\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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Dr. Hamid was a member of Intelligent Drive Team of Vehicle System Engineering Research\r\nGroup (Universiti Teknologi Malaysia). The team leads the Advanced Driver\r\nAssistance Systems (ADAS) and AV-related research in Malaysia, where\r\nprevious collaborators include Proton Holdings Berhad and Smart Mobility\r\nResearch Center (Tokyo). Umar Zakir served as an AV Scientist with\r\nMoovita (Singapore & Malaysia) from 2017-2018, before embarking on a\r\nnew journey as an AV Senior Engineer in Espoo, Finland. 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Breast cancer is the most common type of cancer in women. The incidence of breast cancer is increasing all over the world. The mortality rate of breast cancer decreases in developed countries in parallel with the methods used for diagnosis and treatment, but the rate of breast cancer mortality increases in developing countries [1].
Different treatment methods can be used in breast cancer treatment. Treatment protocols, which are suitable for surgical, radiotherapy, and systematic, can be practiced individually or after one another. While the treatment programs are being developed, the importance of improving the survivability and the quality of life as well as the control of cancer-related symptoms are increasing [2, 3].
Chemotherapy drugs are used in cancer cells to suppress growth and proliferation, to prevent or minimize treatment-related symptoms, and to improve quality of life. However, these drugs, along with their therapeutic and toxic effects, destroy normal cells. Fatigue, loss of appetite, nausea, vomiting, pain, weakness, hair loss, bone marrow suppression, insomnia, mucosal and skin problems, pain, neurological problems, and sexual problems may occur depending on the medication taken after chemotherapy and the tolerance of the individual [4].
During chemotherapy and rehabilitation process of patients, systemic problems, laboratory values, and high fever should be evaluated before and after each treatment session. The patient can continue the exercise program, if the fever is below 38°C, the platelet count is 50, 000 and above, the leukocyte count is 5000-10,000, and the hemoglobin is 8 or above. Besides, symptoms such as nausea, vomiting, and diarrhea should be taken into consideration regarding the quality of the exercise program. The minimal changes in these values lead to differences in the type, severity, and duration of the exercise program [3].
Radiotherapy is one of the preferred methods for the treatment of breast cancer. In the radiotherapy process, skin damage, sensory problems, loss of joint mobility, and bone fracture risk should be taken into consideration, while planning rehabilitation programs. In addition, changes in normal tissue exposed to radiation cause some side effects. Some of these side effects are as follows: fatigue, bone marrow depression, erythema in the skin, pigmentation, burns, hair loss, central nervous system effects, bone growth retardation, radiation pneumonia, pain, and ulcers. When planning rehabilitation programs in patients receiving radiotherapy, it should be aimed to minimize the possible side effects of the treatment and to increase the functionality level of individuals [5].
Patients admitted to oncology outpatient clinics, hormone therapy, chemotherapy, and radiotherapy can experience problems depending on the side effects of drugs. Increasing the quality of life of individuals and minimizing the side effects of treatment is one of the priorities of the health care members working in the field of oncology.
Cancer is a chronic disease that has physical, psychological, and cognitive recovery and aggravation periods. About 33% of cancer survivors reported that the obvious cause of deterioration in the quality of life is fatigue. The primary goal of women with breast cancer and survivors of breast cancer is the improvement of functions affected by cancer-related treatments [6].
The period after diagnosis and treatment means the important adaptations concerning physical, social, cognitive, emotional, and economic aspects for the patients with breast cancer and their immediate circle. The activity participation levels, interests, and quality of life of individuals are reshaped, especially for the survivors. The goals of rehabilitation vary in cancer patients at different stages of the disease. The primary goal is to continue and maintain the quality of life and functionality in the diagnosis phase. It is in the forefront to support improvement in the treatment stage and to prevent the quality of life to be adversely affected. The inclusion of individual submaximal aerobic exercise programs to maintain and enhance the quality of life is the first step in oncologic rehabilitation.
Various scales have been developed to determine the quality of life in breast cancer. Nowadays, there is growing evidence that quality of life in breast cancer should be evaluated in detail. Besides being affected by many factors, the quality of life is subjective and difficult to evaluate. There are few specific questionnaire for cancer: European Organization for Research and Treatment of Cancer (EORTC) Quality of Life Questionnaire and Breast Cancer Supplement (EORTC QLQ—C 30 and QLQ—BR 23), The Functional Assessment of Chronic İllness Therapy General Questionnaire and its Breast Cancer Supplement (FACIT-G and FACIT-B), and The Breast Cancer Chemotherapy Questionnaire (BCQ) [7, 8].
The long process and the side effects of cancer treatment may lead to a decrease in functional capacity. It might lead particularly to the reduction of aerobic capacity, muscle strength reduction, flexibility, changes in body composition, and affecting patients’ health-related quality of life. In recent years, breast cancer mortality is decreasing. However, the need for rehabilitation in the recovery of the reduction in functional capacity due to the side effects of the treatment is increasing [9].
Aerobic exercises, stretching, relaxation exercises, strengthening exercises, combined exercise programs, body awareness training, energy conservation techniques, dance therapy, and yoga are aimed to increase functional capacity in breast cancer patients [10].
Individualized rehabilitation programs should be planned to determine exercise capacity and increase functional capacity in cancer patients. A 6-minute walk test, bicycle ergometer, and walking band can be used under the supervision of physiotherapist with cardiologist recommendation during the evaluation and exercise training.
Cancer rehabilitation in the literature is one of the special rehabilitation approaches in physiotherapy and rehabilitation since 1940. In a study conducted in 1978, the areas where rehabilitation was needed were investigated, and problems were identified in the areas of psychological stress, pain, muscle weakness, daily life activities, ambulation, and family support. Thus, the studies aimed to support the quality of life of cancer patients have gained importance [3].
Currently, studies conducted with cancer patients indicated the impact of exercise on fatigue, pain, muscle strength, functional capacity, and quality of life. Due to cancer treatments and its side effects, changes in physical, functional, cognitive, and emotional well-being may be observed in patients. This situation affects the daily activities and role functions of the cancer patients and clearly emphasizes the need for rehabilitation programs [10].
