Systems and methods for frequency matching a resonant cavity to a light source

Abstract

A method and system for frequency matching a resonant cavity is disclosed. Light is received in a resonant cavity having at least a first mirror and a second mirror that define a path along which the light is reflected. The at least second mirror is operable to change the path length of the resonant cavity. The intensity of the light exiting or reflecting from the resonant cavity is monitored, and an error correction is determined. The second mirror is actuated toward a position relative to the first mirror where the frequency of the light is resonant with the path length. In this way, the resonant cavity is frequency matched to the light, maintaining the resonant cavity in a resonant state.

Description

[Technical Field]

[0001] TECHNICAL FIELD This disclosure relates generally to optical analysis, and more particularly to systems and methods for frequency matching a resonant cavity to a light source. [Background technology]

[0002] Laser modulation in resonant cavity systems is known. Resonant cavity systems traditionally include a chamber (i.e., cavity) with two or more mirrors designed and arranged to repeatedly reflect light along paths between each other. In some cases, the cavity may include two mirrors positioned at opposite ends of the cavity that reflect light between each other along effectively the same path circuit. In other cases, the cavity may include a set of three or more mirrors that define a circuit along which light is reflected. One or more mirrors allow some light transmission, allowing light to be introduced into the cavity.

[0003] Resonant cavity systems are traditionally constructed with mirrors in fixed positions to prevent misalignment that could result in light not being reflected along the desired path, thereby preventing light from building up within them.

[0004] In such systems, a light source in the form of a laser is used to introduce light into the cavity. Because the cavity has a fixed path length, the wavelength of the laser (or its frequency, which is inversely proportional to the wavelength) is chosen so that a multiple of the wavelength of the laser light corresponds to the path length of the cavity between the mirrors. If the cavity only has two mirrors from which the light reflects, the path involves one round trip from the first mirror to the second mirror and back again. The distance between the two mirrors is called the cavity length, which is equal to half the path length. Thus, there is constructive interference of the light within the cavity, but no destructive interference, and the laser is said to be resonating with the cavity.

[0005] The wavelength of laser light is unstable and can change during operation. Since the cavity length is fixed, the wavelength of the laser is modulated to maintain resonance with the cavity. This is traditionally done by stabilizing the laser to the etalon, or via a Fabry-Perot cavity, using a Fabry-Perot interferometer or etalon interposed between the laser and the cavity.

[0006] Figure 1 shows a conventional resonant cavity system 20 used to analyze gas samples. A laser 24 generates a laser beam 28. The laser 24 has an actuator and output coupler that allow adjustment of the length of the laser cavity, and also has an actuator that changes the angle of a grating at the back of the cavity, thereby changing its pitch and therefore which wavelengths it reflects. By adjusting the length of the laser cavity and changing the angle of the grating, the laser can be tuned to a specific wavelength.

[0007] The laser beam 28 passes through the phase modulator 32 and the partially reflective beam splitter 36. A portion of the laser beam 28 passes through the beam splitter 36 and into the resonator chamber 40, which has a front mirror 44a on which the laser beam 28 is incident and a rear mirror 44b at the end of the cavity 48 opposite the front mirror 44a. The remaining portion of the laser beam 28 is deflected into a beam dump 52. The cavity 48 is a Fabry-Perot cavity, which acts to indicate whether the frequency of the laser beam 28 corresponds to the length of the cavity 48 between the two mirrors 44a and 44b. If the laser beam 28 is off-resonance with the frequency of the laser beam 28, the mirror 44a is highly reflective, causing most of the light from the laser beam 28 to be reflected toward the beam splitter 36. A portion of the laser beam 28 is deflected by the beam splitter 36 toward a photodetector 56. The photodetector 56 measures the intensity of the laser beam 28 deflected onto it and sends a corresponding signal to the mixer 60. The function generator 64 generates an oscillation signal and sends it to the phase modulator 32 and the phase shifter 68. The phase shifter 68 shifts the phase of the oscillation signal generated by the function generator 64 and sends the shifted oscillation signal to the mixer 60. The mixer 60 frequency mixes the signal from the photodetector 56 to generate an unfiltered error signal, which it passes to the low-pass filter 64. The filtered signal from the low-pass filter 72 is then amplified by the servo amplifier 76, and the error signal is fed back to the laser 24 to adjust its frequency. Small changes made to the frequency of the laser 24 allow the directionality of the error identified in the error signal to be determined.

