JP2006071431A - Optical resonator measuring device and method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To measure f<SB>FSR</SB>of an optical resonator and group velocity (group refractive index) of a medium in the optical resonator with high precision. <P>SOLUTION: Modulating signals of frequency fm modulated with time are oscillated, phases of light emitted from a illuminant based on frequency fm of oscillated modulating signals are modulated, the optical resonator 15, as a subject matter to be measured, receives the modulated incident light, the intensity of light transmitted through or reflected from inside of the optical resonator 15 among the incident light into the optical resonator 15 is detected, and then a free spectral range f<SB>FSR</SB>of the optical resonator is determined based on the detected intensity of light. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an optical resonator that is applied to a field that requires a standard light source having high coherence at multiple wavelengths, such as optical communication, optical CT, or an optical frequency standard, or a light source that can also use coherence between wavelengths. The present invention relates to an optical resonator measuring apparatus and method for measuring physical properties.

  In the case of measuring the optical frequency with high accuracy, heterodyne detection is performed in which the light to be measured is made to interfere with other light and an electric signal having a generated optical beat frequency is detected. The band of light that can be measured in this heterodyne detection is limited to the band of the light receiving element used in the detection system, and is about several tens of GHz.

  On the other hand, with the recent development of optoelectronics, it is necessary to further expand the measurable band of light in order to perform optical control for frequency division multiplexing and frequency measurement of absorption lines distributed over a wide range.

  In order to meet the demand for an increase in the measurable bandwidth, a wideband heterodyne detection system using an optical frequency comb generator (see, for example, Patent Document 1) has been proposed. This optical frequency comb generator generates comb-like sidebands arranged at equal intervals on the frequency axis over a wide band, and the frequency stability of this sideband is almost equal to the frequency stability of incident light. It is. By heterodyne detection of the generated sideband and light to be measured, a wideband heterodyne detection system over several THz can be constructed.

  FIG. 8 shows the basic structure of the conventional optical frequency comb generator 3.

  The optical frequency comb generator 3 uses an optical resonator 100 including an optical phase modulator 31 and reflecting mirrors 32 and 33 installed so as to face each other with the optical phase modulator 31 interposed therebetween.

The optical resonator 100, the light _{L in} incident at a small transmittance through the reflecting mirror 32, is resonated between the reflecting mirrors 32 and 33, a part of the light _{L out} via the reflecting mirror 33 emitted Let The optical phase modulator 31 is made of an electro-optic crystal for optical phase modulation whose refractive index changes when an electric field is applied, and the frequency applied to the electrode 36 with respect to the light passing through the optical resonator 100. Phase modulation is applied according to the electric signal of fm.

  In this optical frequency comb generator 3, an electric signal synchronized with the time when the light reciprocates in the optical resonator 100 is driven and input from the electrode 36 to the optical phase modulator 31, so that the optical phase modulator 31 is only once. Compared with the case of passing, it becomes possible to apply deep phase modulation of several tens of times or more. As a result, hundreds of higher-order sidebands can be generated, and the frequency interval fm between adjacent sidebands is all equal to the frequency fm of the input electrical signal.

  Further, the conventional optical frequency comb generator is not limited to the above-described bulk type. For example, as shown in FIG. 9, the present invention can also be applied to a waveguide type optical frequency comb generator 20 using a waveguide.

  The waveguide type optical frequency comb generator 20 includes a waveguide type optical modulator 200. The waveguide type optical modulator 200 includes a substrate 201, a waveguide 202, an electrode 203, an incident side reflection film 204, an emission side reflection film 205, and an oscillator 206.

The substrate 201 is obtained by cutting a large crystal such as LiNbO ₃ or GaAs having a diameter of 3 to 4 inches grown by a pulling method into a wafer shape. Processing such as mechanical polishing or chemical polishing is performed on the cut substrate 201.

  The waveguide 202 is arranged for propagating light, and the refractive index of the layer constituting the waveguide 202 is set higher than that of other layers such as the substrate 201. The light incident on the waveguide 202 propagates while being totally reflected at the boundary surface of the waveguide 202. In general, the waveguide 202 can be manufactured by diffusing Ti atoms in the substrate 201 or by epitaxial growth on the substrate 201.

