter Gaussian beam in free space. Without mode-matching lens, the collimated laser was directed into a 67 cm-long optical cavity with an off-axis alignment. The cavity was made of a 4.0 cm-diameter stainless bellow, and two plano-concave mirrors (5.0 cm-diameter, 8 m-curvature radius) were placed at its two sides. These mirrors were all made by ourselves, and their super-polished surfaces (RMS~ 0.06 nm, AFM3100) were deposited with a 29-layer periodic high-reflectivity coating by the ion-sputtering process. Later, their transmittances were
Referring to the HITRAN2004 database [20], it is known that there are some strong absorption lines of gaseous species lying in the spectral tuning range of our laser diode, such as ethyne (C2H2), water vapor (H2O) and giggle gas (N2O). Taking the absorption intensity and the interferences from other absorption lines into account, we chose the absorption line of C2H2 molecule at 6594.388 cm− 1 to carry on our experimental study. Subsequently, we set DFB laser's temperature to 16 °C and scanned the laser current in the range of 20–80 mA, it was then obtained that the laser wavenumber could be turned in the spectral range of 6593.94–6595.06 cm− 1. Furthermore, the relation between the laser wavenumber (cm− 1) and the laser current (mA) could be written as λ = −0:804 × 10
4
2
× i −0:0107 × i + 6595:310
ð9Þ
According to the measurement scheme of OA-ICOS [17], we can first obtain the loss spectrum of optical cavity in this spectral region (the temperature and pressure of gases closed in cavity were measured as 23.5 °C and 101.3 KPa, respectively). As shown in Fig. 3(a), three obvious absorption profiles are observed in the measured spectrum. To obtain the spectral parameters of C2H2, Eq. (4) was used as the object function to fit the measured spectral data using the Levenberg– Marquardt method. The fitted residue is also shown in Fig. 3(b), and the fitted line-width of 0.0720 cm− 1 was very close to the value of 0.0719 cm− 1 derived from the HITRAN2004 database. Therefore, it is believed that the deduced Eq. (4) can perfectly express the real OA-ICOS signal [17]. Additionally, two absorption lines of H2O molecule in this spectral range can clearly be observed in Fig. 3(a). Their spectral linewidths were then determined as ~0.0483 cm− 1 and ~0.865 cm− 1 respectively with the same fitting method, and the calculated absorption intensity ratio of the two lines was obtained as 26.33, which is just less than the value of 27.47 provided by HITRAN database slightly.
Fig. 2. Sketch map of the experimental WM-OA-ICOS system.
Z. Tan et al. / Optics Communications 284 (2011) 852–856
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Fig. 3. The measured spectra of C2H2 and H2O with OA-ICOS and WM-OA-ICOS. (a) is the measured OA-ICOS spectrum and its fitted curve in 6593.93–6595.06 cm− 1, (b) is the fitted residua of OA-ICOS spectrum, and (c) is the 2f-harmonic spectrum measured with WM-OA-ICOS when the modulation amplitude and frequency of laser current were set to 2.26 mA and 1.0 KHz, respectively.
Fig. 4. The OA-ICOS spectra of C2H2 in different concentration and the 2f-harmonic signals at different modulation amplitudes in WM-OA-ICOS. (a) is the measured spectra with OA-ICOS in different C2H2 concentrations, and (b) is the measured relation curves between modulation amplitude of laser wavelength and 2f-harmonic signal intensity in WM-OA-ICOS when the modulation frequency was set to 1.0 KHz.