[0008] Tuning the frequency of laser 24 to match the length of cavity 48 causes constructive interference in cavity 56 when the wavelength of light entering the cavity is resonant with the fixed cavity length. This constructive interference also reduces the external reflectivity of front mirror 52a to laser beam 28, allowing more light to enter cavity 56. Summary of the Invention [Problem to be solved by the invention]

[0009] However, such conventional resonant cavity systems have several limitations. By fixing the cavity length, they can only be compatible with lasers of specific wavelengths, i.e., lasers whose cavity length is a multiple of half the wavelength. Also, depending on the wavelength, phase modulators can be expensive. To match certain wavelengths of light, such as the mid-infrared ("mid-IR"), expensive materials such as germanium are required for the phase modulator. [Means for solving the problem]

[0010] In one aspect, a method for frequency matching a resonant cavity is provided, the method including: receiving light at a resonant cavity having at least a first mirror and a second mirror defining a path along which the light reflects, one or both of the first mirror and the second mirror at least partially allowing light from the resonant cavity to pass therethrough, and the at least second mirror being operable to vary the path length of the resonant cavity; monitoring the intensity of the light exiting or reflecting from the resonant cavity via at least one of the first mirror and the second mirror; determining an error correction from the monitored intensity of the light from the resonant cavity; and actuating the second mirror to a pose relative to the first mirror such that the frequency of the light is resonant with the path length.

[0011] The first mirror may be positioned at a first end of the resonant cavity, the second mirror may be positioned at a second end of the resonant cavity, and the path may be defined between the first mirror and the second mirror.

[0012] The light may be infrared or near infrared.

[0013] The second mirror can be actuated to move in at least one direction toward or away from the first mirror to determine a directionality of error correction applied to the second mirror. The second mirror can be constantly actuated to move alternately toward or away from the first mirror to determine the error correction. The second mirror can be intermittently actuated to move in at least one direction toward or away from the first mirror to determine the error correction. The second mirror can be alternately inactive when a ring-down event occurs and oscillate between ring-down events.

[0014] The method further includes receiving the light at the resonant cavity via the first mirror. The monitoring step may be performed by an optical sensor positioned to monitor light exiting the resonant cavity via the second mirror. The monitoring step may be performed by an optical sensor positioned to monitor light reflected from the first mirror and / or light exiting the resonant cavity via the first mirror.

[0015] In another aspect, a system for frequency matching a resonant cavity is provided, the system including: a resonant cavity having at least a first mirror and a second mirror defining a path along which light reflects, wherein one or both of the first mirror and the second mirror at least partially permits light from the resonant cavity to pass therethrough, and wherein at least the second mirror is operable to vary the path length of the resonant cavity; a light power meter configured to monitor an intensity of the light exiting or reflecting from the resonant cavity via at least one of the first mirror and the second mirror; a logic unit configured to determine an error correction from the intensity of the light monitored by the light power meter; and a mirror actuator system configured to actuate the second mirror toward a pose relative to the first mirror where a frequency of the light resonates with the path length based at least in part on the error correction.

[0016] The mirror actuator system may include at least one piezoelectric actuator connected to the logic unit.

[0017] The first mirror may be positioned at a first end of the resonant cavity, the second mirror may be positioned at a second end of the resonant cavity, and the path may be defined between the first mirror and the second mirror.

[0018] The light may be infrared or near infrared.

[0019] The second mirror may be actuated to move in at least one direction toward or away from the first mirror to determine a directionality of error correction applied to the first mirror. The second mirror may be actuated constantly to move alternately toward or away from the first mirror to determine the error correction. The second mirror may be actuated intermittently to move in at least one direction toward or away from the first mirror to determine the error correction.

[0020] The second mirror may alternately be inactive when a ring-down event occurs and oscillated between ring-down events.

[0021] The system may further include an optical system configured to provide light to the resonant cavity via the first mirror.

[0022] The system may further include a light sensor positioned to monitor light exiting the resonant cavity through the second mirror.

[0023] The system may further include a light sensor positioned to monitor light reflected from the first mirror and / or light exiting the resonant cavity via the first mirror.

[0024] Other technical advantages will become readily apparent to one of ordinary skill in the art after examining the following figures and description.

