Abstract:
An optical resonator by which reflectivity of ring-down cavity mirrors can be altered and enhanced by adding external optical cavities that recycle light to the main cavity. A coupled-cavity ring-down spectroscopy (CC-RDS) is used for controlling the finesse of an optical resonator. Applications include extending the sensitivity and dynamic range of a cavity-enhanced spectrometer as well as widening the useful spectral region of high-reflectivity mirrors. CC-RDS uses controlled feedback of the probe laser beam to a ring-down cavity, which leads to interference between the internally circulating light and that which is fed back through a cavity mirror port.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority to U.S. Provisional Application No. 61/648,100 filed on May 17, 2012. 
     
    
     STATEMENT OF GOVERNMENT INTEREST 
       [0002]    The invention described herein was made by employees of the United States Government and may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of royalties. 
     
    
     FIELD OF INVENTION 
       [0003]    The present invention relates the field of optical resonators, and more specifically to coupled-cavity optical resonator. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0004]      FIG. 1  illustrates an exemplary embodiment of a coupled-cavity ring-down spectrometer. 
           [0005]      FIG. 2  illustrates an exemplary embodiment of a coupled-cavity ring-down spectrometer its corresponding equivalent optical system. 
           [0006]      FIG. 3  is a schematic which illustrates the principle of the coupled-cavity ring-down spectrometer and its corresponding equivalent optical system. 
           [0007]      FIG. 4  is a graph of the theoretical dependence of the effective time constant T eff  on changes in the input and output FBC lengths, ΔL FBM . 
           [0008]      FIG. 5  illustrates the comparison of three sets of measurements with theoretical predictions given by Equation 1.  FIG. 5  further illustrates the measured empty cavity decay time constants together with the corresponding effective finesse. 
       
    
    
     ACRONYMS 
       [0009]    CCRDS—Coupled Cavity Ring-Down Spectroscopy 
         [0010]    CRDS—Cavity Ring-Down Spectroscopy 
         [0011]    DBS—Dichroic Beam Splitter 
         [0012]    FBC—Feed Back Cavity 
         [0013]    FBM—Feed Back Mirror 
         [0014]    RDC—Ring-Down Cavity 
         [0015]    PZT—Piezoelectric Transducer 
       GLOSSARY 
       [0016]    As used herein, the term “absorption coefficient” is the minimum loss-per-unit length (also known as the extinction coefficient). 
         [0017]    As used herein, the term “coupling mirror” means a mirror with a preselected reflectivity value which is variably positioned. 
         [0018]    As used herein, the term “detection limit” means a dimensionless quantity and represents the minimum measurable fractional change in the laser beam intensity as it propagates through the length of the ring-down cavity. The detection limit may be expressed as (u(tau)/&lt;tau&gt;)*π/(Finesse). Where u(tau) is the uncertainty (one standard deviation) of the measured time constant, and &lt;tau&gt; is the mean value of the measured time constant. 
         [0019]    As used herein, the term “displacement” means the difference in position of the coupling mirror due to the change in angle of reflection. 
         [0020]    As used herein, the term “dynamic range” means the range of the largest to smallest absorption strength signal to the largest absorption strength signal as achieved by the overall reflectivity range achieved by a CRDS. 
         [0021]    As used herein, the term “etalonging” means the interference between unwanted reflections from external optical elements back to the ring-down cavity. 
         [0022]    As used herein, the term “finesse” is a dimensionless measurement of the lifetime of the photon in the resonater that indicates the sensitivy of the resonator, and the sensitivity increases the finesse value increases. 
         [0023]    As used herein, the term “piezoelectric transducer” (PZT) means a device that provides micrometric linear translation or which actuates or displaces a coupling mirror. 
         [0024]    As use herein, the terms “recycling mirror” and “feedback mirror” refers to a mirror external to the optical component that reflects light back into a cavity. 
         [0025]    As used herein, the term “reflectivity value” means a numeric value signifying the amount of light reflected from a mirror. A reflectivity value may be varied by positioning a mirror or according to the manufacturing specifications for the mirror. 
         [0026]    As used herein, the term “sensitivity” means is value relecting the smallest quantity of change per unit length that a system is capable of measuring. There is an inverse relationship between sensitity and finess. 
         [0027]    As used herein, the term “time constant” is time quantity which reflects the photon decay life time. 
       BACKGROUND 
       [0028]    An optical cavity resonator is an arrangement of mirrors that forms a standing wave cavity for resonating light waves. 
