Abstract

Cavity ring down (CRD) technique was employed to measure optical losses (absorption and scattering losses), residual reflectance and transmittance of anti-reflectively (AR) coated laser components with transmittance higher than 99.9%. By inserting the AR coated laser component with parallel optical surfaces into the ring-down cavity and measuring the ring-down time versus the angle of incidence with respect to the surface normal, the optical loss and residual reflectance of the laser component were determined respectively at normal and out-of-normal incidences with repeatability of part-per-million level. The transmittance was also determined simultaneously. Experimental results demonstrated that CRD is a simple, inexpensive and fast technique for highly accurate measurements of optical loss, residual reflectance, and transmittance of AR coated laser components widely used in high-power laser systems.

© 2014 Optical Society of America

1. Introduction

Transmittance T, reflectance R and optical loss L (normally includes absorption loss and scattering loss, defined as L=1TR) measurements of optical laser components are routine practice in optical thin film laboratories. For optical components for normal use, optical losses in the order of one percent and higher can be easily determined with sufficient precision (in the 0.1% order) by measuring the reflectance and transmittance via spectrophotometry. On the other hand, an accurate measurement of optical loss in the order of 0.1% and below requires a higher sensitivity as thin-film deposition techniques reach a maturity level consistent with the routine production of dielectric films with optical losses in several hundred ppm (part per million) to sub-ppm range. Currently, the reflectance R and optical loss L of highly reflective (HR) mirrors with reflectance higher than 99.9% have been measured accurately by cavity ring-down(CRD)technique with typical measurement uncertainty of 1ppm or less [1–4]. For anti-reflectively (AR) coated optical laser components with transmittance T higher than 99.9%, the transmittance cannot be measured with sufficient precision by spectrophotometry. CRD is an appropriate technique to measure such high transmittance with repeatability in the ppm level. However, no report on the CRD measurement of transmittance has been found till now.

CRD technique was widely used to measure the optical loss L of optical substrates and laser components. To eliminate the influence of residual reflectance on the optical loss measurement, a component to be measured was inserted in the ring-down cavity in a manner that its surfaces were oriented either at the Brewster angle [5–8] or normal [9–14] to the light beam. On the other hand, in many applications, the residual reflectance of AR-coated components also plays important roles in the system’s performance. For example, the residual reflectance of lenses and windows used in high-power laser systems may have negative influence on the long-term stability of the laser systems, as reflected beams may cause long-term damages to optics in the beam paths or cause optical interference to the laser oscillator. For travelling wave semiconductor optical amplifier (TW-SOA) [15, 16], the residual reflectance of its surface also has important impact on the performance index including bandwidth and gain fluctuation. In these applications, the residual reflectance of AR coatings should be minimized down to ppm (part-per-million) levels by carefully optimizing the coating design and deposition parameters. In this case the determination of the residual reflectance with ppm accuracy is essential for such optimization.

In this paper, for the first time to our knowledge, we report on the application of CRD technique to measure simultaneously the transmittance, optical loss, and residual reflectance of AR-coated laser components. By inserting the laser component into the ring-down cavity (RDC) and measuring the ring-down time versus the angle of incidence with respect to the surface normal of the component, the optical loss and residual reflectance of the laser component can be determined respectively at normal and out-of-normal incidences. The transmittance is determined accordingly.

2. Theoretical Model

For a highly transparent sample with both surfaces AR-coated, when the sample is placed in the RDC with an out-of-normal incident angle so that the reflections from the sample surfaces are out of the RDC, the reflections are deemed as a loss to the ring-down signal. In this case the ring-down signal is expressed as

In=I0(R1R2R32)nexp(2nk)
Where n is the times of round-trip reflection, n=tc/2[L+(ns1)d], with c the speed of light, L the RDC length, and d and ns the thickness and the index of the refraction of the sample, respectively. I0 is the initial intensity of the RDC output signal, In is the intensity of the output light after the light has n-times round-trip reflection in the RDC. R1, R2, R3 are the reflectance of the cavity mirrors for a three-mirror initial RDC. k=k+r, k and r are the optical loss (absorption loss plus scattering loss) and residual reflectance of the sample, respectively.