[0025] For a better understanding of the embodiment(s) described herein, and to show more clearly how the embodiment(s) may be carried into effect, reference will now be made, by way of example only, to the accompanying drawings, in which: [Brief explanation of the drawings]

[0026] [Figure 1] FIG. 1 is a schematic diagram of a prior art resonant cavity system. [Figure 2] FIG. 1 is a schematic diagram of a resonant cavity system according to one embodiment. [Figure 3] 3 is a schematic diagram of a resonant cavity of the resonant cavity system of FIG. 2. [Figure 4] 3 is a flowchart of a general method of frequency locking in the resonant cavity system of FIG. 2. [Figure 5] Figure 5A shows the oscillation of the back cavity mirror of the cavity system of Figure 3 to determine the error correction, and Figure 5B shows the back cavity mirror of the resonant cavity system of Figure 3 actuated towards a pose where the ring-down cavity is frequency-matched to the laser light. [Figure 6] FIG. 2 is a schematic diagram of a resonant cavity system according to another embodiment. [Figure 7] FIG. 10 is a schematic diagram of a resonant cavity system according to a further embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0027] Unless otherwise noted, items depicted in the drawings are not necessarily drawn to scale.

[0028] For simplicity and clarity of illustration, reference numerals may be repeated among the figures where considered appropriate to indicate corresponding or similar elements. Furthermore, numerous specific details are set forth in order to provide a thorough understanding of the embodiment or embodiments described herein. However, those skilled in the art will understand that the embodiments described herein may be practiced without these specific details. In other instances, well-known methods, procedures, and components have not been described in detail so as not to obscure the embodiments described herein. While exemplary embodiments are shown in the figures and described below, it should be understood at the outset that the principles of the present disclosure can be implemented using any number of techniques, whether currently known or not. The present disclosure should in no way be limited to the exemplary embodiments and techniques illustrated in the figures and described below.

[0029] Various terms used throughout this specification may be read as follows, unless the context indicates otherwise: "or" as used throughout is inclusive as if written "and / or," singular articles and pronouns used throughout include their plurals and vice versa, similarly, gendered pronouns include their corresponding pronouns, such that no pronoun should be understood as limiting any description herein to use, implementation, performance, etc., by a single gender, and "exemplary" should be understood as "exemplary" or "illustrating," and not necessarily as "preferential" over other embodiments. Further definitions of terms may be set forth herein, and these may apply to antecedent and subsequent instances of these terms, as understood from a reading of this specification.

[0030] Modifications, additions, or omissions may be made to the systems, devices, and methods described herein without departing from the scope of the present disclosure. For example, system and device components may be integrated or separated. Furthermore, the operations of the systems and devices disclosed herein may be performed by more, fewer, or other components, and the methods described may include more, fewer, or other steps. Furthermore, steps may be performed in any suitable order. As used herein, "each" refers to each member of a set or each member of a subset of a set.

[0031] Various components of a resonant cavity system according to certain embodiments are shown in FIG. 2. In the illustrated embodiment, the cavity system is a cavity ring-down spectroscopy ("CRDS") system 100. A CO laser 104 and a Carbon-13O laser 108 are provided. The CO laser 104 and the Carbon-13O laser 108 are gas tube lasers that oscillate at a series of known frequencies with near-average spacing that can be rapidly selected using a tunable diffraction grating device. Gas tube laser technology has a long history and is a stable and robust method of generating infrared light at precisely known frequencies. Both the CO laser 104 and the Carbon-13O laser 108 emit light in the mid-infrared spectrum.

[0032] The CO2 laser 104 and the Carbon-13O2 laser 108 each have an actuator and output coupler that allows them to adjust the length of the laser cavity, and an actuator that changes the angle of the grating at the back of the cavity, thereby changing the pitch and therefore which wavelengths are reflected. By adjusting the length of the laser cavity and changing the angle of the grating, the laser can be tuned very precisely to a specific wavelength and desired mode quality.

[0033] The CO2 laser 104 generates a first laser beam 112, and the Carbon-13O2 laser 108 generates a second laser beam 116. Depending on the desired optical frequency, either the CO2 laser 104 is tuned to generate the first laser beam 112 while the Carbon-13O2 laser 108 is detuned, or the Carbon-13O2 laser 108 is tuned to generate the second laser beam 116 while the CO2 laser 104 is detuned. In this way, at most only one of the CO2 laser 104 and the Carbon-13O2 laser 108 outputs a beam at any given time, preventing simultaneous coupling of the first beam 112 and the second beam 116. The mid-infrared, and especially the long-wavelength infrared, was chosen as the light source because most volatile organic compounds absorb light in this range. As a result, multiple volatile organic compounds can be measured with a single system. The CO2 laser operates in this wavelength range and has sufficient power and narrow linewidth for ring-down spectroscopy. The use of two lasers increases the range and number of available wavelengths that the CRDS system 100 can use to analyze gas samples.

[0034] The first laser beam 112 is redirected via a mirror 120 on an optical mount towards a beam splitter 124. The beam splitter 124 is partially reflective and partially transmissive and splits each of the first laser beam 112 and the second laser beam 116 into two beams: a sampling beam 128 and an actuation beam 132, which may have the same properties and be of similar intensity as the sampling beam 128. The actuation beam 132 has a primary travel direction TD.