         [0029]    Cavity ring-down spectroscopy (CRDS) is a highly sensitive optical spectroscopic technique that enables very precise measurement of samples that scatter and absorb light. CRDS is used to study gas, liquid dispersed aerosol samples which absorb light at specific wavelengths. CRDS can be used to determine mole fractions of analytes down to the parts per trillion level. 
         [0030]    A CRDS setup measures how long it takes for the light to decay to 1/e of its initial intensity, and this “ring-down time” can be used to calculate the concentration of the absorbing substance present of the sample of the absorbing substance in the cavity. The laser is then turned off in order to allow the measurement of the exponentially decaying light intensity leaking from the cavity. During this decay, light is reflected back and forth thousands of times between the mirrors giving an effective path length for the extinction on the order of a few kilometers. 
         [0031]    A typical CRDS setup consists of a laser and one or more highly reflective mirrors (generally two). The mirrors are placed in optical communication with each on opposite sides of a high-finesse optical cavity. If a sample placed in a cavity absorbs light, the amount of light decreases faster and the photon life is decreased. 
         [0032]    The finesse of an optical cavity is represented as the total phase change (in radians) of the oscillating electromagnetic wave (i.e. the laser beam) over the time that the beam is trapped in the resonator. One exemplary equation that may be used to represent finesse is: 2π (effective path length)/(round-trip path length). Finesse equals π/(1-R) where R is the intensity reflectivity of the ring-down cavity mirror. 
         [0033]    It is desirable to maximize the finesse value of an optical cavity in order to maximize the time a beam is trapped in the resonator, referred to as the photon lifetime. The longer the photon life time, the more sensitive the measurement. 
         [0034]    In addition to finesse there are several other key performance parameters of a CRDS system known in the art. These measurements include wavelength coverage, dynamic range, detection limit and sensitivity. 
         [0035]    CRDS systems may be configured for a specific experimental needs by structurally altering attributes including: (1) distance between mirrors in optical cavity; (2) the angle of reflection of each mirror; (3) the number of mirrors in a cavity; and (4) and the preselected reflectivity value of each mirror. It is also known in the art to use of dielectric films to increase the reflectivity value. 
         [0036]    One problem known in the art is that mirrors for CRDS applications are custom manufactured and have preselected reflectivity value depending on the experimental application for which they are used. The reflectivity value cannot be readily altered after manufacturing resulting in a need for numerous custom mirrors to perform exacting experimentation techniques. 
         [0037]    Another problem known in the art is that custom mirrors generally have an upper bound on their reflectivity. Additionally, commercially available mirrors generally have a maximum reflectivity value of 0.99999. 
         [0038]    It is desirable to increase the maximum attainable reflectivity values available during an experimental process to allow CRDS measurements to be performed over a wider range of physical conditions. 
         [0039]    It is further desirable to increase the key performance parameters attainable by a CRDS system known in the art, including finesse wavelength coverage, dynamic range , detection limit, and sensitivity. 
       SUMMARY OF THE INVENTION 
       [0040]    The present invention uses controlled feedback of the probe laser beam to a ring-down cavity, which leads to interference between the internally circulating light and that which is fed back through one of more coupled cavities mirror port. The channeled use of the interference (etaloning) alters the finesse of the opical resonator in a controlled and quantifiable manner. A couple cavity component may be used for each primary ring-down mirror. In various embodiments the number of coupled cavities may be equal to or less than cto the number of primary ring-down mirrors used in standard ring-down cavity. 
         [0041]    The coupled cavity configuration enhances the performance of a CCRDS apparatus by controlling the finesse of an optical resonator. The coupled cavity configuration also increases the key performance parameters of wavelength coverage, dynamic range, detection limit and sensitivity. 
         [0042]    The invention achieves 10- to 40-fold lower detection limits; 20-fold wider range of concentration. The invention and extends the range more than doubles wavelength coverage for a given set of mirrors. The invention enables laser-based spectrometer methods to be applied over a wider range of physical conditions than with current technology. Exemplary applications include rare and multiple substituted isotopologues 14CO2,13C18O16O; measurement of ultra-low concentrations (&lt;1 part-per-trillion) of gases, aerosols and nanopartles and in environmental monitoring or green house gasses and other trace gas and high-purity gas monitoring. 
         [0043]    The invention also lowers the detection limit of a CRDS in two ways: 1) by increasing the finesse and 2) by reducing interferences (known as etalons) that cause u(tau) to increase. Thus as u(tau) decreases, so does the detection limit 
       DETAILED DESCRIPTION OF INVENTION 
       [0044]    For the purpose of promoting an understanding of the present invention, references are made in the text to exemplary embodiments of a coupled-cavity ring-down spectrometer, only some of which are described herein. It should be understood that no limitations on the scope of the invention are intended by describing these exemplary embodiments. One of ordinary skill in the art will readily appreciate that alternate but functionally equivalent coupled-cavity ring-down spectrometers may be used. The inclusion of additional elements may be deemed readily apparent and obvious to one of ordinary skill in the art. Specific elements disclosed herein are not to be interpreted as limiting, but rather as a basis for the claims and as a representative basis for teaching one of ordinary skill in the art to employ the present invention. 