As the waveguide 202, a LiNbO ₃ crystal optical waveguide may be applied. The LiNbO ₃ crystal optical waveguide can be formed by diffusing Ti on the surface of the substrate 201 made of LiNbO ₃ or the like. When actually manufacturing this LiNbO ₃ crystal optical waveguide, first, a photoresist pattern is prepared on the surface of the substrate 201, Ti is vapor-deposited there, and the photoresist is further removed, so that the micron size is obtained. A thin Ti wire having a width is prepared. Next, this thin Ti wire is heated to thermally diffuse it into the substrate 201.

Incidentally, when this Ti is thermally diffused into the substrate 201 made of LiNbO ₃ , the region where the Ti is diffused has a higher refractive index than the other regions, so that light can be confined. That is, a waveguide 202 capable of propagating light per region where Ti is diffused is formed. Since the LiNbO ₃ crystal-type waveguide 202 manufactured based on such a method has an electro-optic effect, the refractive index can be changed by applying an electric field thereto.

  The electrode 203 is made of a metal material such as Al, Cu, Pt, or Au, for example, and drives and inputs an electric signal having a frequency fm supplied from the outside to the waveguide 202. Further, the propagation direction of light in the waveguide 202 and the traveling direction of the modulation electric field are the same. By adjusting the width and thickness of the electrode 203, the speed of the light propagating through the waveguide 202 may be matched with the speed of the electric signal propagating on the electrode 203. As a result, the phase of the electrical signal felt by the light propagating through the waveguide 202 can be kept constant.

  The incident-side reflection film 204 and the emission-side reflection film 205 are provided to resonate light incident on the waveguide 202 and resonate by reciprocally reflecting light passing through the waveguide 202. The oscillator 206 is connected to the electrode 203 and supplies an electric signal having a frequency fm.

The incident-side reflection film 204 is disposed on the light incident side of the waveguide type optical modulator 200, and light having a frequency ν ₁ is incident from a light source (not shown). Further, the incident-side reflection film 204 reflects light reflected by the emission-side reflection film 205 and having passed through the waveguide 202.

  The exit-side reflection film 205 is disposed on the light exit side of the waveguide type optical modulator 200 and reflects light that has passed through the waveguide 202. The exit-side reflection film 205 emits light that has passed through the waveguide 202 to the outside at a constant rate.

  In the waveguide-type optical frequency comb generator 20 having the above-described configuration, an electric signal synchronized with the time when the light reciprocates in the waveguide 202 is used as a drive input from the electrode 203 to the waveguide-type optical modulator 200. Compared with the case of passing through the waveguide type optical modulator 200 only once, deep phase modulation of several tens of times or more can be performed. As a result, similarly to the bulk type optical frequency comb generator 4, an optical frequency comb having a wide sideband can be generated, and the frequency interval between adjacent sidebands is the frequency fm of the inputted electric signal. Is equivalent to

  The waveguide type optical frequency comb generator 20 is characterized in that the interaction area between light and electric signal is smaller. Since light is confined and propagated in a micron-order waveguide 202 having a refractive index higher than that of the surroundings, by attaching an electrode 203 in the very vicinity of the waveguide 202, the electric field strength in the waveguide 202 is locally increased. It becomes possible to raise. Therefore, compared with the bulk type optical frequency comb generator 3, the electro-optic effect generated in the waveguide 202 is increased, and a large modulation can be obtained with a small amount of power.

JP 2003-202609 A

By the way, in order to operate the optical frequency comb generator having such a configuration at a desired modulation frequency, the free spectral range (Free Spectral) of the optical resonator formed in the optical frequency comb generator is set to the frequency fm to be modulated. Range: f _FSR ) must be an integral multiple of In general, the f _FSR of an optical resonator is, for example, when mirrors are directly attached to both end faces of a crystal and the mirrors face each other to form a Fabry-Perot resonator. Given.

f _FSR = c / (2n _g l) (11)
(Where c is the speed of light in vacuum, l is the crystal length in the light propagation direction in the optical resonator, and _ng is the group refractive index of the electro-optic crystal).
When the refractive index has no wavelength dependence, the above f _FSR is given by the following formula (12) by using the refractive index n of the medium.

f _FSR = c / (2nl) (12)
However, when generating light over a wide band like an optical frequency comb generator, the refractive index dispersion of the material in the optical resonator must be considered. Normally, even if the refractive index for a carrier wave is n, the refractive index for adjacent sidebands is not n. That is, when the wavelength dependence of n is taken into consideration, it can be seen that a group index of refraction as in equation (11) must be used.