Fatigue is the most common symptom in cancer patients. The National Comprehensive Cancer Network has expressed the relationship between fatigue and cancer as a result of the psychosocial interaction of physical, systematic, cognitive, and emotional changes due to long-term treatment. The main purpose of oncologic rehabilitation is to remove the chemicals taken by systemic treatments and radiotherapy, increase the amount of tissues oxygenation, and maintain muscle strength and endurance. Aerobic exercises have an important role in accelerating the excretion of toxic substances accumulated in the body due to the side effects of radiotherapy and chemotherapy and increasing the oxygenation of tissues in order to minimize fatigue complaints [11, 12].
Oncologic rehabilitation is a medical process that aims to reduce the cancer patients’ complaints during the illness, to increase the level of independence, and to increase the quality of life. Studies on conservation, recovery, and development of the physical, environmental, social, cognitive, psychological, and professional functions require experience and multidisciplinary team in the field of oncological rehabilitation. The oncologic rehabilitation team consists of patients, doctors, nurses, physiotherapists, psychologists, nutritionists, dieticians, social workers, speech therapists, and relatives of the patient. Physiotherapists aim to improve the quality of life of cancer patients using individualized exercise programs in the treatment and survival periods starting from the diagnosis stage [12, 13].
While planning individual exercise training in oncologic rehabilitation, the type and stage of cancer, as well as the patient’s complaints, should be considered. Progressive weighing down should be performed to increase muscle performance. This weigh principle means increasing the frequency, intensity, severity, and exercise type gradually and individually. It aims to maximize the cardiopulmonary potential with pretreatment term exercises in cancer. In the treatment term, the aim is to improve the quality of life, the functional capacity of the individual, and to develop their limited skills. In the posttreatment term, the aim of exercise training is to adapt the individual to the physical and environmental changes that may occur in daily life.
The survival duration of breast cancer patients increased due to the developments in cancer treatments. It is important to decrease the treatment-related complications and improve the quality of life during the survival period. Upper extremity limitations, pain, fatigue, sensory problems, the decrease in functional capacity, and loss of muscle strength are common complications in breast cancer patients. In the studies conducted in the field of oncologic rehabilitation with breast cancer patients, it was stated that aerobic exercise programs had an important role in increasing the quality of life and functionality. Furthermore, in the literature, the effects of various physiotherapy applications such as pilates and yoga exercises, complex decongestive physiotherapy applications, strengthening exercises, relaxation exercises, and banding techniques have been shown within the scope of oncologic rehabilitation programs for individuals with breast cancer [14].
Stretching exercises are frequently preferred in physiotherapy and rehabilitation programs, and they are a simple but effective component of treatment when applied correctly. Although the literature on stretching exercises is constantly being updated, physiotherapists are used to improve normal joint movement and physical fitness to reduce muscular fatigue and to improve proprioception and body perception.
Exercises consisting of active stretching and relaxation techniques such as pilates, yoga, and dance therapy can be used in rehabilitation programs in breast cancer patients. These exercises are preferred to support the body image of the individual during the treatment and posttreatment periods, to increase awareness, and to improve the physical fitness of the patient. It is aimed to accelerate the excretion of toxic substances and reduce fatigue complaints by increasing the circulation and muscle feeding with stretching and relaxation exercises [10, 15].
Aerobic capacity refers to the measurement of the functional capacity of the cardiopulmonary system. It is associated with the ability to perform dynamic, medium/high-intensity exercise, which includes the use of long-term, large muscle groups. Aerobic exercises contribute to increase the quality of life by decreasing the fatigue level due to cancer treatment and insulin resistance due to the metabolic structure of the individual with breast cancer [16].
Aerobic exercise training means increasing the energy capacity of the muscle with exercise. Exercise programs are usually prepared considering the frequency, duration, density, and type parameters. The intensity of aerobic exercise progresses from low to medium in breast cancer patients. The heart rate should be 65–80%, and the exercise program should continue for at least 20–30 minutes for the minimum effect [10, 16].
Increasing the level of physical activity in cancer contributes to increase survival rates and quality of life. It has been shown that the mortality rate decreases with regular exercise programs in individuals with breast cancer. Increasing physical activity during breast cancer treatment has an important role in minimizing the side effects of chemotherapy and radiotherapy, providing body awareness, and increasing muscle strength [17, 18].
Physiological responses following aerobic exercise training result in changes in the cardiovascular system and peripheral muscles. With regular aerobic exercise, the capacity to use oxygen in peripheral muscles increases. In addition to endurance exercises, change in oxidative enzyme capacity, fiber type, and capillary density is observed. Lactate accumulation in muscle is reduced, and less carbon dioxide production is achieved during the exercise process. Maximal oxygen consumption, one of the side effects of cancer treatments, decreased, and accumulation of toxic substances causing fatigue complaints increased.
In studies on the effectiveness of aerobic exercise in breast cancer patients and survivors, it was stated that myoglobin levels increased, immune system functions improved, fat destruction was accelerated, functional capacity and quality of life improved, and body composition improved, besides the reduction of fatigue complaints and acceleration of the excretion of toxic substances. In addition, red blood cell counts may decrease in cancer patients as one of the side effects of treatment. This leads to a reduction in physical performance and fatigue, as oxygen requirements cannot be fully met in activities requiring low effort. For this reason, the exercise programs must be personal. The severity of the exercise must adjusted according to personeal needs and the physiological responses. These details are important for cancer rehabilitation [18, 19].
Aerobic exercises in breast cancer patients have been proven to support body image and self-esteem, increase physical performance, weight control, and muscle strength. It is known that the aerobic exercises performed during the chemotherapy period contribute to the reduction of complaints due to side effects and to increase the functional capacity and quality of life. Nowadays, in the field of oncologic rehabilitation, the need for studies involving exercise programs during different treatments in breast cancer patients is increasing.
The word kalistenik is of Greek origin and derived from the word sthenos, which means kallos, and force, which means beauty. It is defined as the art of using your body to improve human physics. Calisthenic exercise is a useful form of exercise because the major muscle groups can be used in paced, rhythmic, different time, number, and intensity, which can be modified and can meet different physical fitness parameters. It can be applied without equipment. These aerobic exercises, which can be used for durability and flexibility, have been shaped by the modification of the Carlson Fatigue Curve test [20].