         [0045]    It should be understood that the drawings are not necessarily to scale; instead emphasis has been placed upon illustrating the principles of the invention. In addition, in the embodiments depicted herein, like reference numerals in the various drawings refer to identical or near identical structural elements. 
         [0046]    Moreover, the terms “substantially” or “approximately” as used herein may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it is related. 
         [0047]      FIG. 1  illustrates an exemplary embodiment of the coupled-cavity ring-down spectrometer  100  which utilizes involves two coupled cavities: input recycle cavity  62   a  and output recycle cavity  62   b.    
         [0048]      FIG. 1  illustrates a first probe beam  10   a  injected through the input coupling mirror  30   a.  The input coupling mirror  30   a  is placed at approximately 45 degrees relative to the probe beam. The first probe beam  10   a  is reflected as a recycled probe beam  10   b  between the input recycling mirror  20   a  and the first primary ring-down mirror  70 . The input recying mirror  20   a  has a second angle of reflection. The PZT actuator  50  microscopically moves the input recycling mirror  20   a  at sub-wavelength intervals to alter the axial displacement of said input recycling mirror  20   a.  The first probe beam  10   a  is injected through the first primary ring-down mirror  70  and reflected back from the second primary ring-down mirror  80  establishing the beam path  90 . Light that leaks out past the second primary ring-down mirror  80  is then recycled back as a recycled output beam  15   b  into the ring-down cavity  60  by the output recycling mirror  20   b  and the output coupling mirror  30   b.  Any light that leaks out beyond the output mirrors creates the output beam  15   a.    
         [0049]    For example one embodiment of coupled-cavity ring-down spectrometer may use a 74 cm long ring-down cavity and a feedback cavity with an approximate finesse of 16, the use of a dual cavity configuration increases the decay time constant from 210 μs to 280 μs, corresponding to an increase of finesse from 2.7×105 to 3.6×105. With the addition of a second feedback cavity, we observe ring-down times as long as ˜0.5 ms, which is equivalent to (1−R)≈4.9×10−6, where R is the effective mirror reflectivity. 
         [0050]      FIG. 2  illustrates the functional equivalence of a coupled-cavity ring-down spectrometer  100  which utilizes first primary ring-down mirror  70  and second primary ring-down mirror  80  which have polished, low-scatter substrates that are coated with layers of dielectric material having variable refractive index. For an empty cavity with lossless mirrors (i.e., no scattering or absorption) of intensity reflectivity R and mirror-to-mirror distance L, the ring-down time constant is given by T 0 =L(cT) −1  where c is the speed of light and T= 1 −R is the mirror transmittance. The absorption coefficient of the cavity medium is inferred by measuring small changes in the ring-down time, and its limit of detection is nominally equal to ε T TL −1 . Here ε T , whose magnitude is influenced by statistical effects such as signal strength and detector and digitizer noise, is the relative standard uncertainty in the measured ring-down time T. In practice, long-term averaging of T to improve measurement precision is often limited by uncertainty and variability in the base losses T×L −1 (cT 0 ) −1  [4,5] that are caused by interference involving unwanted reflections from external optical elements back to the ring-down cavity (RDC). 
         [0051]    This effect, known either as etaloning, spurious reflection, or self-mixing, increases in importance as R approaches unity. As shown below, etaloning leads to an effective RDC mirror reflectivity, R eff  , that can be greater or less than that of the isolated mirror. In CRDS and other cavity-enhanced experiments, etaloning is manifest by slow temporal variation and sinusoidal wavelength dependence in T 0 . This occurs because the effective base losses are sensitive to uncontrolled variations in the phase of the optical feedback (from external cavities) that are caused by drift in\ the relevant optical pathlengths. Since the early days of CRDS, practitioners have been familiar with etaloning effects, and it is now common practice to experimentally reduce this background perturbation using wedged ring-down mirrors, tilted optics, off-axis injection schemes, or antireflective coatings on every interface. Indeed, these steps are required to reach more fundamental detection limits set by the detector noise or the inherent shot noise of the light. 
