CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application No.

62/772,768, filed November 29, 2018, titled“A Waveguide Etalon,” the entire contents of which are hereby incorporated by reference herein, for all purposes.

BACKGROUND

TECHNICAL FIELD

[0002] The present invention relates to optical etalons, and, in particular, to etalons in which electromagnetic waves are guided.

RELATED ART

Definitions

[0003] Unless defined or otherwise required by context, all technical and scientific terms used herein have the same meaning as commonly understood by one of skill in the art to which the invention pertains.

[0004] The term“etalon,” as used herein and in any appended claims, refers to a medium substantially transparent to an electromagnetic wave traversing the medium in an axial direction and having two substantially parallel end facets in planes substantially transverse to the axial direction. The substantially parallel facets are at least partially reflective due either to reflective coating or to a discontinuity in refractive index relative to an adjacent medium.

[0005] The term“wave-guided,” as used herein and in any appended claims, indicates that propagation of an electromagnetic wave within a specified medium is subject to boundary conditions of any sort pertaining to a surface other than the substantially parallel end faces. For example, the electromagnetic wave may be guided within an optical fiber that supports a single transverse mode, or that supports multiple transverse modes, for example. A structure that guides an electromagnetic wave may be referred to as a“waveguide.”

[0006] Single-mode fiber Fabry-Perot interferometers are used in astronomical applications

(such as the fiber Fabry-Perot interferometer produced by Micron Optics of Atlanta, GA), as discussed in the study of Halverson et a ,“ Development of Fiber Fabry-Pirot Interferometers as Stable Near-Infrared Calibration Sources for High Resolution Spectrographs ,” arXiv preprint 1403.6841 (2014), incorporated herein by reference. Temperature control of the fiber Fabry-Perot interferometers may be provided by a thermo-electric controller (TEC). However, to the best of the knowledge of the current inventors, all prior fiber interferometers have required mirrors applied externally to the fiber itself, adding to the cost and complexity of the structure.

SUMMARY OF EMBODIMENTS

[0007] An embodiment of the present invention provides a spectral reference device. The spectral reference device includes an etalon. The etalon has two substantially parallel facets. The two substantially parallel facets are in planes transverse to a propagation axis of an electromagnetic wave. The electromagnetic wave is guided within the etalon. Reflection is provided at each of the substantially parallel facets by a discontinuity in index of refraction along the propagation axis.

[0008] Optionally, any embodiment may also include a waveguide for guiding the electromagnetic wave within the etalon.

[0009] Optionally, in any embodiment, the waveguide may include an optical fiber.

[0010] Optionally, in any embodiment, the optical waveguide may support at most a sole transverse mode at a wavelength characterizing the electromagnetic wave. Optionally, in any embodiment, the waveguide may be configured to support at most a sole transverse mode at a wavelength characterizing the electromagnetic wave. [0011] Optionally, in any embodiment, the etalon may be characterized by a free spectral range of less than 1 GHz. Optionally, in any embodiment, the etalon may be configured to have a free spectral range of less than 1 GHz.

[0012] Optionally, any embodiment may also include a temperature controller. Optionally, in any embodiment, the temperature controller may be configured to maintaining a temperature of the etalon within specified limits.

[0013] Optionally, in any embodiment, the etalon may be externally coated for thermal insulation and regulation. Optionally, any embodiment may also include an external coating configured for thermal insulation and regulation.

[0014] Optionally, in any embodiment, the etalon may be integrated with a resonant medium to provide absolute frequency measurements.

[0015] Optionally, in any embodiment, the resonant medium may include an atomic gas.

[0016] Optionally, in any embodiment, the etalon may be integrated with a second resonant medium to provide absolute frequency measurements. Optionally, in any embodiment, the second resonant medium may include an atomic gas.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The invention will be more fully understood by referring to the following Detailed

Description of Specific Embodiments in conjunction with the Drawings, of which:

[0018] Fig. 1 illustrates an exemplary temperature-stabilized resonant waveguide etalon

(RWE), and its operating principles, according to an embodiment of the present invention.

[0019] Fig. 2 is a graph of power versus frequency, i.e., a spectrum, of a hypothetical exemplary input signal to the RWE of Fig. 1, according to an embodiment of the present invention.

[0020] Fig. 3 is a graph of power versus frequency, i.e., a spectrum, of a hypothetical exemplary output signal of the RWE of Fig. 1, in response to the input-signal of Fig. 2, according to an embodiment of the present invention. [0021] Fig. 4 is a graph illustrating an exemplary output (RWE fringes) of the RWE of Fig.

1, in response to an input narrow-linewidth 780-nm laser whose frequency is scanned across four absorption lines of a natural mixture of atomic ⁸⁷ Rb and ⁸⁵ Rb vapor over a ~6 GHz range, according to an embodiment of the present invention.

[0022] Fig. 5 is an enlarged view of a portion of the graph of Fig. 4 revealing the high density of RWE fringes, according to an embodiment of the present invention.

[0023] Fig. 6 is a graph illustrating results of the RWE of Fig. 1 used to monitor non- linearities in a laser-frequency scan of a current drive distributed feedback (DFB) laser, according to an embodiment of the present invention.

