High Speed Measurement in Spectral Drill using Q-plate and Camera

Seigo Ohno

1 a

, Katsuhiko Miyamoto

2 b

, Shin’ichiro Hayashi

3 c

and Norihiko Sekine

Department of Physics, Tohoku University, 6-3, Aza-Aoba, Aoba-ku, Sendai, Japan

Department of Materials Science, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba, Japan

Terahertz Technology Research Center, National Institute of Information and Communications Technology,

4-2-1 Nukui-Kitamachi, Koganei, Tokyo, Japan

Keywords:

Geometric Phase, Berry Phase, Fabry-P

erot Cavity.

Abstract:

We have proposed a method to scan resonance modes in a Fabry-P

erot cavity applying a geometric phase

shifter, named as spectral drill. When the geometric phase shifter consists of two quarter wave plates and a

half wave plate sandwiched by them is put into a cavity, the resonance modes can be scanned by the rotation

of the half wave plate. Since a mechanical rotation stage has been used for scanning the cavity in our prior

works, the scanning rate was limited by the rotational speed of the stage. In this work, by replacing the half

wave plate to a q-plate with removing the mechanical stage and by taking transmission images by a camera,

we succeeded in 720 times faster acquisition of the transmission spectrum of the spectral drill.

1 INTRODUCTION

Regular separation of resonance modes of a Fabry-

erot (FP) cavity in the spectral region has been used

as a spectral ruler and has been applied to a frequency

marker for the ﬁne spectroscopy and the essential

principle of a frequency comb(Del’Haye et al., 2009).

Since the frequency separation between the resonance

modes depends on the cavity length d, the resonance

frequency can be scanned by changing the cavity

length. The maximum scanning frequency range in

the FP cavity is restricted by physical limitations of

the cavity mirror position or by the tunable range of

physical properties deﬁning the effective light path

length within the cavity. For instance, one of cavity

mirrors is supposed to be mounted on a piezo manip-

ulator for scanning along optical axis. In such case,

the scanning length is limited to only micron order. It

may be enough length for visible light, but short for

the IR range, in which the wavelength becomes longer

than one micron. Other problem for piezo scanner is

on its hysteresis. For the precise measurement, one

has to take care about the reproducibility of the fre-

quency axis because of a piezo hysteresis.

A geometric phase experienced by a light whose

polarization state moves on a Poincar

e’s sphere is

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https://orcid.org/0000-0002-8570-8504

understood as the analogy of the Berry phase ex-

perienced by the wave-function of electron propa-

gating in a vector ﬁeld. The geometric phase of a

light had been investigated by Puncharatnum in old

days(Pancharatnam, 1956). As an application of the

geometric phase of a light, a geometric phase shifter

(GPS) consists of a simple series of phase plates has

been also proposed by some groups for precise con-

trol of the optical phase(Yang et al., 2010) and the

THz-wave phase(Kawada et al., 2016). Recently, the

geometric phase has attracted many researches be-

cause the metasurface technology can control such

geometric phase of a light by designing artiﬁcial

structures(Huang et al., 2012).

We have previously reported an optical conﬁgu-

ration named “spectral drill,” in which a GPS is put

into a FP cavity. In the spectral drill, the resonance

frequency of the FP cavity can be swept continuously

with seamless manner by rotating a phase plate con-

sisting the GPS(Ohno, 2018). The motion of reso-

nance modes moving on the spectral region with ro-

tating the phase plate looks like apparent motion of

grooves on a drill with the rotation. This behavior is

responsible for the name of spectral drill. Since, in

our previous system, the phase plate was mounted on

an auto-rotational stage, the scanning speed of the res-

onance modes was limited by the rotational speed of

the mechanical movement. In this paper, we propose

a method to break this limitation by replacing a phase

plate with a q-plate and using a camera.

Ohno, S., Miyamoto, K., Hayashi, S. and Sekine, N.

High Speed Measurement in Spectral Drill using Q-plate and Camera.

DOI: 10.5220/0008959400970099

In Proceedings of the 8th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2020), pages 97-99

ISBN: 978-989-758-401-5; ISSN: 2184-4364

We believe this method will open new spectro-

scopic applications of a spectral drill.

2 SPECTRAL DISTRIBUTION

A GPS consists of the series of one quarter wave plate

(QWP), a half wave plate (HWP), and another QWP.