Incidentally, when the optical resonator is formed of a bulk crystal as in the conventional optical frequency comb generator 3, an approximate expression that expresses the wavelength dependency and temperature dependency of the refractive index fairly accurately (Selmeier's equation). ) Is reported for each crystal, the group refractive index can be predicted with a certain degree of accuracy, and the optical frequency comb generator can be optimally designed accordingly. Further, in the bulk type optical frequency comb generator in which the optical resonator is constituted by a bulk crystal, by forming at least one of the reflecting mirrors by an external mirror mounted on the movable element, the f of the optical resonator can be obtained. It is also possible to adjust the _{FSR according} to the modulation frequency fm.

  However, in the waveguide type optical frequency comb generator using the waveguide, it is difficult to cope with an external mirror because of the structure of the waveguide, so that it is the same as the bulk type optical frequency comb generator. Measures cannot be taken. In the case of a waveguide type optical frequency comb generator, there is no method for manufacturing a high finesse resonator other than configuring the optical resonator by a reflecting mirror attached to the crystal end face.

Therefore, in order to adjust the modulation frequency fm of the waveguide type optical frequency comb generator to a desired frequency, the group refractive index of the waveguide is accurately measured, and the f _{FSR of the} optical resonator is adjusted to the modulation frequency fm. There is a need.

In particular, the group refractive index of the waveguide is affected by the refractive index dispersion of the material and the structure of the waveguide, so the conventionally known bulk crystal's Cellmeier formula cannot be used, and compared with the bulk type. Thus, it is not easy to obtain the group index of the waveguide type optical frequency comb generator. In addition, since the refractive index dispersion based on the structure has slight variations based on the waveguide creation conditions, it is difficult to accurately predict this at the design stage. For this reason, conventionally, until both ends of the waveguide are polished, a highly reflective film is attached to form a resonator, and a microwave is applied to the electrode to operate the optical frequency comb generator, f The value of _FSR could not be obtained.

Further, the refractive index n of the waveguide constituting the optical frequency comb generator is greatly influenced by the ambient temperature, and the temperature coefficient of the refractive index is about 1 × 10 ⁻⁵ . Therefore, in order to put the refractive index adjustment range of the optical frequency comb generator within the temperature adjustment range according to the installation environment, the group refractive index must be obtained on the order of 1 × 10 ⁻⁵ .

For the reasons described above, it has been extremely difficult to accurately measure the group index of the waveguide before attaching the reflecting mirror and to produce a waveguide type optical frequency comb generator having an optimum f _FSR .

Therefore, the present invention has been devised in view of the above-described problems, and the object of the present invention is to provide an apparatus and method for accurately measuring the f _FSR of an optical resonator and the medium in the optical resonator. An object of the present invention is to provide an apparatus and method for accurately measuring a group velocity (group refractive index).

In order to solve the above-described problems, an optical resonator measuring apparatus to which the present invention is applied is an optical resonator measuring apparatus for measuring physical properties of an optical resonator. A modulated signal oscillating means for oscillating a signal, a phase modulating means for modulating the phase of the light emitted from the light source based on the frequency fm of the modulated signal oscillated by the modulated signal oscillating means, and the phase modulating means Light incident means for making the incident light enter the optical resonator, and light for detecting the intensity of the light transmitted through or reflected in the optical resonator among the light incident on the optical resonator by the light incident means Intensity detecting means; and physical property measuring means for obtaining a free spectral range (f _FSR ) of the optical resonator based on the intensity of light detected by the light intensity detecting means.

In order to solve the above-described problems, an optical resonator measurement method to which the present invention is applied is an optical resonator measurement method for measuring the physical properties of an optical resonator. Light that oscillates a signal, modulates the phase of the light emitted from the light source based on the frequency fm of the oscillated modulation signal, enters the modulated light into the optical resonator as the measurement object, and enters the optical resonator Among them, the intensity of light transmitted through or reflected in the optical resonator is detected, and the free spectral range (f _FSR ) of the optical resonator is obtained based on the detected intensity of light.

In the present invention, a modulated signal having a frequency fm changed with time is oscillated, the phase of the light emitted from the light source is modulated based on the frequency fm of the oscillated modulation signal, and the modulated light is used as the light to be measured. Detects the intensity of light transmitted through or reflected in the optical resonator from light incident on the optical resonator, and the free spectral region of the optical resonator based on the detected light intensity (Free Spectral Range: f _FSR ) is obtained.