[0024] Fig. 7 is a graph illustrating a linearized scan across ⁸⁷ Rb F2 to F' transitions using the RWE fringes, according to an embodiment of the present invention.

[0025] Fig. 8 is a stacked graph showing fringes for independent scans taken at two minutes interval over a period of an hour, as a result of testing an embodiment of the present invention.

[0026] Fig. 9 is a plot of etalon phase shift as a function of time, and Fig. 10 is a plot of corresponding temperature, as a result of testing an embodiment of the present invention.

[0027] Fig. 11 is a graph illustrating an exemplary application of an optical frequency tracker (OFT) that involves rubidium spectroscopy, for example as used in atomic and molecular spectroscopy that require highly-accurate linear laser scans, according to an embodiment of the present invention.

[0028] Fig. 12 illustrates an absolute frequency measurement device, according to an embodiment of the present invention.

[0029] Fig. 13 is a graph of power versus frequency, i.e., a spectrum, of a hypothetical exemplary input signal to the absolute frequency measurement device of Fig. 12, according to an embodiment of the present invention.

[0030] Fig. 14 is a graph of power versus frequency, i.e., a spectrum, of a hypothetical exemplary output signal of the absolute frequency measurement device of Fig. 12, in response to the input-signal of Fig. 13, according to an embodiment of the present invention. [0031] Fig. 15 illustrates working principles of an OFT, according to an embodiment of the present invention.

[0032] Fig. 16 is a graph that illustrates an example of an OFT calibration, according to an embodiment of the present invention.

[0033] Fig. 17 contains a set of graphs that collectively illustrate OFT drift characterization, according to an embodiment of the present invention.

[0034] Fig. 18 illustrates an example of a linearization application of a frequency scan, according to an embodiment of the present invention.

[0035] Fig. 19 is a graph that illustrates an atomic spectra before and after a linearization of the scan, according to an embodiment of the present invention.

[0036] Fig. 20 is a graph that illustrates spectral response of a DFB laser (bottom) recovered from an OFT signal (top), according to an embodiment of the present invention.

[0037] Fig. 21 is a graph that illustrates spectral response of a laser, as a function of drive voltage, according to an embodiment of the present invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

[0038] Embodiments of the present invention provide a resonant waveguide etalon (RWE) that includes a temperature-controlled optical waveguide with two parallel and partially-reflecting end-surfaces, with a photodetector and signal processing methods to realize monolithic light-guided Fabry-Perot (FP) etalon devices. The RWE relies on transverse optical beam confinement using a waveguide cavity medium in place of a non-guiding semi-transparent plate used in traditional FP etalons. This allows guided optical cavity modes for extended beam reflector separations and small free-spectral ranges (FSR) to the MHz level and below. The RWE affords benefits including flexible form factors and assemblies ranging from compact stand-alone units, such as an optical frequency tracker (OFT) unit described herein, to integration into chip-scale devices, as well as ease of fabrication and high operational stability by precluding the need for delicate positioning and alignment of independent reflectors such as mirrors, fiber ends, etc. over long distances. [0039] Etalons with FSRs in the range of MHz and below are desirable in applications including spectroscopy and laser diagnostics. The challenge in realizing short-FSR etalons is in part due to: (1) the need for large coherent-light propagation distances d in free-space or bulk materials, e.g. on the order of meters for MHz FSRs, and (2) sufficient temperature control and mechanical stabilization of large components in traditional free-space or bulk interferometers and etalons.

[0040] The RWE disclosed herein addresses these limitations by providing light confinement and propagation over a fiber-optic waveguide cavity affording both long distances d for short FSRs and maintaining small component volumes, set by the optical fiber volume, for improved thermal and mechanical stabilization. The RWE provides photodiode output with low- FSR interference fringes. Fig. 1 illustrates an exemplary temperature-stabilized RWE 100, and its operating principles, according to an embodiment of the present invention.

[0041] As illustrated in Fig. 1, the RWE 100 includes an optical fiber 102 coiled around an actively-heated thermally-conductive metal bar 110. The single-mode optical fiber 102 has flat- polished end-surfaces 104 and 106, respectively, and forms a resonant waveguide cavity 108 that is wrapped around the thermally-conductive metal rod 110, which is in direct contact with a Peltier element 112 for uniform heating and thermal stabilization across the RWE 100. The RWE 100 is enclosed by thermal insulation, indicated schematically by dashed box 114. A temperature sensor 116 is placed inside the core of the rod 110 for feedback on the temperature to a proportional- integral-derivative (PID) controller 118, which controls the Peltier element 112 for temperature stabilization.

[0042] Fig. 2 is a graph of power versus frequency, i.e., a spectrum, of a hypothetical exemplary input signal 120 (Fig. 1) to the RWE 100. Fig. 3 is a graph of power versus frequency, i.e., a spectrum, of a hypothetical exemplary output signal 122 (Fig. 1) of the RWE, in response to the input- signal 120.