After connecting the output of SR830 to our integrator, the OAICOS system can be applied to measuring the harmonic spectrum of C2H2 molecule. When the modulation amplitude and frequency of laser current were set to 2.26 mA and 1.0 KHz, respectively, the measured 2f-harmonic spectra of C2H2 and H2O are shown in Fig. 3(c). In this case, the integral time of SR830 was 300 ms. Unexpectedly, compared with Fig. 3(a), it can be found that the strong absorption line of water vapor at 6595.078 cm− 1 is not present in Fig. 3(c). We think the phenomenon can be explained from two aspects. First, the cavity output signal near 6595 cm− 1 was so weak that 2f-harmoic intensity detected by SR830 was too low. As we know, the laser current corresponding to the laser wavenumber of 6595 cm− 1 was close to the threshold current of DFB laser, so the laser power at this wavenumber was low. Furthermore, the strong absorption of water vapor reduced the cavity output further. In fact, when we turned the absorption line of water vapor to the middle of scanning region via changing the DFB laser's temperature, we could observe the 2fharmonic spectrum of water vapor at 6595.078 cm− 1 clearly. Second, the modulation amplitude of laser wavelength, which was calculated as 0.03 cm− 1 according to Eq. (9), was far smaller than the linewidth of water vapor, and it also weakened the 2f-harmoic signal. In addition, we can find that the measured 2f-harmoic signal in Fig. 3(c) has an small offset, and it may be due to the RAM effect and the phase shift between the intensity modulation and the laser frequency. According to Eq. (8), it is believed that the optimum modulation amplitude of even-harmonic detection in WM-OA-ICOS reduces with the dying down of the absorption intensity inside the cavity. To validate the conclusion, we set the laser wavelength at 6594.388 cm− 1 by stabilizing the temperature and current of DFB laser (wavelength stability was ~0.003 cm− 1), and measured the relation curves between the modulation amplitude of DFB laser wavelength and the 2f-harmoic intensity under different absorption status. As shown in Fig. 4(a), four absorption profiles at different C2H2 concentrations were recorded by the OA-ICOS technique, and their spectral line-widths were calculated as 0.0713, 0.0720, 0.0720 and 0.0713 cm− 1, successively. In addition, the ratios of absorption intensity to the loss of empty cavity, namely α(v0) ⋅ L / δ0(v0), could also be determined as 17.76, 3.96, 2.08 and 1.03, respectively. Under every absorption status, the integral time of SR830 was set to 1.0 s to obtain a stable 2f-harmoic signal, and the relation curves between the 2f-harmoic intensity and the laser modulation amplitudes were
plotted in Fig. 4(b). From the measured data, the optimum modulation amplitudes under different absorption status could be determined as 0.441, 0.286, 0.249, and 0.194 cm− 1. Obviously, the measured results of Fig. 4(b) can accord with the character of optimum modulation amplitude as Eq. (8). That is to say, the optimum modulation amplitude increases with the absorption loss inside optical cavity. Unfortunately, the calculated optimum modulation amplitude according to Eq. (8), which were determined as 0.682, 0.351, 0.276 and 0.224 cm− 1 respectively based on the measured absorption parameters of C2H2 spectrum, are slightly bigger than the measured results. We think the deviation may be caused by the following reasons: First, the residual interference effect may influence the precision of measured 2f-harmonic intensity. Despite the mechanical vibration was introduced by a micro-pump, the optical interference inside cavity is still inevitable in our present apparatus. Second, the nonlinear character of laser wavelength tuning is ignored, and it may cause the calibration error of laser modulation amplitude. The last reason, which is also the most important, the influence of the adjacent absorption spectral lines may distort the 2f-harmonic spectrum. As depicted in Fig. 3(a) and (c), the spectral lines of H2O at 6594.424 cm − 1 and 6594.698 cm − 1 are very close to the absorption line of C2H2, and its influence on measured 2f-harmoic signal cannot be ignored despite its absorption intensity was so low. Actually, the 2f-harmonic signal of CO2 at different modulation amplitudes have ever been recorded in the referenced literature [14], and their measured results are similar to our experiments and can also confirm our deductions partly.