By Substituting n=tc/2[L+(ns1)d]in Eq. (1), the intensity of the ring-down signal In can be further written as

I(t)=I0(R1R2R32)tc2[L+(ns1)d]exp(tcL+(ns1)dk)=I0exp[cL+(ns1)d(lnR1R2R3k)t]

So that the ring-down time can be given by

τ1=L+(ns1)dc(klnR1R2R3)

When there is no sample in the RDC (empty RDC or initial RDC with k=0,ns=1), the ring-down time is written as

τ0=Lc(lnR1R2R3)

From Eqs. (3) and (4), the optical loss k can be obtained

k=Lc(1τ11τ0)+(ns1)dcτ1

Then

k+r=Lc(1τ11τ0)+(ns1)dcτ1

On the other hand, when the surfaces of the sample in the RDC are normal to the beam path, the reflections from the sample surfaces remain staying in the RDC. In this case the reflections cause no loss to the ring-down signal [10, 12–14]. The ring-down signal In can therefore be written as [17]

In=I0(R1R2R32)nexp(2nk)
or,
I(t)=I0(R1R2R32)tc2[L+(ns1)d]exp(tcL+(ns1)dk)=I0exp[cL+(ns1)d(lnR1R2R3k)t]
In this case the ring-down time can be given by

τ2=L+(ns1)dc(klnR1R2R3)

The optical loss k alone can be determined

k=Lc(1τ21τ0)+(ns1)dcτ2

Once the ring down timeτ0, τ1, τ2are experimentally measured, the optical loss k can be determined via Eq. (10), the residual reflectance r can be determined via Eqs. (6) and (10) and is expressed as

r=L+(ns1)dc(1τ11τ2)
Once the optical loss and residual reflectance of the sample are determined, the transmittance of the sample can be also determined as
T=1kr
The theoretical model shows that by measuring the ring-down time at normal incidence and out-of-normal incidences, the optical loss and residual reflectance, as well as the transmittance of the AR-coated sample can be determined by CRD technique with a typical accuracy in the order of ppm level.

3. Experiment

An optical feedback CRD (OF-CRD) [17] scheme is used in the CRD measurements. A schematic diagram of the experimental OF-CRD setup for measuring the transmittance, optical loss, and residual reflectance of the optical laser components is shown in Fig. 1. A continuous-wave (CW) Fabry-Perot (FP) diode laser (Model IQ1A07, Power Technologies) centered at 1064nm with TEM00 mode output and power approximately 120mW is used as the light source. The output power of the diode laser is square-wave modulated at 100 Hz with a duty circle of 50% by a PC-controlled function generation (FG) card (Model UF2-3012, Strategic Test, Sweden). The RDC is formed by two identical plano-concave mirrors with a diameter of 25.4mm and a radius of curvature r = −100cm and a planar mirror with a diameter of 25.4mm. The RDC mirrors are aligned along their optical axes. The light that leaks out from the RDC mirror (R1) is focused onto a Photo Detector (PD) (Model1811, New Focus) whose output is digitized by a data acquisition (DA) Card (Model UF2-6012, Strategic Test, Sweden) for recording the exponential decay signal. The CRD signals are recorded at the negative edge of the modulation. The sample is mounted on a two-dimensional rotation stage for adjusting the orientation of the sample surface with respect to the beam path. The experimental setup allows an automated, computer-controlled rotation of the sample around x and y directions. A visible diode laser operated at 635nm, is employed for aligning the RDC mirrors.

 figure: Fig. 1

Fig. 1 Schematic diagram of the CRD experimental setup. BS: beamsplitter; PD: photo detector; R1, R2, R3: cavity mirrors; PC: personal computer.

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The sample used in the experiment is a fused silica substrate (Corning 7980) coated with anti-reflective HfO2/SiO2 multiplayer on both sides for 1064nm laser applications. The diameter and thickness of the sample are 30 mm and 2mm, respectively. The anti-reflective multilayer design is Sub/0.345H 1.321L/Air, with H and L represent the layers of high- and low-refractive index materials, respectively. The sample is coated with a vacuum coating equipment (SYRUSpro DUV 1100, Leybold Optics, Germany) with plasma ion assist deposition technology. The theoretical and experimental transmittances versus wavelength are shown in Fig. 2. At 1064nm wavelength, the transmittance measured by a spectrophotometer (Lambda 1050, Perkin Elmer) is approximately 100.0 ± 0.1%. As the transmittance is higher than 99.9%, it could not be measured accurately with the spectrophotometric approach.

 figure: Fig. 2

Fig. 2 Theoretical and measured transmittance spectrum of the AR-coated sample in 900nm-1300nm spectral range.