[0043] In an exemplary embodiment, an RWE 100 includes a 5-meter- long optical resonant waveguide etalon 108 housed in a thermally-controlled package 114. Fig. 4 is a graph illustrating an exemplary output (RWE fringes) 400 of the RWE 100, in response to an input 402 narrow- linewidth 780-nm laser whose frequency is scanned across four absorption lines of a natural mixture of atomic ⁸⁷ Rb and ⁸⁵ Rb vapor over a ~6 GHz range. The 780-nm laser-frequency scan is across four rubidium absorption lines in a vapor cell. The two data traces 400 and 402 are obtained simultaneously by splitting the output of the 780-nm laser source between the RWE 100 and an atomic spectroscopy setup (not shown). Atomic lines identified by four sets of peaks 404, 406, 408 and 410 in Fig. 4 provide absolute laser-frequency references across the scan range.

[0044] Fig. 5 is an enlarged view of a portion 412, indicated by a box, of the graph of Fig. 4 revealing the high density of RWE fringes. The portion 412 includes ⁸⁷ Rb F2 to F' transitions only. The number of fringes between atomic-line references are counted for the FSR determination and calibration.

[0045] To calibrate the FSR, two selected atomic reference lines may be chosen, denoted by black lines 414 and 416 in Fig. 4, to set an absolute frequency scan range 418 covered by the RWE fringes. The FSR is determined by counting the number of fringes and dividing the absolute frequency range 418 by this corresponding number of fringes. For an exemplary RWE 100 operating at 780-nm, we obtain a FSR of about 19.06 ± 0.3 MHz, which is in good agreement with the expected value of about 19.4 MHz for the waveguide etalon length used.

[0046] RWE-based devices provide tools for direct optical monitoring and linearization of laser frequency scans. Non-linearities in frequency scans can arise, for example, in External Cavity Diode Laser (ECDL) due to hysteresis in the piezo component or non-linearities in current drivers in distributed Bragg reflector (DBR) and distributed feedback (DFB) laser due to the lag in the temperature stabilization in fast scans. Linearization of the scan is important for several applications, such as atomic and molecular spectroscopy, material characterization and any other procedure that relies on a frequency dependent measurement using a laser or tool that is assumed to behave linearly. Due to the complexity of the device driving the laser light frequency scan, this is not always the case.

[0047] Fig. 6 provides an example of a non-linear scan from a current drive DFB laser measured using a RWE device. Scan current drive 600 is linear, however response measured using the RWE device (OFT signal fringes 602) is non-linear 604. Line 606 is Rb absorption spectra. Variation in neighboring peak separation across the scan (chirp) is evident.

[0048] In spectroscopy applications, for example, such non-linearities may lead to substantial systematic errors in measurements and calibrations. The disclosed RWE-based device linearizes the measured atomic spectrum from the low-FSR waveguide etalon chirp to recover accurate atomic transitions energies from the measured spectrum.

[0049] The linearization application of RWEs can be extrapolated to any kind of non-linear frequency scan. This has a direct implication of better calibration and reference points for spectrometers and spectroscopic devices. This kind of apparatus are often used in research and industry, for instance several material characterization sciences rely on a fluorescence technical, which includes a frequency scan of an excitation light, and measuring the result of that excitation at specific frequencies. If the machine is miscalibrated or has an intrinsic non-linearity on the scan, this can lead to less precise material properties determination.

[0050] Knowing the etalon FSR, it is possible to recover the frequency range of a scan, without the need of any absolute reference or expensive spectrometer and wavelength readers. Fig. 7 shows a scan across the ⁸⁷ Rb transitions with the Fiber-Etalon fringes. ⁸⁷ Rb F2 to F' transitions are indicated by portions 700 of a line using RWE fringes 702. The transitions peaks are identified by portions 704 of the line. For this plot, the Rb lines are assumed to be unknown, and the peak distances are obtained using the Fiber-Etalon as frequency marker.

[0051] Using only the etalon as frequency reference, one can recover transition energies for a spectrum, such as the one on top. Here, the transitions energies are obtained by measuring the peaks distances relative to the left-most peak. The measured and published values are compared in Table 1.

Table 1 : Comparison of theoretical and measured energy spacing

Identified Peak Theoretical (MHz) Measured (MHz) Error (%)

F2®F 3 0 0 CO F'3®F'2 133.32 133.29 0.02 CO F'3®F'l 211.8 211.55 0.11 F2®F'2 266.65 265.2 0.54 CO F'2®F'l 345.12 344.61 0.15 F2®F'l 423.6 421.99 0.38

[0052] The measured energy values are in good agreement with predicted values. It is important to point that the transition energies were obtained after a single measurement, and without the use of spectrometers or wavelength readers.

[0053] RWEs allow for flexibility in choosing the operating FSR based on the length of the waveguide etalon. Table 2 shows example FSR values for the corresponding RWE lengths.