5. Conclusions In this paper, we have presented a method to deduce the signal expressions of WM-OA-ICOS. To validate the method and its deduced results, some important problems in 2f-harmonic detection of WMOA-ICOS, such as the choice of optimum modulation coefficient of laser wavelength, were studied and experimented. And the measured results have verified our analyses and shown the difference between WM-DLAS and WM-OA-ICOS when the inner absorption of cavity is no longer smaller than the loss of empty cavity. These works can help us to understand the characteristic of WM-OA-ICOS, and may provide some references for the application of WM-OA-ICOS.
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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
The study of wavelength modulation off-axis integrated cavity output spectroscopy in the case of Lorentzian absorption profile Zhongqi Tan, Xingwu Long ⁎, Xianwang Feng, Zhimeng Wei Department of Optoelectronic Engineering, College of Optoelectronic Science & Engineering, National University of Defense Technology, Changsha 410073, China
a r t i c l e
i n f o
Article history: Received 12 May 2010 Received in revised form 24 August 2010 Accepted 28 September 2010 OCIS: 120.2230 120.6200 300.1030 300.6380
a b s t r a c t According to the property of optical cavity and the principle of signals and systems, the mathematical derivations for wavelength modulation off-axis integrated cavity output spectroscopy (WM-OA-ICOS) are presented. And based on the analytical method, the function expression of WM-OA-ICOS signal from Lorentzian absorption profile is obtained. To validate the analyses and deductions, some special cases in 2fharmonic detection of WM-OA-ICOS are studied and experimented with a built compact WM-OA-ICOS apparatus. It is found that the measured results can coincide with the deduced conclusions. The works can provide some references for the application of WM-OA-ICOS in the case of Lorentzian absorption profile. © 2010 Published by Elsevier B.V.
1. Introduction In the past decades, various high-sensitivity absorption spectroscopy techniques, which are mainly based upon the high-finesse optical cavity, have been developed and applied to detecting gas concentration or measuring absorption spectrum [1]. They include cavity ring down spectroscopy (CRDS) [2], phase-shift cavity ring down spectroscopy (PS-CRDS) [3], cavity enhanced absorption spectroscopy (CEAS) [4], integrated cavity output spectroscopy (ICOS) [5], and so on. In these techniques, when the continuouswave laser is used as the light source, the multiple-beam interference inside optical cavity is inevitable because the laser beam is often directed into optical cavity in an on-axis manner. In this case, the coincidence of the narrowband laser frequency with the cavity modes will bring the complexity of their apparatuses and increase their costs. In recent years, some new techniques have been proposed to avoid the interference effect in the high-fitness cavity, such as off-axis integrated cavity output spectroscopy (OA-ICOS) [6–8]. In this technique, the continuous-wave laser is coupled into the optical cavity with an off-axis configuration. And then the interference effect inside the optical cavity is eliminated systematically while preserving the absorption signal amplifying property of such low-loss cavity. In particular, when combining with the wavelength modulation absorption technique [9], the detectable sensitivity of OA-ICOS technique can be improved further. Nowadays, the so-called wavelength modulation off-axis integrated cavity output spectroscopy (WM-OA-ICOS) has
⁎ Corresponding author. E-mail address: [email protected] (X. Long). 0030-4018/$ – see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.optcom.2010.09.072