The fast axis of two QWPs are respectively tilting by

+/ − 45 degrees from the polarization direction of an

incident light. In a usual GPS setup, HWP can be ro-

tated with mounting on a rotational stage(Yang et al.,

2010; Kawada et al., 2016; Ohno, 2018). When the

rotational angle of the HWP is α, the light experi-

ences the geometric phase delay of 2α. Consequently,

a GPS within a FP cavity makes the conﬁned light get

the phase delay of 4α per one round trip. In this case,

the transmission intensity of the cavity can be given

as (Ohno, 2018),

I/I



1 +

(1 − R)

sin

(kd + 2α)



−1

, (1)

where, I

, k, d, and R are the intensity and wavenum-

ber of the incident light, the cavity length, and re-

ﬂectance of the cavity mirrors, respectively. Note that

we assumed all of the reﬂectance of the cavity mirrors

are the same to be R. When the values of reﬂectance

are different and/or the cavity has energy loss by some

reasons, 1−R

can be treated as the effective loss in a

round trip within the cavity. Now, we consider to re-

place the HWP in the GPS with a q-plate. A q-plate is

made of anisotropic molecules, like a liquid crystal or

its polymerized material. It partially works as a HWP,

but the fast axis is gradually rotated m/2 times around

the center of the optics, and is usually used for gen-

erating an optical vortex beam with the topological

charge of m(Marrucci, 2013; Sanchez-Lopez et al.,

2018). When such GPS is introduced into the FP cav-

ity, the transmission intensity distribution in the polar

coordinates (r,θ), whose origin is set onto the cen-

ter of the q-plate, can be derived through modifying

Eq.(1) as,

I(r, θ) = G(r) ·



1 +

(1 − R)

sin

(kd + 2α(θ))



−1

(2)

where, G(r) is the beam power distribution in radial

direction. α(θ) is the tilting angle of the fast axis at

the partial area at the azimuthal position θ on the q-

plate. In mth-order q-plate, the tilting of the fast axis

is distributed as α(θ) =

θ. This means that the reso-

nance condition of kd +mθ = nπ with an integer value

n can be satisﬁed 2m times around the center of the

q-plate. Hence, when we measure the transmission

image around the optical axis of this system, we will

observe 2m fringes in the azimuthal direction around

the center.

3 EXPERIMENT

3.1 Experimental Setup

The experimental setup is depicted in Fig.1. A

beam from a single mode external cavity diode laser

(ECDL), wavelength of 1.55 µm, was incident to a

FP cavity. In the front of the FP cavity, the beam

was gradually diverged via a lens with a short focus-

ing length of 5 cm. In the presenting spectral drill, a

GPS consisting of two QWPs and a q-plate (Thorlabs,

WPV10L-1550, m=1) between them was allocated

within the cavity. Behind the cavity, the transmitted

beam pattern was measured by an InGaAs camera,

which has sensitivity for 1.55 µm. The spectral in-

formation can be measured without any mechanical

rotation of the HWP, whereas, in our prior works, we

have required a rotational stage for the HWP in order

to sweep the geometric phase.

Figure 1: Experimental setup. A geometric phase shifter

(GPS) using a q-plate is put within a FP cavity. GPS: ge-

ometric phase shifter, M1 and M2: cavity mirror, QWP:

quarter wave plate, ECDL: external cavity diode laser.

3.2 Results

A measured image under the condition of the cavity

length d of 3.2 cm is shown in Fig.2. A couple of

bright arms are observed in the image and the tra-

jectory of them draws spiral pattern from the center

to the outer part of the image. These bright curves

are respectively corresponding to the resonance of the

cavity. The number of bright arms of two is just

corresponding to our expected number of 2m since

the value of m in the q-plate was unity. The spiral

shape of the fringes is due to the slight longer cavity

length at the outer side from the center part consider-

ing a gradually diverging beam within the cavity. Al-

though it is not shown here, we have also conﬁrmed

the arms gradually rotate with increasing the wave-

length or cavity length as expecting from Eq.(2).

PHOTOPTICS 2020 - 8th International Conference on Photonics, Optics and Laser Technology

Here, we estimate the frequency sensitivity of this

system when one obtains the frequency change of a

light source from the image. When d = 3.2 cm, the

free spectral range (FSR) of the cavity is derived as

4.7 GHz. The angle of view for a bright area on a arm

from the center position, denote with β, is obtained

as around 20 degrees. Consequently, the sensitivity

for the frequency change can be roughly estimated to

(FSR) · β/(2π/2m) = 0.5 GHz.

In the presenting system, the acquisition rate of a

spectral image was determined by the frame rate of

the InGaAs camera of 60 Hz. In our prior spectral

drill, we used an auto-rotational stage in order to ro-

tate a HWP. Comparing with the rotational speed of

the stage of 30 deg./sec., we considered that 720 times

faster acquisition rate was achieved.

We consider that this acquisition time is sufﬁ-

ciently fast for feedback applications, for example

we are expecting the frequency locking of a single

mode laser within sub-GHz order frequency by per-

forming image analysis to every acquired image. For

more precise frequency locking, the improvement of

q-value of a cavity or a long cavity length will be nec-

essary.

Figure 2: A measured transmission image when cavity

length d = 3.2 cm.

4 CONCLUSIONS

In a spectral drill, we replaced a HWP on a rotational

stage with a q-plate and took the FP spectral image

using a camera for the high speed measurement. We

succeeded in 720 time faster acquisition of the spec-

tra than the prior spectral drill. It will open the new

methodology to control the laser frequency and its ap-

plications.

ACKNOWLEDGEMENTS

This work is partly supported by JSPS KAKEN

(JP18H01908, JP18K04967) and Tohoku University-

NICT matching fund 2019.

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High Speed Measurement in Spectral Drill using Q-plate and Camera