Calisthenic exercises are preferred because of objective evaluation of physical performance, compliance with home exercise programs, and safe application to individuals with chronic disease. The advantage of these exercises is that they can be modified according to the individual and contributes to balance, strength, agility, coordination, and endurance.
Calisthenic exercise practice principles
It is recommended that these exercises be performed in a noise-free environment and accompanied by music.
It is suitable to be rhythmic and counted in order to contribute to the aerobic capacity.
For the 30-minute program, 1–3 exercises should be selected for each category for prone, prone and side-lying, sitting, standing categories, and 60 minutes for each category.
The exercise program should be performed at the same time throughout the treatment, preferably in the morning.
Calisthenic exercises can be performed individually or in groups.
Calisthenic exercises in breast cancer patients can be preferred safely in diagnosis, treatment, and survival stages. Exercise examples that can be applied in breast cancer patients are as follows. These exercises should be applied gradually with the principle of individual weighing and under the supervision of a physiotherapist.
Reciprocal hip flexion and extension in the supine position.
Lifting reciprocal flat leg in the supine lying position.
Setting up a bridge in the supine position.
Hip abduction in the lateral lying position.
Beck extension in the prone position.
Shoulder elevation in sitting position.
The circular movement of the shoulders from the front to the back in sitting position.
Scapula adduction in sitting position (hands on back).
Shoulder flexion in standing position.
Shoulder abduction in standing position.
Reciprocal lateral flexion of the trunk in standing position.
Upward movement on toes with arm up.
Reciprocal hip and knee flexion in standing position.
Half-squat in standing position [16].
Muscle strength is the force that a muscle or muscle group spends against resistance with maximum effort. Strengthening exercises preferred in women with breast cancer to protect and improve the muscular force of the vertebrae and extremities, to improve endurance, increase function and develop the quality of life. Progressive resistant exercise is a method that strengthens the muscle according to the principles of adaptation and weighing down. DeLorme and Oxford techniques are commonly used methods in progressive resistant exercise.
Reduction in bone density, fatigue, decreasing of physical activity as a result of the loss of energy, decrease in the participation of Type I muscle fibers in contraction and loss of strength, anxiety, and depression may be observed depending on the side effects of breast cancer treatments. Strengthening exercises are required to increase muscle function and exercise capacity. In the literature, the most commonly used strengthening exercises in breast cancer patients are progressive resistant exercises. Schmitz et al. reported that there was a 30–50% increase in muscle strength in breast cancer patients who participated in progressive resistance exercise programs for 2 days and 12 months [21, 22].
In oncologic rehabilitation, exercise is recommended for 12 weeks, 3 times a week, 65–80% of the maximum heart rate, and 4–6 severity on the Borg scale. It is important to not to increase the fatigue complaints and maintain the physical performance of breast cancer patients during the strengthening exercises. It is important to not to exercise more than 3 days a week and to plan 1-day exercise and 1-day rest (can be 2 day rest interval according to patient tolerance) for breast cancer patients.
The World Health Organization mandates that exercise repairs physical, physiological, and mental wellbeing in general and that consistent moderate-intensity exercise decreases the risk of cardiovascular disease, diabetes, and cancer [23]. Exercise programs for breast cancer have been reported to contribute to positive outcomes with developed treatment methods [24].
When creating rehabilitation programs, the type and stage of cancer, the needs and expectations of the individual, the progression of the disease, the status of the metastasis, the treatment protocols, and the side effects of the treatment should be considered. Physiotherapists who have an important role in the team of rehabilitation should take a holistic approach to pre/post (remission) treatment periods, active care, protection, and palliative periods.
Determining the duration and frequency of rest intervals in planning the exercise programs that include individual loading principles increases the success of physiotherapy and rehabilitation in parallel with the process of the disease in reducing the fatigue complaints [25].
The pretreatment period is the process in which the disease is recognized by the breast cancer patient. The patient is admitted to the hospital, the diagnosis is made, but the treatments are not started yet. It is a sensitive and anxious period for the patients, and the physiotherapist’s approach to the patient is important for the effectiveness of the treatment. All body systems should be evaluated. The functional status should be determined prior to the treatments, and the effects of the treatments should be demonstrated. Patients and their relatives should be informed about the importance of the starting physiotherapy programs during treatments, survival period, and in the palliative period [3, 26]. The exercises recommended during this period are given in Figure 1.
Exercise recommendation in pretreatment period.
Studies in recent years have shown that exercise, especially moderate-intensity aerobic exercise, has been noted to be advantageous in some studies regarding the breast cancer outcomes, decreasing the mortality rate by >30%, and decreasing recurrence rates for females following a breast cancer diagnosis [27].
It is the period when the treatments started, continued in the breast cancer patient, and the side effects started to be observed. All systems in patients receiving chemotherapy and radiotherapy should be evaluated in detail at frequent intervals. Evaluating and recording the fatigue and pain are important in this period. Functional disability and endurance loss should be considered in planning treatment programs.
Focusing on physiotherapy and rehabilitation programs during the treatment period will enable the patients to adapt to the new period of cancer. Starting the exercise programs at the submaximal level will improve the quality of life of individuals and facilitate their adaptation to treatment by taking into account the side effects that may occur following the first dose of treatment. In the literature, it was stated that it would be effective to give aerobic exercises beginning from the active period in breast cancer patients receiving chemotherapy and radiotherapy [5, 28, 29]. The exercises recommended during this period are presented in Figure 2.
Exercise recommendation in treatment period.
In the recent studies, it has been shown that respirator and functional capacity are increased, and sleeping disturbance, mood disturbance, and anxiety decreased following a 12-week aerobic exercise program in women undergoing adjuvant chemotherapy [30].
The exercise of maintenance and protection period consists of long-term exercises to keep the disease in remission. All systems and circumstances, caused by side effects, should be evaluated in detail at frequent intervals. Findings of different treatments should be noted. Complications such as muscle weakness and posture problems should be considered when planning physiotherapy and rehabilitation programs.
Ongoing physiotherapy rehabilitation studies are needed for women with breast cancer, especially during chemotherapy. Individualized exercise programs are the important parts of the breast cancer treatment in order to reduce the side effects of treatment, to support individuals from physical, functional, and cognitive aspects, and to improve the quality of life [25]. The exercises recommended for this period are presented in Figure 3.