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To measure the transmittance, optical loss and residual reflectance of the sample, the decay time τ0 of the initial RDC is first measured. The sample is then inserted into the RDC near the central position of the cavity and the decay time τ is measured versus the angle of incidence by adjusting the orientation of the sample surface with respect to the beam path with the computer-controlled two-dimensional rotation stage. The optical loss and residual reflectance, as well as the transmittance of the sample are then determined from the ring-down time measured at normal and out-of-normal incidences, obtained from the dependence of the ring-down time on the angle of incidence.

4. Results and discussions

In the experiment, the ring-down signals are recorded immediately at the falling edges of the square-wave modulation. A typical CRD signal and the corresponding best-fit, as well as the fitting error on a linear scale are presented in Figs. 3(a) and 3(b), respectively. The dots in Fig. 3 (a) represent the experimental data, and the solid line represents a single exponential fit. The inserted figure shows that the ring-down signal appears to be highly linear on a logarithmic scale, together with the low fitting error presented in Fig. 3(b), indicating a good single exponential fit. This suggests a negligible contribution of the higher-order modes in the ring-down signal [18, 19]. The high amplitude of the ring-down signal (~0.8V at the beginning) as well as the low noise level indicates a high signal-to-noise ratio (SNR), which allows a precise determination of the ring-down time from a single ring-down signal using a least-squares fitting routine. Higher SNR and therefore higher measurement precision could be obtained by recording and averaging a certain number of ring-down signals.

 figure: Fig. 3

Fig. 3 (a) A typical ring-down signal and the corresponding single exponential fit in a linear scale or in a logarithmic scale. (b) The fitting error representing the difference between the experimental data and the fit.

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To determine the optical loss, residual reflectance, as well as the transmittance of the AR-coated sample, the ring-down time (τ) is measured versus the angle of incidence, and the dependence of the total loss, defined as L0=Lc(1τ1τ0)+(ns1)dcτ, on the angle of incidence is obtained. The results are presented in Fig. 4 (a) for different cavity lengths. The dependence can be divided into three regions. Region 1 (angle of incidence is larger than approximately 1.1 degree for RDC length 0.746m, 1.0 degree for 0.852m, 0.8 degree for 1.036m, and 0.7 degree for 1.036m) represents the case that the reflection of the sample is totally out of the RDC. Region 3 (angle of incidence is smaller than approximately 0.25 degree) represents the case that the reflection of the sample is totally within the RDC. Region 2 represents the case in between. In Region 3 the measured total loss is the sum of the optical loss and residual reflectance, while in Region 3 the measured total loss is only the optical loss. Both are approximately independent of the angle of incidence, as the optical loss and residual reflectance are approximately independent of the angle of incidence when the angle is small (between −2° to 2° here), in agreement with the theoretical predictions (Fresnel’s formula). In Region 2 as the angle of incidence increases, portion of the reflection escapes away from the RDC and the escaped reflection is deemed as loss in the CRD measurement. From Fig. 4(a) the optical loss is determined from the measured total loss in Region 3, the residual reflectance is the difference between the total losses measured in Regions 1 and 3, and the transmittance is determined from the total loss measured in Region 1. Figure 4(b) shows the dependences of the measured optical loss, residual reflectance and transmittance on the RDC length. In the measurements the sample is placed in the middle of the RDC. As expected, the measured optical loss, residual reflectance and transmittance are approximately independent of the RDC length, indicating the high reliability of the measurement results. The measured mean values of the optical loss L, residual reflectance r, and transmittance are 27.3 ± 1.1ppm, 95.8 ± 1.7ppm, and 99.9877 ± 0.0017%, respectively. The low uncertainties indicate the high repeatability of the CRD measurements.

 figure: Fig. 4

Fig. 4 (a) Experimental total loss versus the angle of incidence for different RDC lengths. The sample is placed in the middle of the RDC. Error bar represents the standard deviation of 128 measurements. (b) Optical loss, residual reflectance, and transmittance versus RDC length.