been applied in different fields successfully [10]. For example, 2fharmonic detection technique of WM-OA-ICOS has been used to measure the biogenic NO concentrations in human breath, and the detectable limit was achieved as 2.0 ppbv or better [11,12]. In the past research, the description of harmonic signal and the choice of optimum modulation index in WM-OA-ICOS were often in accordance with the theory of wavelength modulation direct laser absorption spectroscopy (WM-DLAS) [13]. However, in some cases, the traditional theory could not explain reasonably some special phenomena observed in the past experiments of WM-OA-ICOS. For instance, when the absorption loss of gaseous species in optical cavity was no longer smaller than the cavity mirror losses [14], we could find that the measured optimum modulation amplitude of laser wavelength for 2f-harmonic detection in WM-OA-ICOS was obviously bigger than its theoretical value. Beyond this current state, we deduce the universal basis for WM-OA-ICOS with another method in this paper. Furthermore, a set of compact WM-OA-ICOS system was built to verify our analyses and deductions. 2. Theory deduction The off-axis paths between two spherical mirrors of an optical cavity have been well understood and described [6,15], so we do not plan to repeat these contents. In this section, we emphasize the principle deduction of WM-OA-ICOS in the case of Lorentzian absorption profile. As we know, when the interference effect inside the optical cavity is ignored, the off-axis optical cavity can be abstracted into a linear time-invariant (LTI) system, because it is time invariant and satisfies the principle of superposition according to the principle of signals and
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systems [16]. As shown in Fig. 1, the pulsed laser in this case can be regarded as an impulse, and the impulse response h(v, t) of this optical system can be then written as [17] 8 > < hðv; t Þ = k⋅ exp½−t = τ ðvÞ L : > : τ ðvÞ = c⋅½δ0 ðvÞ + α ðvÞ⋅L
ð1Þ
according to the pulsed laser cavity ring down technique. Where k is the coupling coefficient between input light power and the inner power of cavity (traveling in each direction) [6,8], τ(v) is the decay time of light in optical cavity at the laser frequency v, δ0(v) is the total loss of cavity mirror (transmittance plus scattering and absorption), α(v) is the absorption coefficient of gaseous species closed in cavity, and L is the cavity length. Based upon this equation, the output signals of optical cavity excited by different input light signals can be obtained readily via the convolution operation between the input signal and the impulse response function. It is known, when the laser wavelength is modulated in a small spectral region by current tuning the laser diode, the optical system serves as the WM-OA-ICOS scheme. To deduce the basis for WM-OA-ICOS, we suppose the intensity Iin(t) and wavelength v of incident laser are expressed as
Iin ðt Þ = I0 + ΔI⋅ cosð 2π ft Þ ; v = v1 +Δv⋅ cosð 2π ft Þ
ð2Þ
respectively, when the nonlinear character of laser diode is ignored. Thereinto, f is the modulation frequency of laser current, I0 and v1 are the central values of light intensity and wavelength, ΔI and Δv are their modulation amplitudes caused by the current modulation of DFB laser diode, respectively. In the case of no absorption species closed in the cavity, cavity loss is insensitive to the scanning of laser wavelength because the loss spectrum of mirror is almost a smooth curve in a small spectral region. Then the system is still a linear system, and the cavity output signal can be inferred and analyzed with Eqs. (1) and (2). On the contrary, if some absorption species are closed in the cavity, the cavity ring down time (corresponding to the cavity loss) will change obviously with the laser