[0035] The sampling beam 128 is received by a high-speed infrared detector 136, which uses an oscilloscope to measure the amplitude and beat frequency of the sampling beam 128. The beat frequency may indicate the presence of higher-order modes due to suboptimal tuning of the CO2 laser 104 or the carbon-13O2 laser 108. In response to detecting an undesired beat frequency, the corresponding laser 104 or 28 is tuned while maximizing intensity until the amplitude of the beat frequency is minimized or eliminated. If the amplitude of the beat frequency cannot be reduced below an acceptable level, the laser may be tuned to a different wavelength.

[0036] The actuation beam 132 continues to the first optical modulator 140, which deflects the actuation beam 132 onto a mirror 144 on an optical mount. The mirror 144 redirects the light towards a second optical modulator 148, which in turn deflects the actuation beam 132 onto a focusing lens 152. The optical modulators are used to control the intensity of the light beam generated by the laser. In this embodiment, the first and second optical modulators 140, 148 are acousto-optic modulators (“AOMs”) that attenuate the actuation beam 132. In other embodiments, the optical modulators may alternatively be electro-optic modulators. Additionally, although the CRDS system 100 is described as having two optical modulators, in other embodiments, the CRDS system may have fewer or more optical modulators, and the intensity of the actuation beam 132 may be attenuated via other means, such as a shutter.

[0037] The actuation beam 132 deflected by the second optical modulator 148 is focused via a focusing lens 152. As the laser beam, and therefore the actuation beam 132, travels from the CO2 laser 104 or the Carbon-13O2 laser 108, it continues to diverge. The focusing lens 152 focuses the actuation beam 132 back down.

[0038] A mirror 156 on the optical mount then redirects the actuation beam 132 towards the ring-down chamber 160. The two mirrors 144, 156 extend the length of the actuation beam 132 path.

[0039] 2 and 3, ring-down chamber 160 is an elongated tube that defines a resonant cavity therein, referred to as ring-down cavity 164. Front and back cavity mirrors 168a and 168b (alternatively referred to herein as cavity mirrors 168) are disposed at the longitudinal ends of ring-down cavity 164. Cavity mirror 168 is highly reflective both to light directed at it from outside ring-down cavity 164 and to light directed at it within ring-down cavity 164. As a result, while the ring-down cavity 164 is not frequency matched to the operating beam 132, a portion of the operating beam 132, approximately 0.1%, is directed towards and passes through the front cavity mirror 168a into the ring-down cavity 164, and a majority of the operating beam 132, approximately 99.9%, is reflected towards mirror 156. The light reflected towards the lasers 104, 108 is frequency shifted by the AOMs 148, 140 so that the wavelength of the reflected light does not interfere with the generation of the operating beam 132 in the cavities of the lasers 104, 108.

[0040] The cavity mirrors 168 are attached to actuable mirror mounts 172 for adjusting the position and orientation of the cavity mirrors 168. In particular, the front cavity mirror 168a, facing forward of the ring-down cavity 164, is attached to the actuable mirror mount 172 via three mechanized micrometers 176. The back cavity mirror 168b, facing rear of the ring-down cavity 164, is attached to the actuable mirror mount 172 via three piezoelectric transducers 178 with piezos that can be manually adjusted for optical alignment or further adjusted with piezo drivers.

[0041] The angle of each of the cavity mirrors 168 can be changed to align the cavity mirrors 168 sufficiently so that the light beam does not deviate when it enters the ring-down cavity 164. If one of the cavity mirrors 168 is tilted, some of the light will be reflected off the side of the ring-down cavity 164, resulting in a loss of light intensity and, among other things, higher-order modes. The micrometer 176 and the piezoelectric transducer 178 can also be tuned, either individually or simultaneously, to change the length L of the ring-down cavity 164 without affecting the angle adjustment. This allows the ring-down cavity 164 to be tuned so that it resonates with the frequency of the light entering the ring-down cavity 164.

[0042] Focusing lens 152 focuses the laser light to match the optical mode of ring-down cavity 164 so that the minimum waist of the beam is co-located with the minimum beam waist of ring-down cavity 164. The position of focusing lens 152 can be adjusted to match the optical mode of the range of laser wavelengths. In other embodiments, more than one lens may be employed to achieve mode matching.

[0043] A liquid nitrogen-cooled detector 180 is positioned behind the back-cavity mirror 168b to receive the light that escapes through the back-cavity mirror 168b. Detector 180 is an optical sensor that measures the intensity of the light that escapes from the ring-down cavity 164 through the back-cavity mirror 168b. Detector 180 can be replaced by other types of sensors for measuring the intensity of the escaping light.