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In addition, from Eqs. (3), (4), and (9), the ring-down time of RDC with or without sample inside is linearly proportional to the RDC length, and from the slope of this linear dependence the total loss can be determined [10]. Figure 5 presents the RDC length dependence of the ring-down time for the cases of initial RDC (with no sample inside) (τ0), RDC with sample with normal incidence (τ2), and RDC with sample with angle of incidence approximately 1.1 degrees (out-of-normal incidence) (τ1). Evidently, in all three cases good linear dependences are obtained. By taking into consideration the influence of the sample thickness on the dependence, the slopes for the cases of initial RDC (τ0), RDC with sample with normal incidence (τ2), and RDC with sample with out-of-normal incidence (τ1) are 14.41, 12.90, and 9.45 μs/m, respectively. Using Eqs. (10) and (11), the optical loss L and residual reflectance r of the sample determined from the slopes of the linear dependences are 27.1ppm and 94.4ppm, respectively, in excellent agreement with the direct-measurement results, 27.3 ± 1.1ppm and 95.8 ± 1.7ppm, as presented above. In the mean time, the absorption loss of the sample is measured by laser calorimetry (LC) method and the measured absorptance is 19.7ppm, somewhat smaller than the optical loss measured by the CRD technique, as expected. The good agreements among the results obtained with different approaches are an indication of the high reliability of the CRD measurement results.

 figure: Fig. 5

Fig. 5 Ring-down time versus RDC length for initial RDC (with no sample) (τ0), RDC with sample with normal incidence (τ2), and RDC with sample with out-of-normal incidence (τ1).

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5. Conclusions

In summary, for the first time the simple and sensitive CRD technique has been employed to measure simultaneously the optical loss, residual reflectance, and transmittance of AR-coated laser components with transmittance higher than 99.9%. The optical loss, residual reflectance, and transmittance of an AR-coated laser window at 1064nm have been measured to be 27.3ppm, 95.8ppm, and 99.9877%, with uncertainties of 1.1ppm, 1.7ppm, and 1.7ppm, respectively. The low measurement uncertainty and excellent agreement between results obtained with different data-processing techniques have demonstrated that CRD is a highly accurate technique for very low optical loss and residual reflectance measurements of optical components. The accurate measurement of residual reflectance of AR-coated components is expected to find applications on the manufacturing of high-quality AR coatings for high-power laser applications.

References and links

1. G. Schmidl, W. Paa, W. Triebel, S. Schippel, and H. Heyer, “Spectrally resolved cavity ring down measurement of high reflectivity mirrors using a supercontinuum laser source,” Appl. Opt. 48(35), 6754–6759 (2009). [CrossRef]   [PubMed]  

2. H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, and I. Kataoka, “Ultralow-loss mirror of the parts-in-106 level at 1064 nm,” Opt. Lett. 20(6), 530–532 (1995).

3. Y. Gong, B. Li, and Y. Han, “Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity,” Appl. Phys. B 93(2-3), 355–360 (2008). [CrossRef]  

4. A. Duparré and D. Ristau, “Optical interference coatings 2010 measurement problem,” Appl. Opt. 50(9), C172–C177 (2011). [CrossRef]   [PubMed]  

5. C. Stambaugh, M. Durand, U. Kemiktarak, and J. Lawall, “Cavity-enhanced measurements for determining dielectric-membrane thickness and complex index of refraction,” Appl. Opt. 53(22), 4930–4938 (2014). [CrossRef]   [PubMed]  

6. G. A. Marcus and H. A. Schwettman, “Cavity ringdown spectroscopy of thin films in the mid-infrared,” Appl. Opt. 41(24), 5167–5171 (2002). [CrossRef]   [PubMed]  

7. R. N. Muir and A. J. Alexander, “Structure of monolayer dye films studied by Brewster angle cavity ring down spectroscopy,” Phys. Chem. Chem. Phys. 5(6), 1279–1283 (2003). [CrossRef]  

8. J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005). [CrossRef]   [PubMed]  

9. A. Terasaki, T. Kondow, and K. Egashira, “Continuous-wave cavity ring-down spectroscopy applied to solids: properties of a Fabry–Perot cavity containing a transparent substrate,” J. Opt. Soc. Am. B 22(3), 675–686 (2005). [CrossRef]  

10. A. H. M. Smets, J. H. van Helden, and M. C. M. Sanden, “Bulk and surface defects in a-Si: H films studied by means of the cavity ring down absorption technique,” J. Non-Cryst. Solids 299(302), 610–614 (2002). [CrossRef]  

11. K. Egashira, A. Terasaki, and T. Kondow, “Photon-trap spectroscopy applied to molecules adsorbed on a solid surface: probing with a standing wave versus a propagating wave,” Appl. Opt. 49(7), 1151–1157 (2010). [CrossRef]   [PubMed]  

12. R. Engeln, G. von Helden, A. J. A. van Roij, and G. Meijer, “Cavity ring down spectroscopy on solid C60,” J. Chem. Phys. 110(5), 2732–2733 (1999). [CrossRef]  