Exercise recommendation in maintenance/protection period.
Remission period refers to the survival period in which cancer treatments are completed. All systems should be evaluated in detail. Musculoskeletal problems, sensory, motor, and cognitive problems should be examined in detail. When creating physiotherapy and rehabilitation programs, the individual’s specific needs and complaints should be taken into consideration. Loss of muscle strength, poor posture, loss of endurance, and decrease in quality of life are the most common complaints.
Most of the studies related to the breast cancer patients are concerned with the survival period. The effects of aerobic exercises especially on body image, sexual functions, quality of life, functional capacity, and cognitive functions have been confirmed [6, 10, 11]. The exercises recommended during this period are given in Figure 4.
Exercise recommendation in posttreatment period.
In a cohort-longitudinal study, it was observed that fast walking (3 h/week) prior to and following a breast cancer diagnosis in postmenopausal women reduced the mortality rate by 40% [31]. Most importantly, reports in previous systematic reviews suggested that aerobic exercise with moderate-high intensity (50–85% of maximal heart rate), 3 times/week ranging between 8 and 24 weeks, to be the most frequent mode for breast cancer patients and survivors. Similarly, this program may also have a positive effect on the cardiovascular, muscular, and neurological systems. As a consequence, this can lead to improvements in quality of life, such as the ability to deal with daily tasks [32].
According to the definition of the World Health Organization, palliative care is the time when someone is facing a life-threatening illness. It is an approach used to improve the quality of life of patients and their relatives. In this period, rehabilitation programs should be planned considering physical, psychosocial, and mental problems, especially pain. The disability and activity limitations of the body structure and function of individuals should be focused. Improvable/curable functions and the specific needs of the patient are important. Increased muscle strength and locomotor skills should be maintained. Physiotherapy and rehabilitation programs should include daily living activities and the use of ancillary equipment during this period. For this purpose, physiotherapists should determine the need for support equipment and be involved in the adaptation process of the individual and provide the necessary training [3, 33]. The exercise recommendation for this period is given in Figure 5.
Exercise recommendation in palliative period.
Breast cancer is the most common type of cancer among women in the world. The increase in the average lifetime, the change in lifestyle, the spread of screening studies, and the increase in the notification of cancer cases can be considered as the main reasons for the increase in the incidence of breast cancer. Long-term treatment and side effects in breast cancer cause decreasing in the functional capacity of the individual with cancer. Particularly, the decrease in aerobic capacity negatively affects muscle strength, endurance, and body perception, leading to a decrease in quality of life. Besides, symptoms such as systemic problems, blood values results, and high fever during chemotherapy may cause change in the type, duration, severity, and mobilization status of the exercise programs. The practice of aerobic exercise programs during the treatment of breast cancer is important in reducing the side effects, improving physiological health, improving physical functions, and preventing weight gain and maintaining muscle strength. Rehabilitation in breast cancer contributes to the restoration of the problems caused by the disease and its treatment, keeping physical, psychosocial, and occupational functions at the highest level. In women with breast cancer, rehabilitation programs including aerobic exercises are in parallel with the stage of the disease and the treatment process. Also, increasing physical activity level and functional capacity is an important approach in coping with the disease process.
As a result, although there are very important developments in cancer prevention and early diagnosis and treatment methods, a breast cancer diagnosis is rapidly increasing in the world. Cancer patients at the stage of diagnosis continue their daily life routine; they have a high functional level, and they have no side effects. For this reason, many cancer patients state that the quality of life decreases with the onset of treatments, fatigue, long-term hospitalizations, repeated scans, and the effect of drug treatment. Satisfactory and effective applications are needed to maintain the functional status and quality of life of breast cancer patients. Oncologic rehabilitation approaches should be planned and implemented as individual programs adapted to the patients following a comprehensive evaluation of breast cancer patients. Individual rehabilitation programs can be planned as aerobic exercises, pulmonary rehabilitation, body awareness training, and cognitive rehabilitation. It is aimed to maximize the quality of life, minimize complaints, and increase functional capacity with exercise programs in breast cancer patients. More specifically, studies on the appropriate exercise program for breast cancer are needed with a clearer and more comprehensive analysis of the functional capacity and quality of life that are anticipated for positive health outcomes.
We would like to thank our esteemed patients we met during the studies we have carried out in the field of oncologic rehabilitation.
An optical fiber is an extended cylindrical optical waveguide. In its simplest form, it consists of a core having a certain refractive index nc and is surrounded by a clad (sometimes called skin) of refractive index ncl (or ns). An optical fiber is used to guide light through its core, from one end to another, based on the principle of total internal reflection which mandates that nc must be always higher than ncl. Basically, optical fibers are made of highly pure silica glass doped with some impurities in order to increase nc or decrease ncl [1, 2, 3]. Recently, polymeric optical fibers got more attention as alternatives of some glass based optical fibers [1, 4].
Optical fibers are involved in many technological applications such as telecommunications, sensing [4, 5]; fiber lasers and fiber amplifiers [6]; fiber gratings which can act as mirrors [7, 8]; mode converters [9]; modulators; and couplers and switches [10, 11]. Optical fibers are considered ideal optical transmission media since communication cables hundreds of kilometers in length can be obtained with low absorption and low loss due to the purity and cross-sectional uniformity of the manufactured optical fibers. Moreover, accurate tuning of the refractive indices of both core and clad guarantee extremely low scattering loss at the interfaces [1].
The commonly known optical fibers are step index and graded index (GR-IN) optical fibers. The former means that the core’s refractive index is homogeneous while it suffers an abrupt change at the boundary with the clad. For a GR-IN optical fiber, the core does not have a constant value of refractive index but it rather has a radial distribution of refractive index. These two types of optical fibers can be classified into either single-mode or multi-mode optical fibers. Single-mode optical fiber only sustains one mode of propagation while the multi-mode optical fiber can sustain up to hundreds of propagation modes [1, 3]. The number of the propagation modes is related to the numerical aperture of the fiber, which, in turn, depends on the refractive indices of both core and clad.