[0044] The gas sample is loaded into the ring-down cavity 164 by a sample loading system 192. The sample loading system 192 may include a sample storage device, such as one or more thermal desorption tubes, used to collect and deliver the gas sample for testing. Other types of sample storage devices, such as sample bags or cylinders, may be employed. In another exemplary mode of operation, the sample loading system 192 may load the sample directly from the subject. In a specific example, the gas sample is a human breath sample collected from a patient. Because it will be readily apparent to those skilled in the art that there are numerous ways in which a sample may be loaded and unloaded into the ring-down cavity 164, the details of how the sample is loaded and unloaded from the ring-down cavity 164 will not be described herein.

[0045] As previously mentioned, the length L of the cavity 164 between the mirrors 168a, 168b can be controlled by translating the back cavity mirror 168b via the piezoelectric transducer 178. Additionally, the pitch of the back cavity mirror 168b can be controlled via the piezoelectric transducer 178, although in this configuration the pitch of the back cavity mirror 168b is held constant.

[0046] The piezoelectric transducer 178 is controlled by a frequency matching system 196 that matches the length L of the ring-down cavity 164 to the frequency, and therefore wavelength, of the light from a selected one of the operating lasers 104, 108. Note that frequency and wavelength may be used interchangeably herein. During operation, the frequency of a selected one of the operating lasers 104, 108 may drift, causing the ring-down cavity 164 to become out of sync with the light from the selected laser 104, 108. This can result in destructive interference, making it difficult to establish the desired level of light to perform cavity ring-down.

[0047] While conventional resonant cavity systems use methods such as the Pound-Drever-Hall technique to modulate the frequency of a laser to match a fixed-length cavity, the CRDS system 100 uses a different approach by monitoring the light escaping from the ring-down cavity 164 to determine how to tune the length L of the ring-down cavity 164 to the frequency of the laser. The determined adjustment is then used to actuate the piezoelectric transducer 178 and rear cavity mirror 168b toward a position where the cavity length L corresponds to the frequency / wavelength of the laser.

[0048] The frequency matching system 196 includes a lock-in amplifier 200 that receives the monitored intensity signal from the detector 180. A function generator 204 generates a reference oscillator signal. This oscillator signal is received by a phase shifter 208 in the lock-in amplifier 200, which then shifts the oscillator signal so that it is in phase with the reflected or transmitted optical signal. The phase-shifted oscillator signal and the signal from the detector 180 are frequency-mixed by a frequency mixer 212, more simply called a mixer. The mixer 212 outputs a mixed signal, which is filtered by a low-pass filter 216 to remove noise and higher frequencies and amplified via a servo amplifier 220. The filtered and amplified signal provides an indication of how far the light from the selected laser 104, 108, and the ring-down cavity 164 are off-resonant with respect to one another. A proportional-integral-derivative ("PID") controller 224 processes the filtered and amplified signal to provide a closed loop and an error correction voltage that is applied to the oscillator signal from function generator 204. The error correction voltage is then added to the oscillator signal from function generator 204 by summer 228. The added voltage is then used to drive piezoelectric transducer 178 to move rear cavity mirror 168b, frequency matching ring-down cavity 164 to the laser light.

[0049] 2 and 3, once a gas sample is loaded into the ring-down cavity 164, the active selected laser 104, 108 is tuned to a particular wavelength and its light passes through a first optical modulator 140, is reflected off a mirror 144, passes through a second optical modulator 148, and is reflected off a mirror 152 into the ring-down chamber 160. The optical modulators 140, 148 attenuate the operating beam 132 somewhat and modulate its intensity.

[0050] When the operating beam 132 reaches the front cavity mirror 168a, a small portion, approximately 0.1%, penetrates the front cavity mirror 168a and enters the ring-down cavity 164. The majority of the operating beam, approximately 99.9%, is first reflected along the same path toward the selected laser 104 or 108 that is in operation and is frequency shifted by the AOMs 48, 40 so that the reflected light does not substantially interfere with the generation of the operating beam 132.

[0051] Initially, the ring-down cavity 164 is not illuminated. To allow the ring-down cavity 164 to "fill" with light, the length of the ring-down cavity 164 must be matched to the frequency of the light so that the front cavity mirror 168a no longer substantially reflects the beam 132 from the laser 104 or 108 and so that there is constructive light within the ring-down cavity 164. Light then enters the ring-down cavity 164, and because most of the light in the ring-down cavity 164 is reflected between the two cavity mirrors 168, the amount of light, i.e., power, within the ring-down cavity 164 begins to increase as more light is introduced from outside via the operating beam 132. A portion of the light leaks beyond the cavity mirror 168.