         [0052]    In the exemplary embodiment shown, a voltage applied to the PZT actuator  50  allows for displacement of the input feedback mirror  22   a  and output feedback mirror  22   b  to occur. The ring-down cavity time constant is calculated from the etaloning between the input dichroic beam splitter (DBS) mirror  32   a  and output dichroic beam splitter (DBS) mirror  32   b  and the first primary ring down mirror  70  and secondary primary ring down mirror  80 . The input feedback mirror  22   a  and ouput feedback mirror  22   b  are then locked into position when the desired reading is achieved. 
         [0053]    In the exemplary embodiment shown, the coupled-cavity ring-down spectrometer  100  which utilizes a length-stabilized RDC  60  that includes two mirrors, first primary ring-down mirror  70  (flat) and second primary ring-down mirror  80  (plano-concave) with intensity reflectivities R 1  and R 2  respectively, and the other is the input feedback cavity  64   a  and output feedback cavity  64   b  which consists of two mirrors feedback mirrors  22   a  or  22   b  and a DBS miror  32   a  or  32   b.  For the isolated RDC  60 , the geometric mean value of the reflectivity is given by R=(R 1 R 2 )½. However, in the more general case of the coupled-cavity ring-down spectrometer  100  system in which there is retroflection to the main RDC  60 , R 1  and R 2  can be replaced by their respective effective values, which we denote by R 1,eff  and R 2,eff . This enables us to describe an equivalent two-mirror RDC  60  for the coupled cavity system that takes into account the light-recycling influence of the recyling mirrors. Analysis of R 1,eff  and R 2,eff  requires that one include not only the principal reflection occurring at each RDC mirror but also interference by the transmitted field that is fed back through the cavity end mirror from the feedback mirrors. 
         [0054]    In the embodiment shown in  FIG. 2 , the value R 1,eff  can be used to express how time constants change as the mirror R 1,eff  corresponds to the first primary ring-down mirror  70  and is no longer equal to the square of its wavelength-dependent absolute reflectivity |r 1   2 |, as in an isolated RDC system, but is a function of t 1 =(1−r 1   2 )½, φ FBC =2πL FBC λ−1, r DBS , r FBM , t extra , and C 00 , where
       t 1 =(1−r 1   2 )½ is the amplitude transmission of the first primary ring-down mirror  70     φ FBC =2πL FBC λ−1 is the single-pass phase shift experienced by the light within the FBC;   r DBS  is the amplitude reflectivity of the DBS mirrors  30   a  and  30   b;      r FBM  is the amplitude reflectivity of the FBM mirrors  22   a  and  22   b;      t extra  the net amplitude transmission through the FBC medium; and   C 00  is the fundamental transverse electromagnetic mode (TEM 00 ) amplitude coupling coefficient of the feedback beam, respectively.       
 
         [0061]    An expression for R 1,eff  is obtained by evaluating |r 1 +r 2 t 2   1  S FBC | 2 , where the first term corresponds to the directly reflected part (r 1 A inc ) and the second term is the feedback contribution. Here r 2 =−1, and S FBC =C 00 r FBM r 2   DBS t 2   extra e 2iφFBC  Σ ∞   n=0  (r 1 r FBM r 2   DBS t 2   extra e 2iφFBC ) n  is the dimensionless circulating field amplitude, which has undergone multiple round-trips in the external FBC. Evaluating this summation leads to an effective intensity reflectivity for M 1  of where we note that (assuming r 1 ≈1) the second term in the sum corresponds to the Airy transmission formula for a resonator with round-trip losses of r 1 r FBM r 2   DBS t 2   extra  and phase delay of 2φ FBC . 
         [0062]    From Eq. 1, we can calculate the modified RDC time constant in the case of light recycling through the input mirror M 1  by the FBC as T eff =L/(c(1−(R 1,eff R 2 ) ½ )). In  FIG. 2 , the blue (lower) curve shows a calculation of T eff  for an ideally lossless system (t extra =C 00 =1) as a function of the input FBM displacement, ΔL FBC,input =L FBC,input −L FBC,input,0 . These calculations are based on the CC-RDS system experimental values discussed below: L FBC,input,0 =L≈74 cm, R 1 =R 2 =99.9988% (equivalent to T=1.2×10 −5  and corresponding to the measured decay time T 0 =210 μs for the TEM 00  mode of the isolated RDC), R DBS =0.71 for the sagittal field polarization (s polarization) at λ≈940 nm and R FBM =R 1 . Not surprisingly, our analysis indicates that the self-mixing effect leads to a λ/2 periodic L FBC -dependent modulation in T eff  about T 0 . For in-phase self-mixing of the two fields, the original value of T 1 =1.2×10 −5  for M 1  is reduced two-fold to T 1,eff =5.9×10 −6  (T eff,max =280 μs). This change in effective mirror transmittance, which is caused by the addition of the feedback resonator with a finesse of about 16 [F=π√{square root over (Rm )}(1−R m ) −1 , where R m =(R 2   DBS R RDC R FBM ) ¼  is the mean reflectivity of the FBC], corresponds to an increase in F from ˜2.7×10 5  (isolated ring-down cavity) to ˜ 3 . 6 × 10   5  (coupled-cavity case). 