Accurate characterization of optical fibers is required in order to know about their functions and performances. There are many methods of optical fibers characterization such as optical microscopy, electron microscopy, X-ray spectrometry, infrared spectroscopy, light diffraction, light scattering, optical interferometry, and digital holography [1, 3, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]. Optical interferometry is an effective accurate tool for studying and characterizing optical fibers. It depends on the determination of the phase difference between a ray of light transmitting the fiber’s cross-section and a reference ray reaching the interference plane directly without crossing the fiber. This phase shift can be transformed into a refractive index map representing the radial distribution of the refractive index across the fiber or, in other words, the refractive index profile (RIP). Interferometry can detect tiny changes in refractive index if an external effect is applied on the fiber. The change of refractive index can be in situ detected if the interferometer is developed to achieve this task. Interference patterns can be digitally processed and analyzed in order to increase the accuracy of the obtained results [1, 17, 22, 26, 27, 30, 31, 32, 33, 34, 35].
Interference techniques can be classified into either two-beam interferometers such as Michelson, Mach-Zehnder, Pluta polarizing microscope, Lioyd’s mirror, etc., or multiple-beam interferometers such as Fabry-Pérot and Fizeau interferometers [1, 3, 25, 36, 37, 38, 39]. A two-beam interferometer produces a pattern of alternate bright and dark fringes of equal thicknesses when two beams, usually, of equal intensities Io suffering a relative phase difference δ are superposed. The resultant intensity distribution I of the interference pattern is given as:
Multiple-beam interference takes place when light rays fall on two parallel optical plates enclosing a small distance between each other while their inner surfaces are highly reflecting and partially transparent. The intensities of both reflected, I(r), and transmitted, I(t), light distributions that are redistributed due to the multiple-beam interference are given as [40]
where, I(i) is the intensity of the incident light, T and R are the products of the transmission and reflection coefficients of the two surfaces, respectively, while δ is the phase difference between any two consecutive interfered rays.
On the other hand, holography was firstly presented by Gabor in 1947 as a lens-less process for image formation by reconstruction of wave-fronts [41, 42, 43]. It offers 3D characterization such as the depth of field from recording and reconstructing the whole optical wave field, intensity, and phase [41, 42]. Holographic interferometry is a non-destructive, contactless tool that can be used for measuring shapes, deformations and refractive index distributions [44, 45]. The modern digital holography was introduced in 1994 [46, 47, 48]. Moreover, the phase shifting interferometric (PSI) technique was introduced by Hariharan et al. as an accurate method for measuring interference fringes in the real time [49]. Recently, digital holographic phase shifting interferometry (DHPSI) was used to investigate some optical parameters of fibrous materials [17, 18, 21, 26, 27, 28, 29].
In DHPSI, frequently a set of four [20] or five [23, 33] phase shifted holograms with known mutual phase shifts starting with 00 and having 900 separations have to be recorded [21]. These recorded holograms can be represented by:
where a(ζ, η) and b(ζ, η) are the additive and the multiplicative distortions and
or,
In digital holography, the recorded wavefield is reconstructed, based on Fresnel diffraction integral, by multiplying the stored hologram by the complex conjugate of the reference wave r*(ζ, η) to calculate the diffraction field b’(x’, y’) in the image plane, see Figure 1. This can be calculated using the finite discrete form of the Fresnel approximation to the diffraction integral as:
Geometry of digital holographic axes and the planes systems.
The parameters used in this formula depend on the used CCD array of N × M pixels and the pixel pitches Δζ and Δη. The distance between the hologram and the image plane is denoted by d’. The pixel spacings in the reconstructed field of image are:
The convolution of h(ζ, η)r*(ζ, η) can be used as alternative of Fresnel approximation [37]. The resulting pixel spacing for this convolution approach is
In addition, the phase shifted holograms are used to overcome the problems of the d.c. term and twin image, in which the calculated complex wavefield is used instead of a real hologram in the convolution approach.
The intensity and phase distributions in the reconstruction plane are given by
So, the optical phase differences due to phase objects can be extracted.
Mach-Zehnder interference-like system is used as a digital holographic setup as shown in Figure 2 [20, 23, 29, 33]. The optical waveguide sample, such as optical fiber, is immersed in a liquid of refractive index nL near or matching the cladding refractive index nclad of the sample. The interference patterns are recorded using a charge-coupled device, that is, CCD camera.
Mach-Zehnder digital holographic interferometric set-up, S F: spatial filter, L: collimating lens, BS: beam splitter, M: mirror, and MO: microscopic objective.
In this chapter, we illustrate some featured work on interferometric characterization (sometimes, implying digital holographic interferometry) of different optical fibers done by our research group during the last three decades. In Section 2, interferometric characterization of conventional step-index and GR-IN optical fibers is presented. Section 3 illustrates characterization of the conventional optical fibers when they are suffering mechanical bending. In Section 4, interferometric characterization of a special type of optical fibers called polarization maintaining (PM) optical fibers is presented. In the last section, we elucidate thick optical fibers and their interferometric characterization with a special interferometric system, developed in our laboratory, called lens-fiber interferometry (LFI).
In 1994, Hamza et al. derived a mathematical expression to calculate the RIP of an optical fiber by considering the refraction of optical rays at the liquid-clad and clad-core interfaces, see Figure 3 [12]. It was the first time to consider the refraction of the transmitted rays to reconstruct the RIP of a fiber. The derived expressions for calculating the RIP in case of two-beam and multiple-beam interferences, based on Figure 3, are given by Eqs. (12) and (13), respectively.
An incident ray (object ray) is refracted due to a clad-core fiber causing a fringe shift Z when interferes with a reference ray.
where, R is the fiber’s radius and e is the skin’s thickness. nL, ns, and nc are the refractive indices of the immersion liquid, skin, and core, respectively. λ is the wavelength of the used illuminating source. Ls and Lc are the geometrical path lengths inside the skin and the core, respectively. Z is the fringe shift due to the presence of the fiber while h is the interfringe spacing and d is the distance measured from the center of the fiber to the position of the incident ray.