[0052] Light exiting the ring-down cavity 164 via the rear cavity mirror 168b and monitored by the detector 180 is used by the frequency matching system 196 to adjust the cavity length L of the ring-down cavity 164 so that the laser light can efficiently enter the ring-down cavity 164.

[0053] Referring now to Figures 2-5A, a general method 300 for frequency matching the ring-down cavity 164 to laser light is shown. The method 300 begins with monitoring 310 the intensity signal from the detector 180. During operation, the detector 180 is configured to continuously generate a signal corresponding to the intensity of the received light. At the current position, the path length L of the light between the front and back cavity mirrors 168a, 168b is shown. The resonance length RL, which is equal to a multiple of half the wavelength of the light, is also shown. Next, the back cavity mirror 168b is actuated 320 in one direction so that the directionality of any error corrections can be determined. In one configuration, as shown in Figure 5A, the back cavity mirror 168b moves a small distance in one direction (translating in this scenario) and then returns in another direction opposite the first direction, i.e., oscillates or oscillates. In another configuration, the back cavity mirror 168b can be moved a small distance in one direction without first moving the back cavity mirror 168b back. Other ways of moving the back cavity mirror 168b to correct the error and determine its directionality will occur to those skilled in the art.

[0054] Next, the error correction to be applied to the back cavity mirror 168b is determined (330). As previously described, the signal from detector 180 is mixed with a phase-shifted oscillating signal from function generator 204, and the resulting mixed signal is filtered through low-pass filter 216 and amplified through servo amplifier 220. PID controller 224 processes the filtered signal to generate an error correction voltage, which is combined with the oscillating signal from function generator 204 by summer 228. This combined signal is then applied to piezoelectric transducer 178 to translate the edge of back cavity mirror 168b to a position where the cavity length L of ring-down cavity 164 is frequency-matched to the resonant length RL of the laser, as shown in FIG. 5B. That is, cavity length L is a multiple of one-half the wavelength of light from the laser.

[0055] Next, it is determined whether the repeat condition is met (360). During operation, the frequency of the laser light may drift. Therefore, it may be desirable to repeatedly determine an error correction to frequency-match the cavity length to the light. In one configuration, the back cavity mirror 168b can be continuously actuated (i.e., oscillated or oscillated) back and forth within a very small range around the point where the cavity length L is frequency-matched to the laser light, providing continuous fine tuning. In this configuration, the repeat condition would be continuously met. In another configuration, the back cavity mirror 168b could be actuated intermittently at regular time intervals or based on other factors, such as the expected drift of the laser frequency based on how much drift was detected last time, the expected drift range of the laser, etc. Here, the repeat condition would depend on a selected factor or factors. In yet another configuration, the back cavity mirror 168b is actuated continuously between ring-down events and does not oscillate during ring-down events.

[0056] If the repeat condition is met at 360, the method returns to 320 where the rear cavity mirror 168b is actuated to determine the direction of error correction that should be performed.

[0057] In this way, the ring-down cavity 164 can be continuously maintained in frequency match with the laser light.

[0058] The error correction technique used is similar to the Pound-Drever-Hall technique. A symmetric resonator is used, whose complex reflection coefficient is given by

number

[0059] In the conventional laser beam modulation approach using the Pound-Drever-Hall technique, the laser beam is assumed to have an angular frequency ω whose phase is modulated at a frequency Ω, e.g.,

number

number

number

number

number

[0060] Signal ε ω(t) is the resonant frequency ω of the ring-down cavity 164. p When it is consistent with ω(t) passes through zero, so it is an effective error signal. ω(t) is ω0‐ω p is an odd function of ω0‐ω p Depending on the sign of ε ω(t) means that the signs of are different.

[0061] In contrast, the CRDS system 100 modulates the cavity length to frequency match the laser frequency. The length L of the ring-down cavity 164 is modulated as a function of time with a fixed laser frequency ω as follows:

number

number

number

number

[0062] For the same reason as above, when L matches the resonance condition of the ring-down cavity 164, that is, when L=Lp, ε L(t) passes through zero, so the signal ε L(t) is an effective error signal. L(t) L-L p is an odd function of ε L(t) The sign is L-L p Depending on the sign of L ≒ L p This means that the change in the wavelength / frequency of the light entering the ring-down cavity 164 will change the direction of the correction required to move the rear cavity mirror 168b to a position where the length L of the ring-down cavity 164 matches the wavelength / frequency of the light entering the ring-down cavity 164.