Table 2: Example FSR values for corresponding RWE lengths

FSR (MHz) RWE Length (meters)

5 ~20

10 ~10

20 ~5

50 ~2

100 ~1

20 “0.5

500 0.2

1000 0.1

Temperature stability

[0054] The monolithic design of waveguide cavities in RWEs 100 disclosed herein, combined with the small-volume and flexibility of the guiding fiber, allows for highly uniform heating and thermal control. The RWE 100 is enclosed by thermal insulation 114, with a temperature sensor 116 placed inside the core of the rod 110 for feedback on the temperature to the PID controller 118 for temperature stabilization. Fig. 8 is a graph 800 of a stacked series of independent laser scans, each taken at two minutes interval, with active temperature stabilization in the RWE 100 in a laboratory environment. This graph 800 illustrates the fringe-drift in time due to small variations in the temperature (~10 ^~3 K) over an interval of one hour. From the plots, one can see a small drift of the fringes to the right over the course of an hour.

[0055] Fig. 9 is a plot of relative peak position (phase) of fringes versus time and the corresponding rod-temperature variation measured for each scan in Fig. 10, during a test of an exemplary embodiment.

[0056] The plot in Fig. 9 indicates the relative phase shift of the fringes as a function of time. The thermal drift rate is obtained from a linear fit (line 900), which was determined to be about 0.123 ± 0.007 MHz/min or 2 ± 0.1 KHz/sec. The total temperature variation over the hour was about lOmK, and the temperature dependency of the etalon phase shift is about 0.8 MHz/mK.

[0057] The embodiment maintained temperature stable to within a milli-Kelvin, which is sufficient to correlate the etalon drift with temperature drift in Figs. 9 and 10.

Optical frequency tracker

[0058] Optical frequency trackers (OFTs) that include resonant waveguide etalons, according to embodiments of the present invention, provide sub-Mhz frequency resolution and may be used as custom frequency markers with wide ranges of center wavelengths, while requiring low optical power input signals. An OFT provides a complete and compact solution for real-time monitoring and tracking of laser frequency relevant to applications ranging from spectroscopy to laser diagnostics. In spectroscopy applications, the OFT can be used as a tool to rectify non- linearities and interruptions in laserscan behavior. The OFT can track laser frequency with <100 KHz accuracy over scan ranges exceeding tens of GHz by generating a sequence of equidistant frequency markers. In laser diagnostics, the OFT can be implemented to quantify laser performance, such as frequency jitter and drift.

[0059] Compared to traditional wave-meters and interferometers, the OFT provides a low- cost solution optimized for accurate, real-time laser-frequency tracking and monitoring of continuous-wave lasers with narrow linewidths. OFT features include fine frequency marker spacings that can be customized to the user’s application, a rapid response time, high accuracy, and calibration-free operation. The OFT tracking can reach and exceed hundreds of GHz, and its output is a simple voltage signal suitable for integration in high-speed, real-time data acquisition systems.

[0060] The OFT provides a functionality critical to applications such as atomic and molecular spectroscopy that require highly-accurate linear laser scans. One application example in rubidium spectroscopy is illustrated in Fig. 11. Here the frequency of a narrow-line 780 nm laser is scanned across the Rb-85 and Rb-87 D2 transitions (line 1100). The signal generated simultaneously by an OFT (with 19.1 -MHz frequency markers) yields periodic frequency markers (line 1102), which reveal a substantial non-linearity in the laser frequency scan (line 1104). The OFT signal is employed to linearize the measured spectrum and to recover accurate spectral line spacings (line 1106). In the linearized spectrum the atomic reference lines are coincident with their theoretical values (vertical lines, exemplified by vertical line 1108) to within 0.2%.

[0061] Thus, in this application example, the OFT reveals and corrects a nonlinear laser- frequency scan in Rb-85 and Rb-87 saturation spectroscopy. A measured spectrum (line 1100) and the corresponding non-linear laser chirp (line 1104) provided by the OFT output (line 1102) reveals an error of up to 20% (about 200 MHz) in relative Rb line position. An OFT linearized spectrum (line 1106) recovers accurate measurements of atomic line separations to within 0.2% of their theoretical values (vertical lines 1108).

[0062] The OFT Frequency Marker Step Size (FMS) can be fully customized to customer applications. Fibercoupled units, with standard FC angle-cut connector, can also be made. The OFT unit can operate over a large selected optical bandwidth, such as up to about lOOnm, over a wide range of central wavelengths, for example spanning ultraviolet (UV)-visible to near infrared (NIR).

[0063] Table 3 list typical parameters of an exemplary OFT.

Table 3: Typical parameters of an exemplary OFT

Parameter Value (typical) Unit

Operating Central Wavelength 400-700 nm

Bandwidth (Single Mode) 200 nm

Frequency Marker Step Size Range * 10 to 1000 MHz

Frequency Marker Step Accuracy <100 KHz

Frequency Marker Drift <10 KHz/s

Calibration available for 780 and 852nm, inquire for calibration at other wavelengths

Absolute Frequency Measurement

[0064] The resonant waveguide etalon (RWE)/OFT may also be integrated with a stabilized reference to realize an absolute frequency measurement device. Here, the reference provides a known frequency, or set of frequencies, as absolute frequency anchors, from which the waveguide etalon provides relative frequency markers. Absolute/stabilized frequency references may include, for example, atomic references, such as a rubidium and iodine gases, optical references, such as stabilized laser sources, or other reference types that behave as resonant media within a light frequency-range of interest.