In that work, they used Fizeau interferometer to determine the refractive index profile of FOS Ge-doped step-index multi-mode optical fiber with a core radius 19.5 μm. The fiber was immersed in a liquid of refractive index nL = 1.4665, which was a little bit greater than ns while the wavelength of the used illuminating source was λ = 546.1 nm. The Fizeau interferogram of this fiber is shown in Figure 4a. The obtained RIP was compared with the profile calculated for the same fiber when the refraction of light through the fiber was neglected as was usually done by other authors before this work. There was a significant difference between the two profiles, see Figure 4b. Therefore, the refraction through the fiber was recommended to be considered for calculating RIPs particularly when the refractive index of the immersion liquid is not close to the fiber’s refractive index.
(a) An interference pattern of Fizeau fringes, in transmission, for a FOS step-index optical fiber. (b) RIPs of this fiber in case of considering and neglecting the retraction of the crossing rays inside the fiber.
In 2008, another mathematical model was derived in order to determine RIPs of fibers having regular and/or irregular cross-sections [38]. This method was based on immersing the investigated fiber in two liquids with different, but so closed, refractive indices. They applied this method on a single-mode optical fiber, having a small core of radius <5 μm while the fiber’s radius was 60.6 μm, as shown by Fizeau interferograms in Figure 5 when the fiber was immersed in two liquids with refractive indices (a) 1.4589 and (b) 1.4574. The obtained RIP of this fiber is illustrated in Figure 5c showing that this fiber has nc = 1.4630 and ncl = 1.4596. This method was simple and accurate enough to detect such a small core of a step-index optical fiber.
Fizeau interferograms, in transmission, for a single-mode optical fiber when it was immersed in two liquids of refractive indices (a) 1.4589, (b) 1.4574. (c) RIP of the single-mode optical fiber having the interferograms shown in (a) and (b).
A GR-IN optical fiber with a radial refractive index distribution was suggested to be divided into a finite number (M) of concentric layers where each layer has its own value of refractive index, see Figure 6a. The thickness (a) of each layer equals R/M, where R is the radius of the graded-index part. When the ray falls on the fiber at a distance dQ apart from the fiber’s center, the ray refracts through Q layers. The nearest layer to the fiber’s center has a refractive index nQ. The fiber’s RIP can be calculated using Eq. (14) in case of two-beam interference and Eq. (15) in case of multiple-beam interference [13]. Another model was presented in order to get RIP of a GR-IN optical fiber by considering the real path of the optical ray due to the refraction in the core region as well as adding a correction for the ray passing through the immersion liquid [50], see Figure 6b. In this case, the fringe shift was obtained by assuming values for both the profile shape parameter (α) and the difference between refractive indices of core and clad (Δn). A prepared software was programmed to iterate and get the best values of α and Δn and comapre the calculated fringe shift with the experimentally obtained one.
(a) A schematic diagram shows the path of an optical ray crossing Q layers in the core region. (b) A schematic diagram shows the path of an optical ray crossing a GR-IN core optical fiber.
According to Figure 6b, the optical pathlengths of the ray crossing the core
where, R is the core’s radius, k is the minimum distance between the fiber’s center and the bent ray, ε is the half of the angle determined by the two radii that are enclosing the bent ray inside the graded-index region, and γ is the half of the angle between the incident and the emerged rays. Figure 7 shows the interferograms of LDF GR-IN optical fiber when it was investigated by (a) Pluta and (b) Fizeau interferometers. Figure 8 shows the RIPs calculated by these last models for the LDF optical fiber. The last model, presented in 2001 [50], provided more accurate values of the RIP of a GR-IN optical fiber compared with its previous presented model in Ref. [13].
(a) Pluta duplicated image of LDF GR-IN optical fiber and (b) Fizeau interferogram of the same sample. Reference [50] with permission.
A comparison between RIPs of LDF GR-IN optical fiber using the model in Ref. [27] (dots) and model in Ref. [28] (solid curve) in case of (a) multiple-beam Fizeau interference and (b) two-beam Pluta interference. Ref. [50] with permission.
However, the former requires knowing the function describing the index profile while the aim is to find the parameters of this function.
Optical fibers, which are isotropic materials, can suffer a birefringence under external mechanical bending effects [1, 22, 33, 51]. The induced birefringence can be used in sensing applications [52, 53, 54]. However, bending has an unfavorable effect on the optical fibers used in telecommunications where it, sometimes, causes a mode disturbance and consequently a signal attenuation [55, 56]. An approach to calculate the refractive index profile of a bent optical fiber was proposed where the fiber was divided into layers and slabs simultaneously [22]. The refraction of the optical rays at the liquid-clad and clad-core interfaces was considered. Unfortunately, this approach did not consider the change of refractive index inside each slab. Also, the expected change of refractive index due to the release of stresses near the fiber’s free surface has not been considered. However, this approach succeeded to present good information about the variation of mode propagation due to bending.
In 2014, Ramadan et al. calculated the refractive index and the induced birefringence profiles of bent step-index optical fibers using digital holographic Mach-Zehnder interferometer [33]. In that work, they considered two different processes controlling the variations of the refractive index of the bent fiber: (1) the linear refractive index variation due to the applied stress along the bent radius and (2) the release of this stress on the fiber’s surface. The first one is dominant when approaching the center of the fiber while the second one is dominant near the fiber’s free surface and decays on moving toward the fiber’s center. Figure 9 shows the difference between the paths of optical rays through the bent fiber in the compressed and expanded parts. The stress release was supposed to have a radial dependence on the fiber’s radius, which enabled the construction of 2D RIP of the investigated bent homogeneous optical fiber. Based on the expected stress values due to the bending effect, a function describing the RIP was proposed and used to integrate the optical path of the ray traversing the fiber [50]. By adapting the appropriate parameters of this function, the optical phase differences were estimated and matched those phase differences that were experimentally obtained. By this assumption, a realistic induced stress profile due to bending was obtained [33]. DHPSI was used in that study where the recorded phase shifted holograms were combined and processed to extract the phase map of the fiber [18]. By considering both of the mentioned effects, the following function was chosen to describe the RIP of the bent optical fiber [33].
A schematic diagram shows the path of an optical ray crossing a bent homogeneous optical fiber.
where ρ is the strain-optic coefficient, nbf is the refractive index of the bent-free fiber, R is the radius of bending, ro is the radius of the fiber, ncl is the clad’s refractive index, rs is the proposed parameter to control the distance suffering stress release from the surface of the fiber, and x is the distance between the center of the fiber and the position of the incident ray.