[0063] Now, comparing the signal from conventional laser modulation with the signal from cavity length modulation, we see the following.

number

number

number

[0064] In one example, L = 30 cm, λ = 10 μm are used. With an oscillating ring-down cavity 164 (i.e., with an oscillating back cavity mirror 168b), β = 0.1 rad and Ω = 10 16 If we want to obtain an error signal equivalent to a phase modulation of rad / s, the required oscillation amplitude is δL=0.16 nm. For a highly reflective mirror such as R=0.9986, the resulting finesse is approximately:

number

number

[0065] 6 shows a CRDS system 400 according to another embodiment. In this embodiment, the ring-down cavity 164 is frequency-matched to the laser light frequency using a signal from a detector positioned to record light reflected from or escaping the ring-down cavity 164 via the front-cavity mirror 168a. Instead of reflecting the laser beam through a mirror after the focusing lens 152, a beam splitter 404 is used to reflect a portion of the operating beam 132 towards the front-cavity mirror 168a and into the ring-down cavity 164. A portion of the operating beam 132 passes through the beam splitter 404 and is received by a beam dump 408.

[0066] A portion of the light directed toward the front cavity mirror 168a is reflected toward the beam splitter 404. Additionally, a portion of the light from the ring-down cavity 164 may escape via the front cavity mirror 168a and travel to the beam splitter 404. A portion of the light directed from the front cavity mirror 168a toward the beam splitter 404 is reflected toward the AOMs 148, 140, which frequency shift the light to avoid interference with the light being generated by the lasers 104, 108.

[0067] The remaining portion of the light directed toward beam splitter 404 passes through and is recorded by detector 412. Detector 412, like detector 180, is a photosensor that measures the intensity of the received light. Detector 412 generates a signal corresponding to the intensity of the detected light and sends it to the lock-in amplifier 200 of frequency matching system 416. Similar to frequency matching system 196 of the embodiment shown in FIGS. 2 and 3, frequency matching system 416 generates an error correction voltage that is applied to piezoelectric transducer 178 coupled to back-cavity mirror 168b to actuate back-cavity mirror 168b toward a position where ring-down cavity 164 is resonant with operating beam 132.

[0068] The same method 300 as described with respect to FIG. 4 can be employed to frequency match the ring-down cavity 164 to the light.

[0069] While the embodiment described above adjusts the pose of only the rear cavity mirror 168b to accommodate changes in the detection frequency of the laser, in other embodiments, the cavity length L of the ring-down cavity 164 can be changed by moving the front cavity mirror 168b or both the front and rear cavity mirrors 168a, 168b.

[0070] FIG. 7 illustrates a resonant cavity system 500 according to another embodiment. In this embodiment, a resonant cavity 504 has three mirrors that define a path along which light is reflected. A set of three mirror assemblies 508a, 508b, and 508c (hereinafter alternatively referred to as mirror assemblies 508) includes mirrors 512a, 512b, and 512c, respectively (hereinafter alternatively referred to as mirrors 512). The mirrors 512 are attached to mirror mounts 516. The pose (i.e., position and orientation) of each of the mirrors 512 is controllable by a set of piezoelectric transducers 520. A laser 524 is positioned to direct a laser beam entering the resonant cavity 504 toward mirror 512a. The mirrors 512a, 512b, and 512c are positioned and oriented to reflect the laser light along a path having a length L within the resonant cavity 504. Light escaping through mirror 512a is received by detector 528, which sends a signal corresponding to the intensity of the detected light to controller 532. The set of piezoelectric transducers 520 for each mirror 512 is controlled by controller 532. Controller 532 includes the same functionality as frequency matching system 196 of FIG.

[0071] During operation, controller 532 actuates mirror 512a to oscillate slightly via piezoelectric transducer 520. Simultaneously, controller 532 actuates mirrors 512b, 512b to oscillate slightly via their corresponding piezoelectric transducers 520 to accommodate changes in the position of mirror 512a so that the path of light within resonant cavity 504 is maintained. As a result, both the error correction and its directionality can be determined by controller 532.

[0072] To compensate for detected changes in the frequency of the light from the laser 524, the mirror 512a can be moved linearly towards or away from the other two mirrors 512b, 512c, and a corresponding change can be made in the orientation of the mirrors 512b, 512c to maintain the path of the light within the resonant cavity 504.

[0073] In other configurations, controller 532 can nudge mirror 512a in one direction to determine the error correction and its directionality, or nudge mirror 512a in any other manner to obtain the error correction and its directionality. Furthermore, instead of turning mirrors 512b, 512c in response to the translation of mirror 512a, mirrors 512b, 512c can also be translated to maintain a continuous reflection path of light within resonant cavity 504.