[0065] In one embodiment of such an absolute frequency measurement device 1200, input light is split between an atomic vapor-cell reference and a RWE/OFT, as shown schematically in Fig. 12. Fig. 13 is a graph of power versus frequency, i.e., a spectrum, of a hypothetical exemplary input signal 1202 (Fig. 1200) to the absolute frequency measurement device 1200. Fig. 14 is a graph of power versus frequency, i.e., a spectrum, of a hypothetical exemplary output signal 1204 (Fig. 1200) of the absolute frequency measurement device 1200, in response to the input-signal 1202.

[0066] Fig. 13 Here, as the input laser frequency is scanned, the RWE/OFT signal is processed to count frequency steps based on the low-FSR waveguide-etalon fringes, while the atomic vapor-cell output provides absolute frequency anchors (Fig. 14) where the light is resonant with any given atomic transition. The low FSR and correspondingly high frequency resolution of the RWE/OFT output compared to that of the atomic reference, whose absolute frequency markers are sparse and non-linear, allows the input laser frequency to be determined continuously on an absolute scale between atomic reference markers, with an absolute frequency resolution determined by the RWE/OFT frequency resolution.

[0067] From the example of Figs. 12-14, two of the reference lines ( and f ₂ ) match two of the FSR intervals of the RWE, or three fringes. In that case, each of the RWE frequency markers is given by D/3. The total frequency range scanned can be obtained by multiplying all the counted fringes by D/3, and also the absolute frequency interval can be obtained by normalizing the scan to A or A -

[0068] The absolute reference can be chosen based on application, for instance in rubidium spectroscopy a rubidium vapor cell could be used. For applications requiring broader laser wavelength ranges, a molecular iodine cell could be used, for instance, which has a high density of atomic resonances across the visible and infrared (IR). In another embodiment, the RWE and (atomic vapor) reference may also be integrated by embedding a vapor within the RWE itself to provide a single output containing combined absolute and relative reference frequency signals. Similarly, in place of an atomic vapor, a second optical frequency-reference may be passed through the RWE for a combined output.

Ultra-stable optical frequency tracker reference for precision measurements

and laser diagnostics

[0069] Embodiments of the present invention provide a stable frequency tracker that can be used for real-time laser diagnostics, including frequency monitoring of drifts, ripple, and intrinsic non-linearities in frequency scans such as chirps and hysteresis. An optical frequency tracker (OFT) is a monolithic device free of moving parts or multiple optical elements, that incorporates a waveguide capable of generating highly resolved reference fringes. Here, as case studies, we analyze the spectral response of two different kinds of laser source; a DFB laser that has a current dependent frequency drive; and an external cavity diode laser (ECDL) with a mechanically-driven frequency scan. During a spectroscopic measurement, the laser frequency is typically scanned with a known, often linear, drive; the frequency scan range is typically determined by comparing a few points to a known reference such as an atomic spectrum or interferometric fringes. By this method non-linearities are generally ignored. Here we show, though, that despite the linearity of the drive, we observe an intrinsic non-linearity in the laser frequency response significant enough to invalidate a precision spectroscopic measurement, yet small enough to remain undetected by more traditional frequency monitoring methods. To ensure the quality of the measurement we developed a temperature stabilized OFT, with frequency markers in the range of MHz and accuracy of greater than about 20 kHz, combined with an overall stability drift of less than about 10 kHz/s. As results, embodiments of the present invention are able to determine the total frequency scan range without any other reference, linearize a frequency scan to compensate a nonlinear frequency response and measure atomic line transitions within about 0.2% accuracy. These embodiments can also be used as tools for diagnosing laser spectral response, revealing intrinsic chirp inherent in laser systems, noise/ripple levels and hysteretic behavior in frequency scans of the ECDL.

[0070] Laser frequency monitoring is widely used in applications ranging from the search for exoplanets to laser-frequency calibration in telecom systems. Frequency monitoring can be done by comparing the frequency-scanned light with absorption lines in a spectroscopy reference sample, such as an atomic or molecular vapor cell, or with an interferometer or wavelength meter. The drawback of a spectroscopic reference is that spectroscopic lines appear at only specific, discrete wavelengths, and the spacing between such reference lines can be much greater than a typical GHz- scale laser frequency scan. Meanwhile the resolution of an interferometer can be determined by its FSR, given by:

FRS = 2 n ₀ L (1) where c is the speed of light, n ₀ is the index of refraction of the medium, with length L, that the light passes through. The most common interferometers used for frequency referencing are Fabry-Perot interferometers (FPI). On these devices the light travels in an air gap, of length L defined by two partially reflective mirrors, and the interference between the reflected and transmitted light generates resonance markers of the device following equation 1. With a FPI it is possible to achieve resolution on the order of hundreds of MHz. A common adaptation to the Fabry-Perot device is often done by adding a medium of length L where the light travels in {no instead of the air gap. This would automatically increases the optical path ( ngL ) allowing for higher resolution spectra. To obtain narrow resonances, the medium should be temperature stabilized across the whole interferometer length L.