The first term of Eq. (18) gives the bent-induced birefringence,
which is correlated to the generated stress S (r,x) inside the fiber
Eq. (20) evaluates the distribution of stress over the fiber’s cross-section for different bending radii where E is the Young’s modulus of the bent fiber. The signs of Δn are opposite to the signs of tensile and compressive stresses. The tensile stress was chosen to be positive.
Since bending such a step-index optical fiber converts it into a weekly graded-index fiber, Bouguer’s formula [40] was used to correlate the radius, incidence angles, and refractive index of the bent fiber as follows:
where n(x,r) is the refractive index at radius r. By applying this formula at the incidence point, one obtains
This equation was numerically solved to get K satisfying the lower integration limit of the optical path difference for a certain value of x. Based on the model described in Ref. [50], the infinitesimal change in the geometrical distance along the path of the optical ray with respect to the radius variation was given as:
By integration with respect to r, the total path length inside the fiber is:
The optical path length difference between this ray, passed through the fiber, and the reference ray passed through the liquid is:
The phase difference is given as:
Figure 10 shows a set of five shifted holograms of a bent step-index optical fiber with a bending radius R = 8 mm when the incident light was vibrating parallel to the fiber’s axis. They were recorded in order to apply the DHPSI technique and reconstruct the RIP of the bent fiber. The 2π shifted interferogram was analyzed and its reconstructed interference phase map, enhanced phase map, and interference phase distribution are shown in Figures 11a–c, respectively. The refractive index cross-section distribution of the bent optical fiber is shown in Figure 12 while the strain-optic coefficients in compression and expansion were 0.208 and 0.224, respectively.
A set of five shifted interferograms of a bent step-index optical fiber.
(a) The reconstructed interference phase map modulo 2π, (b) its enhanced phase map, and (c) the interference phase distribution.
The refractive index cross-section distribution of the bent optical fiber, R = 8.
In 2017, Ramadan et al. presented a theory to recover the RIP of a bent GR-IN optical fiber inside the core region using DHPSI [35]. They assumed the two different processes controlling the shape of the RIP: (1) the linear variation due to stresses in the direction of the bent radius and (2) the release of the stresses near the fiber’s surface.
The total optical path length of the optical ray crossing the bent GR-IN optical fiber is given by Eq. (27), see Figure 13. The calculated optical path length differences of the interfered rays can be transformed, afterward, into a phase difference map using Eq. (26).
schematic diagram shows the ray tracing in case of traversing bent GR-IN fiber.
with,
Figure 14a shows a set of five phase shifted interferograms for the bent GR-IN optical fiber with bending radius R = 8 mm when the incident light was vibrating parallel to the fier’s axis. The enhanced reconstructed phase modulo 2π and the interference phase distribution of the bent fiber are shown in Figure 14b. Due to the bending process, the GR-IN optical fiber exhibited a birefringence where the RIPs when the incident light vibrated parallel and perpendicular to the fiber’s axis were different, see Figure 15.
(a) A set of five phase shifted interferograms of a bent GR-IN optical fiber. (b) The enhanced reconstructed phase modulo 2π and the interference phase distribution. Ref. [35] with permission.
Refractive index cross-section distribution of the bent GR-IN optical fiber when the incident light vibrates (a) parallel and (b) perpendicular to the fiber’s axis. (c) The birefringence cross-section distribution, R = 8 mm. Ref. [35] with permission.
A PM fiber is any fiber that preserves and transmits the polarization state of the light launched into the fiber even if this fiber is subjected to environmental perturbations [57]. This advantage cannot be verified by conventional single-mode optical fibers outside the laboratory conditions. A PM fiber is tailored to oblige the two orthogonally polarized modes traveling with different velocities (i.e., different propagation constants). This difference in velocities prevents the optical energy from suffering a “cross-coupling” and preserves the polarization state of the transmitted light. Therefore, a PM fiber used in any application requires delivering a polarized light such as in telecommunications, medical applications, and sensing. In interferometric applications, it is used to affirm that the interfered rays have the same polarization states. To maintain such a difference of velocities, the core of the fiber has to be anisotropic either geometrically by making the core cross-section as an ellipse or by applying a uniaxial stress. The most known PM fibers used today are, PANDA, bow tie, and elliptical-jacket fibers. These types are designed by the same way where the cores are flanked by areas of high-expansion glass and shrunk-back more than the surrounding silica then the core is frozen under tension. The birefringence is induced due to this tension, which means creation of two different indices of refraction: a higher index in the direction parallel to the applied stress and a lower index perpendicular to the direction of the applied stress. In the next two subsections, we briefly illustrate both the manufacturing process and interferometric characterization of PANDA and bow tie PM optical fibers.
PANDA PM optical fiber is preferable in telecommunications [57, 58]. It is modified by insertion of stress rods to provide PM properties according to the procedure described in Figure 16. In this process, two holes are ultrasonically drilled along a single-mode optical fiber; then, the stress rods are inserted in these two holes and the fiber is finally drawn [57]. In 2014, Wahba used the off-axis DHPSI to reconstruct the 3D RIP of a PM PANDA optical fiber [23]. The multilayer model was used to calculate the RIP of this fiber in the directions of fast and slow axes. By rotating the PANDA fiber, different interferograms were recorded and analyzed in order to reconstrut the 3D RIP of this fiber, see Figure 17. The reconstructed 3D RIPs of PANDA fiber are shown in Figure 18 when the incident light was vibrating in the direction of (a) fast axis and (b) slow axis.
Manufacturing steps of a PANDA PM optical fiber.
The left column shows three orientations of PANDA PM optical fiber as it was rotated during the characterization process where the slow axis makes an angle (a-i) 0°, (b-i) 45° and (c-i) 90° with the horizontal axis. The middle column shows their reconstructed interference phase modulo 2π while the right column shows their phase difference maps. Ref. [23] with permission.
The 3D RIPs of PANDA PM optical fiber in the directions of (a) fast axis and (b) slow axes. Ref. [23] with permission.