13. S. L. Logunov, “Cavity ringdown detection of losses in thin films in the telecommunication wavelength window,” Appl. Opt. 40(9), 1570–1573 (2001). [CrossRef]   [PubMed]  

14. I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004). [CrossRef]  

15. G. R. Lin, C. L. Pan, and K. C. Yu, “Dynamic chirp control of all-optical format-converted pulsed data from a multi-wavelength inverse-optical-comb injected semiconductor optical amplifier,” Opt. Express 15(20), 13330–13339 (2007). [CrossRef]   [PubMed]  

16. P. Manimaran and M. G. Madhan, “An efficient electrode arrangement for TWSOA based inline detector,” Optik (Stuttg.) 124(19), 3842–3847 (2013). [CrossRef]  

17. Z. C. Qu, B. C. Li, and Y. L. Han, “Measurement of losses in optical components using filtered optical feedback cavity ring down technique,” Proc. SPIE 8206, 82061M (2011). [CrossRef]  

18. H. F. Huang and K. K. Lehmann, “Noise in cavity ring-down spectroscopy caused by transverse mode coupling,” Opt. Express 15(14), 8745–8759 (2007). [CrossRef]   [PubMed]  

19. K. K. Lehmann and D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105(23), 10263–10277 (1996). [CrossRef]  

References

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  1. G. Schmidl, W. Paa, W. Triebel, S. Schippel, and H. Heyer, “Spectrally resolved cavity ring down measurement of high reflectivity mirrors using a supercontinuum laser source,” Appl. Opt. 48(35), 6754–6759 (2009).
    [Crossref] [PubMed]
  2. H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, and I. Kataoka, “Ultralow-loss mirror of the parts-in-106 level at 1064 nm,” Opt. Lett. 20(6), 530–532 (1995).
  3. Y. Gong, B. Li, and Y. Han, “Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity,” Appl. Phys. B 93(2-3), 355–360 (2008).
    [Crossref]
  4. A. Duparré and D. Ristau, “Optical interference coatings 2010 measurement problem,” Appl. Opt. 50(9), C172–C177 (2011).
    [Crossref] [PubMed]
  5. C. Stambaugh, M. Durand, U. Kemiktarak, and J. Lawall, “Cavity-enhanced measurements for determining dielectric-membrane thickness and complex index of refraction,” Appl. Opt. 53(22), 4930–4938 (2014).
    [Crossref] [PubMed]
  6. G. A. Marcus and H. A. Schwettman, “Cavity ringdown spectroscopy of thin films in the mid-infrared,” Appl. Opt. 41(24), 5167–5171 (2002).
    [Crossref] [PubMed]
  7. R. N. Muir and A. J. Alexander, “Structure of monolayer dye films studied by Brewster angle cavity ring down spectroscopy,” Phys. Chem. Chem. Phys. 5(6), 1279–1283 (2003).
    [Crossref]
  8. J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
    [Crossref] [PubMed]
  9. A. Terasaki, T. Kondow, and K. Egashira, “Continuous-wave cavity ring-down spectroscopy applied to solids: properties of a Fabry–Perot cavity containing a transparent substrate,” J. Opt. Soc. Am. B 22(3), 675–686 (2005).
    [Crossref]
  10. A. H. M. Smets, J. H. van Helden, and M. C. M. Sanden, “Bulk and surface defects in a-Si: H films studied by means of the cavity ring down absorption technique,” J. Non-Cryst. Solids 299(302), 610–614 (2002).
    [Crossref]
  11. K. Egashira, A. Terasaki, and T. Kondow, “Photon-trap spectroscopy applied to molecules adsorbed on a solid surface: probing with a standing wave versus a propagating wave,” Appl. Opt. 49(7), 1151–1157 (2010).
    [Crossref] [PubMed]
  12. R. Engeln, G. von Helden, A. J. A. van Roij, and G. Meijer, “Cavity ring down spectroscopy on solid C60,” J. Chem. Phys. 110(5), 2732–2733 (1999).
    [Crossref]
  13. S. L. Logunov, “Cavity ringdown detection of losses in thin films in the telecommunication wavelength window,” Appl. Opt. 40(9), 1570–1573 (2001).
    [Crossref] [PubMed]
  14. I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
    [Crossref]
  15. G. R. Lin, C. L. Pan, and K. C. Yu, “Dynamic chirp control of all-optical format-converted pulsed data from a multi-wavelength inverse-optical-comb injected semiconductor optical amplifier,” Opt. Express 15(20), 13330–13339 (2007).
    [Crossref] [PubMed]
  16. P. Manimaran and M. G. Madhan, “An efficient electrode arrangement for TWSOA based inline detector,” Optik (Stuttg.) 124(19), 3842–3847 (2013).
    [Crossref]
  17. Z. C. Qu, B. C. Li, and Y. L. Han, “Measurement of losses in optical components using filtered optical feedback cavity ring down technique,” Proc. SPIE 8206, 82061M (2011).
    [Crossref]
  18. H. F. Huang and K. K. Lehmann, “Noise in cavity ring-down spectroscopy caused by transverse mode coupling,” Opt. Express 15(14), 8745–8759 (2007).
    [Crossref] [PubMed]
  19. K. K. Lehmann and D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105(23), 10263–10277 (1996).
    [Crossref]