[0071] Embodiments of the present invention may be used to generate stable MHz spacing frequency markers that can be used to characterize laser frequency scans and as diagnostic tools for lasers. An OFT is a device that incorporates a waveguide in an FPI assembly that is compact, monolithic, free of moving parts and temperature stabilized.

[0072] Fig. 15 illustrates working principles of an OFT 1500. A waveguide with index of refraction n and length L is combined with partial reflectors R1 and R2, such that the FRS is on the order of MHz. The whole system is temperature-stabilized to ~mK precision with short term stability <10kHz/s.

[0073] The MHz-spacing of the FSR in the OFT provides a high density of stable, laser- frequency-independent markers. The OFT can be used during laser-frequency scans as a real-time frequency monitoring tool. The high density of frequency markers facilitates determination of the total frequency scan range and also linearization of intrinsically non-linear scans. To explore the capabilities of the device, we show here a case study where we analyze the frequency response of two different laser systems, a DFB laser and an external cavity diode laser (ECDL).

II. OFT Calibration and Operation Principle

[0074] The OFT real-time response to a laser frequency change is converted to a signal having an oscillatory voltage with fixed period proportional to device intrinsic characteristics, based on equation 1. The first step prior its utilization is a single-time calibration of the electrical signal, relative to the spectral change of the laser wavelength of interest. The calibration is a simple process of determining frequency markers spacing (FMS) by counting fringes inside a known energy interval during a laser frequency scan. This energy interval is defined by transition peaks of an atomic spectrum. Since the two lasers used have different central wavelengths, each laser should be calibrated separately.

[0075] Fig. 16 is a graph that illustrates an example of such a calibration. For an ECDL, centered at 1020 nm, the calibration is done by comparing the OFT fringes to an electromagnetic induced transparency (EIT) spectrum of Cs atoms, and for the DFB, centered at 780 nm, a saturation spectrum of ⁸⁵ Rb D2 line may be used.

[0076] The OFT signal (line 1600) is obtained simultaneously with the atomic spectrum

(line 1602) as the laser frequency is changed in time by a linear drive (line 1604). The atomic reference signal is obtained by driving a two-photon resonance of Cs atoms in an EIT ladder configuration using two independent laser sources. The first photon comes from a laser frequency- locked to ground state transition 6S _\ ^® 61’ yi- A second laser outputs 510 nm light that is scanned across Rydberg states labeled as 67 Sm, 65A½ and 65 D _3/ . The second laser is the ECDL centered at 1020 nm followed by a frequency-doubling cavity to reach 510 nm. A small reference beam at 1020 nm is divided before the crystal and coupled into the OFT.

[0077] The positions of the OFT fringes are precisely determined by applying a local quadratic fit around each peak. Once the fringes are counted and each position determined, the calibration is obtained by dividing the number fringes inside a known energy interval by the total energy interval. This OFT yields a constant frequency marker spacing of FMS o = 19.15 ± 0.02 MHz at 1020 nm, and FMS780 = 19.06 ± 0.02 MHz at 780 nm. The frequency marker spacings are stabilized and independent of the laser’s spectral frequency for a range of a few hundreds of GHz.

[0078] After the FMS determination, we measure the stability of the OFT, quantified by the drift rate of the fringes. The measurement includes acquiring several OFT spectra, simultaneously with an absolute reference, where each spectrum is acquired at a different time t. Following the acquisition, the OFT and reference spectra are linearized and frequency-aligned, relative to the reference, in this case an atomic spectrum of ⁸⁵ Rb atoms. For easy visualization of possible OFT drifts, the traces are stacked and plotted in a density plot, where each pixel line, in the y axis, represents the time a trace is acquired, as shown in the top portion of Fig. 17.

[0079] Fig. 17 contains a set of graphs that collectively illustrate OFT drift characterization, according to an embodiment of the present invention. The top graph is a density plot of several OFT spectra acquired at different times t. The bottom graph plots integration (line 1702) of OFT spectra and a reference spectrum (line 1704).

[0080] Each trace is fitted by a sinusoidal function to extract the relative phase of the OFT spectra, with respect to the referenced central frequency. By monitoring the phase evolution of each OFT spectra, we can measure the drift rate presented on the right side of Fig. 17. To filter out electrical noise in the OFT spectra and remove laser power variations, the density plot is built with the fitted function of the OFT traces.

[0081] As noted, line 1702 represents the integrated OFT for all the data acquired over one minute (1050 traces), and line 1704 represents atomic spectra for these data points. The drift rate is obtained by extracting the slope of a linear function fitted to the phase evolution of the OFT spectra (straight line 1700). The short-term stability is determined to be < 10 kHz/s (measured over 1 minute), and the long-term stability is determined to be < 1.6 MHz/h (measured over 12 hours). We attribute this drift to the limit of thermal stabilization of the device (5 mK).

[0082] An example of the linearization application of a frequency scan is shown in Fig. 18.