wavelength scanning, and then yield the lineshape of absorption spectrum. As we know, the system in this case is no longer a linear system. To calculate the cavity output signal under this condition, we can divide the input laser at the time of t into a series of pulsed lasers. Their intensity and wavelength are shown as Eq. (2), and their time interval is expressed as Δt = 2L / c. The cavity output signal at the time t can be then written as the total response of these pulsed lasers, as following: 8 1 +∞ n⋅Δt > > > < I ðt Þ = 2τ ⋅ ∑ fI0 +ΔI⋅ cos½2π f d ðt−n⋅Δt Þg⋅k⋅ exp − τ ðt−n ΔtÞ dΔt ⋅ 1 n=0 > 1 ∞ −x > > :≈ ∫ fI + ΔId cos½2π f ⋅ðt−xÞg⋅k⋅ exp dx 2τ 1 ⋅ 0 0 τ ðt−xÞ
ð3Þ
853
where n is an integer, and τ1 is the ring down time related with the transmittance loss δ1 of mirrors. Here, the cavity output is calculated by dividing τ1 from the inner power of cavity according to the property of optical cavity, and the factor 2 accounts for the fact that the light leaves through both mirrors. To simplify Eq. (3), a hypothesis of f · τ b b 1 is introduced. Since the intensity and wavelength of laser can be regarded as an invariant approximately during the effective integrated time, Eq. (3) is then written as: Iðt Þ = ½I0 + ΔI⋅ cosð 2π ft Þ⋅k⋅τ ðt Þ = 2τ 1 Taking the Lorentzian absorption profile into account [18], and then the output signal of the optical cavity, which is excited by an incident laser modulated as Eq. (2), can be given as: 8 > > > < α ðvÞ⋅L =
S N⋅L π⋅γ ⋅ ½ðv1 −v0 Þ=γ + Δv⋅ cosð 2π ft Þ=γ 2 + 1
> > > : I ðt Þ = ½I0 + ΔI⋅ cosð 2π ft Þ⋅
k⋅δ1 ðvÞ 2⋅½δ0 ðvÞ + α ðvÞ⋅L
ð4Þ
where S is the absorption intensity of gaseous species, N is the absorption molecule density, and γ is the half-width at half-maximum (HWHM) of Lorentzian lineshape. In a special case, a non-modulated laser is used to exit the optical cavity, namely, Δv = ΔI = 0, the cavity integrated output signal can be then obtained to determine the inner absorption of optical cavity, and this is the basis of OA-ICOS. In WM-DLAS, it is known that the light signal can be expressed as h
L
i
I ðt Þ= ½I0 +ΔI⋅ cosð 2πft Þ⋅ exp −∫ α ðvÞ⋅dl ≈½I0 +ΔI ⋅ cosð 2πft Þ⋅½1−α ðvÞ⋅L 0
ð5Þ when α(v) ⋅ L b b 1. Comparing Eqs. (4) with (5), we can find, despite both the WM-OA-ICOS and WM-DLAS are all based on the wavelength modulation technique, their signals have different function expressions. It is known that the modulation amplitude of laser wavelength is a very important parameter for harmonic detection in WM-DLAS, and its optimization value has ever been studied in the past years. In the case of Lorentzian lineshape absorption, the theoretical optimization value for even-harmonic detection, which can maximize the even-order Fourier coefficient of a wavelength-modulated Lorentzian lineshape on resonance, has been deduced as Eq. (6) [19] if not considering the residual amplitude modulation (RAM) effect. ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2ffi Δvnopt n u 2 t η= = pffiffiffi 1 + 1 + n γ 2
ð6Þ
where η and Δvnopt are the optimum factor and optimum amplitude of laser wavelength modulation, respectively. According to this equation, we obtain the maximal 2f-harmonic intensity from the detected signal of WM-DLAS when the condition of Δv ≈ 2.2γ is satisfied. To obtain the optimization modulation value of laser wavelength in WM-OA-ICOS, Eq. (4) is transformed into the same function form as Eq. (5). And it is shown as Eq. (7) 8 i 0 ½I +ΔI ⋅ cosð 2π ftÞ⋅k⋅δ1 ðvÞ ½I0 +ΔI⋅ cosð 2π ftÞ⋅k⋅δ1 ðv0 Þ h > > Iðt Þ= 0 ≈ > ⋅ 1−x > > 2⋅½δ0 ðvÞ + α ðvÞ⋅L 2⋅δ0 ðv0 Þ > > > > < α ðv0 Þ⋅L
0 α ðv Þ⋅L + δ0 ðv0 Þ > > x =" sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > #2 > > > ð Þ ð Þ v −v δ v Δv δ0 ðv0 Þ > 1 0 0 0 > + cosð 2π ftÞ +1 > ⋅ ⋅ ⋅ : γ γ δ0 ðv0 Þ + α ðv0 Þ⋅L δ0 ðv0 Þ +α ðv0 Þ⋅L
ð7Þ
Fig. 1. Schematic diagram of WM-OA-ICOS.