As a result, in the present invention, physical properties such as optical characteristics such as f _FSR and group refractive index of an optical resonator as a measurement target can be evaluated, and in particular, optical signal analysis means such as a spectroscopic device. This is effective in that all signal generation and analysis can be performed electrically without using. In general, electrical frequency analysis has a much higher resolution than optical frequency analysis means. Therefore, in the present invention, it is possible to measure the f _{FSR of the} optical resonator, the group refractive index of the medium, and the group velocity dispersion with high accuracy.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  An optical resonator measuring apparatus 1 to which the present invention is applied is an apparatus for measuring physical properties of an optical resonator 15 as a measurement target, for example, as shown in FIG. The phase modulation unit 12 that modulates the phase of the light emitted from the light source based on the modulation signal having the frequency fm, the light intensity detection unit 13 that detects the intensity of the light from the optical resonator 15, and the modulation signal are generated. In addition, a control unit 14 that measures the physical properties of the optical resonator 15 based on the light intensity detected by the light intensity detection unit 13 is provided. In FIG. 1, a path indicated by a solid line is a light propagation path, and a path indicated by a dotted line is an electric signal propagation path.

  The light source 11 is a light source for generating light of a predetermined frequency. For example, various lasers such as a solid state laser such as Nd: YAG, a semiconductor laser such as GaAs, a gas laser such as ArF, and the like, and external resonance are performed. The light source emits light such as a semiconductor laser that emits light. Incidentally, the light source 11 may emit light based on the control by the control unit 14.

  In the phase modulation unit 12, the modulated signal having a frequency fm synchronized with the time when the light propagates in the phase modulation unit 12 is driven and input from the control unit 14, thereby phase-modulating the light. As a result, a sideband centered on the frequency of light can be generated, but it is not subjected to intensity modulation in terms of time. In addition, the frequency interval between adjacent sidebands is equal to the frequency fm of the modulation signal that is driven and input. In order to set the frequency of the modulation signal to fm according to the frequency interval, the control unit 14 generates a modulation signal having the frequency fm. The light phase-modulated by the phase modulator 12 is incident on the optical resonator 15.

  The light intensity detection unit 13 is a so-called photoelectric conversion element that generates an electric signal p1 according to the intensity of received light. The light intensity detection unit 13 is phase-modulated by the phase modulation unit 12 and further enters the optical resonator 15. The intensity of the light transmitted through the optical resonator 15 or the reflected light is detected. The intensity of the light detected by the light intensity detector 13 is not governed by the phase modulation in the phase modulator 12. The electric signal p1 generated by the light intensity detector 13 is sent to the controller 14 as it is.

In addition to controlling the entire optical resonator measuring apparatus 1, the control unit 14 generates a modulation signal having the frequency fm, receives the electric signal p1 generated by the light intensity detection unit 13, and analyzes it. To do. The control unit 14 identifies a free spectral range (f _FSR ), which will be described later, based on the signal intensity of the electrical signal p1. That is, the control unit 14 has a function as a transmission device that transmits a modulation signal having a frequency fm, and also has a function as a network analyzer that analyzes the electrical signal p1 sent from the light intensity detection unit 13. become. The control unit 14 may include a display surface for displaying the amplitude and phase of the modulation signal having the frequency fm to the user.

Further, the optical resonator 15 as a measurement object by the optical resonator measuring apparatus 1 is an optical resonator used in, for example, a waveguide-type optical frequency comb generator in which a waveguide is formed, but is not limited thereto. However, the optical resonator may be made of a bulk medium. In general, the f _FSR of an optical resonator is, for example, when mirrors are directly attached to both end faces of a crystal and the mirrors face each other to form a Fabry-Perot resonator. Given.

f _FSR = c / (2n _g l) (11)
(Where c is the speed of light in vacuum, l is the crystal length in the light propagation direction in the optical resonator 15, and _ng is the group refractive index of the electro-optic crystal.)
The optical resonator 15 as a measurement target has a phase characteristic that changes at a constant frequency period, and is expressed as f _FSR . In the optical resonator 15, when the phase modulation frequency fm coincides with the f _FSR of the resonator, the relative phase of the sideband undergoes only a change proportional to the order. That is, since the phase modulation in the phase modulation unit 12 is output as it is, the intensity modulation component of the light output therefrom remains 0, and the electric signal p1 photoelectrically converted by the light intensity detection unit 13 In FIG. 5, the component of frequency fm does not appear.

On the other hand, when the frequency fm deviates from f _FSR , the relative phase of the modulation sideband receives a change based on a function of second order or higher with respect to the order, so that the light output from the phase modulation unit 12 is The waveform is subjected to intensity modulation, and the component of f _FSR appears in the electric signal p1 generated by the light intensity detector 13.