The raw OFT signal (lien 1800) is compared to a linearized signal (line 1802). The linearized signal is obtained by fixing each OFT fringe spacing to the calibrated FSM value, in this case for the DFB laser FSM ₇₈ o = 19.06 MHz. The bottom graph 1804 compares the linearized full frequency scan

(line 1806) with the non-linearized (1808). The frequency axis of the non-linearized signal is obtained by normalizing the scan range, such that the position of the last OFT peak is equal to the total number of the OFT peaks multiplied by the FSR780 , ignoring variations in spacings between all of the other OFT peaks along the scan.

[0083] The top plot 1800 of Fig. 18 shows a section of the total scan, where one can see that for the raw data the FMS changes in time or 6 _t is not constant, whereas after the linearization the FMS becomes constant and d/= FMS. The recovered frequency scan from the OFT shows a highly non-linear behavior of the DBF laser. Once the linear spectral change of the laser is obtained, it can be used to accurately measure, for instance, atomic energy transitions in a sample of interest. The OFT signal in Fig. 18 was acquired simultaneously with an atomic spectra of ⁸⁵ Rb and ⁸⁷ Rb atoms. In Fig. 18, line 1800 represents an Rb spectrum with a non-linearized frequency scan, and line 1802 represents the spectrum with a linearized frequency axis.

[0084] Fig. 19 is a graph that illustrates the atomic spectra before (line 1900) and after (line

1902) the linearization of the scan. The frequency scan range was obtained purely by the OFT. The atomic spectra were only translated such that the ⁸⁷ Rb cycle transition is centered in the plot scale. Vertical lines, exemplified by vertical line 1904, indicate predicted theoretical atomic peak positions. The OFT makes it possible to recover all the marked transitions, covered by the scan range, within 0.2% agreement of the theory. Significantly, no extra calibration or corrections on the frequency axis of the spectra are necessary. The result may be obtained solely by the OFT scan show in Fig. 18.

III. Laser Diagnostics

[0085] Another application of the OFT is high resolution, real-time monitoring of frequency scans for laser diagnostics. To illustrate this capability, we present here two case studies of frequency monitoring of two intrinsically different types of laser sources. First, a DFB laser was monitored during a frequency scan of about 2 GHz. This laser was current-tuned, without any moving parts. Secondly, we analyzed the response of a ECDL laser in a symmetric frequency scan of about 7 GHz, where the frequency was change mechanically by a voltage in a lead zirconate titanate (PZT) piezoelectric ceramic component. [0086] The DFB is a compact laser source with a temperature stabilized chip embedded inside a single package. The laser frequency can be current or temperature tuned. For these mea surements, the temperature was stabilized and the current was linearly changed by an external drive at 20 Hz. The laser spectral response is show in the bottom plot of Fig. 20. The frequency scan was recovered using the OFT signal (top plot of Fig. 20). An insert in Fig. 20 is a plot of the derivative of the frequency scan (line 2000) and an oscillatory function adjust (line 2002).

[0087] From the OFT signal of Fig. 20, one can see that there is a transient effect on the frequency scan of the laser defined by two temporal regions. First, the laser frequency starts changing rapidly, then the rate of change decreases until there is no change for a while (2 ^L 3 ms), then the laser frequency starts changing again, reaching a steady state where dF/dt is approximately constant. By recovering the total energy scan (bottom plot) it is possible to see that the frequency changes in different directions during these two periods, quantitatively about 0.5 GHz in one direction, and then about 2.5 GHz in the opposite direction. This initial lag in the frequency scan represents about 25% of the total frequency scan range selected, and is associated to the thermal stabilization of the laser chip at the beginning of the frequency scan. This is a relatively high number that can lead to major inaccuracies in laser scan range calibration or reference lines determination if neglected, for instance, during a spectral measurement.

[0088] The OFT also revealed an intrinsic sub-MHz noise during the scan. The inset in Fig.

20 shows the measured frequency difference between two consecutive points in time SF = (t)— F(t— 1) for this scan. One can see a spectral noise oscillation of 28 kHz (peak-to-peak) and 3 ms period, identified by oscillations in the inset curve 2000 and 2002. We attributed this noise to electric noise/ripple from the current drive unit, based on the laser chip current-to-wavelength conversion factor, a 28 kHz frequency change corresponds to a current oscillation of - 20 nA. This number is below the noise/ripple specifications for the used driver.

[0089] For the ECDL, we monitored spectral response during a symmetric current drive, as illustrated in Fig. 21. Fig. 21 is a graph that illustrates spectral response of a laser, as a function of drive voltage. Colors/shades of gray/line patterns 2100, 2102 and 2104 represent different offset voltages applied to a PZT. In this experiment, offset voltages 15V, 70V and 125V were used, respectively. A bottom insert shows the scan range for each offset, compared to a nominal PZT operation range. A top insert shows the difference in frequency (H) for each curve at the same voltage, when the driver voltage is increased or decreased.

[0090] The frequency axis was obtained by using only the OFT. In this scan, we used a symmetric triangular drive voltage, with amplitude of 28 V ( Vmin = -14 V, Vmax = 14 V), plus an offset central voltage, applied in to the PZT that mechanically change the laser cavity and consequently laser output frequency. Here, we observed a high hysteresis in the laser response, as a function of the driver signal.