         [0063]      FIG. 3  is a schematic which illustrates the principle of the coupled-cavity ring-down spectrometer and its corresponding equivalent optical system. Once the probe-beam intensity has been interrupted, the light leaks out of the ring-down cavity at a rate dictated by its round-trip losses (isolated system). In the coupled-cavity case, the reflected field from the input recycling mirror arises from the direct reflection of the circulating field within the ring-down cavity plus the portion of the recycled probe beam in the feedback cavity that retroreflects from the input recycling mirror and couples back into the ring-down cavity through the first primary ring-down mirror. This coupled-cavity mechanism alters the effective reflectivity of mirror in the equivalent optical system, thus altering the finesse of the ring-down cavity. 
         [0064]    In  FIG. 3 , the blue (lower) curve shows a calculation of the modified RDC time constant, T eff , for an ideally lossless system (t extra =C 00 =1) as a function of the input FBM displacement, ΔL FBC,input =L FBC,input −L FBC,input,0 . These calculations are based on the CC-RDS system experimental values discussed below: L FBC,input,0 =L≈74 cm, R 1 =R 2 =99.9988% (equivalent to T=1.2×10 −5  and corresponding to the measured decay time T 0 =210 μs for the TEM 00  mode of the isolated RDC), R DBS =0.71 for the sagittal field polarization (s polarization) at λ≈940 nm and R FBM =R 1 . Not surprisingly, our analysis indicates that the self-mixing effect leads to a λ/2 periodic L FBC -dependent modulation in T eff  about T 0 . For in-phase self-mixing of the two fields, the original value of T 1 =1.2×10 −5  for M 1  is reduced two-fold to T 1,eff =5.9×10 −6  (T eff,max =280 μs). This change in effective mirror transmittance, which is caused by the addition of the feedback resonator with a finesse of about 16 [F=π√{square root over (Rm)} ( 1−R   m ) −1 , where R m =(R 2   DBS R RDC R FBM ) ¼  is the mean reflectivity of the FBC], corresponds to an increase in F from ˜ 2 . 7 × 10   5  (isolated ring-down cavity) to ˜ 3 . 6 × 10   5  (coupled-cavity case). 
         [0065]    We also display in  FIG. 3  (red/upper curve) the periodic behavior of T eff  when one simultaneously introduces a second FBC, the “output” FBC, to recycle the light that leaks through the output mirror of the. In these simulations, we assume F=31 for the output FBC. Also we suppose that the input FBC (which reinjects the light through M 1 ) is fixed in length to maximize R 1,eff  while the distance between M 2  and the output FBM is varied. In this case, we project that the maximum finesse equals as much as ˜ 2 × 10   6 , with a corresponding T eff  of ˜1.56 ms. 
         [0066]      FIG. 4  illustrates the theoretical dependence of the effective time constant T eff  on changes in the input (lower) and output (upper) FBC lengths, ΔL FBM . While the latter case corresponds to an input that maximizes, both cases consider lossless FBC systems. The line labeled “Isolated RDC” is the nominal observed decay time constant of the isolated system. Parameters correspond to those of our experimental configuration and are given in the text. For ΔL FBM  cases that yield finesse values outside of the extreme, we found that the measurement statistics were highly sensitive to small variations in ΔL FBM . 
         [0067]      FIG. 5  illustrates the comparison of three sets of measurements with theoretical predictions given by Eq. 1. The line labeled “Isolated RDC” is the nominal observed decay time constant of the isolated system, and the curve labeled “Theory” is based on Eq. 1 with experimental parameters given in the text. 
         [0068]      FIG. 5  illustrates the measured empty cavity decay time constants together with the corresponding effective finesse. In (1) the RDC is isolated, while for cases (2) and (3) one FBC is used to change the effective finesse of the RDC through alteration of R 1,eff . In the latter recycling system the finesse for the input FBC for the s- and p-polarization states of the probe beam are 7 and 18, respectively, explaining the differences in modulation depth when the FBM is dithered. Flat data regions correspond to an actively length-stabilized FBC. In (4) a second output FBC was introduced, while the input FBC length was both adjusted and maintained to maximize R 1,eff .