where α(v0) is the peak absorption coefficient. Because the mirror loss in a small spectral range was known as a constant, δ0(v), δ1(v) in Eq. (7) has been replaced by δ0(v0), δ1(v0), respectively. Comparing Eq. (7)
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with Eq. (5), we can find the numerator of modulated signal function is multiplied by a large coefficient 1/ [α(v0) ⋅ L + δ0(v0)] for α(v0) ⋅ L + δ0 (v0) b b 1. This is why WM-OA-ICOS can reach a higher sensitivity than the traditional WM-DLAS in a short cavity. Finally, the optimization value η in WM-OA-ICOS can be determined as ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n u 2 δ ðv Þ + α ðv0 Þ⋅L t η = pffiffiffi 1 + 1 + ⋅ 0 0 n δ0 ðv0 Þ 2
ð8Þ
by referring to Eq. (6). Same as the other methods [13], it is found that the optimization values η of different methods are all the same when δ0 (v0) = 1 − R N N α(v0) ⋅ L (R is the reflectivity of mirrors).
measured as ~0.05% at 6592 cm− 1 (Lambda950, Perkin-Elmer). The light transmitted from the cavity was focused into a detector (PDA10CS, Thorlabs) with a 6.3 cm-diameter lens (focal length 6.3 cm), the detected signal was then sent to a special integral circuit for OA-ICOS measurement or to the DSP lock-in amplifiers SR830 for harmonic detection. To record the stable 2f-harmonic spectrum, the integrator was used again to integrate and digitize the output harmonic signal from the lock-in amplifier SR830, and the laser wavenumber was scanned by current tuning of DFB laser. Once the harmonic intensities of transmitted light signals at different laser wavelengths were recorded, they were sent to the computer via the UART for saving and analyzing. Need to add, to remove the interference effect and improve the stability of cavity output signal further, a micro-pump was mounted on the bellow to dither the cavity length randomly.
3. Experimental apparatus 4. Experimental results and analyses As depicted in Fig. 2, an experimental apparatus is built to verify our deductions and analyses, and it is mainly composed of seven parts, including light source, collimator, low-loss optical cavity, detector, lock-in amplifier, and so on. In our apparatus, a DFB laser (NLK1556STG, NEL) was used as the light source, and it has been integrated with a thermal electric coolers (TEC) and a thermistor sensors. The DFB laser was placed on a butterfly laser diode mounter (LM14S2, Thorlabs), and its temperature and current were controlled by a temperature controller (WTC3243, Wavelength Electronics) and a laser diode driver (LDD200-1P, Wavelength Electronics), respectively. As is known, the central wavelength of laser diode can be tuned in a small spectral range via adjusting its operating temperature or injection current. Accordingly, when the temperature and current of DFB laser were changed in 15–31 °C and 20–80 mA, respectively, it was found that the wavelength of DFB laser could be tuned in the spectral range of 6587–6595.5 cm−1. Furthermore, with the help of a high-precision wavemeter (WA-1500-NIR, EXFO Burleigh) and a spectrum analyzer (WA-650, EXFO Burleigh), the temperaturewavenumber and current-wavenumber coefficients of our DFB laser could be determined accurately. In Fig. 2, to modulate the laser wavelength for WM-OA-ICOS measurement, a sine signal, which came from the reference output of a DSP lock-in amplifier (SR830, Stanford Research Systems), was used as the input signal of LDD200-1P to modulate the injection current of laser diode. Then the modulated narrow-band laser (linewidth ~ 2 MHz) was then passed through a fiber collimator (F240APC1550, Thorlabs), and transformed into a ~1.5 mm-diameter Gaussian beam in free space. Without mode-matching lens, the collimated laser was directed into a 67 cm-long optical cavity with an off-axis alignment. The cavity was made of a 4.0 cm-diameter stainless bellow, and two plano-concave mirrors (5.0 cm-diameter, 8 m-curvature radius) were placed at its two sides. These mirrors were all made by ourselves, and their super-polished surfaces (RMS~ 0.06 nm, AFM3100) were deposited with a 29-layer periodic high-reflectivity coating by the ion-sputtering process. Later, their transmittances were
Referring to the HITRAN2004 database [20], it is known that there are some strong absorption lines of gaseous species lying in the spectral tuning range of our laser diode, such as ethyne (C2H2), water vapor (H2O) and giggle gas (N2O). Taking the absorption intensity and the interferences from other absorption lines into account, we chose the absorption line of C2H2 molecule at 6594.388 cm− 1 to carry on our experimental study. Subsequently, we set DFB laser's temperature to 16 °C and scanned the laser current in the range of 20–80 mA, it was then obtained that the laser wavenumber could be turned in the spectral range of 6593.94–6595.06 cm− 1. Furthermore, the relation between the laser wavenumber (cm− 1) and the laser current (mA) could be written as λ = −0:804 × 10
4
2
× i −0:0107 × i + 6595:310
ð9Þ
According to the measurement scheme of OA-ICOS [17], we can first obtain the loss spectrum of optical cavity in this spectral region (the temperature and pressure of gases closed in cavity were measured as 23.5 °C and 101.3 KPa, respectively). As shown in Fig. 3(a), three obvious absorption profiles are observed in the measured spectrum. To obtain the spectral parameters of C2H2, Eq. (4) was used as the object function to fit the measured spectral data using the Levenberg– Marquardt method. The fitted residue is also shown in Fig. 3(b), and the fitted line-width of 0.0720 cm− 1 was very close to the value of 0.0719 cm− 1 derived from the HITRAN2004 database. Therefore, it is believed that the deduced Eq. (4) can perfectly express the real OA-ICOS signal [17]. Additionally, two absorption lines of H2O molecule in this spectral range can clearly be observed in Fig. 3(a). Their spectral linewidths were then determined as ~0.0483 cm− 1 and ~0.865 cm− 1 respectively with the same fitting method, and the calculated absorption intensity ratio of the two lines was obtained as 26.33, which is just less than the value of 27.47 provided by HITRAN database slightly.
Fig. 2. Sketch map of the experimental WM-OA-ICOS system.
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Fig. 3. The measured spectra of C2H2 and H2O with OA-ICOS and WM-OA-ICOS. (a) is the measured OA-ICOS spectrum and its fitted curve in 6593.93–6595.06 cm− 1, (b) is the fitted residua of OA-ICOS spectrum, and (c) is the 2f-harmonic spectrum measured with WM-OA-ICOS when the modulation amplitude and frequency of laser current were set to 2.26 mA and 1.0 KHz, respectively.
Fig. 4. The OA-ICOS spectra of C2H2 in different concentration and the 2f-harmonic signals at different modulation amplitudes in WM-OA-ICOS. (a) is the measured spectra with OA-ICOS in different C2H2 concentrations, and (b) is the measured relation curves between modulation amplitude of laser wavelength and 2f-harmonic signal intensity in WM-OA-ICOS when the modulation frequency was set to 1.0 KHz.