[0091] From the curves in Fig. 21, one can clearly see the hysteresis of the laser scan, identified by the difference in response associated with the diver polarization and initial position. To quantify the hysteresis, we measured the difference in the laser frequency between the two halves of a cycle during a symmetric drive H, presented in the top inset. A maximum difference of 400 MHz between the two paths, equivalent to ~ 6% of the total scan range, is measured when the PZT is operating at the central range offset. This is a relative high value, if one considers that atomic transition-linewidths are on the order of a few MHz, and hyperfme-energies spacings can range from a few hundreds of MHz, in atomic-ground states, to few MHz in Rydberg states. From Fig. 21, one should also note that the laser response, as a function of drive voltage, is also dependent on the PZT voltage offset. This is a relevant finding, since for several applications the user may calibrate the spectral response of the laser using reference lines at a specific PZT voltage offset. Often, in daily operation, small corrections of the piezoelectric are required to match and correct the frequency. In this scenario, one could naively assume that the response is independent of the voltage offset, leading to inaccurate frequency scan ranges.

[0092] A non-linear response of the laser spectral dependency can also be observed and numerically quantified by adjusting the spectral response curves to the polynomial expression Av(V ) = a + b x V + g x V ² + d x V ³ and comparing terms of different orders. For the three PZT center voltages considered here, the non-linear dependence of the frequency is shown in the 3rd order in Table 4. Table 4 lists values of the spectral response function terms, when the drive voltage increases† (-14 V ® 14 V), and when the drive voltage decreases j (14 V ® -14 V). Table 4: Linear and high-order components of laser spectral response

Offset (V) Linear (MHz/) Quadratic (MHz/V ² ) Cubic (MHz/V) 15 (t) 1570.43 31.50 7.45

15 1575.70 44.68 7.18

70 (t) 1752.87 45.33 8.05

70 1753.94 54.74 9.01

125 1645.65 38.31 4.93

125 1647.12 42.44 4.99

[0093] The non-linear responses of the laser (g and d) are notable high. The maximum quadratic response (54.74 MHz/V ² ) accounts for a total shift of 218.96 MHz across the whole 7.180 GHz scan, reflecting a 3% variation on the total scan range. Numbers of the same order are obtained for the cubic component, showing a total shift of 144.16 MHz, equal to 2% of the total scan.

[0094] Thus, disclosed herein is an ultra-stable reference unit with high spectral resolution, along with some exemplary case studies to diagnose spectral response of current and mechanically tuned lasers. After a one-time characterization, the OFT may be used to linearize a frequency scan and recover atomic reference lines with about 0.2% accuracy, without any other reference. The device can also be used as a tool for real-time laser diagnosis. In an example, presented herein, an embodiment was used to identify a 25% lag in a 2.5 GHz frequency scan of a DFB laser associated with thermal response stabilization of the laser chip, and also a periodic spectral noise in the 10s of KHz range. While using an ECDL, the OFT revealed a hysteresis profile of « 400 MHz in a 7 GHz frequency scan, mostly as a result of the PZT mechanical response, and non-linearities of 3% and 2% (attributed to a quadratic and cubic components, respectively) in the spectral response.

[0095] The embodiments of the invention described herein are intended to be merely exemplary; variations and modifications will be apparent to those skilled in the art. Although any methods and materials similar to or equivalent to those described herein can be used in the practice or testing of the present invention, the preferred methods and materials are described herein. All such variations and modifications are intended to be within the scope of the present invention as defined in any appended claims.

[0096] While the invention is described through the above-described exemplary embodiments, modifications to, and variations of, the illustrated embodiments may be made without departing from the inventive concepts disclosed herein. For example, although specific parameter values, such as dimensions and materials, may be recited in relation to disclosed embodiments, within the scope of the invention, the values of all parameters may vary over wide ranges to suit different applications. Unless otherwise indicated in context, or would be understood by one of ordinary skill in the art, terms such as“about” mean within ±20%.

[0097] As used herein, including in the claims, the term“and/or,” used in connection with a list of items, means one or more of the items in the list, i.e., at least one of the items in the list, but not necessarily all the items in the list. As used herein, including in the claims, the term“or,” used in connection with a list of items, means one or more of the items in the list, i.e., at least one of the items in the list, but not necessarily all the items in the list.“Or” does not mean“exclusive or.”

[0098] Disclosed aspects, or portions thereof, may be combined in ways not listed above and/or not explicitly claimed. In addition, embodiments disclosed herein may be suitably practiced, absent any element that is not specifically disclosed herein. Accordingly, the invention should not be viewed as being limited to the disclosed embodiments.

[0099] As used herein, numerical terms, such as“first,”“second” and“third,” are used to distinguish respective steps, photons, lasers, etc. from one another and are not intended to indicate any particular order or total number of steps, photons, lasers, etc. in any particular embodiment. Thus, for example, a given embodiment may include only a second step, photon, laser, etc. and a third step, photon, laser, etc.