2014 (1)

2013 (1)

P. Manimaran and M. G. Madhan, “An efficient electrode arrangement for TWSOA based inline detector,” Optik (Stuttg.) 124(19), 3842–3847 (2013).
[Crossref]

2011 (2)

Z. C. Qu, B. C. Li, and Y. L. Han, “Measurement of losses in optical components using filtered optical feedback cavity ring down technique,” Proc. SPIE 8206, 82061M (2011).
[Crossref]

A. Duparré and D. Ristau, “Optical interference coatings 2010 measurement problem,” Appl. Opt. 50(9), C172–C177 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2008 (1)

Y. Gong, B. Li, and Y. Han, “Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity,” Appl. Phys. B 93(2-3), 355–360 (2008).
[Crossref]

2007 (2)

2005 (2)

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

A. Terasaki, T. Kondow, and K. Egashira, “Continuous-wave cavity ring-down spectroscopy applied to solids: properties of a Fabry–Perot cavity containing a transparent substrate,” J. Opt. Soc. Am. B 22(3), 675–686 (2005).
[Crossref]

2004 (1)

I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
[Crossref]

2003 (1)

R. N. Muir and A. J. Alexander, “Structure of monolayer dye films studied by Brewster angle cavity ring down spectroscopy,” Phys. Chem. Chem. Phys. 5(6), 1279–1283 (2003).
[Crossref]

2002 (2)

A. H. M. Smets, J. H. van Helden, and M. C. M. Sanden, “Bulk and surface defects in a-Si: H films studied by means of the cavity ring down absorption technique,” J. Non-Cryst. Solids 299(302), 610–614 (2002).
[Crossref]

G. A. Marcus and H. A. Schwettman, “Cavity ringdown spectroscopy of thin films in the mid-infrared,” Appl. Opt. 41(24), 5167–5171 (2002).
[Crossref] [PubMed]

2001 (1)

1999 (1)

R. Engeln, G. von Helden, A. J. A. van Roij, and G. Meijer, “Cavity ring down spectroscopy on solid C60,” J. Chem. Phys. 110(5), 2732–2733 (1999).
[Crossref]

1996 (1)

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105(23), 10263–10277 (1996).
[Crossref]

1995 (1)

Aarts, I. M. P.

I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
[Crossref]

Alexander, A. J.

R. N. Muir and A. J. Alexander, “Structure of monolayer dye films studied by Brewster angle cavity ring down spectroscopy,” Phys. Chem. Chem. Phys. 5(6), 1279–1283 (2003).
[Crossref]

Antonietti, J.-M.

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

Duparré, A.

Durand, M.

Egashira, K.

Engeln, R.

I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
[Crossref]

R. Engeln, G. von Helden, A. J. A. van Roij, and G. Meijer, “Cavity ring down spectroscopy on solid C60,” J. Chem. Phys. 110(5), 2732–2733 (1999).
[Crossref]

Gong, Y.

Y. Gong, B. Li, and Y. Han, “Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity,” Appl. Phys. B 93(2-3), 355–360 (2008).
[Crossref]

Han, Y.

Y. Gong, B. Li, and Y. Han, “Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity,” Appl. Phys. B 93(2-3), 355–360 (2008).
[Crossref]

Han, Y. L.

Z. C. Qu, B. C. Li, and Y. L. Han, “Measurement of losses in optical components using filtered optical feedback cavity ring down technique,” Proc. SPIE 8206, 82061M (2011).
[Crossref]

Heiz, U.

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

Heyer, H.

Hoex, B.

I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
[Crossref]

Huang, H. F.

Jones, H.