Therefore, when the electric signal p1 is observed through the control unit 14 while sequentially shifting the frequency fm of the modulation signal, the intensity modulation is performed when the frequency fm coincides with an integral multiple of f _FSR as shown in FIG. Since the component is minimized, a signal whose output is 0 appears at regular frequency intervals. Therefore, f _FSR can be obtained by measuring the frequency interval.

FIG. 2B shows a case where the vicinity of the minimum region of the intensity modulation component is enlarged. A minimal region of intensity modulation can be seen at the position of the modulation frequency of 12.3 GHz. This minimum region is the 10th minimum value counted from 0 Hz. From this, it can be seen that f _FSR is 1.230 GHz.

Actually, the f _FSR of the optical resonator 15 is measured by searching for a frequency at which the signal intensity of the electric signal p1 is minimized by the control unit 14 as a network analyzer. Next, the length of the optical resonator 15 is measured based on another method, and the group refractive index _ng of the material constituting the optical resonator 15 is obtained by substituting the obtained parameter into the equation (11). It becomes possible.

Furthermore, by using a laser light source capable of changing the wavelength as the light source 11, the wavelength dependency of the group refractive index _ng can be obtained. Group velocity v _g representing light pulses traveling speed in the dispersing medium in an optical resonator 15 is expressed by the following equation using the speed of light c and the group index n _g (13).
v _g = c / _{ng g} (13)
That is, by determining the wavelength dependency of _ng , the group velocity dispersion of the material constituting the medium of the optical resonator 15 can be determined.

As described above, the optical resonator measuring apparatus 1 to which the present invention is applied can evaluate physical properties including optical characteristics such as f _FSR and group refractive index of the optical resonator 15 as a measurement target. In particular, the optical resonator measuring device 1 is a device for measuring the physical properties of the measurement object, but all signals are generated and analyzed without using optical signal analysis means such as a spectroscopic device. This is effective in that it can be performed. In general, electrical frequency analysis has a much higher resolution than optical frequency analysis means. For this reason, the optical resonator measuring apparatus 1 to which the present invention is applied can measure the f _FSR of the optical resonator 15 with extremely high accuracy. In addition, the group refractive index and group velocity dispersion of the medium used in the optical resonator 15 can be measured with high accuracy.

  Further, the optical resonator 15 as a measurement target may be composed of a plurality of reflecting mirrors, but may be one that uses Fresnel reflection generated at the boundary of the medium without using a reflecting mirror. .

  FIG. 3 shows a case where light actually transmitted through the medium in the optical modulator 15 is detected based on the block configuration shown in FIG.

  In order to propagate the light to the waveguide 15 a formed in the optical resonator 15, the light output from the phase modulation unit 12 is incident on the waveguide 15 a via the optical input unit 17. The light transmitted through the waveguide 15 a is taken out via the light output unit 18 and transmitted to the light detection unit 13.

  In FIG. 3, a polarization-maintaining fiber made of PBS or the like may be disposed between the light source 11 and the phase modulation unit 12 and between the phase modulation unit 12 and the light input unit 17. Further, in order to suppress an error due to reflection of the end face in the optical resonator 15, an isolator (not shown) is disposed between the phase modulation unit 12 and the light input unit 17 and between the light output unit 18 and the light intensity detection unit 13. It may be. Furthermore, a mechanism for detecting the DC component of the electrical signal p1 output from the light intensity detector 13 and locking the light source 11 based on the detected DC component may be provided.

Of course, the optical resonator measuring apparatus 1 may evaluate physical properties such as optical characteristics such as f _FSR and group refractive index of a so-called optical frequency comb generator.

  FIG. 4 shows a case where light actually reflected by the medium in the optical modulator 15 is detected based on the block configuration shown in FIG.

  In the configuration shown in FIG. 4, the light modulated by the phase modulation unit 12 is sent to the light input / output unit 21 via the optical circulator 20, and the light reflected from the end face 15b of the waveguide 15a is sent to the light input / output unit 21. Then, the light is extracted and sent to the light intensity detector 13 via the optical circulator 20.

FIG. 5 shows a case where the control unit 14 composed of a network analyzer or the like as described above is divided into an oscillator 24 and a spectrum analyzer 23 that can be frequency tuned. The phase modulation unit 12 modulates the phase of light based on the frequency fm of the modulation signal from the oscillator 24. Also in the configuration shown in FIG. 5, by observing the component of the frequency fm of the electric signal p1 generated by the light intensity detector 13 with the spectrum analyzer 23, the light intensity is minimized when the frequency fm matches f _FSR. Therefore, it is possible to obtain the f _FSR of the optical resonator 15 itself by searching for the frequency at which the spectral intensity is minimized, and consequently to obtain the group refractive index _ng .