After connecting the output of SR830 to our integrator, the OAICOS system can be applied to measuring the harmonic spectrum of C2H2 molecule. When the modulation amplitude and frequency of laser current were set to 2.26 mA and 1.0 KHz, respectively, the measured 2f-harmonic spectra of C2H2 and H2O are shown in Fig. 3(c). In this case, the integral time of SR830 was 300 ms. Unexpectedly, compared with Fig. 3(a), it can be found that the strong absorption line of water vapor at 6595.078 cm− 1 is not present in Fig. 3(c). We think the phenomenon can be explained from two aspects. First, the cavity output signal near 6595 cm− 1 was so weak that 2f-harmoic intensity detected by SR830 was too low. As we know, the laser current corresponding to the laser wavenumber of 6595 cm− 1 was close to the threshold current of DFB laser, so the laser power at this wavenumber was low. Furthermore, the strong absorption of water vapor reduced the cavity output further. In fact, when we turned the absorption line of water vapor to the middle of scanning region via changing the DFB laser's temperature, we could observe the 2fharmonic spectrum of water vapor at 6595.078 cm− 1 clearly. Second, the modulation amplitude of laser wavelength, which was calculated as 0.03 cm− 1 according to Eq. (9), was far smaller than the linewidth of water vapor, and it also weakened the 2f-harmoic signal. In addition, we can find that the measured 2f-harmoic signal in Fig. 3(c) has an small offset, and it may be due to the RAM effect and the phase shift between the intensity modulation and the laser frequency. According to Eq. (8), it is believed that the optimum modulation amplitude of even-harmonic detection in WM-OA-ICOS reduces with the dying down of the absorption intensity inside the cavity. To validate the conclusion, we set the laser wavelength at 6594.388 cm− 1 by stabilizing the temperature and current of DFB laser (wavelength stability was ~0.003 cm− 1), and measured the relation curves between the modulation amplitude of DFB laser wavelength and the 2f-harmoic intensity under different absorption status. As shown in Fig. 4(a), four absorption profiles at different C2H2 concentrations were recorded by the OA-ICOS technique, and their spectral line-widths were calculated as 0.0713, 0.0720, 0.0720 and 0.0713 cm− 1, successively. In addition, the ratios of absorption intensity to the loss of empty cavity, namely α(v0) ⋅ L / δ0(v0), could also be determined as 17.76, 3.96, 2.08 and 1.03, respectively. Under every absorption status, the integral time of SR830 was set to 1.0 s to obtain a stable 2f-harmoic signal, and the relation curves between the 2f-harmoic intensity and the laser modulation amplitudes were
plotted in Fig. 4(b). From the measured data, the optimum modulation amplitudes under different absorption status could be determined as 0.441, 0.286, 0.249, and 0.194 cm− 1. Obviously, the measured results of Fig. 4(b) can accord with the character of optimum modulation amplitude as Eq. (8). That is to say, the optimum modulation amplitude increases with the absorption loss inside optical cavity. Unfortunately, the calculated optimum modulation amplitude according to Eq. (8), which were determined as 0.682, 0.351, 0.276 and 0.224 cm− 1 respectively based on the measured absorption parameters of C2H2 spectrum, are slightly bigger than the measured results. We think the deviation may be caused by the following reasons: First, the residual interference effect may influence the precision of measured 2f-harmonic intensity. Despite the mechanical vibration was introduced by a micro-pump, the optical interference inside cavity is still inevitable in our present apparatus. Second, the nonlinear character of laser wavelength tuning is ignored, and it may cause the calibration error of laser modulation amplitude. The last reason, which is also the most important, the influence of the adjacent absorption spectral lines may distort the 2f-harmonic spectrum. As depicted in Fig. 3(a) and (c), the spectral lines of H2O at 6594.424 cm − 1 and 6594.698 cm − 1 are very close to the absorption line of C2H2, and its influence on measured 2f-harmoic signal cannot be ignored despite its absorption intensity was so low. Actually, the 2f-harmonic signal of CO2 at different modulation amplitudes have ever been recorded in the referenced literature [14], and their measured results are similar to our experiments and can also confirm our deductions partly.
5. Conclusions In this paper, we have presented a method to deduce the signal expressions of WM-OA-ICOS. To validate the method and its deduced results, some important problems in 2f-harmonic detection of WMOA-ICOS, such as the choice of optimum modulation coefficient of laser wavelength, were studied and experimented. And the measured results have verified our analyses and shown the difference between WM-DLAS and WM-OA-ICOS when the inner absorption of cavity is no longer smaller than the loss of empty cavity. These works can help us to understand the characteristic of WM-OA-ICOS, and may provide some references for the application of WM-OA-ICOS.
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