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

Kataoka, I.

Kemiktarak, U.

Kessels, W. M. M.

I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
[Crossref]

Kitajima, N.

Kondow, T.

Lawall, J.

Lehmann, K. K.

H. F. Huang and K. K. Lehmann, “Noise in cavity ring-down spectroscopy caused by transverse mode coupling,” Opt. Express 15(14), 8745–8759 (2007).
[Crossref] [PubMed]

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105(23), 10263–10277 (1996).
[Crossref]

Li, B.

Y. Gong, B. Li, and Y. Han, “Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity,” Appl. Phys. B 93(2-3), 355–360 (2008).
[Crossref]

Li, B. C.

Z. C. Qu, B. C. Li, and Y. L. Han, “Measurement of losses in optical components using filtered optical feedback cavity ring down technique,” Proc. SPIE 8206, 82061M (2011).
[Crossref]

Lim, K. H.

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

Lin, G. R.

Logunov, S. L.

Madhan, M. G.

P. Manimaran and M. G. Madhan, “An efficient electrode arrangement for TWSOA based inline detector,” Optik (Stuttg.) 124(19), 3842–3847 (2013).
[Crossref]

Manimaran, P.

P. Manimaran and M. G. Madhan, “An efficient electrode arrangement for TWSOA based inline detector,” Optik (Stuttg.) 124(19), 3842–3847 (2013).
[Crossref]

Marcus, G. A.

Meijer, G.

R. Engeln, G. von Helden, A. J. A. van Roij, and G. Meijer, “Cavity ring down spectroscopy on solid C60,” J. Chem. Phys. 110(5), 2732–2733 (1999).
[Crossref]

Michalski, M.

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

Mitake, T.

Muir, R. N.

R. N. Muir and A. J. Alexander, “Structure of monolayer dye films studied by Brewster angle cavity ring down spectroscopy,” Phys. Chem. Chem. Phys. 5(6), 1279–1283 (2003).
[Crossref]

Nakamura, K.

Paa, W.

Pacchioni, G.

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

Pan, C. L.

Qu, Z. C.

Z. C. Qu, B. C. Li, and Y. L. Han, “Measurement of losses in optical components using filtered optical feedback cavity ring down technique,” Proc. SPIE 8206, 82061M (2011).
[Crossref]

Ristau, D.

Romanini, D.

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105(23), 10263–10277 (1996).
[Crossref]

Rösch, N.

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

Sanden, M. C. M.

A. H. M. Smets, J. H. van Helden, and M. C. M. Sanden, “Bulk and surface defects in a-Si: H films studied by means of the cavity ring down absorption technique,” J. Non-Cryst. Solids 299(302), 610–614 (2002).
[Crossref]

Schippel, S.

Schmidl, G.

Schwettman, H. A.

Sekiguchi, H.

Smets, A. H. M.

I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
[Crossref]

A. H. M. Smets, J. H. van Helden, and M. C. M. Sanden, “Bulk and surface defects in a-Si: H films studied by means of the cavity ring down absorption technique,” J. Non-Cryst. Solids 299(302), 610–614 (2002).
[Crossref]

Stambaugh, C.

Terasaki, A.

Triebel, W.

van de Sanden, M. C. M.

I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
[Crossref]

van Helden, J. H.

A. H. M. Smets, J. H. van Helden, and M. C. M. Sanden, “Bulk and surface defects in a-Si: H films studied by means of the cavity ring down absorption technique,” J. Non-Cryst. Solids 299(302), 610–614 (2002).
[Crossref]

van Roij, A. J. A.

R. Engeln, G. von Helden, A. J. A. van Roij, and G. Meijer, “Cavity ring down spectroscopy on solid C60,” J. Chem. Phys. 110(5), 2732–2733 (1999).
[Crossref]

Vitto, A. D.

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

von Helden, G.

R. Engeln, G. von Helden, A. J. A. van Roij, and G. Meijer, “Cavity ring down spectroscopy on solid C60,” J. Chem. Phys. 110(5), 2732–2733 (1999).
[Crossref]

Yu, K. C.