  FIG. 6 shows a case where light actually reflected by the medium in the optical modulator 15 is detected based on the configuration shown in FIG.

  Similarly, in the configuration shown in FIG. 6, the light modulated by the phase modulation unit 12 is sent to the light input / output unit 21 via the optical circulator 20, and the light reflected from the end face 15b of the waveguide 15a is input / output. It is taken out via the unit 21 and sent to the light intensity detector 13 via the optical circulator 20.

  FIG. 7 shows an example in which measurement is performed while modulating the frequency of light oscillated from the light source 11.

  An oscillating unit 28 connected to the light source 11 generates an electrical signal having a frequency fs and transmits it to the light source 11. The light source 11 oscillates light modulated based on the electrical signal having the frequency fs.

In general, even when the phase modulation frequency fm does not coincide with f _FSR , when the frequency of light oscillated from the light source 11 coincides with the resonance frequency of the optical resonator 15, it may not appear as intensity modulation. is there. However, in the configuration shown in FIG. 7, light is modulated in advance at a frequency fs that is faster than the scanning time of the modulation frequency fm, so that the frequency of the light at the time of measurement using the modulation frequency fm is the Fabry-Perot resonance frequency. It is possible not to stay in the vicinity. Therefore, even when the center frequency of light matches the resonance frequency of the Fabry-Perot resonator, the intensity modulation component can be observed, and f _FSR can be measured with high accuracy.

It is a block diagram of the optical resonator measuring apparatus to which this invention is applied. It is a figure which shows the result of having observed the electric signal p1, shifting the frequency fm of a modulation signal in order. It is a figure for demonstrating about the example which detects the light which actually permeate | transmitted the medium in an optical modulator based on the block structure shown in FIG. It is a figure for demonstrating about the example which detects the light which actually reflected the medium in an optical modulator based on the block structure shown in FIG. It is a figure shown about the structure which divides a control part into an oscillator and a spectrum analyzer. It is a figure for demonstrating about the case where the light which reflected the medium in an optical modulator is detected. It is a figure which shows the example which measures, adding modulation to the frequency of the light oscillated from a light source. It is a figure shown about the structure of the conventional optical frequency comb generator. It is a figure shown about the structure of the conventional waveguide type optical frequency comb generator.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 Optical resonator measuring device, 11 Light source, 12 Phase modulation part, 13 Light intensity detection part, 14 Control part, 15 Optical resonator

Claims (4)

In an optical resonator measuring apparatus for measuring physical properties of an optical resonator,
Modulation signal oscillating means for oscillating a modulation signal having a frequency fm changed over time;
Phase modulation means for modulating the phase of the light emitted from the light source based on the frequency fm of the modulation signal oscillated by the modulation signal oscillation means;
A light incident means for causing the light modulated by the phase modulation means to enter the optical resonator;
Light intensity detecting means for detecting the intensity of light transmitted through or reflected from the optical resonator among the light incident on the optical resonator by the light incident means;
An optical resonator measuring device comprising: physical property measuring means for obtaining a free spectral range (f _FSR ) of the optical resonator based on the light intensity detected by the light intensity detecting means. Based on f _FSR obtained by the physical property measuring means, a group refractive index _ng is obtained based on the following formula: _ng = c / (2f _FSR 1)
(Where c is the speed of light in vacuum and l is the crystal length in the light propagation direction in the optical resonator)
The optical resonator measuring apparatus according to claim 1. In an optical resonator measurement method for measuring physical properties of an optical resonator,
Oscillate a modulation signal with a frequency fm changed over time,
Modulating the phase of the light emitted from the light source based on the frequency fm of the oscillated modulation signal,
The modulated light is incident on the optical resonator as the measurement target,
Of the light incident on the optical resonator, the intensity of the light transmitted through the optical resonator or reflected is detected.
An optical resonator measuring method, characterized in that a free spectral range (f _FSR ) of the optical resonator is obtained based on the detected light intensity. Based on the obtained f _FSR , the group refractive index _ng is obtained based on the following formula: n _g = c / (2f _FSR 1)
(Where c is the speed of light in vacuum and l is the crystal length in the light propagation direction in the optical resonator)
The optical resonator measuring method according to claim 3.

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