[0074] While certain advantages have been enumerated above, various embodiments may include some, none, or all of the enumerated advantages.

[0075] Those skilled in the art will recognize that many more alternative implementations and modifications are possible, and that the above examples are merely illustrative of one or more embodiments, the scope of which is therefore limited only by the claims appended hereto. [Explanation of symbols]

[0076] 20 Resonant Cavity System 24 Laser 28 Laser Beam 32 Phase Modulator 36 Optical isolator 40 Resonating Chamber 44a Front mirror 44b Rear mirror 48 Cavity 52 Beam dump 56 Photodetector 60 Mixer 64 Function Generator 68 Phase Shifter 72 Low-pass filter 76 Servo amplifier 100 CRDS System 104 CO2 Laser 108 Carbon-13O2 Laser 112 First Laser Beam 116 Second Laser Beam 120 Mirror 124 Beam Splitter 128 Sampling Beam 132 Operation Beam 136 High-speed infrared detector 140 first optical modulator 144 Mirror 148 Second Optical Modulator 152 focusing lens 156 Mirror 160 Ring-down chamber 164 Ring-down cavity 168 Cavity Mirror 168a Front cavity mirror 168b Rear cavity mirror 172 mirror mount 176 Mechanized Micrometer 178 Piezoelectric Transducer 180 Liquid nitrogen cooled detector 192 Sample Loading System 196 Frequency Matching System 200 Lock-in Amplifier 204 Function Generator 208 Phase Shifter 212 Mixer 216 Low-pass filter 220 Servo Amplifier 224 PID Controller 228 Adder 300 ways 310 Monitor the intensity signal from the detector 320 Operate rear mirror 330 Determine error correction 340 Determine the direction of error correction 350 Apply error correction Does it meet the 360 ​​repeat conditions? 400 CRDS system 404 Beam Splitter 408 Beam Dump 412 detector 416 Frequency Matching System 500 Resonant Cavity System 504 Resonant Cavity 508, 508a, 508b, 508c Mirror Assembly 512, 512a, 512b, 512c mirrors 516 mirror mount 520 Piezoelectric Transducer 524 Laser 528 detector 532 Controller L length RL resonance length

Claims

1. 1. A method for frequency matching a resonant cavity, comprising: receiving light in a resonant cavity, the resonant cavity having at least a first mirror and a second mirror defining a path along which the light reflects, one or both of the first mirror and the second mirror at least partially permitting light from the resonant cavity to pass therethrough, and at least the second mirror being operable to vary the length of the path through the resonant cavity; During a ring-down event, the second mirror continuously oscillates; monitoring the intensity of the light exiting or reflecting from the resonant cavity through at least one of the first mirror and the second mirror; determining an error correction from the monitored intensity of the light from the resonant cavity; actuating the second mirror toward a pose relative to the first mirror at which the frequency of the light is resonant with the path length based at least in part on the error correction; A method comprising:

2. 2. The method of claim 1, wherein the first mirror is disposed at a first end of the resonant cavity and the second mirror is disposed at a second end of the resonant cavity, and the path is defined between the first mirror and the second mirror.

3. The method of claim 1 , wherein the light is infrared or near-infrared.

4. 1. A system for frequency matching a resonant cavity, comprising: a resonant cavity having at least a first mirror and a second mirror defining a path along which light reflects, one or both of the first mirror and the second mirror at least partially permitting light from the resonant cavity to pass therethrough, and at least the second mirror being operable to change the path length of the resonant cavity; a light intensity meter configured to monitor the intensity of the light exiting or reflecting from the resonant cavity via at least one of the first mirror and the second mirror; a mirror actuator system configured to actuate the second mirror; a frequency matching system configured to generate a signal to the mirror actuator system to oscillate the second mirror relative to the first mirror during a ring-down event; a logic unit configured to determine an error correction from the light intensity monitored by the light intensity meter; the frequency matching system modifies a signal sent to the mirror actuator system based at least in part on the error correction to actuate the second mirror toward a pose relative to the first mirror where the frequency of the light is resonant with the path length.

5. The system of claim 4 , wherein the mirror actuator system comprises at least one piezoelectric actuator connected to the logic unit.

6. 5. The system of claim 4, wherein the first mirror is positioned at a first end of the resonant cavity and the second mirror is positioned at a second end of the resonant cavity, and the path is defined between the first mirror and the second mirror.

7. A light source for generating the light, The system of claim 4 , wherein the light is infrared or near-infrared.

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