Appl. Opt. (6)

Appl. Phys. B (1)

Y. Gong, B. Li, and Y. Han, “Optical feedback cavity ring-down technique for accurate measurement of ultra-high reflectivity,” Appl. Phys. B 93(2-3), 355–360 (2008).
[Crossref]

Appl. Phys. Lett. (1)

I. M. P. Aarts, B. Hoex, A. H. M. Smets, R. Engeln, W. M. M. Kessels, and M. C. M. van de Sanden, “Direct and highly sensitive measurement of defect-related absorption in amorphous silicon thin films by cavity ringdown spectroscopy,” Appl. Phys. Lett. 84(16), 3079–3081 (2004).
[Crossref]

J. Chem. Phys. (2)

R. Engeln, G. von Helden, A. J. A. van Roij, and G. Meijer, “Cavity ring down spectroscopy on solid C60,” J. Chem. Phys. 110(5), 2732–2733 (1999).
[Crossref]

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105(23), 10263–10277 (1996).
[Crossref]

J. Non-Cryst. Solids (1)

A. H. M. Smets, J. H. van Helden, and M. C. M. Sanden, “Bulk and surface defects in a-Si: H films studied by means of the cavity ring down absorption technique,” J. Non-Cryst. Solids 299(302), 610–614 (2002).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (1)

Optik (Stuttg.) (1)

P. Manimaran and M. G. Madhan, “An efficient electrode arrangement for TWSOA based inline detector,” Optik (Stuttg.) 124(19), 3842–3847 (2013).
[Crossref]

Phys. Chem. Chem. Phys. (1)

R. N. Muir and A. J. Alexander, “Structure of monolayer dye films studied by Brewster angle cavity ring down spectroscopy,” Phys. Chem. Chem. Phys. 5(6), 1279–1283 (2003).
[Crossref]

Phys. Rev. Lett. (1)

J.-M. Antonietti, M. Michalski, U. Heiz, H. Jones, K. H. Lim, N. Rösch, A. D. Vitto, and G. Pacchioni, “Optical absorption spectrum of gold atoms deposited on SiO2 from cavity ringdown spectroscopy,” Phys. Rev. Lett. 94(21), 213402 (2005).
[Crossref] [PubMed]

Proc. SPIE (1)

Z. C. Qu, B. C. Li, and Y. L. Han, “Measurement of losses in optical components using filtered optical feedback cavity ring down technique,” Proc. SPIE 8206, 82061M (2011).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of the CRD experimental setup. BS: beamsplitter; PD: photo detector; R1, R2, R3: cavity mirrors; PC: personal computer.
Fig. 2
Fig. 2 Theoretical and measured transmittance spectrum of the AR-coated sample in 900nm-1300nm spectral range.
Fig. 3
Fig. 3 (a) A typical ring-down signal and the corresponding single exponential fit in a linear scale or in a logarithmic scale. (b) The fitting error representing the difference between the experimental data and the fit.
Fig. 4
Fig. 4 (a) Experimental total loss versus the angle of incidence for different RDC lengths. The sample is placed in the middle of the RDC. Error bar represents the standard deviation of 128 measurements. (b) Optical loss, residual reflectance, and transmittance versus RDC length.
Fig. 5
Fig. 5 Ring-down time versus RDC length for initial RDC (with no sample) (τ0), RDC with sample with normal incidence (τ2), and RDC with sample with out-of-normal incidence (τ1).

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

I n = I 0 ( R 1 R 2 R 3 2 ) n exp ( 2 n k )
I ( t ) = I 0 ( R 1 R 2 R 3 2 ) t c 2 [ L + ( n s 1 ) d ] exp ( t c L + ( n s 1 ) d k ) = I 0 exp [ c L + ( n s 1 ) d ( ln R 1 R 2 R 3 k ) t ]
τ 1 = L + ( n s 1 ) d c ( k ln R 1 R 2 R 3 )
τ 0 = L c ( ln R 1 R 2 R 3 )
k = L c ( 1 τ 1 1 τ 0 ) + ( n s 1 ) d c τ 1
k + r = L c ( 1 τ 1 1 τ 0 ) + ( n s 1 ) d c τ 1
I n = I 0 ( R 1 R 2 R 3 2 ) n exp ( 2 n k )
I ( t ) = I 0 ( R 1 R 2 R 3 2 ) t c 2 [ L + ( n s 1 ) d ] exp ( t c L + ( n s 1 ) d k ) = I 0 exp [ c L + ( n s 1 ) d ( ln R 1 R 2 R 3 k ) t ]
τ 2 = L + ( n s 1 ) d c ( k ln R 1 R 2 R 3 )
k = L c ( 1 τ 2 1 τ 0 ) + ( n s 1 ) d c τ 2
r = L + ( n s 1 ) d c ( 1 τ 1 1 τ 2 )
T = 1 k r

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