A bow tie optical fiber is fabricated on a lathe using the inside vapor-phase oxidation (IVPO) via the process called gas-phase etching to create the required stress [57]. This process is summarized in Figure 19 where a ring of boron-doped silica is purely deposited of boron tribromide in combination with silicon tetrachloride. The rotation of the lathe stopped when a sufficiently thick layer was formed to allow two diametrically opposed sections to be etched away. The final shape of the bow tie and stress levels are controlled by varying the arc through which the etching burner is rotated. Recently, Ramadan et al. estimated the optical phase variations of optical rays traversing a PM optical fiber from its cross-section images [59]. They proposed an algorithm to recognize the different areas of the fiber’s cross-section, which was immersed in a matching liquid and investigated by Mach-Zehnder interferometer.
Manufacturing steps of a bow tie PM optical fiber.
These areas were scanned to calculate the optical paths for certain values of refractive indices and the optical phases across the PM optical fiber were recovered. The experimental interferograms of the bow tie PM optical fiber, shown in Figure 20, were analyzed to extract their optical phase distributions and compare them with the optimized estimated optical phase maps, see Figure 21. This was a direct and accurate method to get information about refractive index, birefringence, and the beat length of a PM optical fiber.
(a and c) Cross-sections of the bow tie optical fiber. (b and d) Experimentally obtained phase shifted interferograms when the incident light vibrates parallel and perpendicular to fiber’s axis, respectively. Ref. [59] with permission.
The calculated and the experimental phase differences of the bow tie optical fiber when the incident light vibrates (a) parallel and (b) perpendicular to the fiber’s axis. Ref. [59] with permission.
Optical fibers having diameters in the order of 100 μm, or less, are convenient to be investigated using interferometric methods when the samples are put in immersion liquids of refractive indices close to the refractive indices of the fibers as described in the previous sections [12, 13]. Optical fibers of diameters bigger than 150 μm cannot be investigated by normal interferometry where the planes of fringes in both liquid and fiber cannot be focused simultaneously. In 2000, Ramadan presented a novel interferometric method to recover such a problem for homogeneous thick optical fibers, commonly used in short-distance data transmission, without using immersion liquids [16]. This type of interference was called lens-fiber interferometry (LFI) since the interference fringes were produced by a combination of an aberrated cylindrical lens and a thick optical fiber. The aberrated cylindrical lens was used to focus a parallel beam on this fiber, which was located in the focal plane of the cylindrical lens [60], see Figure 22.
The ray tracing diagram of an optical ray crossing a homogeneous thick optical fiber.
Two-beam interference produced by the superposition of two optical rays emerging from the fiber was recorded and explained. Due to the aberration of the cylindrical lens, one of these two rays crossed the thick fiber before its center while the other ray crossed after the fiber?s center. Therefore, for each point in the image plane, two rays having two different initial incidence angles on the thick fiber are superposed, see Figure 23. The optical path length of each ray can be obtained by tracing this ray geometrically, as given by Eq. (30), which can be transformed into phase differences for the interfered rays using Eq. (31). The difference in the optical path lengths of each pair of interfered rays can be transformed into an intensity distribution describing the interference fringes using Eq. (32). On the other hand, the scattered rays from the outer surface of the fiber do not contribute in the interference because of the limited range of the incident rays on the fiber. This is in contrast with previous works done by Watkins [14, 15, 61]. By comparing the experimentally obtained interferograms with those reconstructed theoretically as shown in Figure 24, Ramadan was able to determine the refractive index of the investigated thick optical fiber. The advantage is that the used system requires no matching liquid where the experiment is performed when the thick fiber is just held in air. This enables monitoring the probable variation in radius or refractive index of the fiber particularly during the manufacturing process or under external effects.
The relation between the position of each two interfered rays on the screen and their incidence angles on the thick fiber.
(a) A selected and extended part of the obtained interferogram of a thick optical fiber, (b) the enhanced fringes of (a) and (c) the simulated fringes.
where Δ(z1) and Δ(z2) are the optical path lengths of the two interfered rays. In 2004, Hamza et al. developed LFI technique in order to determine the refractive index of the core of a skin-core thick optical fiber [60]. They derived a mathematical expression for the optical paths through the fiber in order to reconstruct the interfernce pattern due to the used fiber when it is used as a thick fiber in the LFI system. By comparing the experimentally obtained patterns with the theoretically reconstructed ones, they were able to estimate the core’s refractive index with an accuracy of 8 × 10−4. Due to its simplicity and applicability, LFI was used, afterward, to measure the refractive index of a liquid [62] and to monitor the thickness variations of a transparent sheet inserted between the cylindrical lens and the thick fiber [63].
This chapter is an attempt to highlight the interferometric techniques used for characterization of optical fibers. Application of two- and multiple-beam interference on different types of fibers is illustrated. Section 2 dealt with conventional optical fibers where we illustrated the theoretical models used to reconstruct the refractive index profiles of these fibers. In these models, the refraction of the light ray traversing the fiber has been considered. Digital holography was explained as an important candidate used for accurate retrieving of phase maps and consequently refractive index profiles of the fibers. In Section 3, we mentioned the problem of fiber bending. Recovering the refractive index profile and mode propagation of a bent fiber considering the refraction of the light rays traversing the fiber is a quite difficult task since bending-induced stresses are responsible for refractive index variations. Also, these stresses are released at the outer surface of the bent fiber. Therefore, we illustrated a successful model that was recently presented to recover the index profile in this case with experimental illustrative data. Another important type of optical fibers is the polarization maintaining optical fibers, which prevent cross-coupling by conserving the state of beam polarization during propagation. In Section 4, we presented interferometric techniques applied on two different polarization maintaining optical fibers, panda and bow tie, to reconstruct their refractive index profiles. Most interference techniques require immersing the fiber in a suitable liquid in order to minimize the phase difference between the fiber and its surrounding medium. In Section 5, an interference technique is presented and applied on a thick optical fiber to recover its refractive index without using an immersion liquid (i.e., in air), which makes the technique suitable for in-situ studying of thick fibers.
The authors would like to acknowledge Prof. A. Hamza, the leader of optics research groups in Mansoura and Damietta Universities, and Prof. T. Sokkar for their continuous support and useful discussions. Also, many thanks to the Optics Research Group members in Damietta University for their useful suggestions and comments.
The authors declare no conflict of interest.
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